Controlling thermal emission of phonon by magnetic metasurfaces

Our experiment shows that the thermal emission of phonon can be controlled by magnetic resonance (MR) mode in a metasurface (MTS). Through changing the structural parameter of metasurface, the MR wavelength can be tuned to the phonon resonance wavelength. This introduces a strong coupling between phonon and MR, which results in an anticrossing phonon-plasmons mode. In the process, we can manipulate the polarization and angular radiation of thermal emission of phonon. Such metasurface provides a new kind of thermal emission structures for various thermal management applications.


Experiment result
The Al/SiO 2 /Al magnetic MTS were fabricated on Si wafer. In fabrication, Al film of thickness 150 nm was deposited on pre-cleaned Si wafer by electron beam evaporation. Amorphous silica films (500 nm ) were synthesized by plasma enhanced chemical evaporation (PECVD) at temperature 300 °C on the Al film, and subsequent in situ annealing was performed for 10 hours. An Al grating was fabricated on the amorphous SiO 2 films by ultraviolent photolithography and subsequent lift-off. The schematic view in Fig. 1(a) exhibits both structure and material information. In experiment, the period and height of grating was fixed as Λ = 6.5 μm and h = 0.05 μm, the width d can be changed through tuning the exposure time in the course of photolithography. Figure 1(b) shows the morphology characterized by a commercial scanning electron microscopy (SEM) of sample with width d = 2.8 μm.
The total thickness of MTS is 0.7 micron which is much smaller than the working wavelength range 11-16 μm.
We measured thermal emission and absorption of sample with FTIR spectrometer. The scanning wavelength range is 11-16 μm. At the same time, we also used FDTD method to calculate the absorption of structures and compare the results with experiment. Firstly, we investigated the MR and phonon separately without coupling effect between them. Figure 2(a) gives the thermal emission and absorption of SiO 2 /Al. Without grating, there is no MR and only phonon is found. Both the measured absorption (blue triangle symbolic line) and thermal emission (red brackets symbolic line) spectra show one faint and broad peak at 12.5 um, along with the measured ones was the simulated absorption spectrum by FDTD method as denoted by the black triangle symbolic line in Fig. 2(a). The data of SiO 2 were referred to ref. 65. The agreement between measured and calculated absorption spectra consolidated our material research base and method reliability. Figure 2(b) gives the calculated absorption spectrum of MTS, where the refraction index of SiO 2 n = 1.47 was used in simulation. In the simulation, the MTS grating periodic is Λ = 6.5 μm and width d = 3 μm under TM polarization (electric field perpendicular to the grating), as we can see, only MR resonance peak is found at 12.5 um. Compared with phonon, the absorption of MR is much stronger which is attributed to the strong magnetic resonance mode [54][55][56][57][58][59][60][61] . Here, the MR mode can be regarded as a kind of plasmonic cavity mode.
For the MTS given in Fig. 1, its thermal emission shows very strong polarization dependence. Figure 2(c) gives TE polarized emission (E field parallel to grating strip). Both the thermal emission and absorption spectra of the MTS in Fig. 2(c) show the similar peculiarity as phonon at 12.5 um given in Fig. 2(a). Here, MR cannot be excited, and only phonon contribute to the emission and absorption. Therefore, these curves are very like those in Fig. 2(a). The calculation agree with experiment quite well.
On the other hand, for TM polarized emission of MTS (E field perpendicular to grating strip) in Fig. 2(d), it is quite different from TE emission in Fig. 2(a). Here, phonon resonance can be still found at the wavelength 12.5 μm. At the same time, the MR can be excited at the same wavelength. This makes MR and phonon overlapped with each other. As a result, the strong coupling occurs between MR and phonon, which will produce two resonance peaks in the curve. In Fig. 2(d), two prominent peaks are obtained at wavelength 11.8 μm and 13.29 μm, which lie on the two sides of 12.5 μm, and are different from peaks of the phonon ( Fig. 2(a)) and the MR ( Fig. 2(b)). In simulations, with including phonon of SiO 2 in the program, the simulated absorption spectra of sample with periodic Λ = 6.5 μm and width d = 3 μm also features two pronounced peaks as denoted by the black triangle symbolic line given in Fig. 2(d). The simulated and measured absorption spectra agree well, which are both in accordance with the thermal emission spectrum. In the following, we will provide a theory model to explain the coupling mechanism.
The absorption and emission polarization dependence of sample can be described by the ratio of TM over TE: P = I TM /I TE . For SiO 2 /Al film, there is no polarization dependence for phonon mode and P = 1. While, for MTS, strong anisotropic property is demonstrated for both theoretical and experimental results as shown in Fig. 3 (experimental result: red line, and theoretical result: blue line). We can see P is very large for the wavelength around the two resonance peaks, while it will approximate unit when the wavelength is far away from the peaks. It means that the polarization dependence is caused by the strong resonance mode of MTS. In the figure, P amounted to forty-fold in calculations, and only about five-fold in experiment. This large discrepancy between theory and experiment is caused by the defects of samples and the aberrations in adjusting the polarizations. Despite all this, the modified anisotropic thermal emission of phonon was still clearly discerned. Beside polarization dependence, the angular dependence of emission and absorption is also changed by MTS. Figure 4(a) and (c) give the results of SiO 2 /Al, in which only phonon exists. As given in ref. 63, phonon near 12.5 μm includes both LO and TO pair mode in the range 1160-1200 cm −1 . Due to Berreman effect of LO phonon in thin film 66 , the interaction between phonon and light will be enhanced by increasing the angle. Then, as shown in Fig. 4(a) and (c), the absorption and thermal emission of SiO 2 /Al film became stronger at larger emission or incident angle. While for MTS in Fig. 4(b) and (d), both the two resonance modes obtain their maximum absorption and emission efficiency at normal angle. For the mode at wavelength 11.8 μm, the absorption and emission do not change  much with angle. While, for the mode at wavelength 13.29 μm, the emission and absorption is reduced greatly around 50 degree. This is caused by strong Bragg scattering at this angle.
In above discussion, we know that the coupling between phonon and MR will produce two resonance peaks. In physics, it is like the normal mode splitting of atoms in cavity [67][68][69] . By putting atom into high-finesse optical cavity, and tuning the parameters of the cavity, the spontaneous emission spectra of the atom featured anti-crossing line-shape, which was attributed to the strong coupling occurred between the atom and cavity. Actually, such mode splitting was also possibly for magnetic polariton structures 55 . In our system, if the MR can be regarded as a cavity and phonon as an atom, the two peaks can be seen as the result of mode splitting. Then if we tune the MR by changing structure parameter, it is possible to produce anti-crossing line-shape near the phonon resonance. For the MTS in Fig. 1(a), its MR resonance wavelength is dependent on the grating width d. Then we can tune MR through changing d. FDTD simulations were performed with varied grating width d of MTS. Figure 5(a) depicted the simulated absorption spectra versus the photon energy and the grating width d, which was changed from 2.6 to 3.6 μm. Pronounced anticrossing behaviour was demonstrated in the absorption spectra, indicating the presence of the strong coupling between MR and the phonon. In experiment, a series of samples with varied width d and fixed period Λ = 6.5 μm were synthesized through changing the exposure time in the process of photolithography. The measured thermal emission spectra of the varied width d grating were shown in Fig. 5(b), where the measurements were performed in normal angle under TM polarization. The pronounced anticrossing behaviour near phonon energy ω = 0.1 ev (λ = 12.5 μm) was also demonstrated in both Fig. 5(a) and (b). The excellent agreement between simulation and experiment render the strong coupling convincible in this system.

