nanoma e ials
A icle
Design o Plasmonic-Wa eguiding S uc u es o
Senso Applica ions
Ja osla Vlˇcek 1,2,*,†, Ja omí Piš o a 1,3,† and Michal Les ˇnák 1,†
1Nano echnology Cen e, VŠB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic
2Depa men o Ma hema ics and Desc ip i e Geome y, Facul y o Mechanical Enginee ing,
VŠB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic
3IT4Inno a ions, VŠB—Technical Uni e si y o Os a a, 708 00 Os a a, Czech Republic
*Co espondence: ja osla [email p o ec ed]
† Cu en Add ess: 17. lis opadu 2172/15, 708 00 Os a a-Po uba, Czech Republic.
Recei ed: 30 July 2019; Accep ed: 26 Augus 2019; Published: 29 Augus 2019
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Abs ac :
Su ace plasmon esonance has become a widely accep ed op ical echnique o s udying
biological and chemical in e ac ions. Among o he s, de ec ing small changes in analy e concen a ion
in complex solu ions emains challenging, e.g., because o he need o dis inguishing he in e ac ion
o in e es om o he e ec s. In ou model s udy, he esolu ion abili y o plasmonic sensing elemen
was enhanced by wo ways. Besides an implemen a ion o me al-insula o -me al (MIM) plasmonic
nanos uc u e, we sugges conca ena ion wi h wa eguiding subs uc u e o achie e mu ual coupling
o su ace plasmon pola i on (SPP) wi h an op ical wa eguiding mode. The dependence o coupling
condi ions on he mul ilaye pa ame e s was analyzed o ob ain op imal ield in ensi y enhancemen .
Keywo ds: su ace pola i ons; plana wa eguide; mode coupling; op ical senso s
1. In oduc ion
The coupling o esonance s a es in a ious op ical nanos uc u es o e s many p omising ways
o he de elopmen o new pho onic de ices. This expec a ion ollows he ecen esul s ob ained o
plasmonic coupled modes occu ing in plasmonic me al-dielec ic nanos uc u es [
1
,
2
]. The coupling
be ween su ace plasmon pola i on and wa eguide mode belongs o he in ensi ely in es iga ed
e ec s, especially as he op ical Fano e ec (OFE) [3,4].
Su ace plasmon esonance (SPR) has become a widely accep ed op ical echnique o s udying
biological and chemical in e ac ions. Among o he s, de ec ing small changes in analy e concen a ion
in complex solu ions emains challenging, e.g., because o he need o dis inguishing he in e ac ion
o in e es om o he e ec s. In pa icula , non-speci ic binding and/o backg ound e ac i e
index changes a e p oblema ic in he mul i-componen analy es, e.g., in medicine, ood sa e y and
en i onmen al applica ions. Typically, he SPR senso is cha ac e ized by i s sensi i i y, pene a ion
dep h, and pe haps e en by ull wid h o hal -minimum (FWHM) o he e lec ance dip. In he angula
in e oga ion mode, he adi ional sensing de ice has an angula sensi i i y o 50–100 deg/RIU, whe e
RIU deno es e ac i e index uni s. I he e lec ance shi
∆R
a ixed incidence angle is de ec ed
ins ead SPR dip angula shi , he sensi i i y mo es abou 30 RIU
−1
[
2
]. Depending on applied
measu ing me hod he esolu ion limi less han 10
−4
can be achie ed [
5
]. Pene a ion dep h gi es
qui e eliable indica ion o he usable dis ance, a which he SPR de ice is sensi i e o changes in he
analy e (≈200 nm a op ical equencies [6]).
To imp o e sensing pa ame e s, se e al di e en ways we e sugges ed o enhance de ec ion limi
o SPR senso s, pene a ion dep h o hose o speci ic applica ion condi ions:
Nanoma e ials 2019,9, 1227; doi:10.3390/nano9091227 www.mdpi.com/jou nal/nanoma e ials
Nanoma e ials 2019,9, 1227 2 o 9
•
adding o pho onic c ys al p ede e mining e ec i e e ac i e index ha suppo ed SPP modes
exci a ion [7–9];
•
implemen a ion o insula o -me al-insula o (IMI) o me al-insula o -me al (MIM) subs uc u es
ha p oduce long- ange su ace plasmons (LR SPP) wi h lowe abso p ion losses [6,10];
•coupling o SPP and wa eguide (WG) modes (see, e.g., [3,11]);
•
dispe sion plasmonic in e ac ion a an in e ace be ween a doped semiconduc o and
a dielec ic [12];
•
applica ions o new ma e ials (e.g., g aphene) and/o speci ic condi ions as c yonic a angemen
a IR equencies [13,14]; and
•some combina ion o he abo e i ems.
