Ex ension o Babine ’s p inciple o plasmonic
me asu aces
Ci e as: Appl. Phys. Le . 119, 161103 (2021); doi: 10.1063/5.0065724
Submi ed: 4 Augus 2021 .Accep ed: 30 Sep embe 2021 .
Published Online: 19 Oc obe 2021
J. D. O iz,
1
J. P. del Risco,
2,3
J. D. Baena,
2,a)
and R. Ma qu
es
4
AFFILIATIONS
1
Facul y o Enginee ing, Uni e sidad de San Buena en u a, Bogo 
a 110141, Colombia
2
Depa men o Physics, Uni e sidad Nacional de Colombia, Bogo 
a 111321, Colombia
3
Depa men o Ma hema ics, Uni e sidad Se gio A boleda, Bogo 
a 111711, Colombia
4
Depa men o Elec onics and Elec omagne ism, Uni e sidad de Se illa, Se illa 41012, Spain
a)
Au ho o whom co espondence should be add essed: [email p o ec ed]du.co
ABSTRACT
Babine ’s p inciple is widely applied in op ics and has been use ul o designing me asu aces wi h dual beha io . Al hough his p inciple can
be igo ously demons a ed o infini ely hin pe ec conduc ing sc eens, i is no exac o any eal sc een. In ac , me als used in plasmonic
me asu aces a e a om good conduc o s, and he hickness o samples is no negligible in compa ison wi h he ypical size o he pa e ned
s uc u e. In his pape , we p opose an ex ension o Babine ’s p inciple alid o plasmonic me asu aces by edefining he concep o
complemen a y sc eens and finding impedance ela ions be ween such sc eens ha ul ima ely leads o a simple ela ion be ween he
ansmission ma ices o wo complemen a y plasmonic me asu aces. The heo y is alid unde he assump ions o he elec oquasis a ic
app oxima ion and plane wa es in he a field. I may find applica ions in he design o op ical plasmonic me asu aces, nanoci cui s, and
nanoan ennas.
Published unde an exclusi e license by AIP Publishing. h ps://doi.o g/10.1063/5.0065724
The ela ed opics o op ical plasmonic me asu aces,
1,2
nanoci -
cui s,
3–6
and nanoan ennas
7
ha e a ac ed much a en ion du ing he
las wo decades. Complemen a i y is a widely used concep in he di -
ac ion heo y ha migh be use ul o new de elopmen s in hese
esea ch a eas. I is closely ela ed o Babine ’s p inciple, which es ab-
lishes ce ain duali y ela ions be ween he fields sca e ed by wo com-
plemen a y sc eens.
8,9
In ac , Babine ’s p inciple has al eady been
applied o designing complemen a y me asu aces a mic owa es,
10
e ahe z,
11
and op ical equencies.
12–18
In hose p e ious wo ks, i
was demons a ed ha he ansmi ance o one me asu ace is like he
eflec ance o i s complemen a y coun e pa , and ice e sa, excep
o some deg ee o de ia ion. Aside om ha , he duali y be ween
elec ic and magne ic fields has been confi med in he nea field o
some specific complemen a y plasmonic s uc u es.
19,20
Howe e ,
while Babine ’s p inciple can be igo ously demons a ed o infini ely
hin pe ec conduc ing sc eens,
8,9
i is no exac o op ical plasmonic
sc eens o which nei he he hickness is negligible no he me als a e
good conduc o s. Ne e heless, e y ecen wo ks
21–23
sugges ha
Babine ’s p inciple is s ill quali a i ely alid o plasmonic s uc u es.
Would i be possible o ex end Babine ’s p inciple o plasmonic
sc eens, maybe by in oducing some co ec ion, and placing i s
applica ion o hese s uc u es on mo e solid g ounds? Along his
Le e , we will show ha his ex ension is possible. Namely, ou ex en-
sion o Babine ’s p inciple will be alid o complemen a y plasmonic