Theory
In this part, a coupled mode theory 64 is established to describe the physical mechanism of the strong coupling between the MR and the phonon. Firstly, let's recur to the common equations that describe two coupled oscillators as:  where μ 1 , μ 2 are the displacements of oscillators under excitation, respectively, and g 1 , g 2 are coupling factor between oscillators and incident field, κ is the coupling factor between the two oscillators 64 . δ is the resonance frequency difference between μ 1 and μ 2 . γ 1 and γ 2 are dissipation losses of oscillators μ 1 , μ 2 , respectively. Here, we choose oscillator μ 2 as the phonon, with inherent resonant frequency ω 0 . And the MR oscillator μ 1 can be manipulated through changing the parameters of the MTS. The Hamiltonian of this two oscillators system can be presented as: Due to the coupling term in Hamiltonian, the mode splitting happens and the two eigen frequencies can be obtained as: (4) 1 2 When the MR resonant frequency is near the phonon frequency ω = 0.1 ev, namely, δ ≈ 0, the strong coupling may occur if κ > > (γ 1 − γ 2 ) 2 67-69 , and the coupled system has two eigen energies, the normal mode splits into two modes, and thus two peaks will be found in absorption spectra.
Here, the mode splitting is like the Rabi splitting of atom in cavity and the Rabi frequency is [67][68][69] : Based on the equation (3), the eigen frequencies of the MTS with varied grating width were numerically calculated, where the parameters of SiO 2 phonon γ 2 = 0.65254(ev) were fitted from the Lorentz formulation. Figure 6 displays the eigen-wavelength versus the grating width d from coupled mode theory (the blanket triangles) and FDTD simulation (the solid red dots). The green dotted line in Fig. 6 indicates the phonon resonance wavelength, and the purple dotted line depicts the MR wavelength varied with the grating width, the error bar gave out the difference value between them and the experiment results. It is evident that the coupled mode theory calculation, the FDTD simulation and the experiment agrees quite well. All the three spectra feature anticrossing characterization. The narrowest frequency is located rightly at the phonon resonant frequency, ω = 0.1 ev, with γ 1 = 1.06896(ev), and thus the detuning δ = 0. Substitute these parameters into formula (4), the coupling coefficient can be obtained as κ = 0.65265(ev). Clearly, κ 2 > > (γ 1 − γ 2 ) 2 , satisfies the strong coupling condition [67][68][69] . Substituting these parameters into Rabi splitting energy band formula (5) 2  1  4  1  2 2 67,70,71 , and we get the Rabi splitting band gap in the anisotropic magnetic MTS as ħΩ rabi = 1.237(ev). Hitherto, from the excellent agreement between simulation and experiment results, we conclude that the thermal emission of SiO 2 phonon at ω = 0.1 ev can be controlled by MTS.

Summary
In this work, we use MTS to control the thermal emission of phonon. The emission peak, polarization and radiation angle can be well manipulated in the process. A coupled mode theory is established to calculate the mode splitting and anti-crossing effect, which agrees with experiment well. In this work, we only consider the phonon inside SiO 2 . Actually, this method can be used to any other materials with different phonon wavelength as the MR can be flexibly tuned to any wavelength. If the fabrication is improved and the MTS have larger resonance Q factor, the plasmon-phonon coupling can be further enhanced. In the future, it can be anticipated that MTS will have many other interesting applications in thermal emission devices.