Pho onics 2025, 12, x h ps://doi.o g/10.3390/xxxxx
A icle
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Fla Emission Silicon Ni ide G a ing Couple s o Lida Op i-
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cal An ennas
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Thenia P ousalidi 1,*, Geo gios Sy iopoulos 1, E ydiki Ky iazi 1, Roel Bo e 2, Cha alampos Ze os 1, Giannis Pou-
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lopoulos 1 and Dimi ios Apos olopoulos
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1 School o Elec ical and Compu e Enginee ing, Na ional Technical Uni e si y o A hens, 15780 Zog a ou,
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G eece
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2 Lionix BV In e na ional, Hengeloses aa 500, 7521 AN Enschede, Ne he lands
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* Co espondence: [email protected] ua.g ;
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Abs ac : Ligh de ec ion and anging (Lida ) is a key enabling echnology o au ono-
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mous ehicles and d ones. I s eme ging implemen a ions a e based on pho onic in e-
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g a ed ci cui s (PICs) and op ical phased a ays (OPAs). In his wo k we in oduce a no el
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app oach o he design o OPA Lida an ennas based on Si3N4 g a ing couple s. The well-
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es ablished T iPleX pla o m and he asymme ic double s ipe wa eguide geome y wi h
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ull e ching a e employed, ensu ing low complexi y and simple ab ica ion, combined
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wi h he low-loss ad an ages o he pla o m. The design s udy aims o op imize he pe -
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o mance o he g a ing couple based adia o s as well as he OPA, hus enhancing he
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o e all capabili ies o Si3N4 based Lida . Uni o m and non-uni o m g a ing s uc u es a e
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conside ed, achie ing θ and φ angles di e gence o 0.9° and 32°, and 0.54° and 25.41°
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espec i ely. Also, wa eleng h sensi i i y o 7°/100 nm is achie ed. Las , he undamen al
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OPA pa ame e s a e in es iga ed, and 35 dBi o peak di ec i i y is achie ed o an 8-ele-
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men OPA.
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Keywo ds: G a ing Couple , Lida , Op ical Phased A ay, Op ical Radia o , Silicon Ni-
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ide
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1. In oduc ion
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Au onomous ehicles, e es ial and ai bo ne, ha e gained popula i y in ecen
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yea s, wi h he au oma ion use cases sp eading ac oss mul iple sec o s and indus ies.
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Thei exis ing and o eseen applica ions ange om he au omo i e and mobili y indus y
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wi h sel -d i ing ca s and au oma ed axis, o ae ospace (au oma ed u ban ai mobili y
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(UAM) scena ios) and d ones [1], sma ci ies, logis ics, manu ac u ing, indus ial appli-
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ca ions and heal hca e [2]. Since au onomous ehicles ope a e in dynamic en i onmen s,
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hey ely on he use o ad anced senso ial echnologies o mapping [3], like he adio
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de ec ion and anging (Rada ) and ligh de ec ion and anging (Lida ). Ex ensi e esea ch
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has aken place in ecen yea s o ad ance he pe o mance and co-in eg a e Rada and
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Lida senso s o au onomous ehicles [4-5].
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Lida is a h ee-dimensional (3D) imaging, mapping and emo e sensing echnique
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ha elies on op ical beam shaping and s ee ing [6] and has eme ged as a p omising so-
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lu ion o au onomous ehicles and d ones. High pe o mance Lida sys ems compa ible
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wi h such applica ions need o enable long- ange powe ansmission wi h low cos , low
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powe consump ion, compac and obus implemen a ions [7]. The high pe o mance
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Recei ed: 31/01/2025
Re ised: 21/02/2025
Accep ed: da e
Published: da e
Ci a ion: To be added by edi o ial
s a du ing p oduc ion.
Copy igh : © 2025 by he au ho s.
