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Evolución a largo plazo de redes ópticas aviónicas Autor: José Manuel Estarán Tolosa Ponente: Juan Ignacio Garcés Gregorio Este informe es parte de los requisitos para lograr la titulación de Ingeniería Superior en Telecomunicaciones por la Universidad de Zaragoza. Este informe representa 18 créditos. Dep. Ingeniería Electrónica y Comunicaciones. Escuela de Ingeniería y Arquitectura Edificio Ada Byron del campus Rio Ebro C/ María de Luna nº 1 50018 Zaragoza España. http://diec.unizar.es/index.php/es/diec/presentacion/presentacion A mi familia. 7 RESUMEN Se ha evaluado el rendimiento de una red óptica aviónica bajo las exigentes condiciones del entorno que típicamente se encuentran en los sistemas aerotransportados. Tasas de error (BER), márgenes de potencia y máximas tasas de transmisión conseguibles se han obtenido a -40oC, 25oC y 90oC. Las vibraciones y los impactos han sido estadísticamente analizados a través de desalineaciones radiales, longitudinales y angulares en los conectores del sistema óptico. El test ha sido elaborado para Non-Return-to-Zero (NRZ). Multiplexación óptica por división en frecuencias ortogonales (OOFDM) con modulación en amplitud y cuadratura (4-QAM, 16-QAM y 32-QAM) se ha propuesto como una opción factible y fiable para dar soporte a las futures y crecientes demandas de ancho de banda. Su rendimiento también ha sido evaluado para cada una de las tres temperaturas. 8 9 ÍNDICE RESUMEN .......................................................................................................................................................... 7 ÍNDICE ................................................................................................................................................................ 9 LISTA DE SIGLAS Y ACRÓNIMOS ..................................................................................................................... 13 1 Introducción ............................................................................................................................................ 15 1.1 Establecimiento del problema ......................................................................................................... 16 1.2 Metodología .................................................................................................................................... 17 1.3 Organización del informe ................................................................................................................ 18 2 Evaluación de software ........................................................................................................................... 19 2.1 Resultados ....................................................................................................................................... 20 2.2 Conclusión ....................................................................................................................................... 21 3 Diseño ...................................................................................................................................................... 23 3.1 VCSEL ............................................................................................................................................... 23 3.1.1 Resultados ............................................................................................................................... 23 3.2 Receptor .......................................................................................................................................... 26 3.2.1 Resultados ............................................................................................................................... 26 3.3 MMF ................................................................................................................................................ 27 3.3.1 Resultados ............................................................................................................................... 27 3.4 10GBASE-SR ..................................................................................................................................... 29 3.5 Optical Orthogonal Frequency-Division Multiplexing (OOFDM) ..................................................... 30 3.5.1 Modulador ............................................................................................................................... 30 3.5.2 Demodulador ........................................................................................................................... 31 3.6 Conclusión ....................................................................................................................................... 31 4 Simulación y resultados .......................................................................................................................... 33 4.1 Non-Return-to-Zero (NRZ) ............................................................................................................... 33 4.1.1 Esquemático ............................................................................................................................ 33 4.1.2 Resultados ............................................................................................................................... 34 4.2 Optical Orthogonal Frequency-Division Multiplexing (OOFDM) ..................................................... 42 4.2.1 Esquemático y parámetros ...................................................................................................... 42 A.1.1 Resultados y conclusión (configuración NRZ) .......................................................................... 44 A.1.2 Resultados y conclusión (optimización) .................................................................................. 44 16 El aprovechamiento del conocimiento acumulado durante la implementación de redes ópticas terrestres y sus componentes constituyen un buen punto de partida y referencia. Sin embargo, las duras condiciones ambientales que se encuentran en los aviones (amplios rangos de temperatura, vibraciones, golpes…) junto con la necesidad critica por la seguridad y la fiabilidad, requieren una adaptación detallada del diseño de la red, los componentes y los estándares al entorno aviónico. Se ha alcanzado un notable progreso en relación a conectores, fibras y transceptores [12] y un nuevo estándar para redes locales (LAN) basadas en multiplexación por longitud de onda (WDM) está siendo desarrollado [13]. Otro aspecto importante es la escalabilidad de la red. La tecnología óptica más moderna es compatible con la antigua pero no al contrario [1]. Es crucial diseñar el sistema teniendo en cuenta futuras exigencias de ancho de banda y seguir ofreciendo una buena calidad de servicio en el tiempo actual. Esto se vuelve una consideración ineludible en aviones, donde la sustitución de los componentes que constituyen la red es más difícil y caro que a nivel de tierra. En este aspecto, las simulaciones se usan para explorar como funcionarán las diferentes opciones y arquitecturas en futuras aplicaciones y establecer límites prácticos de acuerdo con múltiples criterios. Por lo tanto, los resultados obtenidos de simulaciones no son simplemente información extra para confirmar estimaciones sino datos clave que deben ser integrados en la fase de toma de decisiones y diseño del proyecto correspondiente. Las simulaciones deben ser precisas y las condiciones de frontera deben ser claramente especificadas para que los datos sean útiles. Por último, el precio y la modularidad también son factores influyentes. La construcción de una red de bajo coste supone un ahorro en el tiempo presente y un futuro beneficio conforme las piezas de hardware necesiten ser reemplazadas. Una distribución modular garantiza un fácil entendimiento de la red y proporciona la flexibilidad, reconfigurabilidad, escalabilidad y facilidad de mantenimiento que las redes aviónicas necesitan [4]. El trabajo aquí presentado cubre la simulación de una red óptica para su uso en medios de transporte aéreos. La investigación se ha realizado como parte del proyecto DAPHNE (Developing Aircraft Photonic Networks), apoyado por el séptimo programa de marco de trabajo de la Comisión Europea (7th framework programme of the European Comission) (3). 1.1 Establecimiento del problema El principal objetivo fue evaluar el rendimiento de una red óptica específica para la que algunos de los parámetros ya habían sido fijados como resultado de las investigaciones llevadas a cabo durante el desarrollo del proyecto DAPHNE. Por lo tanto, el mayor problema a resolver no fue el diseño de la topología o componentes que satisfacían las necesidades, sino analizar cómo de bien funcionaba dicha red bajo las exigentes condiciones ambientales. Las restricciones se presentan a continuación: 3 www.fp7daphne.eu 17  Trasceptores a 10Gbps de la familia S-light (4). VCSELs integrados a 850nm, chips de fotodiodos PIN de GaAs y electrónica CMOS de bajo consumo. Compatibles con los requisitos ambientales de sistemas aeroespaciales.  Fibra multimodo tipo OM4 (ver APENCIDE A para las especificaciones y APENDICE B para la descripción física)  10 Gigabit Ethernet (10GbE) usando el protocolo de bajo coste 10GBASE-SR. La conformidad con IEEE 802.3ae (10GBASE-SR) implicaba igualmente una restricción en la tasa de transmisión, longitud de la fibra and diversos rangos de operación. Los objetivos de la investigación son:  Para realizar un análisis satisfactorio, la herramienta de simulación debe ser elegida y su precisión evaluada. Esto requiere obtener un material de referencia detallado y escoger únicamente las pruebas verdaderamente relevantes para nuestro caso.  Tras seleccionar el simulador, el modelado debe ser realizado. Es necesario transformar los parámetros físicos y las especificaciones de estándar en variables matemáticas que el software pueda interpretar. Debido a las aproximaciones numéricas, suposiciones y las variadas referencias utilizadas para el desarrollo de la herramienta, la adaptación exacta al formato usado puede llegar a ser compleja e incluso imposible. Los resultados de la simulación deben ser comparados con aquellos obtenidos experimentalmente para diversos casos de modo que el correcto modelado sea confirmado.  Finalmente, la red óptica es simulada. La información apropiada debe ser recogida y examinada. 1.2 Metodología Para conseguir los objetivos previamente mencionados, el trabajo ha sido desarrollado como sigue:  Dos simuladores comerciales diferentes fueron seleccionados (VPITransmissionmaker™ and OptSim™ with MoseSYS™). Su precisión fue analizada para los dos módulos más críticos en nuestro sistema final, es decir, fibra multimodo y diodo laser (VCSEL) a 850nm.  La fibra OM4, el VSEL 850nm y el receptor fueron diseñados de acuerdo con sistemas de medición estandarizados y si conformidad con IEEE 802.3ae (10GBASE-SR) fue confirmada.  El enlace punto-a-punto pretendido fue montado y simulado para modulación NRZ. Se realizaron más de 5000 iteraciones estadísticas para asegurar la mayor precisión en la resolución (~20 horas en total). Además, curvas de tasa de error (BES) vs. potencia óptica recibida, BER vs. distancia, BER vs. voltaje diferencial de entrada al VCSEL y márgenes de potencia fueron estudiados para tres temperaturas diferentes (-40oC, 25oC and 90oC).  Adicionalmente, se propuso OFDM como una Buena técnica de modulación para copar con la demanda de ancho de banda y proporcionar la fiabilidad requerida. Su incursión relativamente reciente en las comunicaciones ópticas motive su estudio y evaluación. El enlace fue reanalizado 4 http://www.d-lightsys.com/ 18 para los formatos de modulación 4-QAM y 16-QAM para cada una de las subportadoras para las tres temperaturas mencionadas. Los resultados son presentados y comparados con NRZ. 1.3 Organización del informe El resto del informe está organizado como sigue. En el capítulo 2 se presentan los resultados obtenidos y las conclusiones en relación a la elección de la herramienta de simulación. El capítulo 3 recoge una descripción del proceso de diseño y la comparativa con las especificaciones del estándar IEEE 802.3 (10GBASE-SR). El capítulo 4 presenta los resultados obtenidos de la simulación del enlace. Finalmente, en el capítulo 5, se extraen las principales conclusiones de la investigación y se proponen futuras líneas de trabajo. 19 2 Evaluación de software Esta sección describe el procedimiento seguido para elegir la herramienta de simulación. Entre los varios aspectos que caracterizan un software de simulación, hay dos especialmente importantes y que la mayoría de las veces suponen un compromiso: precisión y eficiencia. Dada la naturaleza de la red óptica bajo evaluación y las concretas especificaciones eléctricas y ópticas, el hecho de que los resultados se ciñeran a la realidad en la mayor medida posible era especialmente importante incluso a expensas de cierto tiempo de adicional de cálculo. En el contexto del diseño de redes de datos las soluciones exactas son a menudo imposibles de obtener (en términos de recursos de computación) y por consiguiente, todas las suites de simulación usan métodos numéricos elegidos a la discreción del desarrollador que efectúan lo que ellos consideran estimaciones aceptables para, manteniendo la desviación por debajo de cierto umbral, proporcionar soluciones aproximadas. La exactitud de los resultados dependerá de tales técnicas, y deben ser analizados para encontrar aquellos que cumplen mejor con nuestros requisitos. Como se ha comentado, el tiempo de procesado no es tan relevante aquí como la exactitud. Sin embargo, el tiempo de ejecución no debería ser despreciado e incluso menos cuando se pretende hacer una análisis estadístico tan amplio. Algoritmos eficientes y estructuras modulares agilizan y facilitan los cálculos. El usuario debe establecer los parámetros de acuerdo con la simulación concreta que se pretenda hacer para evitar que datos innecesarios sean procesados. Otro punto a considerar es la capacidad y facilidad de interacción con productos de terceros (concretamente MATLAB®) debido a la deseada intención de tener control total de la modulación y demodulación en el presente estudio. Esto permitiría aplicar ecualizaciones especiales de canal, aplicación de sistemas de modulación complejos, calculo eficiente de BER, gestión inteligente de la potencia y en general ayuda a alcanzar un entendimiento más profundo de toda la comunicación. Esta característica puede no estar disponible o puede requerir conocimientos de programación o familiaridad con ellos. Tres posibilidades han sido estudiadas: VPItransmissionMaker™, OptSim™ junto con el modulo ModeSYS™ y nuestra propia implementación del link basada en MATLAB®. A pesar de la flexibilidad y el control que esta última ofrece, se consideró inapropiada como resultado del tiempo necesario solo para crear el escenario correspondiente. Las dos primeras galardonadas herramientas soportan cosimulación con terceros y proporcionan una interfaz gráfica intuitiva y fácil de usar. El principal inconveniente en relación con el uso de suites tan compactas es que se nos permite un nivel limitado de personalización y que los parámetros o su formato no siempre encajan con los que el usuario tiene a su disposición, forzando su adaptación. Otra desventaja es que los módulos son “cajas negras”. Esto significa que los procedimientos matemáticos y algoritmos no son editables, hacienda imposible el entendimiento de la obtención de unos resultados inesperados y, consecuentemente, su optimización o corrección. La importancia de realizar test similares para ambas piezas de software es digna de mención. Es importante enfatizar que no solo es necesario evaluar cómo de bien los resultados de simulación individuales encajan con los reales sino también cual de las herramientas lo hace mejor. Nuestro interés recae sobre la fuente óptica (VCSEL) y el canal (MMF). 