In ou ecen wo k, we analyzed he high e ac i e index wa eguide based on e omagne ic
ga ne [
11
]. Some esul s ob ained he e wi h ela ion o he magne o-plasmonic sensing showed
ce ain pe spec i e by mu ual coupling o he esonan s a es exci ed in pa allel in plasmonic and
wa eguiding sub-sys em. Supplemen ing wo o mo e me al-dielec ic in e aces close o each
o he in o undamen al wa eguide b ings in e es ing e ec s: besides he coupling be ween SPPs
o indi idual in e aces, he o he kinds o combined esonance s a es a e gene a ed dependen ly on
he ma e ial and/o geome ical p ope ies o sepa a e componen s.
This pape is de o ed o he coupling o esonance s a es a ising in op ical s uc u e combining
plana wa eguide (WG) wi h MIM SPR sys em, when he bo h sub-s uc u es ope a e in a angemen
wi h he same coupling p ism. In he nex sec ion, he basic model app oach is desc ibed as ollows.
Plana wa eguide pa ame e s as he backg ound o wa eguide-plasmonic e ec s a e in oduced in
Sec ion 2.1, wi h special a en ion paid o he long- and sho - ange plasmons exci ed in he MIM
complemen ha is analyzed in Sec ion 2.2. Se e al o ms o he coupling wa eguide modes wi h
plasmonic ones a e p esen ed in Sec ion 2.3, and esul ing combined esonance s a es a e discussed
ega ding hei sensing abili y in Sec ion 2.4. In Sec ion 3, he SPP-WG senso se up is p oposed
including sensing abili y exp essed by achie able sensi i i y and esolu ion limi .
Nume ical esul s p esen ed he e we e ob ained using 4
×
4 ma ix me hod based on igo ous
coupled-wa es algo i hm (RCWA, [
15
]) implemen ed as i s own Ma lab code. The p esumed
expe imen al a angemen (de ec ion pa ) o senso esponse analysis is based on lock-in de ec ion
echnique. In he i s s ep o s uc u e es ing, ens o kHz ope a ing equency ange will be applied.
2. Me hods
2.1. Wa eguiding S uc u e
The bismu h-doped gadolinium i on ga ne wa eguide laye o hickness
d
(Bi:GIG,
n2=
2.4619
−
0.0042i) was p epa ed on a gallium-gadolinium ga ne subs a e (GGG,
n3=1.9648
) wi h e ac i e
indices a he wa eleng h 633 nm [
16
]. The p oposed s uc u e was sepa a ed om he coupling p ism
by ai -gap supe s a e. As he coupling p ism mus ha e a ma e ial wi h a ela i ely high e ac i e
index, he u ile p ism (
n=
2.5836) [
17
] was used. This s uc u e enabled gene a ing s anda d TE and
TM guided modes, whe e guided o de was con olled by he Bi:GIG laye hickness (see Figu e 1).
In he s udied plasmonic-wa eguiding s uc u e, he GGG subs a e was na u ally ini e; he wa e
as adjoining analy e (
n=
1.332) was conside ed. The subs a e hickness o 100 nm was ixed in all
simula ions because o i s small in luence on he s udied e ec s compa ed wi h he o he geome ical
pa ame e s o s uc u e. Table 1illus a es pene a ion dep h in o he GGG o he i s h ee mode
o de s o he bo h undamen al pola iza ions o inciden ield.
Since he ai gap sepa a ing men ioned sub-s uc u es is no su icien o ob ain mu ual coupling,
embedding o an app op ia e in e laye is needed, he ma e ial and hickness o which we e speci ied
in ou p e ious simula ions [
11
]. The wa eguide coupling o ces depend p ima ily on he ai
gap hickness; ne e heless, inse ing ano he laye be ween he p ism and WG changed coupling
condi ions di e en ly o he a ious modes, as demons a ed in Figu e 2.
Nanoma e ials 2019,9, 1227 3 o 9
Figu e 1.
(
a
) Plana wa eguide scheme; and (
b
) wa eguide hickness
d
e sus e ec i e e ac i e index
Ne
up o hi d-o de guided modes (
n2
,
n3
deno e e ac i e indices o plana wa eguide and GGG
subs a e, espec i ely).
Table 1.
