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Metal-insulator-metal metamaterial thermal emitters strongly radiate at multiple resonant wavelengths. The fundamental mode, whose wavelength is the longest among resonances, is generally utilized for selective emission. In this paper, we show that parasitic modes at shorter wavelengths are suppressed by newly employed densely-tiled resonators, and that the suppression enables quasi-monochromatic thermal emission. The second-order harmonics, which is excited at half the fundamental wavelength in conventional emitters, shifts toward shorter wavelength. The blue-shift reduces the amplitude of the second-order emission by taking a distance from the Wien wavelength. Other parasitic modes are eliminated by the small spacing between resonators. The densely-tiled resonators are fabricated, and the measured emission spectra agree well with numerical simulations. The methodology presented here for the suppression of parasitic modes adds flexibility to metamaterial thermal emitters.
© 2016 Optical Society of America
1. Introduction
Tailoring thermal emission is one of the key challenges in both academia and industries. Subwavelength structures offer flexibility in design owing to the geometrically controlled electromagnetic resonance. Photonic crystals [1–4], gratings [5,6], cavities [7,8], and metamaterials [9] have successfully controlled thermal emission, toward applications including radiative cooling [3], thermophotovoltaics [1,2,9], and non-dispersed infrared sensing (NDIR) [8]. Especially, metamaterials composed of planar metal-insulator-metal (MIM) resonators [10–28] are attracting much interest because of their simple structures and omnidirectional emission.
There have been several physical explanations for electromagnetic resonances in MIM metamaterials or metasurfaces. They include magnetic polariton [11], impedance matching to the surroundings [29], plasmon resonant patch antennas [30], destructive interference between multiple reflections [31], standing-wave considering lateral dimensions [32], and localized gap plasmon [14,26]. Multiple resonances are excited at the several wavelengths where standing waves are excited. Generally, the fundamental mode, whose wavelength is the longest, is utilized to realize spectral selectivity. Other modes at shorter wavelengths are regarded as parasitic emission. They hamper an incandescent light source with ideal monochromatic emission, and the parasitic emission becomes unignorable in the case that the designed emission wavelength is longer than the Wien wavelength. This is because the emissions at parasitic modes have non-negligible amplitudes compared to the fundamental mode due to the Planck distribution.
In this paper, we demonstrate the suppression of parasitic thermal emission at shorter wavelengths by densely placing the resonators. In [33], we discussed the control of the second-order harmonics enabled by the proximity interactions between diagonally arranged resonators. However, unpolarized behavior, thermal emission or the suppression of other modes was not investigated at that time. In this paper, on ther other hand, square resonators are employed to achieve unpolarized emission at the fundamental wavelength and the maximum interaction between neighboring resonators. Densely-tiled resonators achieve the amplitude reduction of the second-order harmonics through the wavelength shift and the elimination of other parasitic modes.
2. Densely-tiled metal-insulator-metal metamaterial
Figure 1(a) shows a conventional MIM metamaterial consisting of rectangular resonators made of aluminum and silicon. The coordinate system is also shown, and the emission in the xz-plane is considered. The fundamental wavelength is approximately determined by the dimension perpendicular to the emitted magnetic field, and is slightly dependent on the dimension parallel to the magnetic field in the case of normal incidence [34]. In p-polarization, these dimensions correspond to the rectangular width w and the length l, respectively. Here we consider square resonators (w = l) such that the fundamental mode is unpolarized.
Fig. 1 Unpolarized MIM thermal emitters. (a) Conventional MIM metamaterial. The geometrical parameters are: p = 1.96 μm, w = l = 1.26 μm, gx = gy = 0.70 μm, h = 0.10 μm, and d = 0.13 μm. The permittivities of the media are set as εd = 3.422 and εm = 1 – fp2/(f2 + iγf), where f is the frequency, fp = 3570 THz, and γ = 19.26 THz [35]. θ is defined as the angle between the emission and the z-axis. (b) Thermal emission spectra of the conventional MIM metamaterial at a temperature of 400 K. The emissivity of the metamaterial was simulated by CST microwave studio. Emission angles: 0°, 30°, and 60°. The vertical dashed gray lines represent the fundamental wavelength and half the fundamental wavelength. The dotted gray curves show the emission from a blackbody at a temperature of 400 K, which corresponds to the Planck distribution. (c) Densely-tiled MIM metamaterial. The geometrical parameters are: p = 0.89 μm, w = l = 0.87 μm, gx = gy = 0.02 μm, h = 0.10 μm, and d = 0.09 μm. (d) Thermal emission spectra of the densely-tiled MIM metamaterial.