me asu aces composed o ma e ials wi h high alues o he modulus
o he pe mi i i y, which eal pa could be nega i e o egions filled
wi h some plasmonic me al while posi i e in o he egions filled wi h
high pe mi i i y dielec ics. We will no only p o ide a heo e ical o -
mula ep esen ing his ex ension o Babine ’s p inciple bu also com-
pa e i s pe o mance agains he p edic ions based on con en ional
Babine ’s p inciple. We will show ha he ag eemen be ween heo y
and nume ical simula ions using ou ex ension is g ea ly imp o ed o
h ee di e en shapes.
Be o e ex ending his p inciple, i is wo h o summa ize he con-
en ional o m o Babine ’s p inciple which, unde ce ain conside -
a ions, will p omp ly d i e us o a use ul co olla y linking he
ansmission coe ficien s o wo complemen a y pe iodic sc eens
whose pe iod is subwa eleng h (as usual o me asu aces). Le us s a
assuming wo complemen a y hin conduc ing sc eens, one migh be
called he o iginal one while he o he he complemen a y one, bo h
sc eens o hogonal o he z-axis, and loca ed a z¼0.Unde hiscon-
ex , complemen a y means ha bo h sc eens ha e been e ched wi h
Appl. Phys. Le . 119, 161103 (2021); doi: 10.1063/5.0065724 119, 161103-1
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he same pa e n bu in e changing conduc o and ai egions.
Mo eo e ,le hesou cebeplacedin hez<0 hal -space and emi ing
a plane wa e ha impinges no mally on o he sc een. Le us call Einc
and Binc he elec ic and magne ic inciden fields o he o iginal
sc een, while o he complemen a y sc een he inciden fields E0
inc and
B0
inc will be linked o he o me as ollows: E0
inc ¼cBinc and
cB0
inc ¼Einc,beingc he speed o ligh in acuum. Then Babine ’s
p inciple says
8,9
E a cB0
a ¼Einc;
cB a þE0
a ¼cBinc;(1)
whe e E a and B a a e he elec ic and magne ic fields ansmi ed
h ough he o iginal sc een while E0
a and B0
a ha e he same meaning
bu o he complemen a y p oblem. Al hough his is usually called a
p inciple, i is an exac heo em when sc eens a e plana , infini ely
hin, and made o pe ec conduc o .
8,9
Assuming he sou ce is e y
a om he sc een, hen he inciden wa e can be app oxima ed as a
plane wa e. In gene al, he ansmi ed field can be expanded as an
infini y sum o plane wa es. Whene e he uni cell is much smalle
han he wa eleng h, as usual o me asu aces, only a plane wa e
emains a om he sc een. By defini ion, he inciden and ansmi -
ed elec ic fields can be connec ed one ano he h ough E a ¼
Einc
o he o iginal sc een and E0
a ¼
0E0
inc o he complemen a y
sc een, whe e 
and 
0a e he so-called ansmission ma ices.
Simila ly, eflec ion ma ices could be defined by E e ¼
Einc and
E0
e ¼
0E0
inc. They a e jus 2 2 squa e ma ices, because hey a e
linking fields ha a e ans e se o he z-axis and aking in o accoun
bo h co-pola and c oss-pola e ec s (i.e., hey a e, in gene al, non-
diagonal ma ices). Fu he mo e, as a as wa es a e app oxima ed by
plane wa es, he magne ic fields can easily be ob ained om he elec-
ic field by using he well-known o mula B¼ð1=kcÞkE,whe ek
is he wa e ec o and kis he co esponding wa enumbe .
Al e na i ely, when kis pa allel o he z-axis, his o mula can also be
exp essed as ollows:
cBinc
cB a
cB e
cB0
inc
cB0
a
cB0
e
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
9
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>
;
¼01
10
!

