senso s
A icle
E icien Op ical Sensing Based on Phase Shi o Wa es
Suppo ed by a One-Dimensional Pho onic C ys al
Roman Kaˇnok * , Pe Hlubina * , Lucie Gembalo á and Dalibo Cip ian


Ci a ion: Kaˇnok, R.; Hlubina, P.;
Gembalo á, L.; Cip ian, D. E icien
Op ical Sensing Based on Phase Shi
o Wa es Suppo ed by a
One-Dimensional Pho onic C ys al.
Senso s 2021,21, 6535. h ps://
doi.o g/10.3390/s21196535
Academic Edi o s: Ai o U u ia,
Pablo Zubia e, Ne ea De Acha
Mo ás and Diego Lopez-To es
Recei ed: 29 July 2021
Accep ed: 28 Sep embe 2021
Published: 30 Sep embe 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
Depa men o Physics, Technical Uni e si y Os a a, 17. Lis opadu 2172/15,
708 00 Os a a-Po uba, Czech Republic; [email p o ec ed] (L.G.); dalibo [email p o ec ed] (D.C.)
*Co espondence: [email p o ec ed] (R.K.); pe [email p o ec ed] (P.H.);
Tel.: +420-732-851-207 (R.K.); +420-597-323-134 (P.H.)
Abs ac :
In e e ome ic me hods o op ical sensing based on he phase shi o he Bloch su ace
wa es (BSWs) and guided wa es (GWs) suppo ed by a one-dimensional pho onic c ys al a e
p esen ed. The pho onic c ys al, composed o six SiO
2
/TiO
2
bilaye s wi h a e mina ion laye o
TiO
2
, is employed in he K e schmann con igu a ion. Unde esonance condi ion, an ab up phase
change is e ealed, and he co esponding phase shi is measu ed by in e e ome ic echniques
applied in bo h he spec al and spa ial domains. The spec al in e e ome ic echnique employing
a bi e ingen qua z c ys al is used o ob ain in e e ence o p ojec ions o
p
- and
s
-pola ized ligh
wa es e lec ed om he pho onic c ys al. The phase shi s a e e ie ed by p ocessing he spec al
in e e og ams eco ded o a ious alues o ela i e humidi y (RH) o ai , gi ing he sensi i i y o
he RH as high as 0.029 ad/%RH and 0.012 ad/%RH o he BSW and GW, espec i ely. The spa ial
in e e ome ic echnique employs a Wollas on p ism and an analyze o gene a e an in e e ence
pa e n, which is p ocessed o e ie e he phase di e ence, and esul s a e in good ag eemen wi h
hose ob ained by sensing he phase shi in he spec al domain. In addi ion, om he de i a i e
o he spec al phase shi s, he peak posi ions a e ob ained, and hei changes wi h he RH gi e
he sensi i i ies o 0.094 nm/%RH and 0.061 nm/%RH o he BSW and GW, espec i ely. These
expe imen al esul s demons a e an e icien op ical sensing wi h a lo o applica ions in a ious
esea ch a eas.
Keywo ds:
pho onic c ys al; in e e ome y; spec al domain; spa ial domain; Bloch su ace wa es;
guided wa es; K e schmann con igu a ion; ela i e humidi y o ai
1. In oduc ion
Dielec ic s uc u es composed o al e na ing s a i ied media, e e ed o as he one-
dimensional pho onic c ys als (1DPhCs) o he B agg e lec o s, a e in e es ing o hei
op ical p ope ies. Due o a pe iodic modula ion o he e ac i e index (RI), egions o
abandoned ligh equencies— he pho onic band gaps—exis and wi hin hem, ligh is
no allowed o p opaga e h ough he s uc u es [
1
,
2
]. Thus, he 1DPhCs ha e a high
e lec i i y and a e widely used as e lec i e coa ings and il e s [
3
]. The 1DPhCs can
also ac as plana wa eguides [
4
] and he guided wa es (GWs) can be used in sensing
applica ions [
5
–
7
]. Las bu no he leas , he Bloch su ace wa es (BSWs) p opaga ing
along he in e ace o he 1DPhC wi h an ex e nal medium a e widely used in sensing,
including he angula [
8
–
11
] o wa eleng h [
12
–
17
] in e oga ions. Thus, he BSW-based
senso s ex end ma u e echnologies applied in sensing ha ha e se e al applica ions in
di e en ields o biology [
18
], physics [
18
], and chemis y [
18
–
21
]. The BSW s a es exis
wi hin he band gap o a unca ed 1DPhC. Bo h he GWs and BSWs cause a phase jump o
inciden ligh , simila ly o he su ace plasmon esonance (SPR). The e o e, senso s based
on he phase de ec ion o wa es suppo ed by a 1DPhC a e easible [
22
–
27
]. In addi ion,
hey ep esen an al e na i e o ela i e humidi y senso s based on esonances o su ace
Senso s 2021,21, 6535. h ps://doi.o g/10.3390/s21196535 h ps://www.mdpi.com/jou nal/senso s
Senso s 2021,21, 6535 2 o 17
plasmons [
16
], BSWs [
16
], whispe ing galle y modes [
28
], guided modes [
4
,
7
,
29
], pho onic
c ys al modes [30], and lossy modes [31,32].