Submi ed o possible open access
publica ion unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license
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Pho onics 2025, 12, x FOR PEER REVIEW 2 o 16
elies on inc eased ield o iew (FOV), high angula esolu ion, small beam di e gence
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and inc eased scanning speed [8]. T adi ionally, Lida sys ems ha e been based on me-
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chanical implemen a ions wi h ee-space op ics and o a ing pa s [9] ha howe e a e
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no compa ible wi h he compac size, low cos and eliabili y equi emen s, and ha e
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limi ed scanning speed [10]. Mic o-elec o-mechanical sys em (MEMS) Lida is a mo e
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compac al e na i e, showcasing, hough, educed FOV and ulne abili y o mechanical
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shocks. Solid-s a e Lida has eme ged in ecen yea s as ano he echnique ha p o ides
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a scalable and eliable solu ion ha does no include any mo ing mechanical pa s [11]. I
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includes op ical phased a ays (OPAs) whe e he beam is s ee ed by wa eguides ins ead
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o mo ing pa s [12], o Flash Lida ha wo ks like a came a and cap u es he image by
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illumina ing he whole FOV [11]. Howe e , a adeo exis s also o hese me hods, as
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hey showcase limi ed s ee ing angle and de ec ion ange espec i ely.
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In ecen yea s, pho onic in eg a ed ci cui (PIC) based Lida has been gaining mo-
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men um [13]. The ypical choice o PIC based Lida is he Silicon on insula o (SOI) pla -
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o m [10, 14-15] whe e he beam shaping and s ee ing a e pe o med by he silicon chip
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wi h he help o in eg a ed phase shi e s and OPAs based on g a ing elemen s. A sche-
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ma ic o an op ical an enna in OPA con igu a ion based on g a ing couple s is shown in
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Figu e 1. This pla o m o e s many ad an ages. Being compa ible wi h s anda d ma u e
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complemen a y me al-oxide semiconduc o (CMOS) ab ica ion p ocesses i enables he
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de elopmen o cos e icien , low powe , eliable and obus Lida sys ems, based on
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highly in eg a ed OPAs [16]. Compac g a ing an ennas based on one-dimensional (1D)
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OPAs can achie e wo-dimensional (2D) beam s ee ing by wa eleng h uning along he
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longi udinal di ec ion, and by phase con ol along he la e al dimension [16-17]. The in-
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he en ul a-high index con as o he SOI pla o m allows o beam s ee ing as high as
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15o wi h 100 nm wa eleng h uning [18]. Howe e , Silicon (Si) PICs equi e p ecise con ol
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o hei componen s dimensions o op imal pe o mance and a e he e o e suscep ible o
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ab ica ion p ocess e o s. Mo eo e , he SOI pla o m canno suppo high inpu powe
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le els due o he appea ance o non linea e ec s in Si, p ohibi ing i s use in high powe
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sys ems [19]. This limi s he applica ion o SOI PIC based Lida .
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Capi alizing on he ad ances o SOI-based Lida , he Silicon Ni ide (Si3N4) pla o m
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can enhance and u he imp o e he capabili ies and pe o mance o PIC based Lida .
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The Si3N4 pla o m showcases e y low p opaga ion losses and is compa ible wi h high
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inpu op ical powe applica ions due o i s low nonlinea i ies [20]. In combina ion wi h i s
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low index con as , his pla o m is obus o ab ica ion-induced phase a ia ions. Mo e-
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o e , i is anspa en a wa eleng hs below 1150 nm [21] and showcases educed emis-
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sion s eng h o inc eased emi e leng h and small di e gence [22], making i an in e -
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es ing al e na i e o SOI o he de elopmen Lida op ical an ennas [23]. The Lionix T i-
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PleX wa eguide echnology is one o he mos well-es ablished Si3N4 pla o ms. Among
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he di e en wa eguide geome ies i o e s [24], he asymme ic double s ipe (ADS)
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combines he ul a-low loss ad an ages o he pla o m wi h he lowes minimum bend
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adii, equi ing simple ab ica ion p ocesses and o e ing highe yield compa ed o he
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o he geome ies [25]. Mo eo e , i is compa ible wi h s anda d mul i p ojec wa e
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(MPW) ab ica ion p ocesses employing single e ch dep h, and is highly sui able o ap-
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plica ions ha equi e coupling o ex e nal componen s such as ac i e ma e ials. This is
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especially impo an o Lida applica ions, whe e he co-in eg a ion o he Si3N4 compo-
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nen s wi h o he pho onic o elec onic chips and componen s (e.g. indium phosphide o
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he ealiza ion o op ical sou ces) can enable he de elopmen o comple e Lida and Ra-
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da sys ems.
