1. Introduction

Thermal radiation is the phenomenon depicting that any object with a temperature above absolute zero radiates some electromagnetic energy due to the thermal motion of the charged particles within the object. Thermal radiations, as a ubiquitous physical phenomenon, hold great significance for scientific research and engineering applications e.g. in infrared stealth [1], energy utilization [2], and thermal management [3], etc. A traditional thermal emitter (i.e. the blackbody) has the typical characteristics of broadband, omnidirectional, incoherent and polarization independence. However, some advanced applications, have additional requirements for controlling the thermal emissivity at specific wavelengths with narrow bandwidths, such as infrared sensing [4], lighting [5], high-efficiency thermal photodetectors [6], thermal imaging [7] and so on. In the ongoing quest for thermal emitters with superior characteristics, new physics and materials are being extensively explored. In recent years, with the rapid development of photonics and nanofabrication technology, research on artificial structures including plasmonics, metasurface and photonic crystal is becoming more mature and well-developed [8,9]. People can make use of various microstructures made from certain materials to manipulate both the emission spectrum and spatial distribution of thermal radiations. According to Kirchhoff's law of thermal radiation, for any object emitting and absorbing thermal radiations in the thermodynamic equilibrium, the emission is reciprocal to the absorption process. This law allows people to focus on the absorption characteristics and lays out the foundation for a new thermal emitter design. The same structure, upon heating to a high temperature, will emit thermal radiations of the same electromagnetic properties as the absorption. Following this design routine, narrow-band thermal radiation sources working mainly in the mid-infrared (MIR) range have been recently studied in a wider approach [10–12]. Some optical resonances can be excited within the structure to produce efficient absorbers/emitters with a narrow bandwidth through a deliberate selection of the proper material and designing of the structure of the thermal emitter. Thus, changing the structure geometry gives us control over the central wavelength for a large spectral range.

Generally speaking, the narrowband performance can be characterized by the Q-factor, defined as the ratio of the resonant wavelength λ₀ to the FWHM Δλ (Q=λ₀/Δλ), reflecting the coherence property of the radiations. It is reported that a relatively high Q factor (100) can be obtained in the thermal emitters made from polar materials such as SiC [13]. However, due to the limitation in the phononic response of the polar materials, the real part of the permittivity is negative only in the narrow band while the imaginary part is relatively high. As a result, thermal emitters based on polar materials can only have the operating wavelength with low tunability while the emission bandwidth is still not narrow enough. Up till date, several new material platforms have been proposed to achieve narrow-band thermal emissions including multi-quantum well structures [14] and metallic photonic crystals [15]. In particular, the sandwich configuration of metal-insulator-metal (MIM) geometry [16] has attracted widespread attention in metamaterial-based thermal emitters because of their ease of design. Unfortunately, due to the large inherent metal loss and the additional radiative loss in the MIM geometry, the total energy dissipation rate in the MIM resonators is usually high. As a result, the achieved emission resonance is usually wide [17] along with the final emission peak Q value typically at the order of 10 in the MIR band [18]. Therefore, the exploration of new physics and working principles to achieve a narrow-band thermal radiation source remains as an active field, e.g. non-Hermitian selective thermal emitters using metal–semiconductor hybrid resonators [19]. It is of great significance to design inexpensive and reliable narrowband MIR thermal radiation sources with high emissivity and large spectral tunability.

Many studies have been harnessing the concept of BIC [20] in photonics to achieve large Q-factor resonances with high field enhancement greatly impacting to enhance the interaction between light and matter. First proposed in 1929 by von Neuman and Wigner [21], BIC represents an exotic state which is well-bound while its energy is above a certain barrier potential. This superior property has been widely studied and explored in various physics branches including electronics, quantum optics [21], electrodynamics [22], acoustics [23] and nonlinear optics [24]. In electromagnetics, BIC is a resonance with tight spatial confinement and no external leakage while its dispersion is located within the continuum e.g. above the light line. Earlier studies show that BIC with different physical mechanisms can be supported in several photonic systems.