One o he ad an ages o he BSWs suppo ed by 1DPhCs is he ac ha also
s
-
pola ized ligh can be used o hei exci a ion, depending on he s uc u e geome y. Since
he s uc u e is composed o dielec ic ma e ials, abso p ion is e y low and esonance
dips in he e lec ance spec um a e na ow. In addi ion, because o i s chemical s abili y,
sensing using he 1DPhCs can be adop ed in agg essi e en i onmen s. Al hough he
sensing using he e lec ance e alua ion in he spec al domain is mo e o en epo ed
owing o a simple se -up, he phase in e oga ion has some subs an ial ad an ages e en i
he me hod is mo e complex. One o hem is ha esonance phase peaks a e na owe han
he esonance e lec ion dips. Mo eo e , in many cases he esonance e lec ion dips canno
be esol ed and an in e e ome ic me hod o measu e an ab up phase change o e comes
he limi a ion.
In his pape , wo op ical in e e ome ic sensing me hods based on measu emen o
he phase shi o he BSWs and GWs suppo ed by a 1DPhC a e p esen ed. The me hods,
as al e na i es o o iginal app oaches [
33
–
39
], a e applied in bo h he spec al and spa ial
domains, and as an analy e, mois ai o a a ied ela i e humidi y (RH) is used. Fo he
1DPhC unde es we show ha he phase shi s o bo h he BSW and GW can be esol ed
using he spec al me hod. On he con a y, only he phase shi o he GW can be esol ed
using he spa ial me hod. A a speci ic wa eleng h, he phase shi is de e mined as a
unc ion o he RH. The senso pe o mance is e alua ed in e ms o sensi i i y, and in
he case o he BSWs, achie ed sensi i i y o he humidi y is as high as 0.029 ad/%RH.
Simila ly, in he case o he GWs, he sensi i i y eaches 0.012 ad/%RH. Mo eo e , o
show an ad an age o he spec al me hod, de i a i e o he phase shi is pe o med, and
peak posi ion is acked as a unc ion o he RH, gi ing he sensi i i y o he RH as high as
0.094 nm/%RH and 0.061 nm/%RH o he BSW and GW, espec i ely.
The pape is o ganized as ollows. The i s pa is ocused on he ma e ial cha ac e i-
za ion. In he second pa , compu a ional ools used in heo e ical model a e in oduced.
The hi d pa is ocused on a band s uc u e o an in ini e 1DPhC. Then, he heo e ical
esul s a e p esen ed. In he ollowing pa , an expe imen al se -up used in eco ding
he in e e og ams is desc ibed. The las bu one pa is ocused on expe imen al esul s
ob ained by echniques applied in bo h he spec al and spa ial domains. In he inal pa ,
conclusions a e p esen ed.