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Howe e , he Si3N4 has i s own limi a ions. Adequa e beam s ee ing by wa eleng h
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uning emains a challenge due o he limi ed ma e ial dispe sion. Recen de elopmen s
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ha e shown ha s ee ing angles o up o 7o o 100 nm uning ange can be achie ed [22].
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Pho onics 2025, 12, x FOR PEER REVIEW 3 o 16
Mo eo e , he Si3N4 based Lida is no a ma u e echnology. Al hough a ious s udies
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in es iga e Si3N4 op ical an ennas o Lida [26-27] ad ances a e s ill equi ed o achie e
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he desi ed pe o mance combining low di e gence, uni o m emission p o iles and long
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leng h g a ings wi h s anda d ab ica ion echniques. This is especially ele an o Si3N4
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Lida an ennas employing he ADS wa eguide geome y ha ha e no ye been explo ed
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in li e a u e. Howe e , many applica ions can bene i om such implemen a ions, hanks
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o hei a o emen ioned ad an ages, making he esea ch o ADS based Si3N4 op ical a-
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dia o s highly desi able and impac ul.
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This pape in oduces a new app oach o he design o g a ing couple s (GC) o Li-
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da op ical an ennas in he T iPleX Si3N4 pla o m, employing he ADS geome y. The
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e o ocuses on achie ing high pe o mance o OPA based adia o s o Lida sys ems
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ha can be employed in au onomous ehicles and d ones, mee ing he demanding e-
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qui emen s o such applica ions. Mo e speci ically, his design s udy a ge s high FOV o
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he OPAs, inc eased esolu ion and low ecei e losses. The esolu ion depends on he
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beam di e gence, and i can be imp o ed by minimizing he beam di e gence ac oss he
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longi udinal and la e al di ec ions ( he a (θ) and phi (φ) angles di e gence espec i ely).
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The beam di e gence is de e mined by he op ical ape u e o he an enna, and also co -
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ela es o he adia ion uni o mi y h oughou he an enna leng h. In gene al, θ angle di-
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e gence depends on he design o he indi idual g a ing elemen s, while he φ angle
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di e gence depends on he ape u e o he OPA. The ecei e losses can be educed by
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a ge ing a la emission p o ile in he longi udinal di ec ion and achie e g a ings wi h
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long e ec i e a eas (long g a ings) ha can collec ligh wi h inc eased e iciency. A he
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same ime, his wo k a ge s Si3N4 op ical adia o s ha a e compa ible wi h simple ab i-
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ca ion p ocesses and single e ch dep h, ab icable h ough MPWs, wi hou equi ing ac-
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cess o mo e ad anced echniques. Al hough his will signi y limi a ions in he achie ed
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pe o mance, i ensu es ha he designs a e low cos and easily ab icable, a equi emen
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necessa y in many applica ions. This is ensu ed wi h he use o he ADS geome y wi h
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single ull e ch dep h. The design p ocess ou lined in his pape consis s o wo pa s. The
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i s conce ns he design and op imiza ion o he single g a ing elemen , o achie e uni-
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o m emission ac oss long leng h and educe he angles di e gence. The second s ep a -
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ge s he op imiza ion o he OPA s uc u e.