20 El ancho de banda en una fibra multimodo esta principalmente limitado por efectos dispersivos modales. La precisión del software en la emulación del ancho de banda esta inherentemente ligada a su precisión en la precisión o capacidad de simular DMA, MGD y MPD. Las pruebas deben ser realizadas de tal modo que se permita la comparación directa con el material de referencia; lo cual no es siempre fácil. El análisis de DMA fue posible gracias a la descripción exacta de los perfiles de índice de refracción y las representaciones gráficas de los resultados en [14]. Con respecto a MGD y MPD, la principal fuente comparativa de información fue el modelo de 108 fibras de la Universidad de Cambridge (Versión 1.2, Octubre 2004). Dicho modelo considera un set de defectos de índice predeterminados que son representativos de aquellos que se encuentran en las fibras multimodo actualmente desplegadas. Se eligió porque es un modelo de canal que plantea un compromiso entre un escenario pesimista y uno optimista [15] y porque permitía hacer dos test con el mismo paquete de datos. En lo concerniente a los VCSELs, hay tres importantes gráficas que resumen sus características de emisión: luz-intensidad-voltaje (LIV), función de transferencia/s21 y espectro de emisión [16]. El modelado de un VCSEL es una ciencia en sí mismo ([17], [18] y [19]) y por ello se requería una aproximación inteligente al problema. La idea fue utilizar valores por defecto para la composición específica del laser a modelar y ajustar inicialmente aquellos parámetros cuyo impacto en las propiedades de emisión fuera conocido o deducible (longitud de onda, temperatura, eficiencia de inyección ganancia, resistencia térmica, corriente umbral, Resistencia de entrada, elementos parasites, anchura espectral, método de polarización y spotsize entre otros). A pesar de la simplificación, debido al gran nivel de interrelación entre todas las variables, encontrar la combinación deseada conllevó un proceso iterativo largo y de gran carga de trabajo. 2.1 Resultados La Tabla 2-1 muestra los resultados obtenidos para cada uno de los programas y tests realizados. Debido a su gran precisión, posibilidades de configuración, facilidad de uso y buenas referencias, el software finalmente elegido para realizar el diseño y simulación de nuestro enlace fue OptSim™ junto con el modulo ModeSYS™. Un desglose más detallado de las fuentes de información y los procesos de evaluación pueden ser encontrados en el anexo B Tabla 2-1 Resultados de las pruebas efectuadas a las herramientas de simulación. Módulo Test VPItransmissionmaker OptSim (ModeSYS) MMF Atenuación modal diferencial (DMA) No implementado 95%+ precisión Retraso de grupo modal (MGD) 50% cumplen 10 perct. 5% precisión en factores de escala Distribución de potencia de modos (MPD) Desviación 2 avg. / 4 max. Desviación 0.36 avg. / 1 max. VCSEL L-I-V & S21 VCSEL 850nm no implementado Ok 21 2.2 Conclusión Las pruebas realizadas muestran que ModeSYS™ ofrece una modelo de MMF considerablemente más preciso. A diferencia de VPITransmissionmaker™, ModeSYS™ tiene implementado un algoritmo DMA basado en la formula empírica encontrada en [20]. Los resultados de la simulación coinciden con aquellos en [14]. La diferencia de precisión en relación al MPD es abrumadora. El número de errores en la excitación de grupos de modos degenerados (DMG) es 2 para VPItransmissionmaker™ con una desviación máxima de 4 DMGs de alto orden. Por su parte, el número medio de errores con ModeSYS™ es 0.36 con una desviación máxima de 1 DMG de alto orden. La prueba de MGD fue la más complicada de realizar. Se ha probado que VPItransmissionmaker™ ofrece un rendimiento pobre en el cálculo del retraso relativo de modos cuando se utilizan perfiles de índice de refracción particulares. Aproximadamente el 50% de las fibras analizadas no satisfacen el percentil 10. Con respecto a ModeSYS™, los datos a nuestra disposición junto con el formato particular en el que venían dados en el material de referencia impedía una comparación fiable y rápida. Para comprobar el buen funcionamiento, tres publicaciones que probaban el soporte complete del modelo de 81 fibras de la Universidad de Cambridge por parte de ModeSYS™ fueron consultadas y analizadas. Se muestra un error en los factores de escala de los índices de refracción de menos del 5% para tres tipos de fibra diferentes. Además, se estudiaron dos notas de aplicación llamadas “CambridgeModel_case1” y “CambridgeModel_case2” que investigan el efecto de los defectos en el índice en el ancho de banda de la fibra y posteriormente en el diagrama de ojo para enlaces de datos con tasas concretas de modulación. Dichas notas de aplicación trabajan específicamente con el modelo de canal distribuido por la Universidad de Cambridge y muestran de forma clara la similitud y correspondencia de los resultados. Las pruebas sobre el modulo de VCSEL confirmaban que ModeSYS™ era la mejor opción. Mientras que es imposible emular un VCSEL a 850 con el modulo por defecto proporcionado en VPItransmissionmaker™, ModeSYS™ ofrece un modelo matemático completo que además tiene en cuenta variaciones espaciales de la distribución de campo, algo necesario para estudiar el acoplo de modos en una fibra multimodo. Las propiedades físicas fueron analizadas (LIV y s21) así como su rendimiento en un enlace de comunicación de datos. 22 23 3 Diseño Tras garantizar la precisión de los algoritmos y las aproximaciones numéricas usadas en ModeSYS™ para los componentes críticos, esos mismos elementos y el resto de bloques fueron diseñados de acuerdo a las especificaciones y requisitos establecidos dentro del marco de trabajo del proyecto DAPHNE. En primer lugar se presenta el diseño del transceptor (VCSEL y receptor) y de la fibra multimodo. A continuación, se muestra la conformidad con el estándar 10GBASE-SR. Finalmente se explican los principales aspectos considerados en el modem OFDM. El anexo C muestra un desarrollo completo de los esquemáticos utilizados, las especificaciones y los procedimientos seguidos para el diseño y comprobación de la conformidad con IEEE 802.3ae (10GBASE-SR) de cada uno de los componentes. 3.1 VCSEL Los transceptores, los cuales integran un VCSEL AlGaAs a 850nm, son producidos por la compañía francesa D-Lightsys™. Son parte del consorcio del proyecto DAPHNE y son los responsables de desarrollar un módulo a 10Gbps que satisfaga los severos requisitos ambientales. El objetivo es cumplir el estándar 10GbE al tiempo que se logra compatibilidad con las exigentes condiciones aeroespaciales. El producto no es comercial y por lo tanto solo se mostrarán los parámetros estrictamente necesarios respetando el acuerdo de confidencialidad. A diferencia de la verificación del modelo de VCSEL llevada a cabo durante la evaluación del software, en este caso disponíamos de los rangos operativos eléctricos y ópticos en lugar de las curvas LIV y funciones de transferencia. Esas especificaciones proporcionan los valores típicos y los peores casos para un grupo muy concreto de parámetros tales como longitud de onda de emisión, anchura espectral, potencia óptica de salida, voltaje diferencial de entrada, capacidad de entrada, tiempo de subida/caída, amplitud de modulación óptica (OMA) y ratio de extinción (ER) entre los más relevantes. Sin embargo, y a pesar de la completa descripción de funcionamiento proporcionada, los datos eran ligeramente insuficientes para diseñar el diodo laser con precisión suficiente. Por ejemplo, se daba el valor típico para la potencia óptica media de salida pero se desconocía el valor exacto de la corriente de polarización y la temperatura a la que ese valor fue tomado. Este tipo de situación hizo el proceso de diseño considerablemente complicado y algunos valores tuvieron que ser asumidos. 3.1.1 Resultados Las especificaciones para los bloques principales de acuerdo con las hojas de datos se presentan en Tabla 3- 1 (5): 5 Los números en negrita representan estimaciones. 24 Tabla 3-1 Resumen de las especificaciones de los bloques principales en el transmisor. Bloque Parámetro Min Típico Max Unidad PRBS Longitud - 211-1 - - Tasa de transmisión 0.5 - 10 Gbps Generador eléctrico Tipo de flanco - Rampa On/off - - Voltaje diferencial 100 600 950 mV Tiempo de subida/bajada (6) - 30 45 UI (7) Jitter 0 - 0.6 UI VCSEL Longitud de onda 840 850 860 nm Máxima anchura espectral - - 0.85 nm Mínimo OMA -4.3 - - dBm Típico ratio de extinción 3 5 - dB Potencia de salida media -4 -2 -0.7 dBm Temperatura -40 25 90 oC Variación máxima de la potencia óptica de salida dentro del rango de temperaturas especificado - 0.5 1 dB Corriente de polarización - 8 9 mA Respuesta de modulación (8) - 11±1 - GHz No se daba ninguna información sobre el tamaño de haz o la distribución espacial de los campos en la apertura, de modo que se asumió absoluta flexibilidad en este aspecto. Los resultados numéricos para los valores típicos se recogen en la Tabla 3-2 Tabla 3-2 Valores típicos para el modulo VCSEL. Bloque Parámetro Valor Unidad VCSEL Longitud de onda 850 nm Anchura espectral (9) <0.85 nm Resistencia serie 70 Ω OMA -2.7 dBm ER 3.6 dB Potencia óptica de salida media -1.5 dBm Temperatura 25 oC Variación máxima de la potencia óptica de salida dentro del rango de temperaturas especificado (10) 0.25/0.995 dB Corriente de polarización 8 Voltaje diferencial de entrada 600 mV 6Los tiempos de subida/bajada y el jitter se especifican como características ópticas. Debido a la imposibilidad de realizar su ajuste en el dominio óptico, estos dos parámetros son aplicados en el generador de señal eléctrico. 7 Unit Interval. Tiempo normalizado al periodo de la tasa de transmisión. 8 Ancho de banda para Corrientes de polarización dentro del intervalo predefinido [8mA, 9mA]. 9 La anchura espectral no ha sido especificada porque es completamente ajustable con módulos incluidos en el software 10 Para -40oC y 90oC respectivamente 25 Respuesta de modulación 10.2 GHz Nótese que 10Gbps es al máximo flujo de datos nominal conseguible. Esto significa que no es posible lograr el valor típico de ER (5dB) debido a la elevada corriente de polarización necesaria para situar la respuesta de modulación del laser por encima de los 10GHz. Esto, a su vez, es la razón por la ligeramente elevada potencia media de salida. La curva LI resultante para 25oC, -40oC y 90oC y el s21 (25oC and 8mA) son mostrados en Ilustración 3-1. Ilustración 3-1 Curva LI simulada y respuesta de modulación de pequeña señal. La variación de potencia con la temperatura ha sido calculada para una corriente fija de polarización de 8mA; sin embargo, dichas diferencias pueden variar dependiendo de la intensidad de corriente utilizada. A pesar de que se observa en Ilustración 3-1 que las diferencias se reducen claramente para menores corrientes, también se muestra que la corriente umbral aumenta y el ancho de banda disminuye para 90oC y -40oC. La consecuencia es que aparece un compromiso ente estabilidad térmica ratio de extinción y ancho de banda de modulación. La variación de la respuesta de modulación para 7mA, 8mA y 9mA a 25oC así como el diagrama de ojo óptico con jitter desactivado se muestra en Ilustración 3-2. Ilustración 3-2 Respuesta de modulacion de pequeña señal a a 25oC para 7mA, 8mA y 9mA de corriente de bias (izquierda). Diagrama de ojo óptico con jitter desactivado (derecha). 32 33 4 Simulación y resultados En esta sección se muestran y desarrollan los resultados obtenidos en la simulación final del enlace. Está subdividida en dos partes de acuerdo al formato de modulación. La primera corresponde a NRZ, donde las peores situaciones son presentadas así como un completo análisis estadístico para tres temperaturas diferentes (25oC, -40oC y 90oC) y márgenes de potencia. El estándar 10GBASE-SR se utilizó como referencia a lo largo de todo el proceso para establecer límites prácticos para la simulación y asegurar la conformidad en los casos más exigentes. La segunda parte introduce el modem OOFDM en el enlace. 4.1 Non-Return-to-Zero (NRZ) El test con NRZ tiene dos objetivos principales: asegurar el buen funcionamiento del sistema para el caso más básico de modulación en amplitud y servir como comparación para el posterior estudio de OOFDM. Además, hacer un análisis amplio y preciso consolida las bases para futuras implementaciones o pruebas y simulaciones adicionales. Por lo tanto, contemplar los peores casos, márgenes de potencia y realizar un intenso estudio estadístico era muy importante. 4.1.1 Esquemático Ilustración 4-1 Esquemático de la simulación NRZ final. El primer bloque del sistema es un generador de secuencias pseudoaleatorioas que lanza una señal binaria de longitud 211-1. El convertidor binario-eléctrico viene a continuación. La señal eléctrica se inyecta en el VCSEL a través de un modelo ideal de bias-T para generar la señal óptica. El “OPRegulator” emula el control de la potencia de salida integrado en el transceptor. La señal puede ir al receptor directamente para similar B2B o a un acoplador especial que le da una dimensión especial a la potencia óptica de entrada para, de ese modo, realizar un acoplo de los modos a la fibra OM4. El acoplador especial a la salida de la fibra sirve para tener en cuenta la influencia de la distribución especial de los campos en la recepción de la luz dada una apertura circular concreta en el fotodiodo. Finalmente, la luz se transforma en señal eléctrica, se amplifica y se filtra. 34 4.1.2 Resultados La evaluación se ha dividido en dos partes. En la primera se muestra y discute el BER para corrientes de polarización del VCSEL de 7mA, 8mA y 9mA así como el BER en función de la longitud de fibra utilizada. Esto permite el establecimiento de los peores escenarios que se analizan estadísticamente en la segunda parte. 4.1.2.1 25oc Los parámetros de transmisión son fijados a los valores típicos recogidos en Tabla 3-1 y Tabla 3-2. La Ilustración 4-2 muestra el BER vs. potencia óptica de entrada y el BER vs. voltaje diferencial de entrada al laser. Ilustración 4-2 BER vs. Potencia óptica de entrada (izquierda). BER vs. Voltaje diferencial de entrada al VCSEL. 25oC. A pesar de haber fijado 8mA como valor típico de corriente de bias, se observa en Ilustración 4-2 como el ratio de error disminuye conforme la intensidad decrece. Esta tendencia se mantiene hasta aproximadamente 6mA pero por razones de seguridad se fijó 7mA como la mínima considerable. Para confirmar que la reducción de la corriente de polarización no producía saturación en el VCSEL para ningún valor de voltaje de entrada, se realizó un test de BER en función de dicho voltaje diferencial para la potencia de sensibilidad. Los resultados muestran que la curva decrece monotónicamente sin aparentes puntos de inflexión. Estos Buenos resultados permiten establecer 7mA como la corriente de polarización optima para 25oC. Con 7mA, la sensibilidad queda fijada alrededor de los -16dBm lo que ofrece un margen de potencia de 9.9dB para 700m de OM4 y 0.3dB de perdidas por conector de acuerdo a dos tipos diferentes conectores aeroespaciales comerciales (MC5 y la familia AVIO/AVIM). 35 Ilustración 4-3 BER vs. Longitud de fibra MMF. 25oC. En el siguiente test se comprobó el BER en función de la longitud de la MMF y mínima potencia de salida en el laser (-4dBm). La Ilustración 4-3 muestra los resultados donde se observa que el ratio de error es cero. Análisis estadístico En un primer lugar se evaluaron los efectos de la variabilidad de los parámetros más importantes del sistema, no dándoles un valor fijo sino un rango de valores determinado por las hojas de datos o por investigaciones y consultas previas. Posteriormente, con el fin de evaluar la influencia de las vibraciones e impactos en la calidad de la comunicación, el estudio se centró en la desalineación en los conectores al ser los puntos más críticos/débiles de la transmisión. En todos los casos se utilizó distribución gaussiana para la con una desviación típica notablemente exagerada para descartar cualquier caso que pudiera tener lugar en un montaje real. RANGOS DE OPERACIÓN La Tabla 4-1 muestra las variables estudiadas organizadas por módulos. Se presenta la media de la distribución gaussiana y la desviación típica utilizada. Tabla 4-1 Media y desviación típica de la distribución gaussiana de las variables analizadas. Bloque Descripción Media Desviación estándar Unidad VCSEL Longitud de onda 850 10 nm Resistencia serie 70 10 Ω Parásitos 1.1 0.1 pF Tamaño de haz 12 1 µm OM4 Radio 25 1 µm Atenuación 2.1 0.1 dB/km Pendiente en el punto de dispersión cero 0.102 0.001 ps/nm2∙km Longitud de onda de 1315 5 nm 36 dispersión cero Índice 1.481 0.002 - Exponente de perfil 2.065 0.002 - Receptor Ganancia 1600 100 Ω Ancho de banda del LPF 10 0.5 GHz El barrido después de 1200 iteraciones se muestra en Ilustración 4-4. Se observa que ninguna muestra supera un ratio de error de 10-12. El menor margen de potencia obtenido es 7.5dB. Ilustración 4-4 BER después de 1200 muestras estadísticas. Rangos de operación. 25oC. CONECTORES Los valores medios de desalineación y las desviaciones típicas de la distribución gaussiana se muestran en Tabla 4-2. Para el resto de parámetros que no involucraban a los conectores, su valor fue fijado al típico. Tabla 4-2 Media y desviación típica de la distribución gaussiana de las desalineaciones analizadas. Descripción Media Desviación estándar Unidad X-axis offset 0 5 µm Y-axis offset 0 5 µm Z-axis offset 0 5 µm X angular 0 3 grados Y angular 0 3 grados Pérdidas de inserción 0.3 0.05 dB La Ilustración 4-5 muestras los resultados después de 600 iteraciones. A pesar de que el valor medio es bastante parecido al de FIGURE, el valor máximo es sensiblemente mayor (1.54∙10-8). Con el objetivo de averiguar cuál de las desalineaciones tenía mayor influencia, se realizaron tests independientes que demostraron que se necesita una desafortunada combinación de los tres tipos de desalineación para producir BER mayores de 10-12 37 Ilustración 4-5 BER después de 600 muestras estadísticas. Conectores. 