Einc
E a
E e
E0
inc
E0
a
E0
e
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
9
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>
;
¼

R
Einc
E a
E e
E0
inc
E0
a
E0
e
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
9
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>
;
;(2)
whe e 

R ep esen s a 90coun e clockwise o a ion a ound he z-axis.
F om (1) and (2), hedefini ionso 
and 
0in oduced abo e and
wi h he 2 2 iden i y ma ix 
1, i is a s aigh o wa d ask o demon-
s a e he ollowing co olla y:

þ

R
0

R1¼

1:(3)
I is wo h no ing ha , al hough a simila esul has been epo ed in
many pape s in he scala o m þ 0¼1, his ma ix o m is mo e
gene al because i also accoun s o cases p esen ing c oss-pola iza ion
e ec s. In p inciple, he ansmission h ough one sc een could be
guessed om he ansmission o i s complemen a y sc een by using
(3). Howe e , le us emind ha (3) is only alid o sc eens o negligi-
ble hickness and made o pe ec conduc o , which, clea ly, is no he
case o plasmonic me asu aces. Then, we need o eplace i wi h
ano he equa ion sui able o complemen a y plasmonic me asu aces.
Now, le us conside he s uc u e shown in Fig. 1(a), which is a
wo-dimensional (2D) piecewise homogeneous s uc u e filled wi h
se e al media wi h iso opic ela i e pe mi i i ies ei; so, he s uc-
u e is cha ac e ized by he ela i e pe mi i i y piecewise unc ion
eðx;yÞ. I all egions a e filled wi h high pe mi i i ies hen, due o
he con inui y o he no mal componen o eEon he bounda y, he
no mal componen o Ecan be neglec ed inside he me asu ace,
and hus, Eðx;yÞ¼Exðx;yÞ^
xþEyðx;yÞ^
y. Conside ing he uni cell
is much smalle han he wa eleng h and i s hickness is also smalle
han he skin dep h o plasmonic egions, i is also possible o use
he elec oquasis a ic (EQS) app oxima ion:
24,25
he magne ic induc-
ion in Fa aday’s law can be neglec ed o low equencies while he
displacemen cu en densi y in he Ampe` e–Maxwell’s law is s ill
kep because he low equencies a e compensa ed wi h he high al-
ues o pe mi i i y. In his way, he p oblem is simplified o a 2D
p oblem whose elec ic field sa isfies $ ðeEÞ¼0 and $ E¼0,
whe e $ ¼^
x@=@xþ^
y@=@y. In o de o define he complemen a y
p oblem, le us eplace he pe mi i i y eo he o iginal s uc u e
wi h a new complemen a y pe mi i i y, as shown in Fig. 1(b),
defined by
e0ðx;yÞ¼ C1
eðx;yÞ;(4)
whe e C
1
is an a bi a y cons an . I is wo h no ing ha his defini ion
o “complemen a i y” includes he con en ional one as a pa icula
case: when only wo ma e ials a e used his cons an can be chosen as
C1¼e1e2, which means jus an in e change o ma e ials. Unde his
ans o ma ion, he fields inside he complemen a y s uc u e can be
ob ained om hose o he o iginal p oblem as ollows:
E0¼C2e^
zE¼C2e


RE;(5)
whe e C
2
is an a bi a y cons an associa ed wi h he eedom o scal-
ing solu ions om linea equa ions. I can be s aigh o wa dly dem-
ons a ed ha $ ðe0E0Þ¼0and$ E0¼0, by jus eplacing (4)
and (5).This esul includesasapa icula case he esul sp e iously
epo ed in Re s. 26–28 on he e ec i e conduc i i y o 2D wo phase
composi es, which can be ob ained by simply eplacing he ela i e
pe mi i i y eby i =ðe0xÞ,whe e is he spa ial dis ibu ion o
conduc i i y.
FIG. 1. Illus a ion o he uni cells o wo complemen a y me asu aces: he
“o iginal” one (a) and he “complemen a y” one (b). Complemen a y pe mi i i ies
and elec ic fields a e ela ed o Eqs. (4) and (5), espec i ely.
Applied Physics Le e s ARTICLE sci a ion.o g/jou nal/apl
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In o de o desc ibe he esponse o he s uc u e om a mac o-
scopic poin o iew, le us define he a e age elec ic field Ea e as well
as he su ace cu en densi y (coming om he displacemen cu en )
Jsinside he uni cell (u.c.) h ough he in eg als
Ea e ¼1
Aððu:c:
Eðx;yÞdx dy;(6)
Js¼ixe0h
Aððu:c:
eðx;yÞEðx;yÞdx dy;(7)
whe e Ais he a ea o he uni cell, his he hickness o he sample,
and ha monic a ia ion wi h ime eix has been assumed. We can
now define he su ace impedance o he s uc u e, 

Zs,as hema ix
ha ela es he ec o s in (6) and (7) in he ollowing way:
Ea e ¼Ea e;x
Ea e;y

