Design rules for active control of narrowband thermal emission using phase-change materials Maxime Giteau

2025-05-06 0 0 2.73MB 11 页 10玖币

Design rules for active control of narrowband thermal emission using phase-change materials

Maxime Giteau, Mitradeep Sarkar, Maria Paula Ayala, Michael T. Enders, and Georgia T. Papadakis∗

ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain

We propose an analytical framework to design actively tunable narrowband thermal emitters at infrared fre-

quencies. We exemplify the proposed design rules using phase-change materials (PCM), considering dielectric-

to-dielectric PCMs (e.g. GSST) and dielectric-to-metal PCMs (e.g. VO2). Based on these, we numerically il-

lustrate near-unity ON-OFF switching and arbitrarily large spectral shifting between two emission wavelengths,

respectively. The proposed systems are lithography-free and consist of one or several thin emitter layers, a

spacer layer which includes the PCM, and a back reﬂector. Our model applies to normal incidence, though

we show that the behavior is essentially angle-independent. The presented formalism is general and can be

extended to any mechanism that modiﬁes the optical properties of a material, such as electrostatic gating or

thermo-optical modulation.

The ability to control the spectrum, direction, and polar-

ization of thermal emission is critical for applications includ-

ing infrared (IR) sources [1, 2], thermal camouﬂage [3], ra-

diative cooling [4, 5] and energy conversion [6]. In partic-

ular, the possibility of generating spectrally narrowband IR

emission has been the object of a very rich literature [7–14].

While most architectures involve in-plane patterning and/or

a large number of layers to reduce the emission bandwidth,

surface phonon polaritons (SPhPs) offer naturally narrowband

resonances owing to their large material quality factors [15].

In particular, it has been recently shown that few-monolayer

SPhP-based emitters used in a Salisbury screen conﬁgura-

tion [16, 17] (a 3-layer structure consisting of an emitter, a

dielectric spacer, and a back reﬂector, forming a Fabry-Perot

cavity whose resonance wavelength matches that of the emit-

ter) can achieve strong narrowband emission [18].

Another active area of nanophotonics is the active control

of optical properties [19, 20]. Such dynamic modulation can

take the form of electrical gating [2, 13, 21–24], optical bias-

ing [25] or applied strain [26]. In the mid-IR region, the spec-

tral range of interest for thermal emission, a popular approach

for active tuning is phase-change materials (PCMs). These

materials show a dramatic reversible and (for some of them)

non-volatile change in their optical properties upon heating,

leading to a very different spectral response [27–31]. Several

techniques have been developed to induce the phase change

beyond simple thermal heating, which is slow and can result

in signiﬁcant hysteresis [32]. For volatile PCMs, the phase

change can be triggered by laser heating, with a characteristic

switching time of a few tens of nanoseconds [33]. Applying

an electrical current can also result in ultrafast switching in a

few nanoseconds [34]. In the case of non-volatile PCMs, crys-

tallization and amorphization are typically triggered by short

(in the order of nanoseconds, depending on the ﬁlm thickness)

laser pulses [35].

Two classes of materials emerge from this description:

those switching from one dielectric phase to another, with dif-

ferent refractive indices, such as some GeSbTe (GST) com-

pounds [35–38], and those switching from a dielectric to a

metallic phase, such as VO2[32, 39]. PCMs have been

∗georgia.papadakis@icfo.eu

studied for various applications including non-volatile opti-

cal switching [36, 40–44], beam switching and bifocal lens-

ing [45], homeostasis [39], radiative cooling [32] and ther-

mal camouﬂage [46, 47]. They are particularly relevant for

spectrally-tunable narrowband sources [14, 36, 48–50], with

applications in spectroscopy as well as thermophotovoltaics.

However, simple, lithography-free structures tend to have

relatively broadband emissivity [28]. Tunable narrowband

sources have been achieved only for more complex structures,

with an emissivity that is usually not unitary over the whole

range of operation [14, 48, 50]. Furthermore, all these devices

have limited spectral tunability as they rely on the temperature

dependence of a single material’s resonance wavelength.

FIG. 1. Ideal narrowband spectral emissivity upon the phase transi-

tion of a PCM for two conﬁgurations: (a) ON-OFF switching and (b)

Spectral shifting from one resonance wavelength to another.

In this work, we propose a simple framework combining

SPhPs-based resonances and PCMs in a Salisbury screen con-

ﬁguration to design lithography-free narrowband IR emitters

with different properties upon phase transition of the PCM.

We ﬁrst derive analytical conditions for unitary and zero emis-

sivity. We then apply this versatile framework to two conﬁgu-

rations. In the ﬁrst, the emissivity of a single-resonance emit-

ter is turned ON and OFF upon phase transition (Fig. 1(a)).

In the second, which considers two arbitrary emission wave-

lengths, the emission peak switches from one wavelength to

the other (Fig. 1(b)). In both cases, we quantify the per-

arXiv:2210.02155v4 [physics.optics] 18 May 2023

formance of optimized devices, considering both idealized

and real materials. Finally, we show that the emissivity of

these structures shows very little angular dependence, making

them relevant for spectrally-tunable diffuse narrowband ther-

mal emission.