25oC. 4.1.2.2 -40oc La Ilustración 4-6 muestra el BER vs. potencia óptica de entrada y el BER vs. voltaje diferencial de entrada al laser. Ilustración 4-6 BER vs. Potencia óptica de entrada (izquierda). BER vs. Voltaje diferencial de entrada al VCSEL. -40oC. La variación de temperatura a -40oC tiene varios influyentes efectos en el comportamiento del VCSEL: reduce la respuesta de modulación, aumenta la corriente umbral y reduce la resistividad. La dos primeras general la necesidad de elevar la corriente de polarización a 9mA para alcanzar los anchos de banda necesarios para transmitir a 10.3125Gbps y para alejar el punto de trabajo del umbral, de forma que se aumente el factor de amortiguamiento y se reduzcan los overshootings e irregularidades en el diagrama de ojo. El último efecto hace que para un mismo rango de tensión diferencial de entrada, la corriente inyectada sea sensiblemente mayor y, por lo tanto, se llegue a situaciones de saturación con mucha más facilidad. Esto se muestra en el gráfica BER vs. Voltaje diferencial de entrada (a -14dBm y 9mA) en FIGURE, donde se aprecia que a partir de los 650mV la tasa de error se estabiliza e incluso empeora. 38 Ilustración 4-7 BER vs. Longitud de fibra MMF. -40oC. Siguiendo las mismas pautas que para 25oC, se realizó el test a mínima potencia de salida del VCSEL para diversos puntos entre la mínima y máxima distancia de MMF permitida por 10GBASE-SR. Los resultados muestran una transmisión libre de error y con un margen de potencia mínimo de 7.9dB. Análisis estadístico RANGOS DE OPERACIÓN El mismo proceso se realizó para -40oC y los valores de las medias y desviaciones típicas se mantuvieron. La Ilustración 4-8 muestra el barrido estadístico y el correspondiente histograma para -4dBm de potencia de salida del laser, 700m de MMF, 9mA de bias y 600mV de voltaje diferencial de entrada. Ilustración 4-8 BER después de 1200 muestras estadísticas. Rangos de operación. -40oC. La máxima tasa de error es 4∙10-11. El histograma muestra que más del 94% de las muestras están por debajo de 10-20 siendo solo cuatro las que superan 10-12. 39 CONECTORES Ilustración 4-9 BER después de 600 muestras estadísticas. Conectores. -40oC. Sólo el 2% de las muestras son peores de 10-20. El peor caso es 4∙10-8. 4.1.2.3 90oc La Ilustración 4-10 muestra el BER vs. potencia óptica de entrada y el BER vs. voltaje diferencial de entrada al laser. Ilustración 4-10 BER vs. Potencia óptica de entrada (izquierda). BER vs. Voltaje diferencial de entrada al VCSEL. 90oC. A 90oC se produce una reducción de la máxima potencia óptica de salida, un aumento de la corriente umbral, una reducción del ancho de banda de modulación y un incremento de la Resistencia de entrada. Al igual que en el caso anterior, con el fin de alejar el punto de trabajo de la corriente umbral y elevar el ancho de banda de modulación hasta los valores deseados, se utiliza una corriente de polarización de 9mA. A diferencia del caso anterior y a pesar de la gran compresión de rango dinámico (reflejado en la curva LIV), el hecho de que la resistencia serie haya aumentado hace que todo el rango posible de voltaje diferencial de entrada sea soportado por nuestro modelos de VCSEL sin aparente saturación y que la diferencia entre las 40 curvas BER en función del bias sean menos acusadas para potencias por encima de la sensibilidad. Esto se muestra en la curva BER vs voltaje diferencial de entrada en Ilustración 4-10. Ilustración 4-11 BER vs. Longitud de fibra MMF. 90oC. Por último se realizó el cálculo de la variación del BER en función de la longitud de fibra. La Ilustración 4-11 muestra que se consigue una transmisión libre de error con un margen de potencia mínimo de 8.7dB. Análisis estadístico RANGO DE OPERACIÓN Ilustración 4-12 BER después de 1200 muestras estadísticas. Rangos de operación. 90oC. El barrido de 1200 muestras indica que en ningún caso se mejoran los 10-40. El histograma refleja que el 90% de las muestras es menor de 2.10-30 y que todas ellas son menores de 10-20. El mínimo margen de potencia es 7.8dB. 41 CONECTORES Ilustración 4-13 BER después de 600 muestras estadísticas. Conectores. 90oC. El mayor BER realista registrado es 2∙10-4. El histograma muestra que alrededor del 96% de las muestras tienen un BER menor de 10-20 con solo un 1.3% superior a 10-12. 4.1.2.4 Conclusión Se obtuvieron muy buenos resultados para la simulación con NRZ. Las Corrientes óptimas de bias se calcularon para cada temperatura en base al BER. Para dichas corrientes y 600mV de voltaje diferencial de entrada, la peor tasa de error en función de la distancia de fibra se registro a 90oC y no excedía los 10-30. Para 25oC el máximo BER era 10-74 y para -40oC alrededor de 10-40. El mínimo margen de potencia es 7.9dB a -40oC y el máximo 9.9dB a 25oC. Estos resultados prueban que el enlace puede operar con BER por debajo de los 10-12 cuando se utilizan valores típicos. Se debe mencionar que se ha sido asumido la implementación de un sistema de polarización adaptativo. Tal algoritmo debe ser cuidadosamente elaborado y no linealmente interpolado en función de la mínima, máxima y temperatura ambiente. Su cálculo se ha considerado fuera del alcance del presente trabajo. El análisis estadístico mostró que solo cuatro de las 3600 iteraciones superan los 10-12 y ninguna es peor de 10-10. Esto significa que incluso para la peor combinación posible de valores el enlace puede seguir funcionando sobre todo el rango de temperaturas con un BER no peor de 4∙10-11 (obtenido a -40oC). La evaluación de los conectores mostró que a menos que los tres tipos de desalineación (radial, longitudinal y angular) fueran activados, el BER siempre se mantenía por debajo de 10-20. Además, un BER de 10-12 sólo era superado por un 1.1% del número total de muestras (1800). Esto demuestra que a condición de que los parámetros del VCSEL, OM4 y receptor se mantuvieran estables y el link estuviera optimizado para NRZ, el impacto de las desalineaciones es despreciable en nuestro caso. Esto se confirma debido a las notablemente exageradas desviaciones típicas que en cualquiera de los casos serian consideradas inaceptables para un conector óptico orientado a redes aviónicas. Sin embargo, más estudios estadísticos deberían realizarse sobre el impacto de los rangos de operación y desalineaciones como efecto conjunto. 48 49 5 Conclusión Una red óptica predefinida para entornos aviónicos ha sido evaluada. La topología de la red así como el transceptor, canal y estándares de regulación fueron proporcionados y acordados como resultado de la investigaciones llevadas a cabo durante el desarrollo del proyecto DAPHNE, apoyado por la Comisión Europea bajo el FP7. Cinco publicaciones se han presentado durante el desarrollo de la investigación. Una de ellas ha sido aceptada para exposición oral en ECOC’12 y otra fue aceptada y presentada como postdeadline en la pasada OFC/NFOEC´12. Un intense análisis ha sido realizado en lo relativo a la validación de la herramienta de simulación. Dos softwares comercialmente disponibles fueron probados. Para ambos, la precisión de los algoritmos para la emulación de efectos dispersivos modales y la exactitud del modelo de VCSEL a 850nm fueron contrastados resultados experimentales publicados. Se concluyó que ModeSYS™ era la mejor solución para el modelado del sistema pretendido. Las descripciones técnicas y las especificaciones de los componentes deseados para el enlace óptico fueron interpretadas, reformateadas e importadas a ModeSYS™. El buen funcionamiento de los modelos resultantes fue continuamente validado con las hojas de datos proporcionadas y requisitos de rendimiento hasta que un alto nivel de similitud fue conseguido. Posteriormente, se realizó una verificación de la conformidad con IEEE 802.3ae (10GBASE-SR) para el transmisor, canal y receptor. Se concluyó que el modelado era satisfactorio. El enlace fue simulado para NRZ y OOFDM a -40oC, 25oC y 90oC, cubriendo así todo el rango de temperature alcanzado en entornos aviónicos. Además, se llevó a cabo un análisis estadístico para el caso NRZ que comprendía dos fases. La primera consideraba la posibilidad de variaciones en los valores de los parámetros más influyentes en el sistema dentro del rango de operación establecido. La segunda parte evaluaba el rendimiento del sistema cuando desalineaciones radiales, longitudinales y angulares altamente exageradas tenían lugar. Con respecto a NRZ, se obtuvieron excelentes resultados en términos de BER y márgenes de potencia cuando se usaba la configuración típica. El máximo registrado fue 10-31 a 90oC lo cual todavía permitía 8.7dB de pérdidas. La evaluación estadística mostró que dentro de los rangos de operación, solo 4 muestras de 3600 (0.11%) eran peor de 10-12, siendo 4∙10-11 el máximo y todas ellas a -40oC. En lo concerniente a las desalineaciones en los conectores, se requería una fortuita combinación de los tres tipos de desviación para producir BERs peores que, al menos, 10-4. Se comprobó que si uno de ellos era desactivado, los resultados nunca superaban los 10-20. Los resultados para OOFDM mostraron que se pueden conseguir tasas de hasta 20Gbps con modulación 16- QAM por subportadora y mantener el BER por debajo de 10-12 en un sistema optimizado para OOFDM. Por otro lado se concluyó que para velocidades de transmisión menores de 15Gbps NRZ ofrecía resultados comparables con OOFDM/4-QAM con márgenes de potencia considerablemente mayores y simplicidad para todas las temperaturas. Un último test fue desarrollado para OOFDM/32-QAM para demostrar que la 50 ISI y la potencia de ruido en el receptor no permiten incrementar la tasa maxima de transmisión en relación a 16-QAM proporcionalmente al coste técnico y económico implicado. 5.1 Trabajo Futuro Algunas de las posibilidades:  Ejercicios experimentales deben ser desarrollados para confirmar las conclusiones y resultados aquí presentados así como para proporcionar nuevos datos como feedback para posteriores investigaciones.  Una mayor variedad de componentes pueden ser modelados e incluidos en la simulación  Un análisis estadístico combinado de desalineaciones en los conectores y rangos de operación debe ser llevado a cabo.  Una barrido de temperaturas más detallado proporcionaría un conocimiento completo del comportamiento del enlace en las peores condiciones.  OOFDM debería ser analizado estadísticamente.  WDM también podría copar con las necesidades futuras de ancho de banda y proporcionar flexibilidad. 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Traverso et al., “Defining 10GBASE-SR over OM4 media”. Link. [88] J. Lee et al., " 24-Gb/s Transmission over 730 m of Multimode Fiber by Direct Modulation of an 850- nm VCSEL Using Discrete Multi-Tone Modulation," in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2007 and National Fiber Optic Engineers Conference, PDP6, March 2007. [89] T. Kavatzikidis et al., “Performance Study of Optical OFDM for the ACCORDANCE Ultra High-Speed, Long-Reach Access Network,” in FTTH conference2011, Feb. 2011. Link. [90] A.J. Lowery and J. Armstrong, "10Gbit/s Multimode Fiber Link using Power-Efficient Orthogonal- Frequency-Division Multiplexing," Optic Express, vol.13, no.25, pp.10003-10009, Nov. 2005. 55 ANEXOS 56 57 A Theoretical background A.1 Transmitter A.1.1 VCSEL Vertical Cavity Surface-Emitting LASERs are semiconductor Laser Diodes (LDs) whose radiated power, unlike conventional edge-emitting LASERs, is perpendicular to the top surface. The first idea and the initial demonstrations appeared in 1977 [29]. Several investigations in 80s showed some of the good properties and proved diverse advantages of this type of source, boasting the interest and encouraging later research that extended their applications and production [29]. Today, VCSELs are used in computer mice, chip-to- chip, laser printers, high-density optical disks, fiber-in-the-car and of course, short-reach single-channel gigabit-per-second datacom links or parallel transceiver modules on optical fiber ribbons amongst others [30]. A typical layout is shown in Figure A-1. Figure A-1 VCSEL layout [16]. The setting out of the surface-emitting LASERs was motivated by the fully monolithic fabrication of the cavity [29]. This structure itself offers a number of interesting advantages that is increased with the introduction of the vertical cavity. The main advantages of VCSELs are [29]:  The small cavity volume brings the threshold current down to microamperes.  Single-mode operation is possible  Large relaxation frequency allows for high-speed modulation  Passivated surfaces and embedded active region lengthens their lifetime  High power conversion efficiency  Easy coupling to optical fibers due to good mode matching and small nearly circular spot size  VCSELs can be manufactured by monolithic processes reducing the manufacturing cost  The test can be done before dicing 64 Figure A-5 Grade-index profiles of 2 (blue), 2.3 (green) and 1.7 (red) profile exponents. Step-index profile (black). A.2.1.4 Propagation In compliance with geometrical optics, rays propagate by bouncing on the core-cladding interface with different incident angles. Only those for which its phase shift is multiple of 2π will interfere constructively after two reflections and consequently will be guided. This would perfectly explain the propagation over plane waveguides and multimode fibers. But, as the core size becomes comparable to the wavelength (singlemode fibers), a wave-propagation theory is necessary [40]. Besides, despite the inherent complexity of such analysis, it can be extended to multimode fibers as well. In the same way that electromagnetic fields propagate through air or vacuum because they comply with the “wave equation”, those electromagnetic fields coupled into the fiber which are intended to propagate power (17) variations (information) must also fulfill it in our particular medium. All the solutions to the wave equation that satisfy certain boundary conditions and whose special distribution does not change with propagation are known as “modes” (up to now called “rays”) *40] and these can be guided, leaky or irradiative; being the guided ones the responsible for the real transmission. Given the cylindrical shape of the medium, the wave equation is written in the corresponding coordinates as: 𝜕2𝐸𝑧 𝜕𝑟2+1 𝑟𝜕𝐸𝑧 𝜕𝑟 +1 𝑟2𝜕2𝐸𝑧 𝜕𝜙2+𝜕2𝐸𝑧 𝜕𝑧2+𝑛(𝑟)2𝑘0 2𝐸𝑧= 0 (A.4) Notice that the z-component of the electric field has been used. This is because Maxwell’s equations allow us to obtain the rest of the components from only one, hence it is not necessary to solve it for all of them. Usually, the z-component is reckoned [44]. 17 See Poynting Vector. 65 One important thing about using the correct coordinate system is that the solutions are separable simplifying the calculations drastically. Therefore, applying separation of variables, 𝐸𝑧 can be expressed [40]: 𝐸𝑧 𝑟,𝜙,𝑧,𝑡 =𝐾𝐹 𝑟 𝐺 𝜙 𝑍 𝑧 (A.5) Substituting in (A.4) and evaluating the equation: 𝐺 𝜙 =𝑒𝑗𝜌𝜙 𝑍 𝑧 =𝑒−𝑗𝛽𝑧 𝜕2𝐹 𝜕𝑟2+1 𝑟𝜕𝐹 𝜕𝑟+ 𝑛(𝑟)2𝑘0 2−𝛽2−𝜌2 𝑟2 𝐸𝑧= 0 (A.6) (A.7) (A.8) with 𝛽 being the propagation constant of the modes and 𝜌 restricted to integer values since the field must be 2π-periodic in φ. It can be seen that Equation (A.8) is directly dependent on the index profile. In the case of step index, the problem is easily separable into two with constant refractive index: core and cladding. The equation is thereby rewritable as two separate Bessel’s differential equations. After applying boundary conditions, we discard the non-concurrent solutions and take the Bessel function of the first kind of order m (Jm) for the core and the Bessel function of the modified Bessel function of the second king of order m (Mm) for the cladding. The last step to find out the modes is to evaluate both solutions at the core edge and force the continuity of the fields. This yields the “characteristic equation” whose evaluation generates the propagation constant associated to every mode. For grade index fibers no analytical solution exists and the equation needs to be numerically solved. There are some well-known methods of approximation such us “finite differences” that can be used in this context. Modes are uniquely described by its propagation constant: 𝛽=𝑛𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 k0 (A.9) the effective index or 𝑛𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 is the refractive index that a given mode sees along its overall propagation. It is inherently associated with the phase velocity and it is affected by the modes trajectory, medium and wavelength for multimode propagation and exclusively medium and wavelength for singlemode. Guided modes are those for which 𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 𝑘0<𝛽<𝑛𝑐𝑜𝑟𝑒𝑘0 and can be classified according to their field components:  Transverse-Electric (TEm,n): the electric field component in the direction of propagation equals zero.  