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2. Laye s ack and An enna Design Conside a ions
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The pla o m o he de elopmen o he op ical adia o s is he Lionix Si3N4 T iPleX
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pla o m [24-25] and he ADS wa eguide geome y. The mul iple laye s o Si3N4 and Sili-
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con Dioxide (SiO2) allow o make low index con as wa eguides which is bene icial o
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educed sensi i i y o he wa eguided modes e ec i e e ac i e index (ne ) o he wa e-
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guide geome y a ia ion [23]. This esul s in educed emission s eng h and allows o
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achie e long g a ings. A c oss-sec ion o he ADS laye s ack is shown in Figu e 2(b). The
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bo om and op Si3N4 laye hickness is 75 nm and 175 nm espec i ely, while he dis ance
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be ween he wo laye s is 100 nm. The e ac i e index o he ma e ials is nSiO2 = 1.44537
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and nSi3N4= 1.98350 a 1550 nm. Fo ealizing he g a ing ee h, ull e ching is employed
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( emo al o bo h laye s o he Si3N4 ADS laye s ack), a limi a ion imposed by he a ailable
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ab ica ion p ocess. Adhe ing o his limi a ion ensu es ha he p oposed design is ab i-
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cable wi h s anda d ab ica ion p ocesses and minimal ab ica ion isks. As a esul , a
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ixed e ching dep h is conside ed. The nominal wa eguide wid h (w) is 1.1 μm, howe e
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his alue has been a ied in he designed componen s. The design s udy was ca ied ou
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in he spec al ange 1500 nm – 1600 nm, cen e ed a ound 1550 nm.
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Figu e 1: Schema ic o an op ical an enna in OPA con igu a ion based on g a ing couple s. The θ
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and φ angles and he dis ance d be ween adjacen GC elemen s a e no ed.
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Figu e 2: (a) The OPA schema ic o indica e he c oss-sec ional planes. (b) Schema ic o he yz-plane
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c oss-sec ion o he s anda d T iPleX ADS wa eguide. The di e en egions (Si3N4 wa eguide, SiO2
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op oxide laye (TOX) and bo om oxide laye (BOX) and ai op cladding) a e ma ked wi h di e en
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colo s. (c) Schema ic o he side iew (xz-plane c oss-sec ion) o a pe iodic g a ing s uc u e. The
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g a ing pi ch is deno ed wi h Λ and he illing ac o wi h FF. The e ec i e index o he e ched pa
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is n0 and o he une ched pa is n1.
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The p oposed GCs se e as he single adia o elemen s (building blocks) o he op-
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ical an enna and ac as he ligh emi e s and ecei e s o he Lida . They a e a anged
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linea ly in se ies, one nex o he o he wi h dis ance d, in a linea 1D OPA con igu a ion,
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as shown in Figu e 1. Figu e 1 illus a es he θ and φ angles, along he longi udinal and
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la e al di ec ion o he OPA espec i ely. The 1D OPA can ealize beam s ee ing in bo h
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di ec ions, by uning he wa eleng h in he longi udinal di ec ion (θ) and by in oducing
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a phase shi ac oss he g a ing an enna along he la e al di ec ion (φ). The ad an age o
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his con igu a ion is ha 2D beam s ee ing is ensu ed wi h an 1D s uc u e, esul ing in a
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signi ican educed oo p in (o de s o magni ude less) on he chip compa ed o an equi -
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alen 2D s uc u e, conside ing ha o a gi en ape u e size 2D OPA equi es N2 elemen s
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ins ead o N elemen s o he 1D OPA. Mo eo e , in 2D OPAs, he on-chip eal es a e is
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inc eased due o he o e head o he phase shi e s equi ed o beam s ee ing in bo h
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di ec ions.
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3. Design o Single Radia o Elemen
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The building block o he p oposed OPA Lida op ical an enna is he GC. The i s
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pa o his s udy ocuses on he design and op imiza ion o he GC based emi e using
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he Lume ical ini e di e ence eigenmode (FDE) and ini e-di e ence ime-domain
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(FDTD) sol e s. Va ious con igu a ions ha e been explo ed, including uni o m and non-
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uni o m geome ies, o op imize he pe o mance o he single adia o elemen .