Pene a ion dep h o se e al guided modes (550 nm wa eguide laye hickness) in o he
GGG subs a e.
Pene a ion Dep h (nm)
Mode O de 0 1 2
TE 36 44 94
TM 36 47 198
In he p e ious wo k [
11
], he magne o-op ical ac i i y o e omagne ic ga ne was applied as
he p incipal e ec . The e o e, only one gold laye wi h he Al-doped zinc oxide (
n=
1.8) in e laye
was used. Fo he SPP-PWG sys em discussed he e, an in e laye wi h lowe e ac i e index would be
ad an ageous in he p oposed me al-insula o -me al s uc u e (see Sec ion 2.2).
Placing he glass nanolaye (
n=
1.5) impo an ly changes he coupling s eng h be ween p ism
and wa eguide (Figu e 2). The incidence angle
φ
is ela ed o he p ism base/s uc u e in e ace;
in pa icula , o he in e ace p ism base/in e laye in Figu e 2. No e ha he laye hicknesses in
p esen ed schemes do no co espond o he eal si ua ion.
Figu e 2.
Wa eguide esonance s a es dis ibu ion a he angula scale wi hou glass in e laye (cen e
pic u e) and wi h his one.
Inse ing gold ilm o he app op ia e hickness below he wa eguide laye causes angula shi o
TE esonance minima. I enables, among o he s, o achie e he gene a ion o bo h TE and TM modes a
he same incidence angle, acili a ing an impo an g oup o expe imen s. Figu e 3shows one om
esul ing wa eguide modi ica ion.
Nanoma e ials 2019,9, 1227 4 o 9
Figu e 3.
Angula shi o he TE esonance s a es due he Au ilm inse ing (
n=
0.1838
−
3.4310i [
18
])
below he wa eguide laye (ai gap 100 nm, Bi:GIG 520 nm).
2.2. Me al-Insula o -Me al Nanos uc u e
Conside a hin dielec ic ilm o he hickness
sandwiched be ween wo ini e (bu qui e la ge)
me al laye s o he same e ac i e index. Gene ally, he dispe sion ela ion o his symme ic MIM
s uc u e gi es ou esonance s a es ha ep esen wo plasmonic and wo pho onic modes [
19
],
a pa icula se up o which depends on he ma e ial as well as geome ical pa ame e s o SPR
s uc u e [2,10].
In he con igu a ion discussed he e wi h he u ile p ism and SiO
2
gap be ween gold laye s,
he pho onic (i.e., guided) modes canno exis . On he o he hand, one SPP mode su i es o all
alues
o gap hickness. This mode exhibi s odd symme y o longi udinal elec ic ield componen
Ey
, and, consequen ly e en symme y o ans e sal componen
Ez
(no mal o he in e ace) (see
Figu e 4a,b).
Figu e 4.
Elec ic ield componen s in he MIM s uc u e Au–SiO
2
184 nm–Au coupled wi h u ile
p ism. Incidence plane is pe pendicula o he
x
axis. (
a
,
b
) LR SPP wi h odd longi udinal ield
symme y a esonance incidence angle 19.8 deg; and
(c,d) SR SPP
wi h e en longi udinal ield
Ey(z)
symme y, incidence angle 44.4 deg.
Fo su icien ly hick dielec ic in e laye , he o he SPP ype is also suppo ed, ha ing he
opposi e cha ac e is ics o he co esponding elec ic ield componen s (Figu e 4c,d). In ag eemen
wi h desc ibed p ope ies, hese SPPs a e e med asymme ic and symme ic, espec i ely. In bo h
cases, he longi udinal componen s a e con inuous ega ding he bounda y condi ions.
No e ha equen ly used nomencla u e wo ks wi h he long- ange (LR) SPP in he case o
asymme ic longi udinal componen , and sho - ange (SR) SPP in he opposi e si ua ion. This no a ion
Nanoma e ials 2019,9, 1227 5 o 9
is ypical o IMI plasmonic s uc u es, whe e p opaga ion leng h o he symme ic SPP is exp essi ely
less han ha o he asymme ic one [
20
,
21
]. Fo cla i y, we also keep he LR/SR no a ion in his pape .