Transverse-Magnetic (TMm,n): the magnetic field component in the direction of propagation equals zero.  Hybrid (EHm,n, HEm,n): electric and magnetic field components in the direction of propagations differ from zero. The first letter indicates the dominant field. 66 Under the assumption of weakly-guided modes (18), the field components in the direction of propagation are negligible compared to the transversal ones, giving rise to a new sensible nomenclature for the modes: Linearly Polarized modes (LPm,n). Each of them is characterized by the radial (m) [0 up to infinity] and azimuthal (n) [1 up to infinity] orders whose combinations provide every mode with different spatial distribution. Figure A-6 Normalized field intensity of the mode LP01 (left) and LP34 (right) for a 50µm fiber. The mode LP01 corresponds to the HE11 which is the mode that always propagate (multimode and monomode). Its shape (for step index fibers) is very similar to a Gaussian function and if such approximation is used, the deviance is negligible for single mode fibers. The LP34 in Figure A-6 is shown as an example of the symmetry generated by the mode orders. In the refractive index description it is mentioned that although the usual operating windows, indices and sizes allow saying that a 50µm fiber is multimode and a 5µm one is singlemode, this is not strictly correct. The number of modes that propagate depends on the material, the wavelength and its size with respect to such wavelength. Concerning this, there are two parameters that play an important role in determining the total guided modes named “normalized refractive index” and “normalized frequency”. The first one expresses in a range from 0 to 1 any effective refractive index. Those with a value of 0 are those whose value equals the one of the cladding (therefore not guided) and 1 those that equal the core index. The second can be thought of as a figure of merit of the fiber. Its value gives information mainly about the number of propagating modes (19) and how much energy is confined within the core (Marcusse’s approximation to the mode radius for singlemode fibers with 1.2< 𝑉<2.4 [49]). Concerning MMFs, several approximations exist to estimate the number of propagating modes for certain 𝑉 [50]:  Step index: 𝑀=𝑉2 2, with 𝑉>10  Graded/Grade index: 𝑀= 𝛼 𝛼+2 𝑉2 2 18 Mathematically expressed as 𝑛𝑐𝑜𝑟𝑒2−𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 2 2𝑛𝑐𝑜𝑟𝑒2≅𝑛𝑐𝑜𝑟𝑒−𝑛𝑐𝑙𝑎𝑑𝑑𝑖𝑛𝑔 𝑛𝑐𝑜𝑟𝑒 , with ncore and ncladding being the refractive indices of the core and cladding respectively. 19 Any fiber whose normalized frequency is less than 2.405 is singlemode 67 A.2.1.5 Launch conditions In the context of optic communication for MMF-based transmissions, launch conditions correspond to how the optical source illuminates the fiber facet. The way it is done restrict the number of modes that are actually excited and it is crucial to fully understand the performance of the fiber. The measurement of fiber losses and bandwidth is inseparably related to light launching which in turn, depends on the type of optical source. The most conventional sources are light-emitting diodes Light-Emitting Diodes (LEDs) and laser diodes LDs (VCSELs and Fabry-Perot). This section develops on the types of launch scenarios:  OverFilled Launch (OFL) The core is fully and uniformly illuminated. This is produced by most Light Emitting Diodes (LEDs), whose radiation pattern is wide and Lambertian (20). Under these conditions, all the modes that the fiber can support (see section A.2.1.4) are excited.  Radially OverFilled Launch (ROFL) Similarly to OFL, the whole core is illuminated. The difference is that the source is a LD or a SMF ending sufficiently separated from the MMF’s facet. Given this situation, only the modes with cylindrical symmetry (radial modes) are effectively excited hence its name.  Restricted Mode Launch (RML) A small part of the core is illuminated. It arose due to the emergence of VCSELs in 90s, whose spot size was significantly smaller than the cores of the commercial MMFs. This kind is also known as underfilled launch and it allows for selective mode excitation. Quantitatively, the power transmitted from an incoming field to every mode is known as Modal Power Distribution (MPD) and it accounts for the percentage of the input field power that is transmitted to every mode supported in a given fiber. Mathematically, it is the normalized overlap integral of both incident field and mode field [14]: 𝜂𝑚,𝑛= 𝐸𝑖𝐸𝑚,𝑛 ∗𝑑𝐴 2 𝐸𝑖 2𝑑𝐴∙ 𝐸𝑚,𝑛 2𝑑𝐴 (A.10) with 𝐸𝑖 the incident electric field and 𝐸𝑚,𝑛 the modal distribution of the mode LPm,n. A.2.1.6 Distortions Distortions are those undesired mechanisms that keep our link far from ideal. In general, the ideality measurement of a MMF-based communication link such as ours is given by the system’s information transmission capacity or bandwidth (21), which ranges from 0 (no transmission capacity) to infinity. All the distortions have a negative impact on the bandwidth (directly or indirectly) and thereby on the system’s throughput that sometimes can be countered, some other reduced and in the rest just assumed. It is also worthy of mention that some of the impairments are very closely related (attenuation/power- 20 Constant emitted power per area unit and solid angle. 21 This bandwidth should not be mistaken for the optical bandwidth. 68 nonlinearities, chromatic dispersion-Four Wave Mixing (FWM), Self Phase Modulation (SPM)-laser chirp) and its individual treatment is not always simple, implying trade-offs and pragmatic choices. This section describes the main impairments of our channel that affect the bandwidth, how they do it and their best cancelation approach if any. Attenuation Attenuation itself does not limit the bandwidth of the fiber, however, it does affect the total amount of power that reaches the end of the fiber. Since receivers need a minimum amount of power to perform accurately or even work, the losses per meter really represent a factor to consider. Measured in decibels per kilometer (dB/km), the attenuation coefficient depends mainly on the material used for the fabrication of the fiber. Because electromagnetic waves at different frequencies behave differently when they impinge or propagate over certain and given the huge spectrum used for optic communication, it is sensible to measure the attenuation subjected by the light on silica with respect to the wavelength (see Figure A-7). Figure A-7 Loss spectrum of typical singlemode and multimode fibers. Attenuation in fiber is caused by absorption, scattering and radiation ([40], [48]). The improvement of the manufacturing techniques has permitted to lower the attenuation in general, and to create some interesting types of fiber that offer a solution for some individual aspects (“dry fibers” or “bend-insensitive fibers”). Notice in Figure A-7 that MMFs have greater losses than SMFs. This is because the amount of dopants used to make the profiles is lower for SMFs (see section A.2.1.3). Intermodal Dispersion It has been explained that certain types of fibers support more than one mode depending on physical and operational parameters (see section A.2.1.4). It is also known that every single mode is uniquely characterized by its propagation constant (A.9), whose effective index can be expressed as: 69 𝑛𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 =𝑛∙cos 𝜃 (A.11) with 𝜃 being the angle formed by the mode trajectory with respect to the rotational symmetry axis of the fiber. For step fibers the refractive index remains constant throughout the core and therefore, all the modes propagate at the same speed (see section A.2.1.2) but following different paths. Such modes will reach the end of the fiber at different moments (with different delays) generating a multipath situation that causes “pulse spreading”. Simply sticking to Fourier Transform rules, if a signal spreads in time shrinks in frequency; said in other words, our bandwidth decays. In order to address this distortion:  Grade/Graded index fibers: This profile was specifically devised to solve this impairment. Since multimode fibers will unavoidably support more than one mode, this solution gradually changes the refractive index of the core to equalize the channel and force outer modes (longer paths) to propagate faster than the inner ones. This profile is described by a power-law equation whose key parameter is the power coefficient α which, if correctly designed, can totally compensate the delays of meridional rays (22). Such optimum value depends on the index variation with the wavelength (P, profile dispersion parameter), the frequency itself (λ) and the index difference (Δ). Several proposals have been found for the specific formula ([51], [52]) and two situations are distinguished: o No wavelength dependence 𝛼𝑜𝑝𝑡𝑖𝑚𝑢𝑚 = 2(1 −Δ) (A.12) o Wavelength dependence 𝛼𝑜𝑝𝑡𝑖𝑚𝑢𝑚 = 2 1−P +𝐹(Δ, P) (A.13) The profile dispersion parameter is defined as: 𝑃=𝑛𝑐𝑜𝑟𝑒 𝑛𝑔𝑐𝑜𝑟𝑒 𝜆 Δ𝑑Δ 𝑑𝜆 (A.14) with 𝑛𝑔 or core group index: 𝑛𝑔𝑐𝑜𝑟𝑒 =𝑛𝑐𝑜𝑟𝑒 −𝜆𝑑𝑛𝑐𝑜𝑟𝑒 𝑑𝜆 (A.15) 22 Meridional rays are those that propagate within the plane that that contains the fiber’s rotational symmetry axis. On contrary, skew rays are those which propagate describing a spiral as they bounce on the core-cladding interface. Most of the skew rays end up being radiated thus they hardly contribute to the pulse spreading. 70 Although the ideal α exists in theory, in practice it is complicated to build. Within the most common deviations we find axial dips/peaks, inner profile coefficient variation, outer profile coefficient variation and core-cladding interface problems [53]. Notice that some skew rays will not be radiated and although at least one specific profile make the delays independent from such rays [52], they will also have some impact on the pulse spreading.  Singlemode fiber Another more intuitive solution is to force the normalized frequency to be lower than 2.405 by tuning the fiber’s size, wavelength and refractive index. This way, the fiber becomes singlemode and the intermodal dispersion is completely eliminated at the price small tolerances during the fabrication that increase the overall cost of any singlemode-based system. Conventional fibers are usually 8µm to 10µm in diameter for the core and are operated down to ~1100nm.  Restricted Mode Launch (RML) and Offset Launch (OL) As the multipath problem that intermodal dispersion is, reducing the number of paths will result in a better performance. If only those that exhibit lowest relative delay are excited, the improvement would be even greater. This is exactly what RML+OL technique does. While RML helps couple light into a restricted number of modes, the radial displacement of the VCSEL’s spotsize allows selecting those that give better response. If fine enough adjustments are done, it is possible to excite the LP01 mode exclusively having then, virtual singlemode propagation (23). However, that would require precise alignments that would increase the price and make it comparable to the one of a true singlemode set which offers better performance. The real benefit of the RML+OL technique is that, together with grade indices, it provides up to 4- fold bandwidth gain with respect to OFL with much more relaxed alignment constraints than for center launch situations (±5µm of radial offset and 6 degrees in angle) and great stability against environmental influences such as temperature, connector misalignments and mechanical vibrations [8]. The OL technique became feasible in late 90s and its benefits have been widely proved and tested. Group Velocity Dispersion (GVD) This type of distortion is usually negligible compared to intermodal. Notwithstanding, as the fabrication precision of the graded profiles improves and so does the light injection processes, the chromatic or intramodal dispersion has more and more impact on the pulse spreading. Notice that because there is no intermodal dispersion in singlemode fibers, this type mostly becomes the dominant [54]. 23 In general, modal power coupling due to connector misalignment, local bends, scattering or nonlinearities will make the propagation not be purely singlemode. 71 Intramodal dispersion is caused by frequency-dependent variations in the refractive index of the medium. The variations in frequency are due to the unavoidable linewidth that any optical source has (24). Two main subtypes are observed [40]:  Material The physical properties of silica, namely the refractive index, change as it is illuminated with diverse frequencies. This contribution cannot be disregarded either for multimode or singlemode fibers.  Waveguide It has been shown that the propagation constant is a function of the wavelength amongst other parameters. Given the spectral width of the source, every mode may have not only a characteristic refractive index but also a particular wavenumber. The total coefficient is calculated by summing both contributions. The Figure A-8 shows an example of chromatic parameter calculation and representation for standard singlemode fiber. The blue trace corresponds to the material dispersion. The green curve represents the waveguide dispersion and it can be locally changed by varying the fiber’s core radius. The red curve represents the total chromatic dispersion. Figure A-8 Total chromatic dispersion (red) and relative contribution of material dispersion (blue) and waveguide dispersion (green) for a conventional singlemode fiber. It can be observed that there is a wavelength for which the dispersion equals zero. It is usual to work as close to this point as possible though its usage has some drawbacks that need to be evaluated (FWM). Another interesting point is the fact that the waveguide dispersion can be tuned. It allows the creation of the so called “dispersion-shifted fibers” which move the zero dispersion point (around 1.32µm in Figure A-8) up to the third window. 24 Atoms’ energy levels become energy bands when they constitute molecules. Direct modulation causes chirp that in turn enlarges the linewidth. Finally, when the modulation bandwidth becomes proportional to the laser’s linewidth, the latter may expand. 72 Polarization Mode Dispersion (PMD) Although it is the least dominant factor, it cannot be fully compensated. It should only be consider when there is neither intermodal distortion nor GVD and working with high bit rates [40]. It is caused by symmetry variations along the core that make both polarizations be affected differently generating a completely random polarization at the final end of the fiber. The consequence is also a pulse widening that limits the system performance. A.3 Receiver A.3.1 Photodetector Photodetectors or photodiodes (PD) convert light into electric current by exploiting the photoelectric effect. The most conventional semiconductor PDs for data-communication links are PIN and Avalanche (ADPs) however, there are several types that constitute a present alternative for specific applications or a future general-purpose replacement. Some of these are: Schottky-Barrier, Hetero-Interface, Travelling- Wave and Resonant-Cavity [48]. Schottky-Barrier and Hetero-Interface PDs are not often installed but they are being subject of deep research due to the promising properties they have shown so far, Resonant- Cavity show very high quantum efficiency at high bit rates at the price of being wavelength specific and difficult to build and Travelling-Wave exhibit high quantum efficiency at extremely high bit rates compared to PINs (double or triple). A.3.1.1 PIN The p-n junction, generally used as a light emitter, can be used as a light absorber if it is inversely polarized. On contrary to what is done when used as emitter, the already existing electric field in the depletion layer is made thicker by applying an inverse current. This has three main advantages [52]:  As the electric field increases, the carriers leave the depletion layer faster. Higher bit rates supported.  