1. Introduction

All objects are continually generating electromagnetic waves with a spectral distribution that depends upon the temperature of the object [1]. The spectral radiance of room temperature objects such as people, trees, and vehicles peaks at around 10 µm. For hotter objects such as engines, maximum emission occurs at shorter wavelengths. Thus, objects can be “seen” via their radiative emission by detectors operating in the waveband 2–15 µm (mid-infrared band), even without visible light [2]. A critical limitation of conventional mid-infrared detectors, including photon detectors and thermal detectors, is that they lack pixel-level spectral selectivity and polarization selectivity [3]. They only convert the power of the incoming light into readout signals but do not resolve the wavelengths and polarization states at the pixel level. For applications such as hyperspectral imaging and polarization imaging, as shown in Fig. 1(a), conventional mid-infrared detectors have to pair with separate spectral and polarization filters to complete the selection of spectral band and polarization states of the incoming waves. The resulted optical systems are inevitably complicated and bulky.

 

Fig. 1. (a) Conventional infrared detector pixels rely on separate spectral filters and polarizers to resolve the spectral bands and polarization states of the incoming light. (b)Infrared detector pixels with built-in metamaterial absorbers can directly resolve the spectral bands and polarization states. (c) Infrared focal plane array for dual-band polarimetric imaging detection.

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One way to overcome this limitation is to directly tune the spectral selectivity and polarization selectivity of mid-infrared detectors using integrated optical metamaterials, thus mitigating the need for separate spectral filters and polarizers [4–9], as shown in Figs. 1(b) and 1(c). The four pixels with the antenna orientation angle of 0°, 45°,90°, and 135° are regarded as a superpixel. The intensities of the incoming wave measured by the four pixels are I(0), I(45), I(90), and I(135), respectively. Assuming the electric field of the incoming wave has two orthogonal components E_x and E_y. The phase difference between E_x and E_y is ΔΦ=Φx-Φy, the components of Stokes vector can then be written as S₀=|E_x|²+|E_y|², S₁=|E_x|²-|E_y|², S₂=2|E_xE_ycos(ΔΦ)|. The equations that relate E_x, E_y, and ΔΦ, to I(0), I(90), and I(45) are: |Ex|=$\sqrt {\textrm{I}(0 )} $, |Ey|=$\sqrt {\textrm{I}({90} )} $, and |cos(ΔΦ)|=[2*I(45)-I(0)-I(90)]/(2$\sqrt {\textrm{I}(0 )\textrm{I}({90} )} $). Thus the components of Stokes vector can be written in terms of I(0), I(45), I(90), and I(135) as S0=I(0)+I(90), S1=I(0)-I(90), S2 = 2*I(45)-S0. From S0, S1, and S2 the angle of polarization $\textrm{AoP} = \frac{1}{2}\arctan \left( {\frac{{{S_2}}}{{{S_1}{\; }}}} \right)$, and degree of linear polarization $\textrm{DoLP} = \sqrt {\textrm{S}_1^2 + \textrm{S}_2^2} /{S_0}$ can then be calculated [10]. Along this line, Shinpei Ogawa et al. fabricated metamaterial absorbers on the pixels of a-Si based thermopile detectors and realized spectral selective detection and polarization selective detection in the mid-infrared [11,12]. Willie Padilla et al. reported the integration of plasmonic metamaterial absorber with the thin film lithium niobate based pyroelectric detector for wavelength selective detection in the waveband of 8–12 µm [3]. We have also demonstrated a bilayer beam based thermo-mechanical detector integrated with a built-in nanoslot antenna absorber that is both wavelength selective and polarization selective [13,14].

