Mas e in Pho onics “Pho onics BCN”
MASTER THESIS
(T eball de inal de Màs e )
Con ol o he p opaga ion di ec ion o
Bound S a es in he con inuum (BICs)
in liquid c ys al wa eguides
I ena S olić
Supe ised by D .Ma lin Ba al and
D .P o .Da id A igas Ga cía, ICFO
P esen ed on 21 h July 2024
Regis e ed a
Con ol o he p opaga ion di ec ion o Bound S a es in he
con inuum (BICs) in liquid c ys al wa eguides
I ena S olić
Nonlinea op ical phenomena, The Ba celona Ins i u e o Pho onics Science, A . Ca l F ied ich Gauss
3, Cas ellde els (Ba celona) 08860, Spain
E-mail: i ena.s olic@es udian a .upc.edu
Abs ac . A plana wa eguide comp ises mul iple di e en media laye s, whe e ligh is con ined and
ansmi ed in a ilm o co e sandwiched by cladding media. Ligh line equency is an impo an ea u e
o a wa eguide, while wa es wi h equencies below he ligh line o m a ini e numbe o guided modes
ha can p opaga e in he ilm, he ones abo e he ligh line o m a con inuum o adia ion modes. This
hesis will s udy he bound s a es in he con inuum (BICs) in a plana aniso opic wa eguide, which a e
modes ha do no adia e ene gy away om he ilm, despi e ha ing equencies abo e he ligh line o
he wa eguide. Two expe imen s we e conduc ed u ilizing e lec ion spec oscopy o analyze a nema ic
liquid c ys al-based aniso opic plana wa eguide. Nema ic liquid c ys al (LC) is a s a e o ma e ha
exhibi s o ien a ional o de bu no posi ional o de . The aim was o demons a e he exis ence o
pola iza ion sepa able (PS) BICs and he unabili y o in e e ome ic (INT) BICs by applying an AC
ol age.
Keywo ds: Bound s a e in con inuum, nema ic liquid c ys al, aniso opic plana wa eguide
1. In oduc ion
Bound s a es in he con inuum (BICs) a e wa es ha emain localized despi e coexis ing wi h
adia ing wa es in he con inuous pa o he spec um in which wa es ypically ca y ene gy away.1
BICs we e i s p edic ed in he ield o quan um mechanics2, and la e shown o be a gene al wa e
phenomenon ha exis s in many sys ems ha suppo wa e p opaga ion o elec omagne ic wa es,
acous ic wa es in ai , wa e wa es, and elas ic wa es in solids.1 Since he i s demons a ion o
pho onic BICs, he e has been a g ea in e es in hei heo e ical p edic ions in a ious pho onics
sys ems and expe imen al de ec ion.3 In his hesis, we will be ocusing on s udying pho onic BICs in
he aniso opic plana wa eguides.
1.1. Aniso opic media
Aniso opic media is cha ac e ized by ha ing a di ec ional dependency on mac oscopic op ical
p ope ies.3 I can be ound in c ys alline o liquid-c ys alline o m. C ys alline s uc u es a e aniso opic
media when hey ha e a well-de ined c ys al s uc u e (bo h posi ional and o ien a ional o de ) which
a e non-cubic and hei p ope ies a y wi h di e en c ys allog aphic o ien a ions. Liquid-c ys alline
s uc u es do no necessa ily exhibi posi ional o de , as posi ions o he aniso opic molecules can be
comple ely andom, howe e , hey do ha e o ien a ional o de , as aniso opic molecules a e o ien a ed
along one di ec ion.4
Liquid c ys als (LC) exis in mesophase, a luid s a e o ma e ha is in e media e be ween
solid and liquid.4 The e a e se e al ypes o liquid c ys als such as nema ic, smec ic, and choles e ic LC
(see Fig. 1). Nema ic liquid c ys als ha e o ien a ional o de bu no posi ional o de , hei molecules
a e o ien a ed along he same di ec ion and loca ed a andom posi ions.4 The a e age o ien a ion
di ec ion o he molecules in a liquid c ys alline phase is known as he di ec o . Smec ic liquid c ys als
ha e an o ien a ional o de , while hei posi ional o de is in one dimension. The o ien a ion o all
molecules is along he di ec o and molecules a e a anged in laye s wi hin which hei posi ions a e
andom.4 In he choles e ic liquid c ys al, molecules ha e a long- ange o ien a ional o de bu no
posi ional o de , howe e , he molecules pe sis o o m a helix abou he pe pendicula axis.4 A use ul
p ope y o nema ic liquid c ys al is ha he o ien a ion o i s molecules can be con olled by ex e nal
pe u ba ions, such as applying an elec ic ield, magne ic ield, empe a u e, e c.