In this work, we demonstrate a new design strategy for a narrow-band MIR thermal emitter based on the Fabry−Perot (FP) type of BIC mode. This type of BIC is due to the destructive interference between the radiation channels from two resonances [25]. Out of these, one is usually the mirrored image of the other so that they have the same mode distribution and spectral response. We use an array of high refractive index dielectric disks that are supporting the well-known optical resonances of the Mie type and widely explored recently in photonics, e.g. for nonlinear optical applications [26]. When the disk array is separated from a highly reflective substrate by a low refractive index spacer layer with an appropriate thickness, destructive interference between the disk array and its mirror with respect to the substrate can lead to the formation of FP-type BIC. Although the ideal BIC cannot be excited directly by the far-field radiation, and the radiation of resonance energy from the internal of a structure to the external space is completely eliminated, quasi-BIC resonances with ultra-high Q-factor can still be achieved by engineering the thickness of the buffer layer. The Q-factor of the quasi-BIC can be controlled by using a buffer layer thickness deviating from the critical value at different level. Since the substrate is reflective and optically opaque i.e. the transmittance is zero in the frequency range of interest, one only needs to pay attention to the reflection spectrum and evaluate the thermal emission property according to the Kirchhoff's law of thermal radiation. Numerical results show that when a noble metal substrate like gold is used and the metal dissipation is taken into account, an emission resonance with near-unity emissivity and FWHM less than 5 nm can be achieved at the operating wavelength of 4.587 µm. Our results show that when the thickness of the buffer layer is at the critical value, the corresponding radiative Q-factor reaches infinity suggesting that an ideal BIC resonance with no radiation loss can be achieved. By slightly varying the buffer layer thickness, an emission bandwidth comparable to those of the state-of-the-art MIR sources of quantum cascaded lasers (QCL) can be expected. Although many methods have been proposed in the literature to implement narrowband MIR thermal emitters, our proposed design of harnessing the FP-type of BIC is novel and superior due to its simple photonic geometry and the ease of bandwidth control by the buffer layer thickness that receives high precision tunability during the material deposition process.

2. Structure and results

In our design, the sandwich configuration widely used in the thermal emitters based on metallic metamaterial is still adopted except that the top metal layer is replaced by a Ge disk array. Figure 1(a) illustrates the thermal emission process from the structure which consists of a Ge disk array separated by an Al₂O₃ dielectric layer from the Au substrate. The yellow area represents the substrate which is optically opaque for MIR radiations to prevent light from passing through the structure. The substrate also works as the reflective mirror to form the image resonator while it can be heated by applying electric current to provide the high temperature required for the thermal emission. The operation wavelength is determined by the Mie resonance of the disk while the narrow-band operation is achieved by designing the whole system to work in the quasi-BIC state.

 

Fig. 1. (a) Schematic illustration of the working principle of the novel thermal emitter based on the FP type of BIC resonance. The red output beam represents the thermal radiation at the quasi-BIC resonance. (b) Structure diagram of the resonator and its mirror image to form the FP cavity. (c) Cross-sectional view of the unit cell of the structure.

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As shown by the illustration in Fig. 1(b), the FP-type of BIC arises from the coupling between the Mie resonance and its image due to the presence of a gold mirror. When the round-trip phases between the resonance and its mirror add up to an integral times of 2π, the radiations from the resonance and its mirror to the external environment will experience a destructive interference and thus the overall radiation at this frequency is eliminated. This process can be modeled using the temporal coupled mode theory (TCMT) [27]. For simplicity, we ignore the dissipation loss of the gold substrate and assume that it is a perfect electrical conductor (PEC). The structure can be considered as a horizontal resonator with a certain distance from its image under the PEC mirror. The time evolution of the resonance amplitude M = (M₁, M₂)^T can be expressed by Eq. (1) [28]:

We used the finite-element method implemented in the commercial software of COMSOL Multiphysics to evaluate the emission property. It is assumed that the entire structure is two-dimensionally periodic with the period P = 2.3 µm in both the x and y directions. Periodic boundary conditions are used to model lateral periodicity. The relative dielectric constant of gold can be defined by the Drude-Lorentz dispersion model [29]:

According to Kirchhoff's law of thermal radiation, the absorbance of a structure A(ω) can be used to model the emissivity E(ω). Since the Au substrate is optically thick to result in zero transmittance, the absorbance A(ω) = 1−T(ω)−R(ω) can be simplified as A(ω) = 1−R(ω) where T(ω) and R(ω) represent the transmittance through and the reflectance from the whole structure, respectively. Therefore, it is only necessary to study the absorption characteristics of the structure under different excitations and the final results will represent the emission characteristics of the structure. This method has been widely used in the study of metasurface based thermal radiation sources. According to coupling mode theory, the amplitude of the absorption peak depends on the ratio of the external loss rate (γ_Me) to the internal loss rate (γ_M0) in terms of cavity parameters [32]:

The results of TCMT show that the roundtrip phase of FP-type of BIC is critical. As shown in Fig. 1(b), the Ge disk array at the top and the Au electrode at the bottom can act as a perfect pair of mirrors to capture waves in the alumina dielectric layer. Figure 2(a) presents the simulated absorption spectra at different Al₂O₃ thicknesses while keeping the Ge disk radius constant. The formation of FP-BIC at the “critical point” is observed by varying the thickness of the alumina dielectric layer in the range of 0.37-0.46 µm. The influence of structural parameters on the radiation properties of structures is further studied. The numerical simulation results in Fig. 2(b) show that the Q factor first increases and then decreases with the increase of the Al₂O₃ layer thickness while the other parameters are kept unchanged. The total quality factor (Q) satisfies the following relation [33]:

 

Fig. 2. (a)Simulated Al₂O₃ thickness-dependent absorbance spectra. (b)The Q factor as a function of the thickness of the Al₂O₃ medium layer.

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Figure 3(a) represents the emission spectrum calculated for the thickness of alumina as t = 0.383µm. We assume that the normal incidence is excited by a linearly polarized plane wave in the x direction. According to the Kirchhoff's law of thermal radiation, the incident light used in our calculations has the same properties as the radiation from the designed thermal emitter. The results show that when the resonant frequency is 4.587µm, the emission spectrum of ultra-narrow linewidth is obtained. The emissivity at the resonance reaches near unity and the emission bandwidth is about 5 nm. A single emission line at 4.2-4.8 µm can be observed in Fig. 3(a). In order to better understand the principle of BIC resonance in the FP cavity supported by this structure, we further plot the distribution of electric and magnetic fields in Fig. 3(b). As, it can be seen in the Fig. 3(b), the magnetic field and circular loop shaped electric field are indeed concentrated in the top Ge layer.

 

Fig. 3. (a) Normal normalized emission spectrum of Ge disk array; The illustration shows the narrow-spectrum response of the device at a wide band scale (4.2-4.8 microns). (b) The distribution of H and E fields at the resonant frequency of the structure.

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The main point of our design is to use the FP type of BIC to eliminate the radiative loss. Thus, the total loss of the system is only determined by the material absorption, which should be minimized to maximize the Q factor of the resonance. Although gold is used in the above calculations, it can be replaced by another material of silver, which is more economic and has even lower absorption loss. Considering the general loss of silver is a quarter of that of gold, the improvement of the emission bandwidth by a factor of four can be expected. Furthermore, the low-index spacer layer can work to protect the silver from oxidation.

Although the geometry employed to achieve the FP-type of BIC resonance in this work is quite similar to those in [19], we note that the underlying physics is different. In [19], the thermal emission requires the excitations of a pair of coupled oscillators with extreme asymmetry in optical losses to result in the passive PT-symmetry. That's why the metal substrate of tungsten is used to realize a lossy image of the near-lossless resonance in Si resonators. However, in this work the resonator and its mirror image in Fig. 1(b) should have the same loss to fulfill the requirement on the magnitude for the destructive inteference to occur.

3. Conclusion

Concludingly, in this paper, we demonstrate a new design strategy for a narrow-band mid-infrared thermal emitter using the FP-type BIC mode. When a high refractive index disk supporting Mie resonance is separated from a high reflective substrate by an appropriate thickness of a low refractive index spacer layer, the destructive interference between the resonator and its mirror with respect to the substrate can lead to the formation of FP-type BIC. By designing the thickness of the buffer layer, the quasi-BIC resonance can achieve the the ultra-high Q factor (>10³) along with an ultra-narrow bandwidth in the MIR region. We have numerically demonstrated that a mid-infrared thermal emitter operating at a wavelength of 4.587 µm has a full-width half-maximum resonant emissivity of less than 5 nm for an approximately unit resonant emissivity even considering metal dissipation. One can also change the geometry of a Ge disk array to tune the resonance based on the scaling invariance property of Maxwell equations, thus thermal radiations at other frequencies across the entire mid-infrared band can be realized. This is also advantageous over other MIR sources whose operation wavelengths are restricted by the energy level of the amplification medium. By changing the thickness of the spacer layer, the emissivity at different frequencies can be optimized. In addition, our design uses regular materials of Ge and alumina, eliminating the requirement for fancy III-V semiconductors which need the expensive growth techniques like molecular beam epitaxy (MBE). Our proposed new thermal radiation source with the advantage of ultra-narrow bandwidth has potential practical applications due to its economy and ease of fabrication process.