2. Theo e ical Model
2.1. Ma e ial Cha ac e iza ion
The mul ilaye s uc u e unde s udy is shown in Figu e 1a, and i ep esen s a
1DPhC consis ing o six SiO
2
/TiO
2
bilaye s and a e mina ion laye o TiO
2
. The 1DPhC is
deposi ed on a glass subs a e and employing an imme sion oil, he subs a e is a ached
o a coupling p ism made o BK7 glass in he K e schmann con igu a ion. In Figu e 1b, a
de ail image o he s uc u e p o ile ob ained by a scanning elec on mic oscope (SEM) is
shown, e ealing di e en laye hicknesses. To cha ac e ize he hin laye s, he a iable
angle spec oscopic ellipsome y (VASE) measu emen was employed. Da a ob ained
by he VASE we e p ocessed using he Comple eEASE so wa e (J.A. Woollam Co., Inc.,
Shanghai, China) and he hicknesses o he laye s we e de e mined, as summa ized in
Table 1.
Senso s 2021,21, 6535 3 o 17
Mois ai
TiO2
T1
S1
S6
T7
glass subs a e
imme sion
liquid
TiO2
SiO2
SiO2
BK7 p ism
α
θ
e
z
x
y
(a)
(b)
Figu e 1. (a) A coupling p ism wi h a pho onic c ys al unde conside a ion. (b) SEM image o he pho onic c ys al.
Table 1. Thin laye hicknesses ob ained by he VASE.
Laye Thickness (nm) Laye Thickness (nm)
T187.65 S1120.21
T279.09 S2101.75
T377.28 S3109.24
T480.74 S4108
T580.89 S5127.3
T676.85 S6125.02
T764.41 e 6.96
Mo eo e , he RI dispe sions o he laye s and o he subs a e we e also de e mined
as a esul o i ing he da a ob ained by he VASE. In he case o he glass subs a e, he RI
as a unc ion o wa eleng h is exp essed by Cauchy o mula
nsub(λ) = A−Bλ+Cλ2−Dλ3, (1)
whe e alues o cons an s ob ained by he VASE a e
A=
1.51824,
B=
0.19112
µm−1
,
C=
0.019391
µm−2
and
D=
0.07108
µm−3
, when wa eleng h
λ
is in mic ome e s. The RI
dispe sion o hin ilms is desc ibed by o mula
n2
i(λ) = A+Bλ2
λ2−C2−Dλ2, (2)
whe e
A
,
B
,
C
and
D
a e cons an s and
i
= TiO
2
, SiO
2
indica es he ma e ial. Thei alues
ob ained by he VASE o TiO
2
a e
A=
0,
B=
4.672,
C=
0.22935
µ
m,
D=0µm−2
.
The cons an alues ob ained o SiO
2
a e
A=
1.348,
B=
0.756,
C=
0.10683
µ
m,
D=0.00975 µm−2
. The ob ained ela ions a e alid in a wa eleng h ange om 376 nm o
1700 nm. Simila ly, he RI o he BK7 p ism is desc ibed by a h ee e m Sellmeie o mula
speci ied elsewhe e [40], alid in a wa eleng h ange om 0.3 µm o 2.5 µm.
A he op o he e mina ion laye , he e is a ough su ace. To con i m he ough
su ace, a squa e o 10
µ
m
×
10
µ
m chosen on he su ace was inspec ed by he a omic
o ce mic oscopy (AFM) and da a ob ained we e p ocessed using Gwyddion so wa e. A
Senso s 2021,21, 6535 4 o 17
opog aphy image o he 1DPhC su ace co ec ed by a la su ace sub ac ion is shown in
Figu e 2, and he a e age oughness Ra= (1.302 ±0.37)nm was ob ained.
Figu e 2. A opog aphy image ob ained by an AFM measu emen .
Unde assump ion ha he a e age oughness is smalle han he wa eleng h o
in e ac ing ligh , he ough su ace can be app oxima ed by a laye o an e ec i e medium.
In he case o he B uggeman e ec i e media app oxima ion (EMA), he dielec ic cons an
ee desc ibing he laye sa is ies he equa ion
ea−ee
ea+2ee
+ (1− )eb−ee
eb+2ee
=0, (3)
whe e
ea
end
eb
a e dielec ic cons an s o media
a
and
b
, espec i ely, and
∈<
0, 1
>
is a
ac ion o medium
a
in he e ec i e medium laye . By de aul , se -up o he Comple eEASE
so wa e, 50% o oid is assumed ( = 0.5, eb= 1) in he models.