In he aniso opic media, he e ac i e index is a second- ank enso .4 A coo dina e sys em can
always be chosen so ha o -diagonal elemen s o he enso a e ze o, in which case diagonal elemen s
a e called p incipal e ac i e indices 𝑛1, 𝑛2, and 𝑛3.4 Uniaxial c ys al is a special case o aniso opic
media which has wo equal e ac i e indices ha a e di e en om he hi d one 𝑛1= 𝑛2= 𝑛𝑜≠ 𝑛3=
𝑛𝑒.4 These e ac i e indices a e called o dina y and ex ao dina y and a e he e ac i e index
expe ienced by wa es wi h pola iza ion pe pendicula and pa allel o he op ic axis, espec i ely.
Bi e ingence is one o he ea u es o he aniso opic medium whe ein he p opaga ing elec omagne ic
wa es o di e en pola iza ions ha e di e en dielec ic esponses.5 I can be calcula ed as he
di e ence be ween 𝑛𝑒 and 𝑛𝑜. Posi i e uniaxial c ys als ha e an ex ao dina y e ac i e index g ea e
han he o dina y e ac i e index 𝑛𝑒> 𝑛𝑜, while he opposi e is ue o he nega i e uniaxial c ys als
𝑛𝑒< 𝑛𝑜.4
Figu e 1. Di e en ypes o liquid c ys als a e p esen ed: a) nema ic; b) smec ic; and c) choles e ic
LC.
1.2. Modes in a wa eguide
An op ical wa eguide is a s uc u e o con ining and ansmi ing ligh . Plana dielec ic op ical
wa eguide consis s o h ee laye s, longi udinally ex ended along he 𝑦 axis in he shape o a slab, as
shown in Figu e 2. The ilm is he cen al laye , posi ioned be ween wo cladding laye s; he op laye
(co e ) and he bo om laye (subs a e).5 A s ep-index wa eguide has alues o e ac i e index ha
change ab up ly be ween laye s.5 Op ical wa eguides a e no mally guided sys ems, bu hey can also
be an i-guided sys ems. In guided sys ems, ilm is made o high e ac i e index media, while subs a e
and co e a e made o low e ac i e index media.4 Ligh is con ined in he ilm only in one di ec ion
and is guided u ilizing o al in e nal e lec ion, he adia ion o ene gy in o he co e and subs a e is
minimized.5 In he an i-guided sys em, he ilm is made o low e ac i e index media, and he subs a e
o he co e is made o highe e ac i e index media. The ligh wa e is no con ined in he ilm, i
adia es om he ilm in o he media wi h a highe e ac i e index.3
Fo a single homogenous medium, solu ions o Maxwell´s equa ions exis o any alue o
p opaga ion cons an smalle han he p oduc o he e ac i e index o he medium, 𝑛, by he acuum
wa enumbe , i.e., 𝑘𝑦< 𝑛𝑘0.3 Fo a plana wa eguide s uc u e ha consis s o mul iple di e en
ma e ials, he ligh wa e is no allowed o ha e e e y alue o p opaga ion cons an 𝑘𝑦, bu jus a
speci ic se o 𝑘𝑦 alues, due o he need o sa is y he bounda y condi ions.3 The suppo ed modes all
in o wo g oups, a ini e numbe o disc e e guided modes, and leaky modes, which a e imp ope
solu ions o Maxwell’s equa ion ha all wi hin he con inuum o adia ion modes.3 Leaky modes
p o ide an excellen desc ip ion o he ield in he icini y o he wa eguide, while he imagina y pa
o he p opaga ion cons an desc ibes he adia ion losses.