Because the depletion layer gets thicker, the number of absorbed photons is higher. Increased efficiency  The widening of the active region with respect to the material extension reduces the parasitics. Improved electric bandwidth. Nonetheless, p-n PDs have a great disadvantage that makes them unsuitable for >1Gbps datacom systems [55]. Some electron-hole pairs that are created outside the active region end up entering because of their intrinsic mobility. This generates current that drastically limits the systems bandwidth. PINs come to solve that problem. By adding a slightly n-doped intrinsic layer between the p-doped and n-doped silicon (P-I-N), the depletion layer is made much thicker in comparison with the p/n zones. This solution, which is adjustable, keeps or 73 augments the advantages of the p-n junction and reduces noticeably the diffusion current given that p/n zones can be much thinner. To characterize a PIN diode, there are two important parameters: Quantum Efficiency (QE) and responsivity. They are very closely related and they give information about the number of electrons per photon generated (ideally 1). These parameters are usually accompanied with the wavelength since they directly depend on it. Responsivity can be seen as a QE that besides, accounts for the energy variation at different wavelengths. A.3.1.2 Avalanche PhotoDiode (APD) Avalanche PDs are PINs subjected to a very high reverse polarization. The aim is to create strong enough electric field so that the electrons generated by the photoelectric effect collide with other electrons transmitting the necessary energy to push them up to the conductive level thereby creating an electronhole pair [55]. This is called “impact ionization” which results in “avalanche breakdowns”, hence their name. This gain of this type of photodiodes ranges between 10 and 100 what means that a single electron can produce from 10 to 100 electron hole pairs [55]. The structural difference with respect to PIN is the addition of a lightly p-doped segment between the ndoped and the intrinsic layer. This is where the gain generation takes place. Exactly as for PINs, the alloys and materials used for their fabrication restrict their wavelength range. This type of laser is more complex to use and more expensive than PIN but it offers a very high sensitivity. The first window is conventionally used for SR communications whose attenuation is not big enough to need of such high sensitivity. However, they are commonly used for long-haul or link length measurements [48]. A.3.2 TransImpedance Amplifier (TIA) TransImpedance Amplifiers are devices installed right after the PDs. They convert current into voltage and avoid the two principal problems that arise when dumping all the output current into a simple resistor. Because the PDs usually have non-negligible capacitance, if the load resistor is very high, the RC transient will increase and the electrical bandwidth will drop accordingly. On contrary, if the resistance is very low, there will be low gain and the Signal-to-Noise Ratio (SNR) will be insufficient. TIAs provide considerably faster RC transient and very high gain (tunable if necessary) [56]. Schematic shown in Figure A-9. Figure A-9 Transimpedance amplifier schematic. - + Vcc Vo Rgain C PD TIA 80 One of the things that makes a good software is the proper use of assumptions and approximations to skip unnecessary calculations and save time but still being accurate. This handling must be checked and it is basically the major source of errors. The concrete application and affordable margins will also play a significative part in determining how acceptable certain results are; for instance, assuming that there is not Polarization Mode Dispersion (PMD) in a short-reach 1Gbps transmission does not induce so much deviation as when it is assumed for a high-speed long-haul link. This section summarizes the used tools for the evaluation/design of MMF and VCSEL in our specific optical link. A.5.1 MultiMode Fiber (MMF) A.5.1.1 Indirect bandwidth measurements (physical characterization) These tools are used to make a deep and selective study of the causes of the distortion in the MMF. They are used to estimate the precision of the simulator and find out where the possible deviations are owed to. Mode Dependent Attenuation (MDA) Mode Dependent Attenuation is one of the three mode-depending distortion effects in a MMF and it has a strong influence in its characteristics [67]. It is caused by Rayleigh scattering, absorption and loss on reflection at the core cladding interface [20]. These loss mechanisms act differently on each mode, changing their individual attenuation coefficients. This effect does not have to be necessarily symmetrical or sensible given the random nature of the causes of such dispersions. Strictly, the response of each of the loss mechanisms should be calculated to find out the exact influence on the MDA and build up a combined function. Nevertheless, this is complicated given the varied number of generated parameters that would not be easy to give correct numerical values [20]. Instead, separate and usual measurements of the fiber’s attenuation in the three transmission windows are done. The extrapolated function can be easily introduced in the simulation tool. In [20] the following formula is proposed: 𝛾 𝑥,𝜆 =𝛾0 𝜆 +𝛾0 𝜆 𝐼𝑝[𝜂 𝑥− 1 𝑀 𝜆 2𝛼 𝛼+2] (A.16) with 𝛾0 𝜆 being the intrinsic fiber attenuation, 𝐼𝑝 is the pth order modified Bessel function of the first kind, 𝜂 is a weight constant, 𝛼 is the profile exponent and 𝑀 𝜆 is the number of modes, which for graded-index fibers is: 𝑀(𝜆) = 𝛼 𝛼+ 2 𝑉2 2 (A.17) 81 Usually, MDA is also referred as Differential Mode Attenuation (DMA) to emphasize the fact that it is the difference in the attenuation of the modes what causes the impact. DMA affect the bandwidth by attenuating some modes so strongly that they do not contribute to the modal delay anymore. It can be inferred that if those modes with highest differential delay are filtered off, the attainable transmission rate can increase. Mode Group Delay (MGD) As it has been explained in section A.2.1, multimode fibers support many modes uniquely characterized by its propagation constant. All these guided modes with different velocities reach the end of the fiber at different time instants generating a multipath situation that reduces the attainable bandwidth. These group delays are a crucial property to describe the dispersion of signal transmitted over a MMF and its mitigation requires a detailed understanding of the results [68]. They are collected in the Modal Group Delay (MGD) measurement. Under the assumption of weakly-guided modes, modes can be grouped in LPs, which are modes whose field components in the direction of propagation are negligible compared to the transversal ones. Besides, under those conditions, some LPs hold very similar group velocities thus they affect equally to the pulse spreading. This allows grouping them into numbered Degenerate Mode Groups (DMGs) [69]. The modes within a certain DMG will fulfill the following requirement [51]: 𝐷𝑀𝐺𝑁𝑈𝑀𝐵𝐸𝑅 = 2 ∗𝑛+𝑚−1 (A.18) From the formula above, one can infer that the higher the DMG number, the more LPs contains. A consequence of this is that a radial light injection with a fixed spot size will excite a larger amount of modes the farther it is from the core center. This provides good modal noise immunity and stability despite the reduced dispersion [14]. One important advantage of the MGD study is that the injection condition dependence is, to some extent, eliminated from the intermodal distortion effect. It yields delay times for every DMG, which are selectively excited. MGD is also important to account for possible modal power coupling, since power transfer between modes is seen as a superposition of pulses with various group delays. This influence is clearly demonstrated in [70] where strong coupling in mode-division-multiplexed systems using coherent detection has been beneficial due to the modal dispersion reduction., MGD is often represented in a graph. In the Y axis the relative propagation delays with respect to the mode LP01 (DMG1). In the X axis the DMGs (see Figure A-13). The total amount of DMGs depends on the number of propagating modes. 82 Figure A-13 MGD plot. It shows the dependence of relative propagation delay on mode group numbers for different cases of profile exponent values. [71]. As it can be seen in Figure A-13, there some expected tendencies depending on the profile exponent. If it is larger than the optimum, high order modes reach the opposite end later than the LP01 and vice versa. The three lines on the picture represent ideal alpha profiles. In practice it is impossible to obtain such straight lines but they exhibit curvatures and diverse oscillations owed to fabrication imperfections. For instance, a collapse during the production may generate an on-axis dip. Since the profile deviation is located in the center region, low order modes will propagate much faster that they should; this produces an oscillating MGD (like a sawtooth wave). Another example is when the profile exponent does not keep constant throughout the radius. If so, the relative propagation delay turns into a curved line rather than a straight one. Mode Power Distribution (MPD) It has been explained that RML limits the number of modes that are actually excited. If some of them do not contribute to the distortion, there could be a huge improvement of the bandwidth. It can also happen that imperfections in the fiber’s cabling or fabrication cause that two neighboring modes yield very different delay times, resulting in a bandwidth close to the one obtained under OFL conditions. It is crucial to assure that an accurate mode excitation is calculated and that it corresponds to real parameters. Mode Power Distribution (MPD) determines whether only modes with similar velocities or the worst-case combination of modes will propagate along the fiber [51]. It is represented in a 2-D plot with Y axis being the percentage of the total power coupled for every DMG on the X axis. Figure A-14 shows a concrete example of MPD graph. DMG Relative propagation delay [ns/km] 83 Figure A-14 MPD for a 62.5µm multimode illuminated with the output of a SMF that produces a 7µm Gaussian spot size at 1300 nm. The radial offset is 17µm. MPD might be also called “mode coupling”. It should not be mistaken for power cross-coupling between guided modes in optical fibers. A.5.1.2 Direct bandwidth measurements (standards) The next procedures represent regulated techniques for the determination of the MMF bandwidth. They are used to assure the fiber’s compliance according to a certain transmission standard, which is often the relevant value in the development of a certain data-communication link. The obtaining of satisfactory results based on any standard guarantees the good working within very well defined operational limits. When simulating, it is crucial to make sure that your system’s behavior is sensible by comparing the results with these reliable and official references. Differential Mode Delay (DMD) The OFL and RML techniques are used for the bandwidth characterization of LED-based and VCSEL-based systems at less than 1Gbps respectively [72]. However, the appearance of VCSEL-based 10Gbps standard (IEEE 802.3ae) motivated the development of a more precise and complex standard for 50µm laseroptimized MMFs at 850nm called Differential Mode Delay. It characterizes the modal structure of a gradedindex MMF without taking into account the type of laser source to predict the bandwidth [72] [73]. The measurement is conducted in accordance to IEC 60793-1-49 (2006) that replaces TIA-455-220-A (2003) and it consists of measuring pulse/impulse responses of the fiber for a SMF launch which radially scans the end-face of the fiber in increments of certain amount. The output graphs are called DMD plots and they provide dispersion cartographies that show where the fastest and slowest DMGs are located across the 84 fiber core. The picture is then compared with “DMD masks” defined by ANSI/TIA or ISO/IEC, which establish minimum requirements for the DMD in order for the fiber to have certain transmission capabilities. For the measurements, the mode field diameter is specified to be 5±0.5µm and the special resolution of the lateral scan is 1µm. With regard to the pulse duration, it depends on the estimated fiber class which is to be analyzed. For instance low resolution DMD for OM1 and OM2 use semiconductor lasers that generate 80ps to 100ps pulse, however, high quality fibers (OM3+/OM4) require very short duration pulses (around 10ps) which are achieved with Titanium Sapphire lasers [51]. The DMD is defined in Fiber Optic Test Procedure 220 (FOTP 220) as the maximum difference between the 25% (quarter maximum) threshold of the leading and trailing edges. The standard divides the radius into three reference intervals for the DMD (see Figure A-15): inner section (5-18µm), outer section (0-23µm) and sliding sections (5µm width at 7, 9, 11 and 13µm offset launch) [51]. Figure A-15 Illustration of a DMD plot with the reference measurement regions superimposed. It was measured after 300m of parabolic alpha profile at 1300nm. The standard definition contains the balanced combinations of the sections that need to be met for a fiber to belong to a certain fiber class which in turn, has associated a minimum bandwidth. These specifications are calculated for 300m-long reels. As an example, the DMD specifications for OM3 fiber type are shown in Table A-3. Table A-3 DMD specifications for OM3 fiber. Specifications Inner DMD (ps/m) Outer DMD (ps/m) Sliding DMD (ps/m) 1 ≤0.33 ≤0.33 ≤0.25 2 ≤0.27 ≤0.35 ≤0.25 3 ≤0.26 ≤0.40 ≤0.25 4 ≤0.25 ≤0.50 ≤0.25 5 ≤0.24 ≤0.60 ≤0.25 6 ≤0.23 ≤0.70 ≤0.25 OUTER INNER SLIDING 85 Encircled Flux (EF) Covered in the IEC 61280-4-1 Ed2 (June 2009) standard, Encircled Flux measures the amount of optical power that emanates from a source and that penetrates a specific region of a fiber end-face as defined by prescribed radius limits [73]. It defines the launch specifications for diverse wavelengths and core diameters in order to standardize the illumination conditions. It was firstly devised to provide an ideal general model of the output of an 850 nm VCSEL to allow mathematical modeling of laser-optimized fibers for the emerging high-speed Gigabit Ethernet networks (10Gbps, 40Gbps and 100Gbps). Later on, it was used as a method to define mode fill and increase the consistency in the bandwidth and loss measurements [74] not only for 850nm but also 1300nm and 62.5µm fibers to account also for “legacy” setups. It can be used as an independent reference or in conjunction with DMD to extrapolate the so-called effective modal bandwidth (EMB) that takes into consideration both delays and optical source field distribution for >10Gbps links [73]. EF is represented in a 2-D plot where the Y axis expresses the percentage of the total power transmitted within a circle of certain radius (X axis). Mathematically expressed as: 𝐸𝐹 𝑟 = 𝑖(𝑟,𝜃)𝑟𝑑𝑟𝑑𝜃 𝑟 0 2𝜋 0 (A.19) with 𝑖(𝑟,𝜃) being the normalized light intensity of the source. Effective Modal Bandwidth Computed (EMBc) Effective Modal Bandwidth Computed or Calculated EMB is a technique that reckons the worst case bandwidth that the fiber may exhibit when coupled to a VCSEL [51]. Therefore, it takes into consideration the type of source utilized. It consists of weighting each of the radial traces of the DMD plot by unit-less fractions specified for ten lasers that are representative of more than 10000 standard-compliant and commercially available VCSELs. These weights, generated from regulated EF calculations, are compiled in ANSI/TIA-492.AAAC-B (2009) which also reports the EMBc measuring procedure and a full description of DMD. The standardized procedure follows the next steps [22]: 1. DMD calculation 2. Weighting the DMD radial traces with the corresponding ten factors (ten for each position) 3. The scaled pulses are summed up for each laser option. This generates ten scaled DMD plots. 4. The worst-case plot is multiplied time 1.13. The result is the EMBc This system is mostly used by MMF manufacturers to assure 10Gbps (or more) compliance of the fiber for any existing type of VCSEL. Notice that, if the source is fixed and known, EMBc calculation is not necessary given that the field produced is very specific. 