The mul ilaye de ec ion s uc u e is sensi i e o changes in RI o he ex e nal medium
(analy e) o he 1DPhC. Since he change in he RI o mois ai due o RH change is e y
low (
∆RI ≈
3.6
×
10
−7
ob ained [
41
] o wa eleng h
λ
= 532 nm, empe a u e
= 20
◦
C,
a mosphe ic p essu e p= 1013.25 hPa and RH change om 30% o 80%), he mechanism o
sensi i i y o he p oposed senso o mois ai (see nex Sec ions) has o be caused by o he
phenomena. One o hem is adso p ion o wa e molecules on he ough su ace [
42
,
43
]
o he 1DPhC. To gain insigh in o he e ec , we simula e i by in ol ing con ibu ion o
dielec ic unc ion o wa e in calcula ions o he B uggeman EMA. I can be done using o
Equa ion (3) ecu si ely. Fi s , he RI dispe sion o wa e can be desc ibed by a ou e m
Sellmeie o mula [44]
n2
w(λ)=1+
4
∑
n=1
Aiλ2
λ2−λ2
i
, (4)
whe e he cons an s
Ai
and
λ2
i
alid o empe a u e o 20
◦
C a e
A1=5.684027565 ×10−1
,
A2=
1.726177391
×
10
−1
,
A3=2.086189578 ×10−2
,
A4=
1.130748688
×
10
−1
,
λ2
1=5.101829712 ×10−3µm2
,
λ2
2=1.821153936 ×10−2µm2
,
λ2
3=
2.620722293
×
10
−2
µm2,λ2
4=1.069792721 ×10 µm2.
Senso s 2021,21, 6535 5 o 17
Then he dielec ic unc ion
e0
e
con aining con ibu ions o ai and wa e is ob ained
using Equa ion (3), conside ing
ea=n2
w
and
eb=
1 o ac ion o medium
a
(wa e )
∈<
0, 1
>
, whe e o
=
0
→e0
e =ea
and o
=
1
→e0
e =ew
. A e ha , he
inal dielec ic unc ion
ee
in ol ing con ibu ions o TiO
2
and p e iously de e mined
e ec i e medium is ob ained, conside ing ea=n2
TiO2and eb=e0
e , wi h ixed =0.5.
2.2. Ma ix Fo malism
In e ac ion o elec omagne ic wa es wi h dielec ic pe iodic s uc u es can be e ec-
i ely desc ibed by he 2
×
2 ma ix me hod [
45
,
46
], assuming ha he media a e homo-
geneous and iso opic. Fi s , a s uc u e o
N
laye s sandwiched be ween wo semi- ini e
media is conside ed, as shown in Figu e 3. Ampli udes o igh and le p opaga ing plane
wa es a e ep esen ed by
Ai
and
Bi
, espec i ely, while he supe sc ip
0
indica es ha he
wa e is a he le bounda y o he laye .
B0
B0
B0
A0
A1
A2
B10
B10
A10
A20
AN
AN+10
BN
BN+10
AN0
BN0
x
z
dN
01
12
23
(N-1)N
N(N+1)
Figu e 3. A s uc u e o Nlaye s unde s udy.
The co esponding igh and le p opaga ing modes can be ep esen ed as column
ec o s, and hese ec o s a he wo sides o he in e ace
ij
a e ela ed ia so-called
dynamic ma ix Dij
Ai
Bi=Dij Aj0
Bj0!, (5)
whe e
Dij =1
ij 1 ij
ij 1, (6)
and
ij
and
ij
a e he e lec ion and ansmission coe icien s o he
ij
- h in e ace, espec-
i ely. These coe icien s a e gi en by
ij =




kix−kjx
kix+kjx o s-pol. wa e,
n2
ikjx−n2
jkix
n2
ikjx+n2
jkix o p-pol. wa e, (7)
and
ij =




2kix
kix+kjx o s-pol. wa e,
2n2
ikjx
n2
ikjx+n2
jkix o p-pol. wa e, (8)
whe e
kix =k0[(nl)2−(n0sin θ)2]1/2
is he no mal componen o he wa e ec o o
he ligh wa e in he
i
- h medium. When a wa e p opaga es h ough he
i
- h laye , a
phase change
kl l
o
−kl l
is in oduced, depending on whe he he wa e is igh o le
p opaga ing, espec i ely. Thus, he modes on he wo side bounda ies o he
i
- h laye a e
ela ed ia

Senso s 2021,21, 6535 6 o 17
Aj0
Bj0!=PiAj
Bj, (9)
whe e
Pl=eikl l0
0 e−ikl l(10)
is he p opaga ion ma ix. Pu ing all his oge he , a ma ix equa ion ha ela es he wa e
ampli udes in subs a e and supe s a e can be ob ained
A0
B0=MAN+1
BN+1, (11)
whe e he o e all ans e ma ix is exp essed as
M=M11M12
M21M22= [
N
∏
i=1
D(i−1)iPi]DN(N+1). (12)
The complex e lec ion coe icien o he s uc u e is a a io o he e lec ed wa e
ampli ude
B0
o he inciden wa e ampli ude
A0
. Assuming ha no ligh is inciden om
he supe s a e (BN+10=0), using Equa ion (12) we ob ain
s,p=| s,p|eiδp,s=M21
M11
, (13)
The phase di e ence be ween
p
- and
s
-pola ized ligh wa es can hus be de e mined
as ∆(λ) = δp(λ)−δs(λ).