A ans e se mode in a wa eguide is a speci ic ans e se ield dis ibu ion pa e n ha is ixed
along he longi udinal p opaga ion axis 𝑦 and sa is ies he wa e equa ion, meaning ha ampli ude and
pola iza ion a e main ained cons an .5 Ligh can be guided in one o mul iple modes.5 The op ical modes
ha a e suppo ed in he wa eguide a e ea u es ha a e in luenced by he p ope ies o he op ical
media o laye s and he wa e equa ion bounda y condi ions. The modes can no mally be ei he
ans e se elec ic-TE (S pola ized in special case) o ans e se magne ic-TM (P pola ized) depending
on he di ec ion o he elec ic and magne ic ield w. . he di ec ion o p opaga ion.5 Howe e ,
wa eguides in ol ing aniso opic media can also suppo hyb id modes, which ha e all six componen s
o he elec ic and magne ic ields.6
In Figu e 2, an asymme ic plana dielec ic s ep-index wa eguide is in oduced, which is
cons an along he 𝑦 and 𝑧 axes, while along he 𝑥 axis laye s o di e en ma e ials a e placed. The
e ac i e indices o ilm, subs a e, and co e a e deno ed as 𝑛𝑓, 𝑛𝑠 and 𝑛𝑐 espec i ely. The
p opaga ion di ec ion is along he 𝑦 axis. To de ine he op ic axis o ien a ion, Pola angle 𝜃 is de ined
wi h espec he 𝑥 axis, and azimu hal angle 𝜙 gi es o a ion abou 𝑥 axis and is de ined wi h espec
he 𝑦 axis.3 When no ol age is applied, bo h he op ic axes o he ilm and subs a e a e in he y-z plane,
hen he azimu hal and pola angles o bo h he ilm and subs a e emain he same, a si ua ion known
as aniso opy symme y. The aniso opy-symme y b eaking akes place when, ei he he ilm’s
azimu hal o pola angle is changed wi h espec o he subs a e. This can be achie ed o a plana
wa eguide wi h a liquid c ys al ilm by applying an AC ol age. The pola -symme y b eaking happens
when ol age is applied in he o hogonal di ec ion (ou o plane) and he pola angle 𝜃 is changed,
whe eas, he azimu hal symme y-b eaking si ua ion is achie ed by applying an in-plane ol age.
Figu e 2. Wa eguide cell and he used coo dina e sys em ea u ing 𝑦 axis as he p opaga ion
di ec ion, laye s o di e en ma e ials along he 𝑥 axis, and cons an ma e ial p ope ies in he
𝑧 di ec ion. Addi ionally, in case no ol age is applied, he op ic axis is posi ioned along he
𝑦 axis. The applied ol age can esul in op ic axis o ien a ion exp essed in e ms o pola and
azimu hal angles.3
Fo an inciden wa e o wa eleng h 𝜆0, a e i en e s he medium o ela i e dielec ic
pe mi i i y 𝜖𝑟 , he alue o he wa enumbe cons an is3:
𝑘 = 2 · 𝜋
𝜆0 · √𝜖𝑟 = 𝜔0
𝑐· 𝑛 = 𝑘0𝑛
(1)
The momen um o he wa e 𝑘
󰇍
can be decomposed in o wo componen s along he 𝑥 and 𝑦 axes, 𝑘
󰇍
=
𝑘𝑥𝑥 + 𝑘𝑦𝑦 , whe e 𝑥 and 𝑦 a e uni ec o s. The 𝑦 componen is 𝑘𝑦= 𝑘 · sin𝜃 , and he 𝑥 componen
is 𝑘𝑥= 𝑘 · cos𝜃, whe e 𝜃 is he angle. Fu he , no malizing componen s o each ma e ial 𝜅𝑥=𝑘𝑥
𝑘0 and
𝑁 = 𝑘𝑦
𝑘0 , whe e N is he mode e ec i e index, i is a dimensionless pa ame e ha has he meaning o
he e ac i e index ha he mode senses and i can be e e eded o as no malized p opaga ion cons an ,
we ge (𝜅𝑥𝑓)2+ 𝑁2= 𝑛𝑓2.3 Fo in e nal e lec ion o happen, angle 𝜃 has o be g ea e han he c i ical
angle o each su ace 𝜃𝑓𝑠 =sin−1 𝑛𝑓
𝑛𝑠 and 𝜃𝑓𝑐 =sin−1 𝑛𝑓
𝑛𝑐 .5 The ligh line o a ma e ial 𝜔 = 𝑐𝑘0
𝑛 is a
cu o equency.4 Wa es wi h equencies below he ligh line canno be ansmi ed o he cladding
and a e e anescen , while wa es wi h equencies abo e he ligh line can p opaga e in he cladding.4
Fo a wa eguide whe e 𝑛𝑓> 𝑛𝑠 , 𝑛𝑐 , he e a e guided modes and adia ion modes. Guided modes