We consider a two-layer stack consisting of an emitter with

complex refractive index neand thickness deon top of a spacer

with a real refractive index nsand thickness ds. It is sur-

rounded by two semi-inﬁnite media: an upper medium with

real refractive index niand a back reﬂector with a complex

refractive index nb. The general architecture is illustrated in

Fig. 2(a). The emitter layer supports a SPhP resonance at

wavelength λe, and its relative permittivity is εe=n2

e. We also

deﬁne the optical thickness of the spacer as ∆s=nsds. We

restrict our analysis to normal incidence, and discuss its ex-

tension for oblique angles towards the end of the manuscript.

Using Kirchhoff’s law of thermal radiation, we describe emis-

sivity as ε=1−R, where R=|r|2is the reﬂectivity, rbeing

the Fresnel reﬂection coefﬁcient of the system. We consider

the incident medium to be air (ni=1) and the back medium

to be a perfect reﬂector (1/nb→0). The following results are

derived and generalized in the Supplemental Material [51],

starting from ref. [52]. Assuming ℑ(εe(λe)) 1 (ℑmeaning

the imaginary part), the emitter thickness required to achieve

unitary emissivity (resonance) at wavelength λeis:

de=λe

2πℑ(εe(λe)),(1)

whereas the spacer’s optical thickness is:

∆ε=1

s=m+1

2λe

2,m∈N,(2)

where Nis the set of all natural numbers, including zero. On

the contrary, imposing the condition of zero emissivity and

considering the same emitter thickness (Eq. 1), the spacer’s

optical thickness becomes:

∆ε=0

s=mλe

2,m∈N(3)

Therefore, if ℑ(εe)1, then deλe(Eq. 1), hence we

can neglect the impact of the front layer on the resonance

conditions, leading to the resonance and anti-resonance wave-

lengths of a simple Fabry-Perot cavity (Eqs. 2-3).

The emissivity of such a system can be actively tuned be-

tween 0 and 1 by modifying the optical thickness of the spacer,

∆s=nsds. This can be achieved with PCMs. In particular, a

PCM that switches from one dielectric phase to another di-

electric phase, with different refractive indices nα

sand nβ

s, can

be used directly as the spacer. The index change upon phase

transition modulates the optical thickness and thus the emis-

sivity of the system (Fig. 2(b)). Alternatively, a PCM that

switches from a dielectric phase to a metallic phase can be in-

serted between two spacer layers such that the thickness of the

cavity itself changes upon phase transition (Fig. 2(c)). In its

FIG. 2. (a) Salisbury screen conﬁguration considered for unitary and

zero emissivity: a thin emitter is placed on top of a dielectric spacer,

above a back reﬂector. (b-c) Two ways to modify the optical thick-

ness of the spacer. (b) When the PCM has a dielectric-to-dielectric

transition, it can be used as the spacer. (c) When the PCM has a

dielectric-to-metal transition, it can be used as a reﬂector hiding a

second spacer which only plays a role in the dielectric phase.

metallic phase, the PCM behaves like a perfect reﬂector, and

the spacer thickness is dα

s, while in its dielectric phase, the

spacer becomes the combination of the two spacers and the

PCM, with a total thickness dβ

s. Note that for the two-layer

model (Fig. 2(a)) to be analytically valid, the PCM should ei-

ther be extremely thin or have the same refractive index as the

spacer when the PCM is in its dielectric phase. The model al-

lows for unitary emissivity at the resonance wavelength to be

achieved either in phase αor β(depending on the thickness

of the spacer(s)).

In the following, we illustrate this framework with two

examples, the ﬁrst one pertaining to ON-OFF switching of

thermal emission at a certain wavelength upon phase transi-

tion, and the second one regarding spectral shifting between

two frequencies, where the emission wavelength is arbitrarily

tuned. In both cases, we present the results obtained with both

idealized and real materials. The simulations are performed

using an in-house transfer matrix method [53]. The refractive

index spectra used for all materials considered are represented

in the Supplemental Material [51]. The materials considered

in this work, with the exception of the PCMs, show negligible

dependence in their permittivity with temperature.

As a ﬁrst illustration, we design a system with narrowband

unitary emissivity in phase αand zero emissivity in phase

β. The ﬁgure of merit for evaluating the performance of the

switch can be deﬁned as the difference in emissivity between

the two phases, at the resonance wavelength λeof the emitter:

ϕswitch =εα(λe)−εβ(λe).(4)

For ideal materials, ϕswitch should be unity. By considering

Eqs. 2-3 in this particular system, we derive the ON and OFF

conditions, respectively, for the optical thickness of the PCM

spacer:

∆α

s=mα+1

2λe

2,mα∈N,(5)

∆β

s=mβ

λe

2,mβ∈N,(6)

which imposes

∆α

∆β

=2mα+1

2mβ

.(7)

Note that, to minimize the thickness of the spacer, the in-

dices mαand mβshould be as small as possible.