The hicknesses o lossy me allic laye s mus be su icien ly small in eal si ua ions. The e o e,
44-nm gold ilm a he wa eleng h 633 nm in applied K e schmann con igu a ion was used. This is he
eason ha men ioned common Au sublaye hickness is p ese ed in he designed s uc u e. The size
o single MIM pa s impo an ly in luences he pa ame e s o plasmonic esonance s a es ha b ings
an ad an age by SPP-WG coupling. Figu e 5illus a es exci a ion o he bo h kinds o SPPs o wo
s a es wi h symme ic geome y bu o di e en dielec ic slab, and he asymme ic case, when he i s
gold laye hickness p edomina es. LR SPPs exci ed close o 25 deg exhibi small dependence on MIM
geome y, whe eas he SR SPPs a e ha dly modi ied.
Figu e 5.
Plasmonic esonance s a es in he MIM s uc u e wi h hin Au ilms: he LR SPR minima on
he le (
φ≈
25
◦
); and he SR SPR dips on he igh . The nanome e alues o laye hicknesses in he
legend a e o de ed om he closes o he p ism o he ai subs a e.
2.3. SPP–PWG Coupling
Conside he example when he dielec ic wa eguide in e laye in Figu e 2(g een componen
below he p ism) is supplied by he symme ic MIM plasmonic s uc u e discussed in he p e ious
subsec ion. In he combina ion wi h wa e analy e, we ob ain he esonance esponse in Figu e 6.
The TE wa eguide modes a e p ac ically supp essedk he weakly coupled mode TM
0
is ou side he
igu e. Howe e , he wa eguide coupling o TM
1
mode is enhanced by he na ow SR plasmonic
mode.
Figu e 6.
Re lec ance esponse om plasmonic-wa eguiding s uc u e wi h ma ked esonance s a es.
Fini e laye hicknesses in nm ( om op o bo om): 22/100/22/80/480/100.
The coupling be ween plasmonic and wa eguiding modes can be eached using se e al me hods
ollowing he SPP ype and WG mode o de as well. Besides changes o wa eguide condi ions (gap
and/o wa eguide laye hickness), he geome ical pa ame e s o MIM sub-s uc u e enable e icien
uning o e lec ance esponse.

Nanoma e ials 2019,9, 1227 6 o 9
A ising o SR SPP dips a highe incidence angles (Figu e 5) leads o he coupling wi h he low
o de wa eguide modes simila o in he p e ious example. This is easily ealized by he hickness
asymme y in MIM componen s o he o m 10
/ i/
34, whe e
i
is he dielec ic in e laye hickness
aken as use -speci ic pa ame e . In Figu e 7, he SR SPP coupling wi h he TM
1
wa eguide mode is
modeled h ough small changes o he hickness i.
Figu e 7.
Mu ual coupling o he TM
1
wa eguide mode and he sho - ange plasmonic mode o he
laye hicknesses o he s uc u e 10/ i/34/80/450/100 (see p e ious igu e o explana ion).
We obse e he enhancing o TM
1
coupling o ces caused by he wi ness o plasmonic esonance
s a e. An inc ease o he in e laye hickness leads o he angula shi o SPP dip ha successi ely
goes ac oss he WG esonance minimum. This phenomena is usually e e ed as he op ical Fano e ec
(OFE) (see, e.g., [3] and e e ences he ein).
On he con a y, he coupling o ces o TM
3
mode p edomina e compa ed o he LR SPP mode
(see Figu e 6). Since he mu ual coupling demands an alignmen o bo h esonance s a es, we a enua e
he WG coupling o ces by enla gemen o ai gap up o 300 nm oge he wi h he applica ion o he
opposi e MIM asymme y compa ing wi h he p e ious case. The esul ing e lec ance esponse in
Figu e 8is again o he OFE ype.
Figu e 8.
Mu ual coupling o he TM
3
wa eguide mode and he long- ange plasmonic mode uned by
he isize. The laye p opo ions a e speci ied o each s uc u e.
A ine uning o he SPP-WG coupling is again ealized h ough he dielec ic in e laye hickness.
Simila ly, in his case, we can speak abou he OFE.