86 A.5.2 VCSEL It is now known that this LDs exhibit some little desirable features that, although are present in many other sources, are noticeably more marked in VCSELs. Some of the possible factors are multimode operation, carrier diffusion, secondary pulsations in the turn-off transient and, above all, the thermal behavior [17]. Given their special impact, all these influencing factors require of a model that account for them (at least thermal dependence). Its development need of a very a deep physical insight that ends up in complicated and very computational demanding simulators. From the data transmission point of view, there are a group of key parameters which can be extracted from the three VCSEL’s representative curves that allow the engineer to evaluate if the LD meets the pursued requirements or not. Nonetheless, the design of a VCSEL that satisfies those concrete specifications (downstream) is something completely different. In such case, a complete understanding of the model parameters and their specific impact on the communication-relevant figures of merit is required in order to tune the laser’s properties within sensible/realistic intervals. Here, the three main characterizing curves of a VCSEL are introduced. A.5.2.1 Light-to-current-to-voltage (L-I-V) The name comes from Light-Intensity-Voltage and it shows the output optical power and the device voltage with respect to the input current. It gives information about the maximum optical output power, threshold current, input impedance, safe current ranges, rollover region and some other thermal-dependent effects [17] [18] [16] . Figure A-16, shows a VCSEL’s LIV curve for a particular bottom emitting AlGaAs laser *17]. The blue, red and green traces represent the output power at 25oC, 50oC and 75oC respectively. Their slope is given by the thermal resistance and the maximum power is achieved at the so-called “rollover current”. From that point on, the laser’s self-heating changes the physical properties and the power drops. Notice that it is a progressive process. The linear range for the output power is comprised between 5mA and 15mA. It can be also observed the threshold current increases with the temperature from 2.5mA to 3mA. The voltage function is represented in black and it exhibits non-linear behavior at low currents. The electrical input impedance can be estimated from its slope (25). The LIV curves can vary considerably from laser to laser depending on the layout and materials used. In order to illustrate this, two more LIV curves are shown in Figure A-16 and Figure A-17 for index-guided InGaAs and a thin oxide AlGaAs 65. 25 The laser behaves as a diode and, in theory, the resistance should me infinity in the other polarization 87 Figure A-16 LIV curves for AlGaAs VCSEL in (left) and index-guided InGaAs VCSEL(right). The most remarkable difference between AlGaAs and InGaAs plot is the variation of the voltage with the temperature. From top to bottom, they correspond to voltages at 25oC, 50oC and 75oC. Figure A-17 LIV of thin oxide AlGaAs VCSEL. The special property of the thin oxide AlGaAs is that it shows no output power that at 75oC. This is due to the excessive increase of the threshold current and the degradation of the slope efficiency [75]. A.5.2.2 S21 / transfer function The next tool to characterize a VCSEL is the response of the system at different wavelengths or “dynamic response”. This can be expressed either with the s21 parameter to account only for the device input impedance or with the transfer function, that considers the “source” impedance to account for possible mismatch at the input. 88 Figure A-18 Small-signal modulation response (s21) for 3 different drive currents [76]. The measurement of the modulation bandwidth of a laser is strictly relevant when direct modulation is used. The transfer function provides information about the maximum reachable bandwidth (3dB bandwidth (BW)) for a given bias current. Figure A-18 shows an example of s21 for a particular 850nm VCSEL with an active region comprising multiple In0.072Ga0.928As quantum wells to improve differential gain and reliability. It exhibits an especially high bandwidth at 10mA (>20GHz) and the key parameters and physical composition are described in [76]. Owed to the carrier density variations (see section A.1.2.1), LDs present resonances in their frequency responses which are proportional to the bias current and inversely proportional to the carrier and photon lifetime in the cavity. This can be clearly seen in Figure A-18, where two peaks at around 7.5GHz and 13Ghz are generated with 2mA and 5mA respectively. On the other hand, the damping factor is proportional to the bias, causing a fading of the peak as the injected current increases. A.5.2.3 Spectrum The linewidth, center wavelength and general spectral properties are also relevant in any LD characterization. Typically, the optical spectrum of a VCSEL is narrower than that of a Fabry Perot (FP) laser and broader than that of a Distributed Feedback Laser (DFB) which is designed for single wavelength operation [34]. In general, the linewidth has a direct impact on the optical link performance through chromatic dispersion hence it is convenient that the light spectrum is as confined as possible at the center frequency. For its part, undesired offset of the center frequency or instabilities may cause unexpected attenuation, pulse-spreading and a great performance worsening in case of coherent detection. 89 B Software evaluation: references and procedures B.1 VPItransmissionmaker™ Because High-Speed Optical Communications Group already had licenses at their disposal, this CAD tool was the first one to be evaluated. This award-wining (26) program has been designed for modeling all types of photonic systems and networks and it has been reference for more than 650 publications up to 2010 [77]. It offers an intuitive modular graphical interface, a robust simulation scheduler and satisfactory signal representation. Nevertheless, it was not until the version 8.6 was released (March, 2011) that several enhancements on the MMF module and power coupling capabilities were included. This fact casted doubt about the precision of the multimode transmission and spatial field distributions. No information was found concerning the VCSEL. B.1.1 MMF module B.1.1.1 Differential Mode Attenuation (DMA) REFERENCE The test was carried out based on the results found in [14]. In the experiments, two different types of fiber were tested; labeled fiber A and fiber B (see Table B-1). The MMF was illuminated through a SMF lens launch technique, which produced a 3 µm spot size. The laser in the end facet of the SMF was a FP at 1300nm. The method utilized to measure the DMA is the following: 1. Perform a radial sweep of the laser’s core. Measure the overall fiber loss over a short length of fiber (2m for fiber A, 0.3m for fiber B) for every position. The losses observed are only owed to light injection. The curve is normalized to set the maximum power at 0 dB. 2. Perform a radial sweep of the laser’s core. Measure the loss over a long link length (1Km for fiber A, 0.8Km for fiber B) for every position. This measurement accounts for the losses due to light injection, propagation and DMA. The curve is normalized to set the maximum power at 0dB (propagation loss removed). 3. Normalize the latter with respect to the first one in order to remove the light injection dependent attenuation. The resulting graph represents the DMA. In [14], this third step is skipped and a combined plot of step one and two is shown instead. In such case, it is the difference between the traces what determines the DAM effect at a given radial offset. Simulations are also performed to support the results obtained in practice. One of the assumptions is a Gaussian shaped near-field distribution out of the SMF-lens launch. The results are shown in Figure B-1. 26 Optical Society of America Technical Excellence Award 1999 96 With the intention of illustrating the impact of a variation of the MGD in the DMD, the following mathematical development of (B.1) is presented: 𝐼𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒𝐷𝑀𝐷= 1 𝐶𝜏𝑚 𝑀𝐴𝑋 𝑂𝐹𝐹𝑆𝐸𝑇 𝑚=0 𝐾1,𝜏 𝑚𝜏1+𝐾2,𝜏 𝑚𝜏2+⋯ =1 𝐶𝜏1 𝐾1,𝜏 1𝜏1+𝐾2,𝜏 1𝜏2+⋯ +1 𝐶𝜏2 𝐾1,𝜏 2𝜏1+𝐾2,𝜏 2𝜏2+⋯ +⋯= =𝜏1 𝐾1,𝜏 1 𝐶𝜏1+𝐾1,𝜏 2 𝐶𝜏2+⋯ +𝜏2 𝐾2,𝜏 1 𝐶𝜏1+𝐾2,𝜏 2 𝐶𝜏2+⋯ +⋯ (B.2) The mean DMD is obtained as described above. The normalization with respect to the minimum allows ascribing the whole DMD to a single DMG. Therefore: 𝑚𝑒𝑎𝑛𝐷𝑀𝐷=𝜏𝜏𝑀𝐴𝑋 𝐾𝜏𝑀𝐴𝑋,𝜏 1𝐶𝜏1+𝐾𝜏𝑀𝐴𝑋,𝜏 2𝐶𝜏2+⋯ (B.3) Associating 𝜏𝑀𝐴𝑋 to the maximum delay for the scaled MGD, the same procedure can be done to calculate the mean DMD generated by the scaled index profiles (𝑇𝑀𝐴𝑋) : 𝑚𝑒𝑎𝑛𝐷𝑀𝐷=𝑇𝑇𝑀𝐴𝑋 𝐾𝑇𝑀𝐴𝑋,𝑇 1𝐶𝑇 1+𝐾𝑇𝑀𝐴𝑋,𝑇 2𝐶𝑇 2+⋯ (B.4) The information provided in the model comprises 𝜏𝑛 and 𝑃𝑛,𝜏 𝑚 for every offset. For its part, 𝑇𝑛 is obtained through simulation. The number of excited modes (𝑁𝑛,𝜏 𝑚) can be calculated based on 𝑃𝑛,𝜏 𝑚 and applying (2.18). However, there is not explicit or implicit information about the light coupling for the test performed by the University of Cambridge on the scaled profiles. This prevented us from transforming the simulated 𝑇𝑛 into DMD plots with (B.4). The next most accurate option to assess the accuracy of VPItransmissionmaker™ implied the assumption that the factor accounting for light coupling in (B.3) and (B.4) was very similar. This is not a bad approximation given that the launch conditions are very clearly stated (see Table B-3) and that the profile scaling sticks to little modifications of the perturbations rather than a complete remake of the index contour [79]. In such case, the ratio between the mean DMDs can be expressed as: ∆𝐷𝑀𝐷 % =𝜏𝜏𝑀𝐴𝑋 𝐾𝜏𝑀𝐴𝑋,𝜏 1𝐶𝜏1+𝐾𝜏𝑀𝐴𝑋,𝜏 2𝐶𝜏2+⋯ 𝑇𝑇𝑀𝐴𝑋 𝐾𝑇𝑀𝐴𝑋,𝑇 1𝐶𝑇 1+𝐾𝑇𝑀𝐴𝑋,𝑇 2𝐶𝑇 2+⋯ ≈𝜏𝜏𝑀𝐴𝑋 𝑇𝑇𝑀𝐴𝑋 (B.5) Because the idea behind scaling the profiles is to make the DMD difference equal to zero, it is not a bad approximation to assume that at least the tendency of the MGD curves is maintained. This means that the 97 DMG that causes the maximum delay is likely to be the same for both scaled profile and scale MGD. This would permit to rewrite (B.5) as: ∆𝐷𝑀𝐷 % ≈𝜏𝜏𝑀𝐴𝑋 𝑇𝑇𝑀𝐴𝑋 ≈𝜏𝑀𝐴𝑋 𝑇𝑀𝐴𝑋 (B.6) With this method, the ratio of the DMDs is calculated and compared with the ratio of the maximum absolute delays in the MGDs. The more similar the more accurate the simulator is. Given the little usage and the poor future perspective of OM1 fibers, it was not possible to find information about the DMD ranges for this type of fiber. Nevertheless, it was observed that the ratio between the minimum “outer” DMD and the maximum one for OM3 and OM4 was around 50%. Since the DMD calculated by the University of Cambridge could be considered “outer” type (see Table B-3) this factor of proportion was also assumed for our 62.5µm fibers. Based on that and accounting for the error caused by the approximation, it was decided to establish the fifth part of it as the validation percentile (10%) for the ratio deviations. That is, it will be considered that there is good agreement when the difference keeps below 10%. The evaluation procedure is structured as follows 1. Estimate the difference between the red circle and the black circle for the fiber under test in APPANDIX. Calculate the ratio. 2. “A” case: Pick the maximum absolute value of the blue and red traces. Calculate the ratio. (B.6) 3. “B” case: Pick the absolute value of the red trace at the position of the maximum value of the blue trace. Calculate the ratio. (B.5) 4. Ratio comparison As a general consideration, it must be said that the delays at the highest DMGs (18, 17 and even 16) should not be taken into so much consideration as the rest. The modes within these groups propagate very close to the core-cladding boundary and at those radial positions the propagation is unpredictable. Those modes end up being radiated most of the times; therefore, associating a “propagation” delay to them is meaningless. The results are summarized in Table B.5. Table B-5 Individual delay ratios and similarity result. Green shaded cell are hits, red cells are misses. ∆𝑫𝑴𝑫 % ∆𝑴𝑮𝑫 % 𝒎𝒊𝒏 ∆𝑫𝑴𝑫 % ,∆𝑴𝑮𝑫 % 𝒎𝒂𝒙 ∆𝑫𝑴𝑫 % ,∆𝑴𝑮𝑫 % FIBER #7 0.9482 0.9702 97.73% FIBER #17 1.00755 1.2103 83.24% FIBER #31 0.809523 0.8008 98.92% FIBER #37 1 0.8441 84.81% FIBER #51 8.9 - - FIBER #59 1 1.1379 87.88% FIBER #61 0.9756 0.8488 87% FIBER #65 0.9389 1.0294 91.20% FIBER #81 0.6043 0.8946 67.54% 98 FIBER #95 0.7407 0.8691 85.22% FIBER #101 0.9350 0.9609 97.30% FIBER #103 1 0.9526 95.26% FIBER #105 0.985 0.7858 79.77% Five of the fibers are above the threshold, what means that more than 61% are in disagreement. The results correspond to the ratio calculated with (B.5). FIBER #51 and #81 are discarded according to Cambridge recommendation. B.1.1.3 Mode Power Distribution (MPD) REFERENCE The reference used for measuring the power-coupling accuracy of VPItransmissionmaker™ is Cambridge 108-fiber model [78]. Together with MGDs and spectra for each of the fiber, a spreadsheet with 18 power coefficients (18 DMGs considered) for each of the 31 radial positions is included. Expressed as the percentage of power coupled, anything below 0.5% is neglected and rounded down to zero. Notice that we are working with DMGs and not modes hence considerable less power that 0.5% of the total is actually coupled into the modes contained in the corresponding DMG. The measurements are done with the launch conditions summarized in Table B-3. SCHEMATIC Similarly to the MGD case, the CAD tool generates a text file with the coupling coefficients for a given radial offset and spot size whose values are introduced in the MMF module itself. MATLAB® was used for postprocessing the data and to perform the evaluation. RESULTS Two things are important regarding power coupling: the power percentage and the concrete DMGs into which it is being injected. Both aspects are accounted in the analysis. Firstly, the power coefficients have been plotted with respect to the DMGs and compared qualitatively. The spot size in the simulator is set to 7µm FWHM with Gaussian field distribution. For the ease of representation, only 8 of the 31 curves are presented in Figure B-6. They correspond to radial offsets of 0µm, 4µm, 8µm, 12µm, 16µm, 20µm, 24µm and 28µm. Besides, the coefficients have been joined with a continuous trace. It should be clarified that any value within DMGs (non-integer) may not be exact and should not be considered. 99 Figure B-6 Percentage of power coupled into each DMG for different radial positions. The blue curve represents the coupling coefficients provided by the University of Cambridge and the red trace the coefficients calculated with the simulator. It can be seen that the amount of power coupled into the main DMGs (for offsets higher than 4µm) according to Cambridge model is noticeable greater than the one calculated with the simulator. The difference is in average 4% that represents approximately between 13% to 22% of the maximum percentage coupled to one mode (expect for offsets from 0µm to 4µm). Furthermore, and despite Figure B-6 is not the best representation, is can be foreseen a wrong excitation based on the excessive width of the individual red curves. Note that as the offset increases, the power spreads over a larger number of DMGs. This is because the degeneracy of the modes is approximately twice the group number [14] and hence, a selective excitation of a high order DMG will divide the power into a larger number of modes than for instance DMG 1 (only LP01). In order to check if the excited modes are the correct ones, Figure B-7 is presented Figure B-7 Number of excited modal groups as a function of the radial offset. The FWHM spot size of the source is 7µm with Gaussian field distribution. 100 It is observed that there is hardly agreement between both references. Albeit some discrepancy is expected for high order modes, in any case a difference of 4 DMGs could be reached (33% of the target maximum). The differences for low order modes are also high, with a maximum of 3 missing DMGs at 3µm, 4µm, 5µm offset. The average number of mistakes is 2. B.1.2 VCSEL module The analysis of the VCSEL module performance in VPItransmissionmaker™ was as short as decisive: the range of nominal emission frequency goes from 50THz up to 300THz. This means that it cannot be used for simulations with wavelengths higher than 1000nm. Given the special interest in using the first window, the only option would have been to create our VCSEL model. B.2 OptSim™ (ModeSYS™) Due to the limitations found in the previous software, it was decided to test this well-known simulator. ModeSYS™ supports the design and simulation of multimode optical communication systems. With a primary focus on data communication applications, it allows both temporal and spatial analysis of optical signal and their propagation. Similarly to its counterpart, it provides together with OptSim™ an intuitive graphical interface and lab-like measuring instruments. B.2.1 MMF module B.2.1.1 Differential Mode Attenuation (DMA) REFERENCE Same reference as for VPItransmissionmaker™ SCHEMATIC Replicating the setup in [14]: Figure B-8 Schematic for DMA test in ModeSYS™- From left to right: LASER, spatial coupler, MMF, multiband to singleband converter and optical power meter. The “Mb2Sb” is used to collapse every mode into one unique optical signal. Given that the only 101 intention is to measure the power, it is convenient to treat them as an aggregate group rather than as individual entities. The multimode fiber and LASER are adjusted according to the description in section B.1.1.1. The coupler is ideal (neither insertion loss nor misalignments) and it is necessary to couple spatially distributed fields into MMF. The “scan” button is used to sweep the offsets and represent the power variation in correspondingly. The power values were saved in a text file and imported into MATLAB®. RESULTS DMA is explicitly implemented in this simulator. It requires the user to fill out two fields: order of the modified Bessel function of the first kind and scaling factor (see (2.16)). Based on the attenuation tendency observed in Figure B-1 (constant attenuation and decay for high offsets), the order of the Bessel function was set to one. In order to find the correct or most approximate value for the scaling factor, a range within 1 and 30 was scanned (finally set to 21). It is important to realize that the formula for the DMA does not depend on the distance although the physical effect does. This is somehow confusing but it facilitates a lot the determination of the scale factor. The result for fiber B is shown in Figure B-9. Figure B-9 Normalized loss vs. launch offset after 2m and 1km of fiber B. The blue trace corresponds to the attenuation for 0.3mtransmission link and the red line represents 800m transmission. The offset was ranged between 15µm and 35µm to avoid unnecessary computational load and increase the precision of the representation. High level of agreement is exhibited by using 20µm, 25µm and 30µm as reference points. According to Figure B-1, their values should roughly be -1dB, -4dB and -15dB. This is exactly what is observed in Figure B-9. Similar results were obtained for fiber A, whose profile had to be readapted to the new format supported by ModeSYS™. 