Here, we consider the conﬁguration where the PCM is used

as the spacer (Fig. 2(b)), as it is the simpler conﬁguration.

Based on Eq. 7, the refractive index ratio should correspond

to:

nα

nβ

=2mα+1

2mβ

.(8)

Such a conﬁguration is only constrained by the refractive

indices of the PCM. One promising material for this applica-

tion is Ge2Sb2Se4Te1(GSST), which shows a large refractive

index ratio, close to 3/2, in the IR frequency range between its

crystalline phase (ns

α≈4.60) and its amorphous phase (ns

β≈

3.19) [54]. Therefore, from Eq. 8, we consider mα=mβ=1.

For the sake of illustration, here, we consider a SiC [55, 56]

emitter with a resonance wavelength λe=12.6µm. Its thick-

ness, determined from Eq. 1, is de=3.7 nm.

FIG. 3. Spectral emissivity for both PCM phases, shown with the

blue and red curves, in the ON-OFF switching conﬁguration, using a

3.7 nm-thick SiC emitter with a dielectric-to-dielectric PCM. Dashed

line: Assuming an idealized PCM and a perfect back reﬂector. Solid

line: Considering a GSST spacer and a silver back reﬂector.

For the ideal conﬁguration, we consider a dispersionless

and non-absorptive GSST with refractive indices nα

s=4.60

and nβ

s=3.19 on top of a perfect reﬂector, so as to satisfy the

refractive index ratio of Eq. 8 for mα=mβ=1. The ﬁgure of

merit is maximized for a spacer thickness ds=2.015 µm, cor-

responding to near-ideal ON-OFF switching, with ϕswitch =

0.996 (Fig. 3). This spacer thickness is the average of the val-

ues predicted by eqs. 5-6 (2.054 µm and 1.975 µm , respec-

tively). The width of the resonance is determined by that of

the SPhP mode in SiC. We note that even with an imperfect re-

fractive index ratio, we can achieve a ﬁgure of merit extremely

close to unity, demonstrating the imperfection tolerance of the

approach.

For a realistic conﬁguration, we consider the complex re-

fractive indices of GSST [54] and silver [57], for the PCM

layer and back reﬂector, respectively. The PCM thickness is

set to ds=2.035 µm (very close to the ideal case), as it max-

imizes the ﬁgure of merit. As can be seen in Fig. 3, the ON-

OFF switching remains extremely effective, with ϕswitch =

0.980. Nonetheless, we note that emissivity in the crystalline

phase is signiﬁcantly broadened due to parasitic absorption in

the PCM and the Ag back reﬂector (3). The origin of this

broadening and strategies to mitigate it are discussed in the

Supplemental Material [51].

The framework discussed above can be extended to sev-

eral thin emitters stacked on top of each other (or an emitter

with several SPhP resonances) to achieve a spectral shift in

the emissivity in the two PCM phases. This can be achieved

as long as there is no signiﬁcant spectral overlap between the

SPhP modes of the two thin emitters. Here, we consider a

system with two emitters, referred to as e1and e2henceforth.

These emitters support a SPhP resonance at wavelengths λe1

and wavelength λe2, respectively. The aimed operation is to

achieve unitary emission at wavelength λe1in phase αand

unitary emission at wavelength λe2in phase β(Fig. 1(b)). We

deﬁne a ﬁgure of merit to quantify the quality of the spectral

shift, which should approach unity in the ideal case:

ϕshi f t =1

2hεα(λe1)−εβ(λe1)+εβ(λe2)−εα(λe2)i

(9)

We assume the spacer is dispersionless, such that

nα/β

s(λe1) = nα/β

s(λe2) = nα/β

s. Based on Eqs. 2-3, the sys-

tem must satisfy at once the following four equations:

∆α

s=m1+1

2λe1

2,m1∈N,(10)

∆α

s=m2λe2

2,m2∈N,(11)

∆β

s=m3+1

2λe2

2,m3∈N,(12)

∆β

s=m4λe1

2,m4∈N,(13)

which imposes a wavelength ratio:

λe2

λe1

=2m1+1

2m2=2m4

2m3+1(14)

It is impossible to ﬁnd four integers (m1-m4) that satisfy

Eq. 14 exactly. Nonetheless, one can achieve a spectral shift

close to optimal if the two integer ratios in Eq. 14 are close to

each other. We emphasize that this approach allows arbitrar-

ily large spectral shifts in emissivity, provided the availability

of materials with the desired resonance frequencies, the trans-

parency of the spacer material in that spectral range, and the

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Designrulesforactivecontrolofnarrowbandthermalemissionusingphase-changematerialsMaximeGiteau,MitradeepSarkar,MariaPaulaAyala,MichaelT.Enders,andGeorgiaT.PapadakisICFO-InstitutdeCienciesFotoniques,TheBarcelonaInstituteofScienceandTechnology,Castelldefels,Barcelona08860,SpainWeproposeananalyticalfram...

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Design rules for active control of narrowband thermal emission using phase-change materials Maxime Giteau

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