While metamaterials have proved to be an invaluable tool to tailor the responses of mid-infrared detectors pixels, their potentials have not been fully exploited yet. This is largely because the traditional way of designing metamaterials is to select an overall pattern based on prior known physical principles and intuition, and then iteratively fine-tune the structure by brute-force parameter sweep simulations [15]. The problem with this hand-tuning method is that it can only handle simple geometries with small sets of parameters, such as single-sized nanodisks, nanorods, nanocrosses, nanostrips, and so on [16–21]. On the other hand, advanced lithographic tools such as electron beam lithography (EBL) and extreme ultraviolet lithography (EUV) can generate patterns with feature size down to sub-10 nm [22–25]. This allows human designers to explore much more complex geometries and uncover unprecedented optical characteristics. To efficiently optimize the many design degrees of freedom associated with complex geometries, it is necessary to use computer algorithms to assist the search of the vast parameter space for optimal design [26–31]. Towards this end, we reported an inversely designed polarization selective metamaterial absorber based on a metal-insulator-metal (MIM) structure with multi-sized nanostrip antennas as the top layer [32]. A computer program based on particle swarm optimization (PSO) algorithm was developed to handle the structural parameters such as the widths of the nanostrips and the gap sizes between neighboring nanostrips. The optimal design found by the PSO program can achieve high spectral absorption in the specified 3–5 µm band.

One problem with the PSO algorithm-based program is that the number of nanostrips in a period needs to be pre-designated before the optimization. In other words, the basic pattern of the multi-sized antennas is pre-determined, while the PSO program only adjusts the structural parameters. The designer needs to compare the results of the computer-generated designs with a different number of nanostrips and choose the best one. In this paper, we developed a computer program based on the genetic algorithm (GA) [33,34]. This evolutionary algorithm begins with a randomly generated pixelated pattern to search for the optimal design of the MIM absorber with a top layer of multi-sized antennas. The GA automatically modifies the pattern of the multi-sized antennas in each iteration and eventually finds polarization selective designs with high spectral absorption in two infrared atmospheric windows: 3–5 µm and 8–12 µm.

When the demonstrated absorbers are built into thermal detectors, two issues will affect the overall detector performance: 1) the MIM structure is not infinitely large anymore, but limited by the pixel size of the detectors. To find a suitable pixel size, a numerical study is conducted to find out how the spectral absorption of the MIM structure changes as the pixel size is reduced. 2) The overall polarization selectivity of the detector is not only decided by the optical absorption of the TE polarization and TM polarization but also affected by the temperature increases caused by the two polarization states. A photothermal analysis is performed to reveal the difference in the local temperature increases under TE polarization and TM polarization, respectively. The corresponding impact on the overall polarization selectivity of the detector is also evaluated.

2. Simulations and results

It is well known that the MIM structure with a single-sized nanostrip antenna has a narrowband absorption peak, and the wavelength is proportional to the width of the nanostrip. When nanostrip antennas with different widths are appropriately arranged in a unit cell, their absorption spectra can be superimposed to form a broad absorption band. Figure 2(a) shows the MIM structure consisting of a gold backplate, a silicon spacer, and a top layer of multi-sized nanostrip antennas that are periodic in the x-direction and infinitely long in the z-direction. Lumerical FDTD solutions, a finite-difference time-domain (FDTD) method based simulator, is used to simulate a unit cell of the periodic structure, as described by the 2D simulation region in Fig. 2(a). Periodic boundary conditions are applied to the left side and right side of the unit cell, and perfectly matched layer (PML) boundary conditions are applied to the top and bottom of the 2D simulation region. A normally incident plane wave source is applied above the structure as the excitation, and the electric field of the incident wave is polarized in the x-direction (TM mode). The gold backplate is thick enough to eliminate the transmission of the incoming wave (T = 0). A power monitor is placed above the plane wave source to collect the reflected waves and calculate the power reflection coefficient R. The calculation of the power absorption coefficient A is thus simplified to A ≡ 1 – R.

 

Fig. 2. (a) Configuration of the 2D unit cell used to simulate the metal-insulator-metal based metamaterial absorber with multi-sized nanostrip antennas as the top layer. (b) The process of optimizing the metamaterial absorbers with Genetic Algorithm, and the absorption spectra of the optimized structures in (c) 3 µm – 5 µm and (d) 8 µm – 12 µm, respectively. The refractive indices of gold and silicon provided by Lumerical FDTD solutions can be found in Ref [35].