102 B.2.1.2 Mode Group Delay (MGD) Unlike VPItransmissionmaker™, ModeSYS™ do not generate the MGD plot. Instead, it creates a file that contains the modal delays influenced by the launch conditions in a way which is not described. This means that the result is completely dependent on, at least, the spot size and radial offset. This complicates enormously the calculation of the relative MGD even assuming that the impact of the launch conditions is known and reversible. It requires undoing the DMG groups, invert the effect mode by mode, group them back in DMGs and perform the comparison described in section B.1.1.2. Notice that the first 18 DMGs contain 190 modes in total and that this process should be repeated for each of the 13 fibers at least for two different offset positions. This possibility was discarded as a result of the excessive workload and time needed. Owed to the possibility of calculating the DMD in ModeSYS™, the next option was to calculate the simulated DMDs and compare with the corresponding results obtained by the University of Cambridge. This was a straight-forward and more reliable method since no assumption is taken and it is not necessary to calculate ratios for indirect comparison. However, as explained in section B.1.1.2, the DMD definition in the 108-fiber model differs from the one in the software. The first one is called “mean DMD” and the second corresponds to the standardized method described in TIA-455-220. This fact prevented us from making a reliable validation as it was impossible to modify the DMD module in ModeSYS™ and transform it to calculate a mean DMD. Furthermore, the results from both definitions could not be compared since the relation of proportion between them was not known with sufficient precision. Consequently, the publications presented by the RSoft Design Group regarding the simulation of communication links based on the 81-fiber model (previous version to 108-fiber model) ([80] and [81]) together with the application notes called “CambridgeModel_case1” and “CambridgeModel_case2” in *82] were evaluated. [80] was a mere exposition of results without any direct comparison or conclusion. However, in [81] it was proved that an error of less than 5% in the scaling factors is achieved for three different fibers of the 81-fiber model. The tests are done based on the mean DMD and impulse response instead of MGD, which constitutes a much more reliable and decisive validation method for the modal delay algorithm. The application notes investigate the effect of index distortions in the 81-fiber model on fiber performance and, subsequently, on eye diagrams in data-modulated multimode link. The calculation of the resulting MGDs is included as well as bandwidths. No reason was found so as not to trust the good results obtained by the design group. B.2.1.3 Mode Power Distribution (MPD) REFERENCE Same reference as for VPItransmissionmaker™ SCHEMATIC 103 Figure B-10 Schematic for MPD test in ModeSYS™. The LASER spot size is set to 7µm which corresponds to 4.2µm of beam width for Laguerre-Gaussian mode profile. The wavelength used is 1300nm. The offset is increased by one every iteration (31 iterations). Notice that it was not necessary to terminate the link. The text file is formatted and imported into MATLAB® RESULTS Figure B-11 shows the MPDs for 0µm, 4µm, 8µm, 12µm, 16µm, 20µm, 24µm and 28µm of radial offset. Figure B-11 Percentage of power copled into each DMG for different radial positions. The blue curve represents the coupling coefficients provided by the University of Cambridge and the red trace the coefficients calculated with the simulator. It can be observed a considerable increment of the accuracy in the power percentage compared with Figure B-6. The average difference of the power coupled into the two most excited DMGs for each offset is reduced from 4% to 0.78% (more than 5-fold accuracy increment). In the worst case, that percentage constitutes 5% of the maximum power coupled into one mode (offsets of 28µm and higher). For its part, Figure B-12 shows the excited DMGs for every offset. 104 Figure B-12 Number of excited modal groups as a function of the radial offset. The FWHM spot size of the source is 7µm with Gaussian field distribution. It can be seen that it does not exist deviance at all for the first 17µm. From that point on we approach the core-cladding interface (7µm FWHM spot size) and some oscillation is comprehensive. Besides, the maximum deviation never exceeds 1 DMG fault (8% of the target maximum) and the tendency is followed perfectly. B.2.2 VCSEL module ModeSYS™ provides a VCSEL model that takes into consideration the spatial distribution of the output field so that it can be combined with the MMF through a spatial connector. Besides, the module not only sticks to general behaviors but other important ones such as spatial hole burning, lateral carrier diffusion, thermally dependent gain and thermal carrier leakage are all accounted for. The study of the physical model was beyond the reach of this investigation however, it was necessary to assure that it behaved properly when introduced into a communication system. Given the confidentiality and in some cases uncertainty about the exact values of the physical parameters that characterize a VCSEL, it resulted impossible to provide any more accurate test than a graphical comparison of the LIV, s21 and Back-to-Back (B2B) eye diagrams. REFERENCES The references used are [76], [83] and [84]. They provide complementary information about a very similar VCSEL model developed in the Department of Microtechnology and Nanoscience in Chalmers University of Technology. It generates 9mW of maximum output power and has 20GHz bandwidth at 10mA (very high speed). The series resistance is around 80Ω, the slope efficiency 0.7-0.8W/A and the current threshold is 0.6mA. Figure B-13 shows the LIV at 25oC and s21 for three diverse bias currents. 105 Figure B-13 Targeted LIV curve and small-signal modulation response [76]. Another parameter that can be estimated from the LIV is the turn-on voltage, which is around 1.7V. The capacitance is mostly canceled in order to reach such high modulation frequencies. The s21 shows the progressive increment of the damping factor with the bias current for a fixed photon lifetime inside the resonance cavity. Once the response of this concrete laser was estimated, [85] was used to include it into a full transmission simulation. The authors used the VCSEL in [85] to launch a 4-PAM signal into an OM4 at 12.5GBd and 15GBd, which is equivalent to 25Gbps and 30Gbps. The 4-PAM modulation was achieved by decorrelating two binary signals of 27-1 length and 900mV and 450mV amplitude. The experiment is done over 200m and 300m fiber spans and the propagated signal is received with an amplified photodiode of 12GHz BW. The error counting is done through an adapted On-Off Keying (OOK) BER tester under the assumption of high enough SNR to consider that errors are exclusively caused by neighboring symbols. The formula utilized to calculate the total bit error rate is: 𝐵𝐸𝑅=1 8(𝑃01 +𝑃10 + 2𝑃12 + 2𝑃21 +𝑃23 +𝑃32) (B.7) with 𝑃𝑥𝑦 being the conditional probability of receiving 𝑦 when 𝑥 was sent. SCHEMATIC LIV & s21 The VCSEL module in ModelSYS™ has its own test feature. The user selects the plot or report wanted and the result is presented in an autogenerated graph or a text file respectively. It is not necessary to select any PRBS length, bit rate or voltage/current modulation input levels to check the LIV and s21. The temperature point and the bias current are provided within the same test tool hence it is not necessary to change them 112 Max. Linewidth - - 0.85 nm Min. OMA -4.3 - - dBm Typ. ER 3 5 - dB Avg. Output power -4 -2 -0.7 dBm Temperature -40 25 90 oC Max. Output power variation over the specified temperature range - 0.5 1 dB Bias current - 8 9 mA Mod. Response32 - 11±1 - GHz No information about the spot size or field distribution was provided hence absolute flexibility was assumed. Consequently, the encircled flux analysis was not required. C.1.2 Procedure Firstly, the PRBS block and the binary to electrical converter are adjusted with the parameters from the table. With regard to the bit rate, it was set to 10Gbps given that a compliance with 10GBASE-SR standard was intended. Because of that, we had to assure the best agreement possible between simulation and requirements at that specific bit rate. The rise/fall time was set to 30ps (66% of the maximum) and the differential input voltage to the laser was fixed at 600mV. Concerning the VCSEL, its modeling consisted of tens of iterative sweeps of parameters. Starting from the AlGaAs predefined model, the variables were progressively tuned from the most stable and clear (wavelength, driving system or room temperature) to the most uncertain ones (thermal gain, parasitics, turn-on voltage or current injection efficiency). The LIV and s21 were constantly checked to assure reasonable behavior and thereby restrict at maximum the sensible intervals for the parameters based on the operational ranges provided. Special care was put in the stability of the laser with respect to the temperature (check “Max. Output power variation over the specified temperature range” in Table C-1) since it turns crucial in avionic networks; where the ranges are drastically larger than in ground level. The extinction ratio was checked with “EyedB” and the OMA with “EyeW”. The linewidth was measured with “Spectrum” at 3dB. C.2 Receiver C.2.1 Schematic and specifications 32 Bandwith at bias currents within the predefined interval [8mA,9mA]. 113 Figure C-2 Schematic utilized for the receiver design. The “PRBS”, “ElecGen” and “VCSEL” are responsible for the signal generation. The outgoing data stream passes through “PowerNorm” that regulates the average optical power to set it at a certain level preestablished by the user. Finally, the signal is converted to electrical in the PD, amplified in the TIA and filtered in the LPF. All these stages are embedded in the “receiver” block. The rest of the blocks are measuring tools like power meters, eye mode in scopes, OSAs and BERtester. The electrical and optical specifications are collected in Table C-2 (33). Table C-2 Specifications for the receiver. Parameter Min Typ Max Unit Wavelength 760 850 860 nm Max. Linewidth - - 1 nm Max. Average optical power -5 -3 0 dBm Optical sensitivity at 10Gbps - -15 -12 dB Differential output voltage 200 400 700 dBm C.2.2 Procedure Following the natural route of the ligh/current, the PD was the first device faced. As the type (PIN) and the composition (GaAs) were given, the only parameter to be set was the quantum efficiency (QE). It is defined as the degree of effectiveness of the incident radiant flux for producing current [21] and it is a different way of expressing the PD responsivity. The output of the adjusted photodiode was analyzed in order to calculate the necessary gain in the TIA to generate values within the range of the differential output voltage (see Table C-2). This is done modifying the feedback impedance of the transimpedance amplifier. When reasonable values were obtained, the noise power was adjusted to achieve the target sensitivity. For this, the LPF’s cut-off frequency was set to 10GHz and “PowerNorm” was set to -15dBm. The tuning was done accordingly to the BER result. 33 Bold numbers represent estimations. 114 C.3 MMF C.3.1 Schematic and specifications Figure C-3 Schematic used for the MMF design. The “MML” block is a mode-locked laser. It simulates the response of a 5µm mode field diameter Titanium Sapphire laser to generate the necessary 10ps FWQM pulses for the DMD test on OM3+ and OM4 fibers. The spatial coupler is responsible for the radial scan of the OM4’s end face every 1µm. After propagation, the pulses are collected and processed into the DMD module, which builds the DMD plot and calculates the accumulated time spread. The receivers and “TransFunc” are used to follow the evolution of the bandwidth with every change. Recalling what was discussed, the DMD specifications provide maximum delays for each of the three intervals. One fiber that remains below those particular values, guaranties certain transmission capabilities certified by the committee. For OM4, the particular delays are still under discussion but a first draft has been released (see Table C-3). Table C-3 DMD specifications for OM4 fiber [51]. Specifications Inner DMD Outer DMD Sliding DMD 1 ≤0.10 ≤0.30 ≤0.11 2 ≤0.11 ≤0.17 ≤0.11 3 ≤0.14 ≤0.14 ≤0.11 C.3.2 Procedure The general parameters from the datasheet were loaded into the OM4 module. The most relevant ones and their values are summarized in Table C-4. 115 Table C-4 List of specifications reported in Darka’s datasheets for their OM4 fiber. Parameter Value Unit Attenuation (850nm) <2.2 dB/km Zero dispersion wavelength 1295≤λ0≤1340 nm Zero dispersion slope ≤0.105 ps/nm2∙km Group refractive index (Typ.) 1.482 - Refractive index difference 1 % The core refractive index was approximated through the group refractive index as first approach. The Sellmeier’s equation (FORMULA) for fused silica was used as an approximation for the refractive index variation with respect to the wavelength. The dispersion wavelength was initially set to 1315nm, the zero dispersion slope was established at 0.102 ps/nm2∙km and 2.1dB/km for the attenuation. The effects of material dispersion on group velocity were taken into consideration. The group refractive index was introduced and the profile dispersion parameter was set to zero at the beginning. This allowed us to set an initial value of 2.07 to the profile exponent based on the estimation in [51] of the optimum coefficient for 50µm silica fibers at 850nm. The DMA feature was deactivated at first. This was done in order to see the actual delay of high order DMGs on the DMD plot and thereby understand the impact of each parameter. Once the starting values were established the corresponding adjustment was performed. The process can be simplified in the next four steps: 1. Variation of the profile exponent and core refractive index 2. Check MGD 3. Adjustment of the profile dispersion parameter 4. Check DMD The MGD was used because its generation was almost instantaneous and it can be associated indirectly to the DMD behavior hence saving a lot of time. The impact of the chromatic dispersion parameters was also tested however, the DMD hardly showed any variation for values within the ranges in Table C-4. Consequently, those parameters together with the refractive index difference remained the same as initially. C.4 10GBASE-SR C.4.1 Specifications All the specifications were obtained from the 10GBASE-S definition (Short Wavelength Serial PMD) in the IEEE 802.3ae standard. 