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3.1. P inciple o Ope a ion
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Among he g a ing pa ame e s, he mos ele an o his design s udy ha will be
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used in he design p ocess a e he e ec i e e ac i e index o he g a ing pe iod (ne -g a ing),
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he emission angle (θ) and he coupling cons an (k).
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In a g a ing s uc u e, he e ec i e index o a g a ing pe iod ha consis s o an
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une ched pa wi h e ec i e e ac i e index o he suppo ed mode n1 and an e ched pa
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wi h e ec i e e ac i e index o he suppo ed mode n0, wi h illing ac o FF, as shown
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in Figu e 2(c), is gi en by (1)
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𝑛𝑒𝑓𝑓−𝑔𝑟𝑎𝑡𝑖𝑛𝑔 =𝐹𝐹 ∗ 𝑛1+(1 − 𝐹𝐹)∗ 𝑛0. (1)
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Fo ou s uc u e, since he e ched pa consis s only o SiO2 due o ull e ching, we assume
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he e ec i e e ac i e index in he e ched pa o be equal o he e ac i e index o SiO2
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(n0 = nSiO2).
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The emission angle θ o a g a ing is ela ed o he pi ch Λ, he ope a ing wa eleng h
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λ and he ne -g a ing, acco ding o he B agg condi ion exp essed in (2) [28]
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sin(𝜃)=𝑛𝑒𝑓𝑓−𝑔𝑟𝑎𝑡𝑖𝑛𝑔−𝜆
𝛬
𝑛𝑆𝑖𝑂2 . (2)
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The coupling cons an k exp esses he e ec i e e ac i e index con as be ween he
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high and low index sec ions o a g a ing pe iod [27] and is gi en by (3).
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𝑘 = 𝑛1 − 𝑛0
𝑛𝑒𝑓𝑓−𝑔𝑟𝑎𝑡𝑖𝑛𝑔∗ 𝛬. (3)
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k ela es o how as (o e how many pe iods) he powe will be sca e ed ou side o he
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GC. Fo low loss wa eguide pla o ms, ha ing low k can help ealize GCs wi h long e -
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ec i e leng hs. One way o achie e low k is by a ying he wa eguide wid h along he
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GC leng h [29]. In applica ions ha a ge uni o m emission p o iles, apodiza ion o k
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along he leng h is desi able o enginee ing he emission p o ile.
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3.2. Uni o m Design
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The simples GC con igu a ion in e ms o design and ab ica ion complexi y is a
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uni o m GC whe e he geome ical pa ame e s ( illing ac o (FF), wid h, pi ch (Λ)), cho-
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sen o op imal pe o mance, emain cons an h oughou he GC leng h. The e ec i e
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index o he g a ing (ne -g a ing), gi en by (1), is also cons an ac oss a uni o m design. Uni-
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o m GC con igu a ions we e in es iga ed and simula ed in his s udy. A op iew o he
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uni o m g a ing is shown in Figu e 3.
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Figu e 3: Side iew o he uni o m GC, showing he cons an pi ch, FF and wid h ac oss he di ec ion
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o p opaga ion.
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Figu e 4: Simula ed θ and φ angles di e gence (a) a ying he g a ing wid h o ixed leng h o 50
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μm and (b) a ying he g a ing leng h o ixed wid h o 2 μm.