Re lec ance o he s uc u e can be exp essed as a squa ed modulus o he coe icien
Rs,p=| s,p|2. (14)
2.3. Band S uc u e
To unde s and he shape o he e lec ion spec a, he band s uc u e concep , simila
o he solid-s a e physics, can be used. Conside ing an in ini e 1DPhC, he pe iodici y leads
o exis ence o allowed and o bidden bands— he wa es a some equencies can p opaga e
h ough he 1DPhC, whe eas some o he canno . Using he 2
×
2 ma ix o malism de-
sc ibed in he p e ious sec ion, he ansmission ma ix ha links elec ic ield ampli udes
a he inpu and a he ou pu o one bilaye (one uni cell) o a pe iodic s uc u e can
be ob ained. Unde assump ion ha he RI in he 1DPhC is pe iodically modula ed, he
Bloch’s heo em can be applied, which s a es ha a solu ion o he wa e equa ion has a
o m o a plane wa e modula ed by a pe iodic unc ion wi h he same pe iod as he RI. In
esul ing eigenp oblem, eigen alues o he ansmission ma ix a e ela ed o he Bloch
wa e numbe
K
. Fo de i a ion, see [
45
] and esul ing equa ion o
p
-pola ized ligh is [
16
]
cos(KΛ) = cos (ka⊥a)cos (kb⊥b)−1
2 n2
bka⊥
n2
akb⊥
+n2
akb⊥
n2
bka⊥!sin (ka⊥a)sin (kb⊥b), (15)
whe e
a
,
b
and
Λ
a e hicknesses o he laye s and a bilaye hickness, espec i ely,
ki⊥=q(niω
c)2−β2
,
i=a
,
b
is a no mal componen o a wa e ec o in co espond-
ing medium and
β
is a p opaga ion cons an . Equa ion (15) gi es dependence o he
p opaga ion cons an
β
on he angula equency
ω
. Regions whe e
cos(KΛ)<
1 a e
ela ed o p opaga ing wa es ( eal
K
). In he case o
cos(KΛ)>
1, he wa es a e e anes-
cen (imagina y
K
). In Figu e 4a, a band diag am o he in ini e s uc u e composed o
SiO
2
/TiO
2
bilaye s is shown. He e, educed a iables
¯
β=βΛ
2π
and
¯
ω=ω
c
Λ
2π
we e used
Senso s 2021,21, 6535 7 o 17
and as hicknesses o he SiO
2
and TiO
2
laye s, a i hme ic means o he hickness alues
ob ained by he VASE we e used (
a
= 115 nm,
b
= 78 nm). The whi e egion ep esen s a
pho onic band gap, while he blue egions ep esen he allowed bands. The ed c osses
a e ela ed o su ace wa es exci ed on a ini e 1DPhC consis ing o 100 SiO
2
/TiO
2
bilaye s
(when subs a e is glass and supe s a e is ai ) o a ious angles o incidence. I can be
seen ha hei posi ions a e in he pho onic band gap and hus hey a e iden i ied as he
Bloch su ace wa es.