The metamaterial at a temperature of 400 K emits infrared light with an amplitude given by multiplying the emissivity of the metamaterial by the Planck distribution, as shown in Fig. 1(b). The metamaterial is designed to emit the light at a wavelength of 10 μm with unity emissivity in the normal direction. We see that there are emissions originating from the multiple parasitic resonances at wavelengths shorter than 7 μm, especially at oblique angles. The amplitudes of these emissions are not negligible compared to the emission at 10 μm because the parasitic wavelengths are close to the Wien wavelength. The power ratio between these parasitic modes and the fundamental mode, which is here defined by the ratio of the integrated radiances in the wavelength range of 3-7 μm to that of 8-12 μm, is 0.27 at an angle of 60°. The ratio becomes larger as the emitter temperature rises or the fundamental wavelength increases, which means that the quality of the emitter as a monochromatic source is degraded.
The densely-tiled metamaterial emitter shown in Fig. 1(c) successfully reduces the parasitic emission as shown in Fig. 1(d), and its effect is attributed to the small gap between square resonators. There is only one parasitic emission at a wavelength shorter than 4 μm, which is significantly shorter than the original parasitic main peak at 5 μm in Fig. 1(b). The wavelength shift of this parasitic mode reduces the amplitude of the parasitic emission, because the amplitude of the Planck distribution reduces as the wavelength becomes shorter in this wavelength range. As a result, the integrated radiance between 3 μm and 7 μm at an angle of 60° is suppressed from 11.8 Wsr−1m−2 to 4.0 Wsr−1m−2 thanks to the small gap between resonators. For the fundamental mode, the wavelength and the peak emissivity remain almost unchanged, while the bandwidth is slightly enlarged [36].
Figure 2 shows the angular thermal emissivity of the MIM metamaterials in both polarizations. Numbers of modes including the third-order harmonics, mode A, mode B, and surface plasmon polariton (SPP) are excited in the conventional emitter in the wavelength range between 3 μm and 7 μm, while they are successfully eliminated in the densely-tiled metamaterial emitter. The suppression of SPP is attributed to the small spatial period, because the SPP is excited around the angle where the first-order diffraction changes from evanescent to propagating.
Fig. 2 P- and s-polarized angular emissivity in the wavelength range from 3 μm to 15 μm. (a) Conventional MIM metamaterial. (b) Densely-tiled MIM metamaterial. Fund., 2nd, 3rd, and SPP denote the fundamental mode, the second-order harmonics, the third-order harmonics, and surface plasmon polariton, respectively. The right hand side of the panel shows emissivity in p-polarization and the left hand side shows that in s-polarization.
The remaining parasitic mode in p-polarization in the densely-tiled resonator is the second-order harmonics. The second-order harmonics in the conventional metamaterial appears at a wavelength of 5 μm, which is half the fundamental wavelength. On the contrary, the wavelength ratio of the fundamental mode to the second-order mode is larger than twofold in the densely-tiled resonators. The wavelength ratio decreases as the emission angle becomes larger, and it indicates that the phase difference between neighboring resonators in the x-direction plays the key role in the control of the wavelength ratio. Figure 3(a) shows the magnetic field distribution at the fundamental mode. Since the directions of the magnetic fields in the neighboring resonators in the x-direction are the same, the magnetic fields in neighboring resonators interact in a constructive way. Such a constructive interaction red-shifts the fundamental wavelength because the effective width is enlarged. The fundamental wavelength in the densely-tiled resonators is the same as that in the conventional resonators although the width of the rectangle is smaller, because the proximity interaction does not occur in the conventional resonators. Figure 3(b) shows the magnetic field at the second-order mode, and antiparallel magnetic field is excited in each resonator. Thus, the directions of the magnetic fields in the neighboring resonators in the x-direction are opposite. Consequently, the proximity interaction at the second-order mode is smaller than that at the fundamental mode. This means that the effective width for the second-order mode is approximately constant compared to that of the fundamental mode. The proximity interaction is destructive in the case that the emission angle is small, where each resonator is excited at almost the same phase. This explains why the second-order mode is dependent on the angle. Note that the proximity coupling in the y-direction also contributes to increase the fundamental and the second-order wavelengths, i.e. the effective length is enlarged.