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Fo he design p oposed in his pape , FF was chosen equal o 0.5. The nex pa ame e
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ha was in es iga ed is he wid h. The nominal wid h in his pla o m is 1.1 μm, and i s
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minimum alue o p ope con inemen o he mode in he wa eguide is 700 nm. Hence,
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wid h alues g ea e han 1 μm we e in es iga ed. The wa eguide wid h a ec s he ligh
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con inemen wi hin he wa eguide in he la e al dimension. A he same ime, la ge wid h
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alues inc ease he equi ed dis ance (d) be ween adjacen GCs (shown in Figu e 1) in he
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OPA o a oid e anescen iled coupling and c oss- alk be ween he OPA channels. Las ,
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as he wid h inc eases, we en e he mul i-mode egime, which should be a oided. The e-
212
o e, a s udy o he wid h impac on he OPA pe o mance (angles di e gence) is neces-
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sa y o op imize i s alue. To his end, 3D-FDTD simula ions we e pe o med a ying he
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wa eguide wid h be ween 1 μm and 4 μm wi h s ep o 0.5 μm, while keeping he o he
215
pa ame e s cons an (leng h = 92.6 μm, FF = 0.5). The simula ed θ and φ angles 3dB di e -
216
gence is shown in Figu e 4(a). These esul s indica e ha as he wid h inc eases, he φ
217
di e gence will dec ease (10.4% o dec ease o wid h a ia ion be ween 1 and 4 μm),
218
while θ di e gence is mono onically a ec ed (9% o inc ease o wid h a ia ion be ween
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1 and 4 μm). Since he θ di e gence is close o 1o, his ansla es o 0.1o o change, ha is
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conside ed small in e ms o absolu e alue o he applica ion. Taking in o accoun he
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a o emen ioned limi a ions and o ensu e ha he spacing equi emen s in he OPA s uc-
222
u e will emain easonable, wid h up o 2 μm should be chosen.
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As a second s ep, he e ec o he GC leng h a ia ion is s udied, o op imize i s alue.
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3D-FDTD we e pe o med, his ime a ying he GC leng h be ween 25 μm and 200 μm,
225
while keeping he wid h cons an o 2 μm and he FF o 0.5. The esul ing simula ed θ and
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φ angles 3dB di e gence is shown in Figu e 4(b). We obse e ha bo h he θ and φ di e -
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gence is educed as he leng h inc eases. Fo leng h o 92.6 μm, he θ di e gence is 0.94°,
228
while he φ di e gence is 33.92°. Fo leng hs longe han 160 μm he di e gence alues
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s a o con e ge. Fo leng h o 208 μm alues o he θ and φ di e gence as low as 0.63°
230
and 28° can be achie ed. This signi ies a θ and φ di e gence educ ion o 81% and 55.5%
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espec i ely, o he in es iga ed leng h inc ease om 25 μm o 200 μm.
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Figu e 5: Le : op iew o he emission p o ile o he uni o m g a ing o wid h o 2 μm and leng h
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o 100 μm. The Ez componen ield dis ibu ion is shown wi h he colo scale. Righ : 1D plo o he
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emission p o ile along he dashed line o he le igu e.
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Figu e 6: Calcula ed emission angle θ o he a ield p o ile, a ying he wa eleng h in he ange 1.5
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- 1.6 μm, o uni o m ee h p o ile and pi ch 926 nm. The elec ic ield in ensi y is shown wi h he
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colou scale.
240
Las , he pi ch is eely chosen acco ding o (2), o achie e he desi ed emission angle.
241
Fo emission angle o a ound -10o, which is a ypical alue o adia o s, he pi ch is se o
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926 nm. These alues esul in op imal pe o mance o he uni o m g a ing, while mini-
243
mizing he θ and φ angle di e gence. A 3D-FDTD simula ion was epea ed wi h he se-
244
lec ed geome ical pa ame e s. The op iew and side iew o he simula ed emission p o-
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ile o he g a ing a e shown in Figu e 5. The ex ac ed θ and φ angles di e gence is 0.9o
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and 32o espec i ely. I is wo h no ing ha he φ di e gence is la ge because hese simu-
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la ions do no ake in o accoun he comple e OPA s uc u e, bu only he single adia o
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elemen .