happen i 𝜃 > 𝜃𝑓𝑐 , 𝜃𝑓𝑠 in o he wo ds, i he e ec i e index N is la ge han he maximum o 𝑛𝑠 and
𝑛𝑐 , 𝑁 > 𝑚𝑎𝑥(𝑛𝑠,𝑛𝑐).3 These a e modes ha ha e equencies below he ligh line in he co e and
he subs a e and because o ha emain con ined in he ilm. Guided modes a e disc e e and exis only
i he p opaga ing wa e o ms cons uc i e in e e ence wi h i sel while p opaga ing, which depends
on he 𝑘𝑥 componen . Radia ion modes appea i 𝑁 < 𝑚𝑎𝑥(𝑛𝑠,𝑛𝑐) and o m a con inuum o
equencies abo e he ligh line. Wi hin he con inuum o adia ion modes, he e a e esonances wi h
high con inemen in he ilm which a e desc ibed by he so called leaky modes. These a e he imp ope
solu ions o Maxwell’s wa e equa ion whe e he imagina y pa o he solu ion ma hema ically
ep esen s he adia ion loss.3,5 They a e cha ac e ized by ene gy being coupled o he adia ion channel
and being adia ed away om he ilm.3 Radia ion channels a e wa es ha adia e ene gy away om
he ilm, hey can appea in he co e , subs a e, o bo h.3
1.3. Bound s a es in he Con inuum in aniso opic media
In he aniso opic plana wa eguides, BICs a e modes ha don´ adia e ene gy away and
emain localized in he ilm, e en hough hei equencies a e abo e he ligh line o he wa eguide, in
he pa o he spec um ha co esponds o he con inuum o adia ion modes.3 Fo BICs, he coupling
o he con inuum o adia ion modes in he subs a e o co e ia he adia ion channel does no happen.
One way o explaining his phenomenon is app oached by he leaky mode o malism.3
Leaky modes a e modes abo e he ligh line, ha a e pa ially con ined inside he ilm, unlike
o he adia ion modes.3 As a leaky mode p opaga es inside he ilm along he 𝑦 axis, i a enua es
exponen ially, because i couples o he adia ion modes in he subs a e, co e , o bo h.3 Consequen ly,
he e is exponen ial ene gy g ow h in he ans e se di ec ion in he immedia e su ounding, because o
he lux conside a ion, as ene gy conse a ion law applies.3 This loss o ene gy is desc ibed by he
imagina y pa o he complex p opaga ion cons an , 𝑘𝑦= 𝑁𝑘0, o he leaky mode.3
Semi-leaky modes a e cha ac e ized by ha ing only one adia ion channel in he cladding,
p o ided by ei he o dina y o ex ao dina y wa e, while he o he wa e is e anescen .3 Fo a semi-
leaky mode o exis in he wa eguide wi h an aniso opic subs a e and iso opic ilm, 𝑁 needs o be
si ua ed be ween he e ac i e indices o he subs a e and below he e ac i e index o he ilm such
ha one o he ails exponen ially decays o gi e a guiding p o ile and he o he ail has an exponen ial
ise co esponding o he adia ion in he con inuum.3 Simila ly, in case bo h ilm and subs a e a e
aniso opic, semi-leaky modes happen o 𝑁 being be ween any e ac i e indices o he ilm and he
subs a e, as shown in Figu e 3.3 Gene ally, bo h guided and leaky modes can be suppo ed by plana
uniaxial wa eguides when 𝑛𝑜𝑠 < 𝑛𝑒𝑓.3 Howe e , he case o Figu e 3 le co esponds o an an i-
guiding s uc u e as 𝑛𝑜𝑠 > 𝑛𝑒𝑓, and only leaky modes a e suppo ed. Addi ionally, pu e ans e se
Figu e 3. Re ac i e indices o he iso opic ilm a e shown on he le and o he aniso opic
ilm on he igh . In he case o an aniso opic subs a e, o dina y and ex ao dina y e ac i e
indexes a e nos and nes, and in he case o an aniso opic ilm, hey a e no and ne . The blue line
ep esen s he mode p opaga ing in he ilm and he co e , he ed line ep esen s he ex ao dina y
wa e ha ge s con ined, while he g een line ep esen s he o dina y wa e which in his case
se es as he adia ion channel.