Fig. 3 Magnetic field snapshot at the interface of the top metal square and the dielectric layer in the densely-tiled resonators. (a) Fundamental mode, 9.99 μm, 30°, p-polarization. (b) Second-order mode, 3.66 μm, 30°, p-polarization. Four periods are shown because the emission at an oblique angle is considered and the phase relationship between neighboring resontaors is important. P, E, B denote the directions of the poynting vector, electric filed, magnetic field of emission, respectively. The poynting vector is in the xz-plane. Pink arrows schematically represent the directions of the magnetic fields.
In the conventional metamaterial, mode A at 4.27 μm is excited in both polarizations, and mode B at 6.40 μm is excited in s-polarization. Both modes are suppressed in the densely-tiled metamaterial resonators. Figure 4(a) shows the snapshot of the fields at mode A. We consider the fields at positions α and β, which are located at the edges of the square, in order to elucidate the physical mechanism of the suppression. The magnetic field at position α is in the positive x-direction, and it is perpendicular to the edge of the square. The magnetic field at position β is also perpendicular to the edge of the square, but is in the negative x-direction. In the case that the square resonators are placed densely, the magnetic field at position α and that at position β of the neighboring resonator interact destructively. As a result, the excitation of mode A is strongly suppressed in the densely-tiled resonators. The same scenario is applied to mode B.
Fig. 4 Magnetic field snapshot of the parasitic modes in the conventional metamaterial. (a) Mode A, 4.27 μm, 0°, p-polarization. (b) Mode B, 6.40 μm, 30°, s-polarization.
Next, we further investigate how the proximity interaction suppresses the parasitic modes by varying the gap. Here, we consider p-polarized emission at an angle of 60°, and thus the emitted magnetic field is in the y-direction. The gap gx in the x-direction and the gap gy in the y-direction, are swept independently as shown in Fig. 5(a) and 5(b), respectively. The width and the length are kept at a constant value of 1.26 μm, while the period in the x- or the y-direction changes according to the gap values.
Fig. 5 Emissivity profile at an angle of 60° in p-polarization as a function of (a) gx, (b) gy, and (c) g = gx = gy. The horizontal axis is log scale. Other geometrical parameters are: w = l = 1.26 μm, h = 0.10 μm, and d = 0.13 μm. The gap gy in (a) and the gap gx in (b) are kept at 0.70 μm. Half the fundamental wavelengths are plotted as blue curves.
The fundamental wavelength increases as the gap becomes smaller in both cases. In Fig. 5(a), the fundamental wavelength is nearly constant when the gap gx is large, and it increases rapidly when gx is smaller than 0.1 μm. This indicates that the proximity interaction in the direction perpendicular to the magnetic field is negligible when the gap is larger than the thickness of the dielectric layer. On the contrary, the fundamental wavelength is constant when gy is smaller than 0.1 μm as shown in Fig. 5(b). This suggests that the magnetic field profile is the same as that of the grating (gy = 0 μm) when gy is smaller than 0.1 μm.
Interestingly, the second-order wavelength is kept almost constant in Fig. 5(a), which is thought to be due to the small interaction between antiparallel magnetic fields in neighboring resonators in the x-direction. In contrast, the proximity interaction in the direction parallel to the magnetic field increases both the fundamental and the second-order wavelengths as shown in Fig. 5(b).
The emissivity profile obtained by varying both gaps simultaneously is shown in Fig. 5(c), and it corresponds to the emitters with unpolarized fundamental emission shown in Fig. 1(a) and 1(c). The interactions in the x-direction and the y-direction constructively increase the fundamental wavelength, while the second-order wavelength red-shifts slightly. Moreover, mode A disappears as the gap becomes smaller, as previously discussed. The third-order resonance vanishes from this wavelength range when the square size becomes smaller in order to set the fundamental wavelength to be 10 μm.
3. Experimental investigation
The fabrication of the thermal emitter started from the deposition of three layers onto a silicon substrate. Aluminum, amorphous silicon, and aluminum layers were deposited sequantialy by magnetron sputtering. Then the resist pattern was formed by the electron-beam lithography (F5112 + VD01, Advantest). We employed dry-etching rather than lift-off to transfer the resist pattern into the top aluminum layer. Dry-etching avoids a narrow resist pattern, which is required to form a small gap in the case of lift-off.