116 Figure C-4 Fiber optic cabling model It is important to remark that the IEEE 802.3 group assumes a link operation over a reasonable range of environmental conditions related to temperature, humidity, and physical handling (such as shock and vibration). The final implementation of the network will need the usage of specific aerospace connectors such as Diamond AVIM connector family and the Deutsch MC3 MkII and MC5. Up to date, there is no OM4 equivalent for airborne systems. Its re-design or protection will be necessary as well as for the rest of conventional components which will be exposed to those strict conditions and whose official adaptation has not been stipulated yet. Another important consideration is the ease of splicing and maintenance which should be as simple and reliable as possible. In this regard, there are some mechanical splicers that have been proved to pass most stringent aerospace qualifications (see [86]) C.4.2 Transmitter A direct comparison between the PMD requirements and D-lightsys’ emitter is presented in Table C-5. Table C-5 Comparison between 10GBASE-SR transmitter requirements and D-lightsys’s transmitter. Description 10GBASE-SR D-lightsys transceiver Units Signaling speed (nominal) 10.3125 10 (34) GBd Wavelength 840 to 860 840 to 860 nm Max. RMS spectral width 0.45 0.85 nm Max. Average launch power -1 -0.7 (35) dBm Min. Average launch power -7.3 -4 dBm Min. OMA -4.3 -4.3 dBm Extinction ratio 3 3 dB Max. RIN -128 -117 dB/Hz Encircled flux See footnote36. See Figure C-6 - Eye mask definition {X1, X2, X3, Y1, Y2, Y3} {0.25, 0.40, 0.45, 0.25, 0.28, 0.40} See Figure C-5 - 34 The maximum bit rate is determined by the modulation response at a certain temperature and bias. No information is provided about signaling speed variation but it is plausible to assume that 10.3125Gbps is attainable with a correct control and adjustment of both parameters. 35 The transceiver is Class 1M according to IEC 60825-1 but the output power can be adjusted through a 2-wire serial interface to keep it below -1dBm. 36 The encircled flux at 19 μm shall be greater than or equal to 86% and the encircled flux at 4.5 μm shall be less than or equal to 30% when measured into Type A1a (50/125 μm multimode) fiber per ANSI/TIA/EIA-455-203-2001. 117 For the sake of simplicity, it is assumed that the RMS spectral width and Relative Intensity Noise remain below 0.45nm and -128dB/Hz respectivelty. It should be noticed that these parameters, as well as the signaling speed, are readily tunable in the simulator to keep them below maximum ratings. Encircled flux and eye mask tests are done with ModeSYS™. Figure C-5 Optical eye diagram and the 10GBASE-SR eye mask specification. Figure C-5 illustrates a combined plot of the optical eye and the corresponding eye mask. For the eye to fulfill the 10GBASE-S specifications, it has to contain the calculated eye mask inside the aperture. Such mask is built according to the format described in the standard. Notice the normalization. Figure C-6 Encircled flux of the VCSEL model and reference masks. As described above, the modal field distribution of the VCSEL must have less than 30% of the total radiated power within the first 4.5µm and more than 86% between 0µm and 19µm to be deemed compliant with the 10GBASE-S PMD. Figure C-6 shows the VCSEL’s EF for a center launch (0µm offset) with 15µm diameter Laguerre-Gaussian spot size. It is widely contained in the acceptable operational region. The conclusion is that all the parameters fully comply with the specifications with the exception of the uncertainty about the RIN and linewidth assumptions. 118 C.4.3 Receiver A direct comparison between the PMD requirements and D-lightsys transceiver is presented in Table C-6 (37). Table C-6 Comparison between 10GBASE-SR receiver requirements and D-lightsys’s receiver. Description 10GBASE-SR D-lightsys transceiver Units Signaling speed (nominal) 10.3125 10.3125 GBd Wavelength 840 to 860 840 to 860 nm Max. Average receive power -1 0 dBm Min. Average receive power -9.9 -15 dBm Max. SRS in OMA -7.5 -15.5 dBm Max. Receive electrical 3 dB upper cutoff frequency 12.3 12.3 GHz Max. Return loss -12 -12 dB The receiver shall be able to tolerate, without damage, continuous exposure to an optical input signal having a power level equal to the Max. Average receive power plus at least 1 dB. Besides, a received power below Min. Average receive power cannot be compliant; however, the lower limit is said to be purely informative thereby it will not be regarded as long as we stay below it [25]. In any case, the requirements are met. The Stressed Receive Sensitivity is the way how sensitivity is specified in 1GbE standards. It establishes the maximum OMA of the incoming signal at which the receiver is required to attain BER equal or lower than 10-12. Compliance is achieved when the receiver is equal or lower than the standard. In our case, it was measured with conformance test signal at TP3 [25] for BER = 10–12. Concerning the maximum 3dB bandwidth of the LPF, since the filter it is not part of the transceiver it is assumed to equal the standard. C.4.4 Channel and power budget The specifications for 50µm MMF at 850nm and their comparison with the simulation results are gathered in Table C-7. 37 Bold numbers represent estimations. 119 Table C-7 Comparison between 10GBASE-SR channel requirements and OM4 model. Description 10GBASE-SR OM4 model Unit Min. OM4 operational distance 550 550 m Max. OM4 operational distance N/A 700 (see fotnote38) m Max. Insertion loss 2.6 (39) 2.6 dB Max. Fiber cable attenuation 3.5 2.2 dB/km Zero dispersion wavelngth 1320 1315 nm Max. Zero dispersion slope 0.11 0.102 ps/nm2∙km As indicated in the standard, the maximum operational distance is calculated based on an allocation of 1.1dB40 total connection and splice loss, leaving 1.5dB for fiber attenuation. In the worst case of 2.1dB/km the maximum reachable distance is 714.28m (700m). The attenuation after 550m of OM4 fiber at 2.1dB/km is 1.155dB, what leaves 1.445dB margin for connectors and splices. In simple point-to-point links where two connectors are used, this corresponds to two connectors of 0.3dB41 loss and six 0.15dB42 splicings. C.5 Optical Orthogonal Frequency-Division Multiplexing (OOFDM) C.5.1 Modulator C.5.1.1 Design parameters The design parameters are chosen with respect to the previously stated constraints. Table C-8 presents the summary. Table C-8 Design parameters for the OOFDM modulator. Description Value Unit Number of subcarriers 256 - Modulation per channel 4/16/32-QAM - Training sequences 2 - Cyclic prefix 1 % Oversampling 2/4 - IM mode DCO-OFDM - 38 Maximum reachable distance assuming BER≤10-12 39 It includes losses due to connectors, splices and fiber attenuation (OM3 reference). It should be noted that when IEEE 802.3ae was released in 2002, the fiber with the best performance was OM3. 40 This number results of the estimated adaptation of 10GBASE-S power budget requirement to the OM4 fiber type [87]. Connectors and splices are much more precise for OM4 and thereby the loss reduction. 41 Maximum registered for OM4 being 0.2dB/0.25dB the typical value for aerospace connectors. 42 Maximum splice losses of Draka’s bend-insensitive 850 MMF. 120 PAPR handling Clipping - Sampling rate Variable GS/s The number of subcarriers is determined by a combined trade-off. Given a fixed bandwidth, increasing the number of channels assures almost completely flat fading hence facilitating the equalization and making it more accurate. Besides, the number symbols per OFDM symbol is greater and this increases the effective bit rate. On the other hand, it will worsen the maximum PAPR thereby raising the non-linear effect of clipping or the necessary dynamic range of the DAC. Furthermore, the subcarriers get closer and closer within the available bandwidth and this makes the whole system more sensitive to ICI. All in all, and based on different literature ([88] and [89]), the number of channels was set to 256. The constellation per subcarrier is chosen to be M-QAM owed to the benefits that it offers respect to other modulation formats when applied on OFDM [59]. With regard to the number of bits per symbol, several possibilities were implemented (2, 4 and 5). The determination of the channel response is done through the analysis of the distortion undergone by two training sequences. These sequences are built so that all subcarriers are excited with equal magnitude and phase. At the receiver, the transfer function is calculated seizing on the fact that FFT transformation is required. According to [58] two training symbols is a reasonable choice because it gives 3dB lower noise level by simple averaging both symbols. The cyclic prefix was roughly calculated according to maximum expectable delay per meter and maximum tested distance. As it has been explained above, the maximum delay was set to the closest maximum affordable outer DMD (0.14ps/m). In the worst-case channel modulation (BPSK), 256 channels, 10.3125Gbps and 1km fiber reel, it does not exceed 1% of the symbol duration (~0.6%). Another important aspect is the oversampling factor. Oversampling in OFDM is absolutely necessary to fulfill the Nyquist criterion before the DAC conversion. Some studies have shown that a factor of 1.5 is sufficient [59] however, it was fixed to 2 or 4. The latter for representation issues. Notice that an excessive oversampling for a steady sampling rate will increase the symbol duration and hence the effective bit rate. This highlights the importance of choosing the lowest factor possible. Biasing the output stream was the technique used to guarantee unipolar driving signal. Despite the powerefficient advantages of other alternatives it was chosen to stick to the cost-effective network requirement and take advantage of the unavoidable biasing of the VCSEL (directly modulated) to solve two problems with only one solution: creation of a unipolar signal and population inversion with only one bias current. The peak-to-average control was decided to be done through clipping. It is the simplest method and it gives the best error ratio for a certain SNRb according to [90] compared to other solutions. However, it generates an undesired noise called “clipping noise” due to the selective truncation of concrete peaks and also OOB noise. To solve the latter the signal is filtered with a Hamming window, taking advantage of the reconstruction filter after DAC. That is, one filter offer solution for both OOB noise generated after clipping and reconstruction of the oversampled signal. 121 Finally, the sampling rate is chosen depending on the rest of variables in order to attain the mandatory 10.3125Gbps (±100ppm). C.5.1.2 Process description The binary bit sequence could be taken either from ModeSYS™ when the module was integrated in the optical link or from a predefined set of pseudorandom sequences. After loading the binary vector and replicating it to create a longer stream, it was divided into 256 parallel channels (one for each subcarrier) and transformed into symbols according with the chosen constellation. Once the data was formatted, the necessary replication and complex conjugation for DMT was performed. After that, the IFFT was calculated and the output matrix was transformed into a vector to create the digital OFDM symbol frame. Right after including the training sequences, the cyclic prefix was added and the signal was clipped. The next block is the DAC conversion. Firstly, the normalized amplitude range is transformed into values within the differential input voltage limits of the transceiver. Once this was done, up-sampling and LPFing were applied to generate the final outgoing data stream. C.5.2 Demodulator C.5.2.1 Design parameters No special parameters need to be reported. The ADC works at the same rate as DAC, the number of inputs in the FFT is the same as outputs in the IFFT, the length of the discarded window is exactly the same as the cyclic prefix duration and the demodulation is done according with the chosen constellation in the transmitter. C.5.2.2 Process description Before setting the receiver in the default mode, two things needed to be done: calculate the optimum sampling point and the channel’s transfer function. The first one was done by setting the wanted parameters in the transmitter and launching a 27-1 PRBS sequence into the channel. The received signal was correlated with the ideal PRBS and the resulting deviation utilized to set the optimum sampling point in the first position of the vector. With regard to the channel’s transfer function, it was calculated from the averaged transfer function obtained from the pair of training sequences. The coefficients were stored and applied at each of the FFT outputs (1-tap equalizer). From this point on the regular working mode was established. The incoming electrical signal was sampled every 2 starting from the first position in the vector. The cyclic prefix was removed and the resulting stream was serial-to-parallel converted and FFTed. The outputs were equalized with the calculated coefficients and parallel-to-serial converted in order to perform the 1/0-mapping from the corresponding modulation format. Once the binary stream was ready, two forms of BER calculation were implemented: error counting 128 Figure D-9 Histogram of the real dimension (left) and received 16-QAM constellation (right). The estimated BER is 8∙10-17. Despite the symbols in the constellation are more defined compared to 25oC, there is a lower concentration of samples in the optimum levels; it is reflected in the histogram. The consequence is that, as the Gaussian fitting algorithm disregards those bins with small concentration compared to the maximum, the result for 25oC are thinner bells that yield improved BER. This should be taken into consideration and use the estimated BERs as qualitative references exclusively. The sensitivity is around -7.5dBm. Similarly to 25oC, the power margin is around 1.5dB. D.3 90oC D.3.1 4-QAM The BER is the worst of all cases for 4-QAM modulation per subcarrier. The histograms show a higher accumulation of samples in the optimum compared to -40oC however, the rest of observations are considerably more spread than for any other temperature. This can be inferred from the difficulties to make an exact Gaussian matching of the whole level (see Figure D-10). Figure D-10 Histogram of the real dimension (left) and received 4-QAM constellation (right). 129 The mentioned spreading is also visible in the constellation when compared with 25oC. Despite this effect, the BER is still widely below error free. The counted errors equal zero and the estimated error rate is 2∙10-67. The sensitivity equals -14dBm, leaving a minimum power margin of 7.9dB. D.3.2 16-QAM Against what was expected based on the worse performance for 4-QAM, the results obtained at 90oC on 16-QAM are better than for any other temperature. The estimated BER equals 10-25 and the symbols are perfectly defined in the histogram (see Figure D-11). Figure D-11 Histogram of the real dimension (left) and received 16-QAM constellation (right). The sensitivity experiences an improvement of 1.5dB (-9dBm) with respect to 25oC and -40oC, permitting a power margin of 3dB. 130 E Estándares de fibra multimodo en la industria y distancias típicas de transmisión soportadas Regulating standards: Industry Standards Fiber Type ISO/IEC 11801 Type OM4 fiber Type OM3 fiber Type OM2 fiber IEC 60793-2-10 Type A1a.3 fiber Type A1a.2 fiber Type A1a.1 fiber TIA/EIA 492AAAD 492AAAC-B 492AAAB-A ITU G.651 G.651 G.651 Using ISO/IEC 11801 notation, the standardized (gray) and typically supported transmission distances for diverse standards [59]: 131 F Especificaciones para diversos tipos de fibras ópticas comercialmente disponibles Draka: Bend-Insensitive OM4 fiber Draka: Regular OM4 fiber Draka: Regular OM2 fiber Draka: Regular OM1 fiber Corning: Bend-Insensitive OM4 fiber Corning: Regular OM1 fiber 132 G Rendimiento del proceso de escalado de perfiles de índice de refracción en comparación con el método habitual de escalado de retraso modal [78] DMD scaling results (blue dots: unscaled DMD; red circles: DMD after usual scaling process; black circles: DMD of the scaled refractive-index profile): 133 H Publicaciones  R. Rodes, J. Estaran, B. Li, M. Mueller, J. B. Jensen, T. Gründl, M. Ortsiefer, C. Neumeyr, J. Rosskopf, K. J. Larsen, M. Amann, and I. Tafur Monroy, “100 Gb/s single VCSEL data transmission link,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 and National Fiber Optic Engineers Conference , PDP5D.10 March 2012.  R. Rodes, J. Estaran, T.T. Pham, E. Hviid, I. Tafur Monroy, “Next Generation WDM-PON enabling Gigabit Per-User Data Bandwidth,” Conference Proceedings of 3nd Annual Workshop on Photonic Technologies for Access and Biophotonics, 2012, University of California, Berkeley, California, Jan. 2012  J. Estaran, R. Rodes, T. T. Pham, M. Ortsiefer, C. Neumeyr, J. Rosskopf, I. Tafur Monroy, “Quad 14Gbps L-Band VCSEL-based System for WDM Migration of 4-lanes 56Gbps Optical Data Links,” accepted for oral presentation ECOC’12.  R. Rodes, T. T. Pham, J. Estaran, M. Iglesias Olmedo, I. Tafur Monroy, “GigaWaM WDM-PON System Demonstrator: 10Gbps/2.5Gbps Bidirectional Link Performance.”  J. Estaran, J. J. Vegas Olmos, G. A. Rodes, I. Tafur Monroy, “Bidirectional uncompressed HD video distribution over fiber employing VCSELs,” submitted IPC´12. 134