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Figu e 6 illus a es he θ angle wa eleng h sensi i i y as ex ac ed om he a ield
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da a. Wi h he uni o m design, 7o o θ angle wa eleng h s ee ing is achie ed, wi h 100 nm
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o wa eleng h shi , om 1500 nm o 1600 nm. Howe e , i is e iden om Figu e 5 ha
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his componen has an exponen ial emission p o ile and canno mee he design a ge o
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uni o m emission and long e ec i e leng h. This is expec ed because he uni o m design
254
has a cons an k, and gi en ha e e y pe iod ecei es less inpu ligh han he p e ious,
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due o he ligh ha is emi ed upwa ds, he esul ing emission p o ile will showcase an
256
exponen ial decay. The e o e, o achie e mo e uni o m emission p o iles, non-uni o m
257
g a ing p o iles ha e been in es iga ed, as desc ibed in he nex pa ag aph.
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3.3. Non-uni o m Design
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Due o he pe o mance limi a ions o he uni o m design, non-uni o m con igu a-
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ions we e also in es iga ed o achie e mo e uni o m emission p o iles. The non-uni-
261
o mi y conce ns he geome ical pa ame e s o he design and sugges s ha along he
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g a ing leng h some o he design pa ame e s a e being a ied. Taking in o accoun he
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ab ica ion p ocess limi a ions, and o ensu e compa ibili y wi h Lionix T iPleX pla o m
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ab ica ion p ocesses ha enable only ull e ching, he pa ame e s ha can be a ied a e
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he wa eguide wid h, he illing ac o and he pi ch.
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The geome y a ia ion o he non uni o m g a ing is designed o ensu e a cons an
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emission angle θ ac oss he g a ing leng h, o low θ angle di e gence and inc eased es-
268
olu ion in he longi udinal axis. Acco ding o (1) and (2), o ensu e a cons an emission
269
angle he induced geome y a ia ion needs o be designed ca e ully. In his s udy we
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a y he wid h and FF, keeping he pi ch alue cons an , and conside ing only ully e ched
271
wa eguides. A op iew and a side iew o he non-uni o m design a e shown in Figu e 7
272
le and igh espec i ely. Mo eo e , he geome y a ia ion a ge s uni o m emission
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dis ibu ions. To achie e his, he k o e e y pe iod should g adually inc ease ac oss he
274
g a ing leng h. Inc easing k is achie ed by dec easing he FF ( o app oach FF o 0.5 ha
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Pho onics 2025, 12, x FOR PEER REVIEW 8 o 16
esul s in s onge emission) and inc easing he wid h ac oss he g a ing leng h, which
276
leads o inc easing emission a e [27].
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278
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Figu e 7: (Le ) op iew and (Righ ) side iew o he in es iga ed non-uni o m g a ing design wi h
280
a ying wid h and FF.
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Figu e 8: Calcula ed e ec i e e ac i e index o he TE0 mode a ying he wa eguide wid h.
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The design p ocess s a ed wi h FDE simula ions using Lume ical MODE sol e .
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Fi s , he e ec i e index o he undamen al TE mode o a wa eguide c oss-sec ion (n1)
285
a ying i s wid h, is calcula ed, gi en he ADS T iPleX laye s ack. The esul s a e shown
286
in Figu e 8. In he ADS T iPleX pla o m, o c ea e he g a ing ee h he Si3N4 is ully
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e ched, emo ing bo h laye s o he Si3N4 laye s ack ha a e illus a ed in Figu e 2(b).
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The e o e, he e ched pa o he g a ing geome y consis s o SiO2. Since he e is no wa e-
289
guiding ma e ial in he e ched pa and he FDE sol e canno calcula e any suppo ed
290
modes, we assume he alue o he e ec i e e ac i e index o he e ched pa (n0) o be
291
equal o he alue o he e ac i e index o SiO2 (nSiO2). Using (1) and he calcula ed n1
292
alues, i is hen possible o compu e he ne -g a ing, o he di e en wid h and FF combina-
293
ions. This is shown in Figu e 9.