2.4. Sensing Abili y o Plasmonic-Wa eguiding Sys em
Conside he SPP-WG sensing de ice as in Figu e 6ope a ing in he angula in e oga ion mode
wi h TM pola ized op ical beam. The e lec ance inc emen
∆Rp
a a e e ence incidence angle is
de ec ed as he esponse on small changes o analy e e ac i e index
∆na
. Thus, he sensi i i y
S
and
esolu ion limi min(∆na) a e exp essed as
S=∆Rp
∆na
[RIU−1], min(∆na) = δRp
S[RIU], (1)
Nanoma e ials 2019,9, 1227 7 o 9
whe e
δRp
is he minimal limi o a gi en se up. The abo e indings allow designing o he senso ic
s uc u e wi h op imal ope a ing pa ame e s. A i s , we exploi he enhancing o coupling o ces
by LR SPP coupling wi h a WG mode o high o de ha implies su icien pene a ion dep h o he
p obe ield in o he analy e. Choosing an app op ia e e e ence incidence angle is he o he impo an
s ep. Wa eguide esonance dips a e no ad an ageous o he modula ion because o hei s eepness,
and oo weak a iabili y ela ing o a change o analy e e ac i e index. Howe e , when he LR SPP
dip is “locked” on o wa eguide one, he esul ing op ical Fano e ec no only p oduces enhanced
elec omagne ic ield ac oss he s uc u e bu also leads o span o WG dip. Thus, he esul ing coupled
esonance s a e disposes o equi ed sensing p ope ies.
3. Resul s and Discussion
We showed ha he mu ual coupling o SPR modes exci ed in MIM s uc u e wi h guided modes
in linked wa eguiding sub-sys em allows es ablishing a ious coupled esonance s a es o ma ing
a o able condi ions o senso ic applica ions. The 140 nm dielec ic s ip oge he wi h he 170 nm ai
gap led o qui e close compa able e lec ion dips ha c ea e sensi i i y inc ease o coupled esonance
s a e (Figu es 9and 10).
Figu e 9.
Mu ual coupling o he TM
3
wa eguide mode and he long- ange plasmonic
mode: (
a
) laye hicknesses 0/140/0/170/470/100 (WG modes only); and (
b
) laye hicknesses
34/140/10/170/470/100 (coupled esonance s a es).
Figu e 10.
Illus a ions o he sensi i i y analysis: (
a
) de ails o e lec ance cu es co esponding o he
scale o analy e e ac i e index in igu e (
b
) wi h ma ked e e ence incidence angle; and (
b
) linea i y
o he Rp s. nadependence.
The segmen o e lec ance cu e be ween g een poin s in Figu e 9b is he mos e icien o
he sensi i i y es ing because o i s linea i y and sui able s eepness. De ailed isualiza ion o he
successi e shi o e lec ance esponse as a unc ion o he analy e e ac i e index a iance is illus a ed
in Figu e 10a. The esponse cha ac e is ics o he sensing elemen wi h p oposed pa ame e s a e:
sensi i i y,
S=
49.5 RIU
−1
; esolu ion limi , 2
×
10
−4
RIU; and
δRp=
0.01. The minimal s ep be ween
Nanoma e ials 2019,9, 1227 8 o 9
he neighbo ing cu es a he e e ence incidence angle (see he blue e ical line in he Figu e 10a) is
∆Rp=0.05.
Al hough compa ison s udies o he SPR and SPP-WG senso s showed less sensi i i y in he
second case ([
2
] and e e ences he ein), he designed s uc u e may achie e equi alen esul s as a
pu e SPR a angemen , namely by he be e igu e o me i . As he ypical SPR senso s a e based on
he esponse analysis ep esen ed by a plasmonic esonance minima, in p esen ed s udy, we exploi ed
p ope ies o wa eguide esonance dip modi ied by op ical Fano e ec .
I needs o be emphasized ha he linea i y o he sensi i i y on he in e al om 1.330 o
1.335 (Figu e 10b) ensu es eliable senso unc ionali y. Mo eo e , he conca ena ion o plasmonic
nanos uc u e wi h wa eguiding subs uc u e leads o ield in ensi y enhancemen , enabling an
imp o emen o esolu ion abili y.
Au ho Con ibu ions:
J.V. pe o med he simula ions, p epa ed he igu es, and w o e he ini ial e sion o he
pape . J.P. p oposed he p ojec , p o ided he o e all guidance, and supe ised he inal e sion. M.L. checked
and comple ed he applica ion ou pu s.
Funding:
This wo k was pa ially suppo ed by he Minis y o Educa ion, You h and Spo s o he Czech Republic:
by he Na ional P og am o Sus ainabili y (NPU II) p ojec “IT4Inno a ions Excellence in Science—LQ1602”.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Abb e ia ions
The ollowing abb e ia ions a e used in his manusc ip :
FWHM ull wid h o hal -maximum
IMI insula o -me al-insula o
MIM me al-insula o -me al
OFE op ical Fano e ec
SPP su ace plasmon pola i on
SPR su ace plasmon esonance
WG wa eguide
LR long- ange
SR sho - ange
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