00.1 0.2 0.3 0.4 0.5 0.6
0.2
0.25
0.3
0.35
0.4
0.45
¯
β
¯
ω
0.38 0.42 0.46
0.34
0.36
0.38
0 0.2 0.4 0.6 0.8 1
0.2
0.25
0.3
0.35
0.4
0.45
Re lec ance
¯
ω
0.88 0.92 0.96
0.34
0.36
0.38
(a) (b)
Figu e 4.
(
a
) A band diag am o an in ini e mul ilaye s uc u e. Red c osses a e ela ed o he Bloch s a es. Inse shows
posi ions o he esonance s a es in de ail. (
b
) Re lec ance o he s uc u e wi h 100 bilaye s as a unc ion o
¯
ω
. Ligh is
p-pola ized, angle o incidence is θ=48◦. Inse shows a shallow esonance dip ela ed o he Bloch su ace wa e.
In Figu e 4b, he e lec ance o he s uc u e wi h 100 bilaye s o SiO
2
/TiO
2
as a
unc ion o
¯
ω
is shown. The 2
×
2 ma ix o malism was used in calcula ing he e lec ance,
assuming app oxima e ex inc ion coe icien s o TiO
2
and SiO
2
laye s o
kTiO2=
1.6
×
10
−3
and
kSiO2=
3.4
×
10
−4
, espec i ely [
16
,
17
]. This igu e clea ly shows ha he Bloch su ace
wa e esonance shows up as a shallow dip in he e lec ance spec um.
3. Theo e ical Resul s
To gain quan i a i e unde s anding o he e lec ion spec a, he e lec ance o he
1DPhC was compu ed in he wa eleng h domain, as shown in Figu e 5a, using he 2
×
2
ma ix me hod. The ex inc ion coe icien s
kTiO2
and
kSiO2
gi en in he p e ious sec ion
we e conside ed in he calcula ions, o enla ge esonance dips occu ing in he e lec ance
spec a (o he wise hey would be no obse able). In he case o
p
-pola ized ligh , h ee
esonance dips a e obse ed in he gi en wa eleng h egion, a na ow dip app oxima ely
a
λBSW =
551.5 nm co esponds o he BSW, while b oad dips a
λp
GW1=
483.7 nm and
λp
GW2=
677.9 nm, espec i ely, co espond o guided wa es. This is suppo ed by he
no malized op ical ield dis ibu ion o
p
-pola ized ligh in he 1DPhC shown in Figu e 5b.
The op ical ield is p opo ional o
|Hy|2
, whe e
Hy
is magne ic ield componen . The
enhanced op ical ield in ensi y a he wa eleng h
λBSW
co esponds o cha ac e o he
BSW ield wi h exponen ial en elopes, while he in ensi ies a wa eleng hs
λp
GW1
and
λp
GW2
a e enhanced inside he s uc u e and hus hei cha ac e s co espond o guided
wa es. In he case o
s
-pola ized ligh , wo esonance dips a e obse ed in he Figu e 5a
a wa eleng hs
λs
GW1=
474.5 nm and
λs
GW2=
735.1 nm, delimi ing he bo de s o he
pho onic band gap o s-pola ized ligh .
Senso s 2021,21, 6535 8 o 17
450 500 550 600 650 700 750 800
0
0.2
0.4
0.6
0.8
1
Wa eleng h (nm)
Re lec ance
Rs
Rp
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
20
40
60
80
Dis ance om he subs a e/1DPhC in e ace (µm)
No malized op ical ield in ensi y
λp
GW1=483.7 nm
λBSW =550.7 nm
λp
GW2=677.9 nm
(a) (b)
Figu e 5.
(
a
) Theo e ical e lec ance o he 1DPhC as a unc ion o wa eleng h o bo h
p
and
s
-pola ized ligh . The dip a a
wa eleng h o app oxima ely 551.5 nm is associa ed wi h he Bloch su ace wa e. (
b
) No malized op ical ield dis ibu ion
o p-pola ized ligh in he s uc u e. Angle o incidence θ=41.9◦.
The heo e ical esponse o he p oposed senso can be shown o di e en wa e
amoun adso p ion on he ough su ace o he 1DPhC, al hough he dependence on he
RH change is unknown. In Figu e 6a, he phase esponse o he senso o illing he ough
su ace wi h wa e is shown o wa e ac ions
= 0, 0.2, 0.4, 0.6, 0.8 and 1. As can be seen,
a ed shi occu s o highe wa e ac ion
. De i a i e o he phase shi as a unc ion o
wa eleng h is shown in Figu e 6b. Ex eme poin o he de i a i e is ela ed o he so-called
esonance wa eleng h λRa which he BSW is exci ed.