¼Zs;xx Zs;xy
Zs;yx Zs;yy

Js;x
Js;y

¼

ZsJs:(8)
By applying iden ical defini ions (6) and (7) in he complemen a y
me asu ace, and using (4) and (5), i is eadily shown ha he comple-
men a y a e age elec ic field E0
a e and he complemen a y su ace cu -
en densi y J0
sa e ela ed o he o iginal ones as
E0
a e ¼ C2
ixe0h


RJs;(9)
J0
s¼ixe0hC
1C2


REa e:(10)
Ye , E0
a e and J0
sa e ela ed by he complemen a y su ace impedance


Z0
sas: E0
a e ¼

Z0
sJ0
s, hen, when we pu oge he his defini ion wi h
(8)–(10), we di ec ly ela e bo h su ace impedances. Wi h he acuum
wa e numbe k¼xffiffiffiffiffiffiffiffiffi
e0l0
pand he acuum impedance
Z0¼ffiffiffiffiffiffiffiffiffiffiffi
l0=e0
p, he final esul is


Z0
s

R

Zs

R1¼Z2
0
4K


1;(11)
whe e
K¼h2k2C1=4:(12)
I ecalls a p e ious heo em epo ed in Re s. 26–28 o he e ec i e
conduc i i y o 2D la ices o conduc i e cylinde s, which can be
deduced om (11) as a pa icula case by using C1¼e1e2and
ei i=ðixe0Þ. I is also closely ela ed o he p ope y
ZZ
0¼Z2
0=4 epo ed by Booke
29
and Deschamps
30
o pe ec ly
conduc ing complemen a y sc eens, which can be ob ained om
(11) when K¼1, and he o diagonal componen s o he su ace
impedance ma ix a e ze o.
Now, le us use s anda d bounda y condi ions a he me asu ace
o sol e he ansmission ma ix om he su ace impedance ma ix.
Fi s , by imposing he con inui y o he angen ial componen o he
elec ic field hen Einc þE e ¼Ea e ¼E a,whichisequi alen o


1þ
¼
. Second, due o he ound su ace elec ic cu en , he mag-
ne ic field mus sa is y he ollowing discon inui y ela ion: ^
zðBinc
þB e B aÞ¼l0Js, which is equi alen o 

1


¼Z0


Z1
s
.
In his way, we ha e go a sys em o wo linea equa ions wi h wo
unknown ma ices, 

and 
, ha can be easily sol ed o ge he ans-
mission ma ix

¼

1þZ0
2


Z1
s

1
:(13)
Recip ocally, he su ace impedance is 

Zs¼ðZ0=2Þ½
1

11.Since
i is an a bi a y choice wha is he o iginal o complemen a y sc een,
i is clea ha we can w i e a ela ion analogous o (13) o 
0and 

Z0
s.
The e o e, by using (11), we can es ablish a di ec ela ion be ween
bo h ansmission ma ices, which is

