Super-Octave Metamaterial Absorbers for the Infrared

The GA optimizer was employed to identify a metallic nanostructure array that simultaneously maximizes absorption over a broad bandwidth while also giving a wide-FOV and polarization- independent response, targeting an MMA with a high minimum absorptivity of greater than 90% over an angular range of ±40° and having more than an octave of bandwidth across the 2 gm to 5 gm mid-IR range. Absorber geometries were optimized using both Au and Pd metals for the ground plane and patterned nanostructure layer in order to compare the performance of these two materials. As described later in the next section, the higher optical loss of Pd as compared to Au provides significant advantages in terms of reliable nanofabrication of the MMA structure. Polyimide was selected for the dielectric substrate and superstrate layers because of its nondispersive optical properties over the target wavelength range. In order to accurately account for the material dispersion in the design, the measured optical constants (n and k) of the Au, Pd, and polyimide thin films were used during the design optimization.

The GA evolved all of the adjustable design parameters, including the thickness of each layer, the unit cell period, and the patterned metal feature geometry, to identify a four-layer MMA that meets the target optical performance metrics. The metal-ground plane layer thickness was fixed at 100 nm, which is several times the skin depth for both Pd and Au. By minimizing the cost function in Eq. (8.3), the GA evolves the nanostructure pattern and layer thicknesses to have near-unity absorption over all of the test wavelengths and incidence angles. For the first mid-IR broadband MMA design, 16 test wavelengths were specified in approximately equally spaced frequency intervals over the range from 2 gm to 5 gm, and the test incidence angles were chosen to be (вф) = {(0°,0°), (40°,0°), (40°,45°)}, which covers an FOV of up to ±40°. Throughout the evolutionary process, structures that do not meet predefined nanofabrication constraints were assigned a high cost and were eliminated from subsequent candidate populations [89]. This ensured that the optimized structure could be fabricated without adjustments to the screen geometry. Operating on a population of 24 chromosomes, the GA converged to the MMA structure shown in Fig. 8.5a with minimized cost in 86 generations. The optimized thicknesses are 30 nm for the patterned Pd nanostructures and t1 = 398 nm and t2 = 429 nm for the top and bottom polyimide layers. The unit cell period is a = 851 nm on both sides with a pixel size of 57 nm. The optimized unit cell geometry seen in Fig. 8.5a is complex, containing several identifiable features, including a cross dipole centered in the unit cell, a large loop centered in the unit cell and interconnected between unit cells, and four smaller, isolated loops centered at the corners of the unit cell. These nanostructure elements and the coupling between them support multiple electromagnetic resonances and work in consort to produce high absorption across the target broad mid-IR band.

The simulated absorptivity of the MMA is calculated from the scattering parameters according to A = 1 - R, where R is the reflectance. Figure 8.6a shows the simulated absorptivity for unpolarized, TE-polarized, and TM-polarized light. The normal incidence spectra in Fig. 8.6a demonstrate that the minimum spectral absorptivity for this structure is greater than 90% over the entire 1.90 gm to 5.47 gm range with a high average value of 98.8% across this band. It is evident from these spectra that the broadband absorption is due to the merging of multiple strong resonances positioned at optimized wavelengths across the band. The peak values of normal incidence absorptivity occur at 2.13 gm, 3.0 gm, 3.7 gm, and 5.05 gm. Figure 8.6a also shows two-dimensional contour plots of the predicted angular dependence of the absorptivity from normal в = 0° up to в = 55° off-normal incidence for all polarizations. These simulations reveal that at an incidence angle of в = 55°, more than an octave bandwidth is achieved with a minimum absorptivity of 89.5% and that an average absorptivity of 94.7% is maintained over the 2 gm to 5 gm band, which is wider than the targeted FOV used for optimization. Comparing the TE and TM responses in Fig. 8.6a, we can see that the TM absorption at the long wavelength edge of the absorption band drops off more quickly with increasing incidence angle, whereas the dip in absorptivity around 4.5 gm becomes more pronounced for TE polarization at large incidence angles. These small changes in the MMA response with increasing incidence angles are associated with slight shifts in peak position, strength, and bandwidth of the dominant resonances found at normal incidence.

(a) Simulated and (b) measured angular dispersion of the absorption

Figure 8.6 (a) Simulated and (b) measured angular dispersion of the absorption

spectra for the MMA design shown in Fig. 8.5. From left to right: Normal incidence absorptivity for unpolarized, TE, and TM illumination. Contour plots of absorptivity as a function of wavelength and angle of incident from normal up to 55° incidence under unpolarized (second column), TE (third column), and TM (right column) illumination.

In order to understand the contribution of different parts of the nanostructure geometry to the broadband absorption, the electric volume currents excited within the MMA were simulated at the wavelengths with peak absorption (2.13 gm, 3.0 gm, 3.7 gm, and 5.05 gm) and at one wavelength outside the band (1.5 gm) for normally incident, TE-polarized illumination. The top views of the current distributions are shown in Fig. 8.7, revealing that outside the absorption band at 1.5 gm, the electric current in the MMA is negligible. By contrast, at wavelengths corresponding to peak inband absorption, large electric currents and field enhancements are found on different parts of the Pd nanostructure array. The central crosses support the highest current at the shortest 2.13 gm wavelength. At the intermediate 3.00 gm and 3.70 gm wavelengths, the current distribution spreads from the central cross to include the large and small loops, and at the longest 5.05 gm wavelength, the electric current is high on all parts of nanostructure except the central cross.

Top view of the current distributions in the nanostructured Pd screen under normal incidence illumination at the wavelengths 1.50 цт, 2.13 цт, 3.00 цт, 3.70 цт, and 5.05 цт

Figure 8.7 Top view of the current distributions in the nanostructured Pd screen under normal incidence illumination at the wavelengths 1.50 цт, 2.13 цт, 3.00 цт, 3.70 цт, and 5.05 цт.

Compared to other MMAs that excite magnetic resonances [45], the strong broadband absorption in this MMA comes entirely from electric resonances. The relatively thick polyimide substrate layer prevents strong coupling between the patterned nanostructure and the ground layer, inhibiting loop currents associated with magnetic responses. Cross-sectional views of the electric volume currents confirm that large currents are only present on the Pd nanostructure layer and not on the ground plane. Hence, the simulation results demonstrate that the broadband performance is achieved by exciting multiple closely spaced electric resonances on the singlelayer nanostructure array.

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