elec ic (TE) and ans e se magne ic (TM) modes a e suppo ed in case he ligh p opaga es along one
o he p incipal axes o he dielec ic enso , o he wise, modes a e hyb id.3
The e a e wo ypes o BICs in aniso opic plana s uc u es, pola iza ion sepa able (PS) BICs
and in e e ome ic (INT) BICs.3 PS BICs a e a subse o symme y-p o ec ed BICs whose o igin is
ela ed o he pola iza ion o he adia ion channel in he cladding being o hogonal o he pola iza ion
o he p opaga ing mode.7 In he case o posi i e uniaxial ilm and nega i e uniaxial subs a e, he
pola iza ion o he mode p opaga ing along he 𝑦 axis is TE, and he pola iza ion o he adia ion channel
in he subs a e is TM, so he mode can’ couple o he adia ion channel o he o hogonal pola isa ion.3
The PS BICs exis only o p opaga ion di ec ions along he p inciple axes, whe ein he mode is pu e
TM o TE, o he wise, modes a e hyb id o any o he p opaga ion di ec ion.3 PS BICs exis o all
wa eleng hs o which he e is a leaky mode.3 INT BICs occu o p opaga ion di ec ions ha a e o -
axis o in o he wo ds ha a e no along any o he p inciple axes.3 The o igin o INT BICs is due o he
des uc i e in e e ence a he in e ace be ween he ilm and he cladding.3 INT BICs a e in e es ing,
because he modes a e hyb id, and hei pola iza ion, p opaga ion di ec ion and exis ence equency can
be uned by ca e ully choosing he wa eguide pa ame e s. Sol ing he dispe sion equa ion gi es he
solu ions o 𝑁 whe e he modes exis . The dispe sion equa ion gi es he alues o N whe e leaky and
guided mode (only leaky in an i-guiding s uc u es) exis s. Howe e , i is no a su icien condi ion o
p o ide in o ma ion abou he BICs exis ence and loca ion in he pa ame e space, pa icula ly INT
BICs.3 The e o e, an addi ional auxilia y condi ion is imposed, which s a es ha he ampli ude o he
adia ion channel needs o be ze o.3 Plana wa eguides wi h iso opic ilm and aniso opic subs a e can
suppo PS BICs, bu no INT BICs, while plana wa eguides wi h bo h ilm and subs a e being
aniso opic, can suppo bo h PS BICs and INT BICs.3 In he case o he plana wa eguide wi h
aniso opic ilm, PS BICs a e only suppo ed when he cladding and ilm op ic axes a e aligned and
pa allel o he wa eguide in e ace (aniso opic symme ic s uc u es) and o ligh p opaga ing along
one o he p incipal axes.7 INT BICs can exis o aniso opy symme y b oken s uc u es and when
ligh is p opaga ing o -axes di ec ion.