0¼

R1

1
½


1ð1KÞ

1

R:(14)
I ep oduces he co olla y p e iously ob ained om con en ional
Babine ’s p inciple, exp essed in (3),onlywhenK¼1(see hesupple-
men a y ma e ial o examples wi h K1) bu , in gene al, K6¼ 1
and equency dependen as indica ed in (12). The e o e, Eq. (14) can
be conside ed as an ex ension o Babine ’s p inciple o complemen-
a y plasmonic me asu aces. I is wo h o emind, howe e , ha his
o mula was ob ained unde he assump ion o he EQS limi , which is
alid o sc eens wi h subwa eleng h pe iodici y, low a ia ion o fields
along he z-axis inside he me asu aces, and high pe mi i i ies. Since
hese cons ains a e usually ulfilled by plasmonic me asu aces ope a -
ing a op ical equencies, his heo y is expec ed o be use ul o he
analysis o hese s uc u es.
To alida e ou heo y, h ee couples o complemen a y plas-
monic me asu aces using di e en shapes will be nume ically simu-
la ed. We will ocus ou a en ion in he in a ed ange o equencies.
Fo all cases, we will use silicon (Si) and sil e (Ag) no only because
hey a e ex ensi ely used in plasmonics bu also because hey bo h
ha e high pe mi i i y in he in a ed ange and, a he same ime,
hey p o ide a big con as o pe mi i i y, which migh be desi able
o designing complemen a y s uc u es. The ela i e pe mi i i y o Si
is almos cons an wi hin he conside ed equency ange, wi h a negli-
gible imagina y pa , and can be app oxima ed as eSi 11:9.
31–33
On
he o he hand, he pe mi i i y o Ag depends s ongly on he e-
quency wi h a D ude–Lo en z beha io desc ibed by eAg ¼1x2
p=
ðx2þixcÞ, whe e he plasma equency is xp¼1:375 1016 ad/s
and he collision equency is c¼3:12 1013 s1; hese pa ame e s
ha e been ob ained om Re . 34. As a fi s example, we will analyze
he complemen a y sc eens shown in Figs. 2(a) and 2(b),whicha e
made o al e na ing Si and Ag ba s. Pe iodic bounda y condi ions a e
used a he edges o he s uc u es. A bi a ily, (a) may co espond
wi h he o iginal p oblem while (b) wi h he complemen a y one.
Following he same a gumen s o Re . 6, o y-pola ized (x-pola ized)
inciden wa es, i can be in e p e ed as a plana nanoci cui wi h se ies
(pa allel) connec ions o nanoinduc o s ep esen ing he Ag egions
(nega i e pe mi i i y below he plasma equency) and nanocapaci-
o s ep esen ing he Si egions (posi i e pe mi i i y). By passing
om he o iginal o he complemen a y s uc u e, each egion swi ches
om he nanoinduc o o he nanocapaci o and ice e sa. The com-
plemen a y p oblem is defined no only by he in e change o ma e i-
als bu also by he 90 o a ion o he pola iza ion s a e o he inciden
wa e, which means ha se ies (pa allel) connec ions swi ch o a
pa allel (se ies) connec ion in he complemen a y p oblem. Unde
hese assump ions, i can be shown ha (11) is sa isfied. In ac , we
ha e nume ically compu ed he ansmission coe ficien s h ough
bo h sc eens by using he comme cial so wa e CST Mic owa e S udio
om 50 o 300 THz o , equi alen ly, om 1 o 6lm. The plo s o
Applied Physics Le e s ARTICLE sci a ion.o g/jou nal/apl
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Fig. 2 show simula ed ansmission coe ficien s (solid lines) as well as
he cu es de i ed om (3) (dashed lines) and (14) (do ed lines) by
using he nume ical esul o he complemen a y sc een. A e y good
ag eemen be ween ou heo y, i.e., (14), and he elec omagne ic sim-
ula ions has been ound while he esul s coming om con en ional
Babine ’s p inciple, i.e., (3), show a significan de ia ion om he sim-
ula ed esul s. Al hough Fig. 2(a) shows a big de ia ion in he phase
abo e 250 THz, i is no ac ually ele an i we conside ha he co e-
sponding magni ude is nea ze o. (The phase is indefini e a ze o.) I is
also wo h no ing ha , due o he mi o symme ies o he s uc u e
espec o he x-plane and y-plane, he o diagonal elemen s o he
ansmission ma ices cancel ou and hen only he diagonal compo-
nen s a e depic ed in Fig. 2.
The esponse o he o me s uc u e was poo ly dispe si e and
dissipa i e. To check ou heo y o s uc u es p esen ing s ong dis-
pe sion and dissipa ion, which is he common si ua ion o me asu a-
ces as well as me ama e ials based on esona ing pa icles, he
ansmission coe ficien s h ough a sc een made o spli ings and i s
complemen a y sc een ha e been compu ed in he ange om 15 o
65 THz. Thei uni cells and hei geome ical pa ame e s a e ully