The thermal emission spectra of the fabricated metamaterials were evaluated by Fourier-transformed infrared (FTIR) emission spectroscopy. The sample temperature was monitored by a K-thermocouple, and was regulated to be 400 K by a heater. The spectra at an angle of 50° are shown in Fig. 6. Multiple parasitic modes are observed in the conventional metamaterial at wavelengths shorter than 7 μm. The parasitic mode with the largest amplitude, which corresponds to the second-order harmonics, has a wavelength longer than the half the fundamental wavelength. In contrast, the densely-tiled metamaterial suppresses the parasitic modes. As discussed, this is realized by the suppression of modes A and B as well as the shift of the second-order wavelength to be shorter than half the fundamental wavelength. The measured spectra were reproduced by the numerical simulations. The baseline of the emission, which is the radiance at off-resonant wavelengths, is relatively higher than that in the numerical simulation in Section 2, because lossy amorphous silicon was employed as the dielectric layer.
Fig. 6 Fabricated MIM thermal emitters. (a) SEM image of the conventional resonators. (b) Zoom-up of the model utilized in numerical simulations. (c) SEM image of the densely-tiled resonators. (d) Thermal emission spectra of the conventional resonators. (e) Thermal emission spectra of the densely-tiled resonators. The emission angle is 50° and emitter temperatures are 400 K. The red solid and the blue dashed curves are measured and simulated emission spectra, respectively. The vertical dashed gray lines represent the fundamental wavelength and half the fundamental wavelength. The dotted gray curves show the emission from a blackbody at a temperature of 400 K. In the numerical simulations, the permittivities are εd = 13 + 1i and εm = 1 – fp2/(f2 + iγf), where fp = 3570 THz and γ = 19.26 THz. The geometrical parameters of the conventional resonators are: p = 2.25 μm, w = l = 1.33 μm, gx = gy = 0.92 μm, h = 0.10 μm, and d = 0.25 μm. The dielectric layer is overetched with a depth of dOv = 0.15 μm. The width wNOv of the non-overetched area around the aluminum patch is 0.07 μm. The geometrical parameters for the densely-tiled resonators are: p = 1.25 μm, w = l = 1.05 μm, gx = gy = 0.20 μm, h = 0.10 μm, d = 0.25 μm, and dOv = wNOv = 0.07 μm. These parameters are consistent with SEM images.
The emitter with various gap values were also fabricated and measured. For this experimental parametric study, the nominal gaps in the x- and the y-direction take the same value, and they span from 0.1 μm to 0.5 μm in the design. The nominal width of the square is fixed to be 0.85 μm. The resonant wavelengths were measured by microscopic reflection spectroscopies at an angle around 30°. The fundamental wavelength shown in Fig. 7(a) depends on the gap, while the second-order wavelength is nearly constant. This tendency is consistently seen in the simulated result in Fig. 5(c). The maximum ratio between the second-order and the fundamental wavelengths is around 2.7, which is almost the same as the simulated maximum ratio although the nominal gap values are different (0.1 μm and 0.02 μm). This is attributed to the narrow gap (~0.05 μm) of the fabricated metamaterial as shown in Fig. 7(b), as well as thicker dielectric layer (d = 0.25 μm) compared to the numerical study in Section 2.
Fig. 7 (a) Measured resonant wavelength of the fundamental and the second-order modes as a function of the nominal gap. The dashed gray curve represents half the fundamental wavelength. (b) SEM image of the MIM metamaterial with a nominal gap of 0.1 μm. The actual gap width is retrieved as 0.05 μm from the image.
4. Conclusion
We have realized a quasi-monochromatic thermal emitter by suppressing parasitic modes, which are excited in the conventional MIM thermal emitters. Such suppression was achieved by the densely-tiled resonators. The second-order resonant wavelength is shifted toward shorter wavelength, and it enables the suppression due to the Planck distribution. Other parasitic modes are eliminated due to the destructive interaction between magnetic fields in neighboring resonators. The conventional and the densely-tiled metamaterials were fabricated, and the thermal emission spectra and the resonant wavelengths were measured. The measured results are supported by numerical simulations.
Acknowledgment
The samples were fabricated using an electron-beam (EB) lithography apparatus (F5112 + VD01) donated by the Advantest Corporation at the VLSI Design and Education Center (VDEC) of the University of Tokyo, through MEXT Nanotechnology Platform Project. We acknowledge the staff of Takeda Sentanchi Cleanroom including Y. Mita, T. Sawamura, and E. Lebrasseur. We thank T. Nakajima from Tokyo metropolitan industrial technology research institute for emission FT-IR measurement. We acknowledge I. Takahashi for dry-etching, and A. Miura for dicing wafers. We also acknowledge K. Hanamura for fruitful discussions.
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