In he p esen hesis, we demons a e he exis ence o PS BICs in a liquid c ys al-based
wa eguide using e lec ion spec oscopy. Addi ionally, we explo e he unabili y o he BICs by
applying an AC ol age o he sys em in he 𝑥 di ec ion pe pendicula o he in e ace planes. Applying
an ou -o -plane AC ol age esul ed in he b eaking o pola symme y and hus, PS-BICs disappea s,
becoming leaky modes o INT-BICs.
2. Implemen a ion
2.1. Ma e ial p ope ies
Table 1. Ma e ials used o o m a wa eguide ( * alues o e ac i e indices aken om he websi e 8 )
empe a u e (˚C)
wa eleng h (nm)
O dina y
e ac i e index
Ex ao dina y
e ac i e index
5PCH LC
25
632
1.4870
1.6070
*PVA
Room empe a u e
632
1.4814
–
*Calci e
Room empe a u e
632
1.6557
1.4849
*SF11
Room empe a u e
632
1.7787
–
The op ical wa eguide used in he expe imen has a calci e subs a e, 5PCH liquid c ys al (LC)
o he aniso opic ilm and ai is he co e . To couple he modes a he ilm-subs a e in e ace using
e lec ion spec oscopy, SF11 hemisphe e p ism is used. The e o e, he LC ilm wa eguide has SF11
pla e as he op co e which is a con inua ion o he e ac i e index o SF11 p ism o p ism coupling
a he ilm-subs a e in e ace. When he cell is used in he expe imen , i is hea ed be o e use o main ain
he mesophase s a e o he LC. The index-ma ching liquid o 𝑛 = 1.78 is illed be ween he SF11 p ism
and he cell.
2.2. Sample p epa a ion
SF11 and calci e a e cu in o pla es wi h dimensions 10𝑚𝑚 ×10𝑚𝑚. The pla es a e cleaned
wi h he ace one. Nex , anspa en Indium Tin Oxide (ITO) elec odes a e deposi ed on he su aces o
SF11 and calci e pla es. The hickness o he elec odes is di ec ly p opo ional o he ime o spa e ing,
so he calcula ed hickness o he elec odes o 24 minu es o exposu e is a ound 0.08μm. One side o
each pla e is exposed o UV ligh o 20 minu es o make hei su aces mo e hyd ophilic. The d ops o
PVA a e pu on he hyd ophilic su aces whe e hey sp ead o co e almos he whole su ace.
A e wa ds, he spin-coa ing akes place. Fo each pla e, spin coa ing is done o 1 minu e a he speed
o he spin o 3000 pm and he esul is a coa ed su ace o he expec ed hickness o 50-60nm. The
coa ed samples a e hen pu in he o en o one hou a he empe a u e o 90 ˚C and hen o 2 hou s a
he empe a u e o 120 ˚C, o ha den he coa ed PVA. A e wa d, he coa ed samples a e ubbed wi h a
el e clo h on a o a ing olle . Rubbing aims o eo ien he long chains o he PVA polyme along he
ubbing di ec ion because he ubbed su ace will la e ensu e he plana alignmen o he liquid c ys al
ha will be pu in con ac wi h i in he ollowing s eps. The ubbing akes place in he di ec ion o he
op ic axis o he bi e ingen subs a e which is al eady de ined be o e he p ocedu e. A e ha , he
o ma ion o a cell akes place, he pla es a e pu on o one ano he e y p ecisely, wi h a space be ween
hem. The p essu e is applied on he op and bo om su aces, and hen he cell is pu in o he acuum
chambe o 180 minu es o he laye o ai be ween he pla es o be emo ed, a e which wo ou o
ou sides o he cell a e sealed wi h he NOA61 glue and he UV lamp. Fo he glue o u he ha den,
he cell is pu in o he UV chambe o he du a ion o 12 hou s. The 5PCH LC in he o m o he liquid
is pu inside he glass pla es u ilizing capilla y o ces. The sample is hen le a he empe a u e o 120
˚C o hal an hou , o sp ead along he space be ween he co e and he subs a e, a e which he
empe a u e is slowly dec eased o 50˚C and he cell emains a his empe a u e o 3 hou s. Finally,
he las wo edges a e sealed ollowing he same p ocedu e ha was conduc ed o sealing he i s wo
edges.