specified in Fig. 3. Fo (a), a spli ing o Ag is embedded in a laye o
Si while ma e ials appea in e changed in (b). The plo s o Fig. 3 show
he simula ed ansmission coe ficien s (solid lines) as well as he
cu es de i ed om (3) (dashed lines) and (14) (do ed lines). I can
be app ecia ed how he cu es ob ained wi h ou heo y by using (14)
ag ee wi h he simula ions much be e han (3), which comes om
con en ional Babine ’s p inciple. Once again, we can a gue ha o
diagonal componen s o 
, i.e.,
xy
and
yx
, a e canceled ou because o
he mi o symme y espec o he y-plane.
As a las example, in o de o demons a e he alidi y o ou he-
o y o cases ha p esen c oss-pola iza ion e ec s, we decided o
o a e he p e ious spli ings by 45as shown a he op o Fig. 4.This
figu e also shows he simula ed esul s (solid lines) as well as he cu es
de i ed om (3) (dashed lines) and (14) (do ed lines) wi hin he
ange be ween 15 and 65 THz. The diagonal componen s o he ans-
mission ma ix
xx
and
yy
exac ly ma ch each o he because o he mi -
o symme y espec o he diagonal di ec ion. Howe e , nei he he
x-plane no he y-plane a e mi o planes, hus, in his case, a non-
ze o esponse is obse ed o he o diagonal componen s
xy
and
yx
which, by he way, a e also equal one each o he . As in he p e ious
FIG. 3. T ansmission coe ficien s (magni ude and phase) h ough wo di e en spli
ing me asu aces made o sil e (Ag) and silicon (Si). The geome ical pa ame e s
a e a¼250 nm, 0¼100 nm, g¼10 nm, w¼30 nm, and h¼25 nm. Plo s show
simula ed esul s (solid lines) as well as cu es de i ed om (3) (dashed lines) and
(14) (do ed lines).
FIG. 4. T ansmission coe ficien s (magni ude and phase) h ough wo di e en spli
ing me asu aces made o sil e (Ag) and silicon (Si), whe e he spli ings a e o i-
en ed a 45 espec o he la ice axes. The geome ical pa ame e s a e
a¼250 nm, 0¼100 nm, g¼10 nm, w¼30 nm, and h¼25 nm. Plo s show sim-
ula ed esul s (solid lines) as well as cu es de i ed om (3) (dashed lines) and
(14) (do ed lines).
FIG. 2. T ansmission coe ficien s (magni ude and phase) h ough wo di e en pa -
allel s ip g a ings made o sil e (Ag) and silicon (Si). Thei uni cells a e shown on
op whe e he geome ical pa ame e s a e w1¼50 nm, w2¼10 nm, and
h¼25 nm. Plo s show simula ed esul s (solid lines) as well as cu es de i ed om
(3) (dashed lines) and (14) (do ed lines).
Applied Physics Le e s ARTICLE sci a ion.o g/jou nal/apl
Appl. Phys. Le . 119, 161103 (2021); doi: 10.1063/5.0065724 119, 161103-4
Published unde an exclusi e license by AIP Publishing
04 June 2025 14:00:05
examples, ou heo y summa ized in (14) app oaches he simula ions
be e han (3) (con en ional Babine ’s p inciple).
In conclusion, we ha e ex ensi ely analyzed he concep o com-
plemen a i y and he applicabili y o Babine ’s p inciple o plasmonic
me asu aces. The defini ion o complemen a y sc eens is gene alized
in such a way ha he con en ional defini ion, in ol ing only he
in e change o wo ma e ials, is con ained as a pa icula case. This
analysis leads o an ex ension o Babine ’s p inciple summa ized in
(14). We nume ically demons a ed ha ou heo y ep esen s a sub-
s an ial imp o emen o h ee di e en geome ies. Aside om ha ,
we eel ha i is qui e gene al and can be applied o o he complemen-
a y plasmonic me asu aces ope a ing in he op ical ange.
Fu he mo e, he ela ion be ween complemen a y impedances shown
in (11) may find applica ions o designing complemen a y nanoci -
cui s and nanoan ennas ope a ing in he in a ed ange. This will be
explo ed in an upcoming wo k.
See he supplemen a y ma e ial o in o ma ion ela ed o he
chance o eco e ing he alidi y o con en ional Babine ’s p inciple o
o mula (3) by choosing a sui able hickness o which K1ina
wide ange o equencies.
This wo k has been suppo ed by he Minis e io de Ciencia e
Inno aci
on wi h EU FEDER Funds (P ojec No. TEC2017-84724-
P), by he Colombian Go e nmen h ough COLCIENCIAS
(P ojec No. 1101-521-29389), and he Uni e sidad de San
Buena en u a (P ojec No. CBI013-012-2018).
DATA AVAILABILITY
The da a ha suppo he findings o his s udy a e a ailable
om he co esponding au ho upon easonable eques .
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Applied Physics Le e s ARTICLE sci a ion.o g/jou nal/apl
Appl. Phys. Le . 119, 161103 (2021); doi: 10.1063/5.0065724 119, 161103-5
Published unde an exclusi e license by AIP Publishing
04 June 2025 14:00:05