294
F om he esul s shown in Figu e 9 i is e iden ha o speci ic pai s o wa eguide
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wid h and FF, he ne -g a ing emains cons an . These con ou lines, shown wi h black lines
296
in Figu e 9, a e he desi ed egions om which he wid h-FF pai s can be ex ac ed. The
297
design me hodology includes pa i ioning he a ailable wid h ange in N alues o p o-
298
duce he wid h-FF pai s, as i will be desc ibed sho ly. Thus, i is ensu ed ha he emis-
299
sion angle θ is also cons an . Mo eo e , he emission p o ile o he g a ing is no longe
300
exponen ial, bu becomes mo e uni o m. This is achie ed because ac oss he g a ing
301
leng h he FF dec eases app oaching 0.5, while he wid h inc eases, leading o an inc eas-
302
ing k. Fo a gi en con ou line, he co esponding coupling cons an k has been calcula ed
303
acco ding o (3). Figu e 10 illus a es k o h ee o he con ou lines o Figu e 9. I can be
304
obse ed ha o all con ou lines, k is simila , and i g adually inc eases as he wid h
305
inc eases, acco ding o he design a ge .
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Pho onics 2025, 12, x FOR PEER REVIEW 9 o 16
307
Figu e 9: ne -g a ing o he undamen al suppo ed mode calcula ed ia FDE simula ions, a ying he
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wa eguide wid h and FF. The black lines a e he con ou lines o he plo s along which he ne -g a ing
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has a cons an alue. The selec ed con ou line is ma ked wi h he pink s a s.
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Figu e 10: The calcula ed coupling cons an k o he di e en wid h alues ac oss he g a ing, o
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h ee o he con ou lines.
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I is no ed ha he e a e mul iple con ou lines one can wo k wi h. A choice be ween
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he a ailable op ions mus he e o e be made a ge ing op imal pe o mance. In e ms o
315
keeping he emission angle cons an , all con ou lines a e equi alen . Howe e , he e a e
316
wo mo e c i e ia ha can help make he bes choice.
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The i s one conce ns he compa ibili y o he design wi h he ab ica ion p ocess
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capabili ies. The FF should emain below 0.9 o compa ibili y wi h he accep able mini-
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mum ea u e size o app oxima ely 100 nm ( o pi ch a ound 1 μm, FF should be be ween
320
0.1 and 0.9). Mo eo e , he FF s ep should be as la ge as possible, leading o la ge s eps in
321
he g a ing ee h leng h and compa ibili y wi h he minimum s ep size. This is sa is ied
322
when choosing a con ou line wi h la ge slope in he whole wid h ange. The same is ue
323
in he la e al di ec ion whe e la ge wid h s eps a e desi able o compa ibili y wi h mini-
324
mum s ep size. Fo a gi en GC leng h ( ixed amoun o GC pe iods and pa i ioning s eps
325
N), inc easing he u ilized wid h ange will inc ease he wid h s ep. No e ha we choose
326
o wo k wi h wid h la ge han 1 μm o p ope con inemen o he undamen al mode
327
wi hin he wa eguide. Mo eo e , wid hs la ge han 2 μm a e no desi able since hey
328
impose limi a ions in he spacing be ween he a ay elemen s and ull OPA size, and also
329
signi y ope a ion in he mul imode egime.
330
A second c i e ion o choosing he con ou line is he k alue. Al hough be ween he
331
di e en con ou lines he k alues a e simila , we see om Figu e 10 ha k shows a la ge
332
a ia ion in he 1-1.5 μm wid h ange, compa ed o he 1.5-2 wid h ange. The e o e, he e
333
is a ade-o be ween ha ing a la ge k a ia ion and an accep able wid h size. All hings
334
conside ed, he con ou line ha bes i s all c i e ia is ma ked wi h pink s a s in Figu e 9
335
and has ne -g a ing=1.495.
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual au-
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ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
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people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
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