In his hesis, we a e explo ing he p ope ies o an aniso opic wa eguide, wi h posi i e uniaxial ilm,
nega i e uniaxial subs a e, and aniso opic co e (ai ac s as a co e ). This is an an i-guiding s uc u e
ha doesn´ suppo any guided modes because he highes e ac i e index o he s uc u e is in he
subs a e and no in he ilm, i is he o dina y e ac i e index o he subs a e. Type o he liquid c ys al
used in he expe imen is nema ic, and he ype o wa eguide cell ha is o med is called 𝜋-cell.
3. Measu emen
3.1. Expe imen al se up
The se up used o e lec ion spec oscopy u ilizing p ism coupling is a modi ied O o-
K e chmann con igu a ion.9 The inpu ligh om he He-Ne lase (𝜆 = 632.8 𝑛𝑚) is guided by an
op ical ibe o he ibe collima o . Collima ed ligh passes h ough he pola ize whe e 𝑝 o 𝑠
pola isa ion can be selec ed. As he nex componen , a lens ocuses ligh on o he cell. Ligh alls on o
he hemisphe ic p ism made ou o SF11 so he p ism coupling akes place and index-ma ching liquid
is placed be ween he p ism and he wa eguide. Due o he pa h di e ence o e lec ed wa es by he
di e en sample laye s, in e e ome ic inges will be o med. Re lec ed ligh passes h ough he
p ecision sli , collima ing lens, and alls on o he beam spli e . A e he beam spli e , pa o he ligh
is ansmi ed and alls on he CCD came a, and pa o he ligh is e lec ed and alls on he
pho omul iplie ube (PMT). The signal om he PMT is collec ed by he oscilloscope, while he signal
om he came a is di ec ly ead by he cus om PC applica ion. Fo applying ol age, he elec odes o
he cell a e connec ed o he wa e o m gene a o . The wa eguide is placed on a o a ing s age which
o a es 360° du ing he p ism coupling, o a y he op ic axis o ien a ion. The se up is con olled using
he in-house de eloped LABVIEW so wa e, which was modi ied o his p ojec o au oma e he
o a ion s age and collec ou pu in ensi y h ough he CCD came a.
Figu e 4. The expe imen al se up used o e lec ion spec oscopy o he wa eguide cell.
3.2. P ism coupling
A high e ac i e index op ical p ism is used as a su ace couple o coupling inciden ligh o
he ilm in he op ical wa eguide. As we a e in e es ed in he in e ace be ween he ilm and he
subs a e, he p ism is made o SF11 glass, he same ma e ial as he op pla e o he wa eguide. In his
way, when index-ma ching liquid is used, only a hin laye o ITO and PVA sepa a es he p ism om
he liquid c ys al ilm. Thus, in his way, he p ism is close o he ilm which has he mode wi h a gi en
equency (𝜔), pola iza ion, and momen um. The e o e, e icien p ism coupling is ensu ed by phase
ma ching in he di ec ion o p opaga ion a phenomenon known as us a ed TIR e anescen coupling,
ollowing he phase-ma ching condi ion 𝑁 = 𝑛𝑝∙sin𝜑 , whe ein np is he e ac i e index o he
p ism.10
3.3. The expe imen
Two sepa a e expe imen s we e conduc ed, bo h u ilizing he modi ied O o-K e chmann con igu a ion
shown in Figu e 4, and he men ioned wa eguide sample.
Figu e 5. (a) Top iew o he sample on he o a ing s age. (b) The expe imen al se up.
The i s expe imen ha was conduc ed was measu ing he e lec ed wa es using he CCD
came a. The ligh was di ec ed on o he wa eguide sample and e lec ed ligh ha ell on o he came a
was collec ed. The sample was posi ioned on o he o a ing s age, and measu emen s we e conduc ed
o di e en alues o azimu hal angle 𝜙, achie ed by o a ing he sample in a sweep om 0° o 360°,
wi h an inc emen o 1°. Addi ionally, he whole p ocess was epea ed o di e en alues o he
inciden angle 𝜑, as a sweep om 34° o 36° deg ees. Following his, in he image p ocessing s age,
images we e s i ched oge he bo h ho izon ally ( o conca ena e all he azimu hal angles aken) and
e ically ( o conca ena e all he measu ed angles o incidence), o c ea e an image whe e he ho izon al
axis co esponds o he azimu hal angle, and e ical axis co esponds o he angle o incidence o 𝑁.