530 540 550 560 570
2
4
6
8
10
Wa eleng h (nm)
Phase shi ( ad)
=0
=0.2
=0.4
=0.6
=0.8
=1
530 540 550 560 570
0
0.2
0.4
0.6
Wa eleng h (nm)
De i a i e o he phase shi ( ad/nm)
=0
=0.2
=0.4
=0.6
=0.8
=1
(a) (b)
Figu e 6.
(
a
) Theo e ical phase shi as a unc ion o he wa eleng h wi h he inc easing ac ion o wa e
in he e ec i e
medium laye . (b) De i a i e o he phase shi as a unc ion o wa eleng h.
Senso s 2021,21, 6535 9 o 17
4. Expe imen al Se -Up
To measu e phase shi s o wa es unde esonance condi ions, in e e ome ic ech-
niques applied in bo h he spec al and spa ial domains a e employed. In Figu e 7, an
expe imen al se -up employing he spec al in e e ome ic echnique is shown. A compo-
si ion o he se -up and a measu emen p ocedu e a e desc ibed in he ollowing pa . A
ligh beam is gene a ed by whi e-ligh sou ce WLS (halogen lamp HL-2000, Ocean Op ics,
Dunedin, FL, USA), guided by op ical ibe OF and hen i passes h ough collima ing
lens CL. The collima ed beam (o diame e app oxima ely 1 mm) passes h ough linea
pola ize P (LPVIS050, Tho labs, New on, MA, USA), wi h op ical axis-o ien ed 45
◦
wi h
espec o he plane o incidence, and bo h pola iza ion componen s
s
and
p
a e gene a ed.
An op ical pa h di e ence be ween he componen s is in oduced by bi e ingen qua z
c ys al BC o hickness
d
= 6 mm, so ha in e e ence inges ha e app op ia e pe iod in
esul ing in e e og ams. The ligh beam hen e lec s om he mul ilaye s uc u e which
was p epa ed by a me hod o spu e ing (Meop a, Pˇ e o , Czech Republic), p ima ily made
as a B agg e lec o .
BC
P
(45◦)
CL
MO
A
(45◦)
analy e
ou pu
S
OF
ROF
PC
WLS
HS
con olle boa d
inpu
sensing chambe
Figu e 7.
Expe imen al se -up consis ing o whi e-ligh sou ce WLS, op ical ibe OF, collima ing lens CL, pola ize P,
bi e ingen c ys al BC, a coupling p ism wi h a mul ilaye s uc u e and a sensing chambe , humidi y senso HS, analyze
A, mic oscope objec i e MO, ead op ical ibe ROF, spec ome e A and pe sonal compu e PC.
A linea pola ize used as analyze A (LPVIS050, Tho labs) wi h op ical axis-o ien ed
45
◦
wi h espec o he plane o incidence p ojec s he pola iza ion componen s in o one
di ec ion o pola iza ion, so hey may in e e e. Then, he ligh beam is launched by
mic oscope objec i e MO in o ead op ical ibe ROF (M15L02, Tho labs) and hen led
o he spec ome e (USB4000, Ocean Op ics). As a esul o he p ocedu e, a spec al
in e e og am is ob ained. The angle o incidence on he ai /p ism in e ace is adjus ed
o be
α=
24
◦
(see Figu e 1). The analy e is mois ai wi h di e en RHs app oxima ely
om 35% o 80%. To con ol he RH, a sys em including pe is al ic pump PP (BT100M,
2xYZ1515x, Baoding Chuang Rui P ecision Pump Co., L d., Baoding, China) and wa e
ank WT is employed (see Figu e 8). To inc ease he RH, oom ai is pushed by he PP
o he WT (bellow he wa e le el) and humidi ied ai lows om he WT o he sensing
chambe , when ap 1 is opened and ap 2 is closed. To dec ease he RH, oom ai is injec ed
by a an and lows o he sensing chambe , while ap 2 is opened and ap 1 is closed. The
Senso s 2021,21, 6535 16 o 17
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