The inal image would demons a e he a ious modes suppo ed by he wa eguide along wi h he
exis ence o PS BICs. As he s a posi ion o he o a ing s age doesn’ co espond o he ze o alue o
he azimu hal angle, om he inal image we need o gene a e he use ul pa which co esponds o he
alues o he azimu hal angle om 0° o 180°.
In he second expe imen , he wa e o m gene a o was used o apply he AC ol age on o he
elec odes and gene a e he ol age on and o s a es. The applied ol age induces a change in he pola
angle posi ion o he op ic axis which causes he pola -symme y b eaking. The applied ol ages we e
a sweep in he ange o ampli ude alues om 1𝑉 o 10𝑉 wi h he 1𝑉 inc emen . The signal was
sinusoidal wi h he 1𝑘𝐻𝑧 equency. A e passing he beam spli e , pa o he ligh alls on o he PMT,
which is connec ed o he oscilloscope. Two measu emen s we e ca ied ou , i s highes o de mode
and hen he second highes o de mode we e examined one by one, by changing he incidence angle
alues. On he oscilloscope, we can de ec he change in he ou pu in ensi y when he ol age is applied.
This would help us unde s and he swi ching dynamics o he BICs in he co esponding modes.
4. Resul s and Discussion
4.1. Resul s o he i s expe imen
Figu e 6 demons a es he esul s o he e lec ion spec oscopy when a TE (S pola ized) wa e
is inciden on he wa eguide. We obse e he change in e lec ed in ensi y due o he di e en azimu hal
angles o mul iple angles o incidence. The ed dashed lines ep esen alues o o dina y and
ex ao dina y e ac i e indices o he subs a e. As we can see, by changing he azimu hal angle, he
o dina y e ac i e index emains cons an , while he ex ao dina y e ac i e index is a con ex
unc ion. The black dashed lines ep esen alues o o dina y and ex ao dina y e ac i e indices o he
ilm.
Figu e 6. In he inal image, e lec ion images a e s i ched oge he , so ha he ho izon al
axis ep esen s di e en alues o he azimu hal angle, and he e ical axis ep esen s
di e en angles o incidence.
Since i is a mul imode sys em, we obse e a ious leaky modes o di e en e ac i e indices
and each o he modes co esponds o he speci ic e ec i e index, N which a e he solu ions o
Maxwell’s equa ions. In he expe imen al Figu e 6, when a TE wa e is inciden on he wa eguide and
we collec he e lec ed image. The leaky modes a e shown as e lec ion dips as he e is ansmission
h ough he sample due o he mode adia ion o he subs a e. Howe e , we obse ed he solu ions o
he leaky mode exis in he egion whe e he ex ao dina y e ac i e index o he ilm is g ea e han
he ex ao dina y e ac i e index o he subs a e only. The es o he e lec ion dips a e some B ag
in e e ences whe e ei he ansmission o e lec ion is a o depending on he inciden angle and le
local alue o he ex ao dina y e ac i e indices. When he op ic axis becomes pe pendicula o he
di ec ion o p opaga ion (a Φ = 90°), we obse e he blue bands ( e lec ion dips) o leaky mode s a
o disappea esul ing in maximum e lec ion a Φ = 90° o he highe o de mode. In his case, a
PS-BIC wi h TE pola iza ion exis s, which is o hogonal o he o dina y (o TM) adia ion channel,
esul ing in o al e lec ion. This is in ag eemen wi h he li e a u e, whe e BICs ha e been demons a ed
as ze os o adia ion ampli udes and expe imen ally hey canno be coupled om he con inuum,
he e o e, showing a maximum e lec ion poin s whe e he leaky mode e lec ions anish.