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The process of optimizing the pattern of the multi-sized nanostrip antennas in a unit cell using genetic algorithm (GA) is shown in Fig. 2(b). In each unit cell, the top layer (“antenna layer”) of the MIM structure is evenly divided into N sections, and each section can be filled with air or gold, represented by a binary digit 0 or 1, respectively. The antenna layer is thus described by an N-digit string (“encoding”). The value of N is determined by both the resolutions of nanofabrication tools and the speed of the computers that carry out the FDTD simulations. At the beginning of the optimization process, the GA program executed in MATLAB sends 50 randomly generated N-digit strings (“individuals”) to the FDTD simulator to designate the original patterns of the antenna layer. In each iteration, the FDTD simulator simulates the 50 MIM structures with the designated antenna patterns and returns the computed figure-of-merits (FOMs) of the 50 MIM structures to the GA program. Here the FOM is defined as the averaged spectral absorption coefficient of the TM mode in the specified 3 µm – 5 µm band or 8 µm – 12 µm band. The idea of GA is to screen out individuals with poor adaptability while excellent traits will be continuously accumulated, resulting in perfect individuals with specific characteristics. Here “excellent traits” are defined as individuals with higher FOMs, while “perfect individuals” refer to the individuals with the highest FOM. Specifically, the GA program uses the strategies of “roulette” and “elitist preservation” to select the “parents” of the next generation from the 50 “individuals” based on their FOMs [36,37]. The roulette strategy decides whether an individual is chosen as the parent of the new generation based on its normalized FOM. Individuals with higher FOMs are more likely to be chosen as the parents, and the GA program memorizes the individual with the highest FOM (current optimal solution) as the “elitist individual”. When the 50 parents of the new generation are determined, they are arranged into 25 pairs to perform the crossover operation. In the crossover operation, the two parents in each pair have an 80% chance to exchange the digits in their strings (gene), and each digit has a 50% chance to be exchanged. The individuals resulted from the crossover operation are then placed into the next generation. If the two parents in a pair do not exchange digits, they are directly placed into the next generation. After the crossover operation, the GA program randomly selects 15% of the individuals in the new generation to perform the mutation operation. To perform the mutation operation on an individual, the GA program randomly picks 15% of its digits and change the value of each picked digit from 0 to 1, or from 1 to 0 (invert the bit). When the mutation operation is finished, the parent with the highest FOM (elitist individual) directly displaces the first individual of the new generation to prevent its excellent traits from being lost (elitist preservation). After these steps, the number and arrangement of nanostrips in the patterns of the new generation of individuals become different from those in the parents. This is the difference between the GA program in this paper and the PSO program in our previous work [32]. The new generation of individuals is then sent to the FDTD simulator to find their FOMs. The optimization process iterates for 150 generations, and the individual with the highest FOM in the 150th generation is selected to generate the final optimized structure (“decoding”).

The insets in Figs. 2(c) and 2(d) present examples of two optimized structures for 3 µm – 5 µm band (“MWIR absorber”) and 8 µm – 12 µm band (“LWIR absorber”), respectively. The MWIR absorber shown in Fig. 2(c) has a period of P₁ = 2.55 µm, with a 120 nm thick silicon spacer between a 100 nm thick gold backplate and a 50 nm thick antenna layer. The unit cell is evenly divided into N = 30 sections, so the optimized antenna layer is described by a 30-digit string, specifically “001110001111011101111101111000”, where “1” represents an 85 nm wide nanostrip filled with gold, while “0” represents an 85 nm wide nanostrip filled with air. Therefore, the antenna layer consists of five gold nanostrips with widths of 255 nm, 340 nm, 255 nm, 425 nm, and 340 nm, respectively. The air gaps between adjacent nanostrips are 340 nm, 85 nm, 85 nm, 85 nm, and 425 nm, respectively. The simulated absorption spectrum of the optimized structure contains five spectral peaks: λ₁ = 3.09 µm, λ₂ = 3.31 µm, λ₃ = 3.69 µm, λ₄ = 4.05 µm, and λ₅ = 4.61 µm, respectively, and the average absorption coefficient of TM mode in the 3 µm – 5 µm band is 0.728. Similarly, the LWIR absorber shown in Fig. 2(d) has a period of P₂ = 7 µm, with a 200 nm thick silicon spacer between a 100 nm thick gold backplate and a 50 nm thick antenna layer. The unit cell is evenly divided into N = 50 sections, so the optimized antenna layer is described by a 50-digit string, specifically “011111111001111110111011 11111010111111111011111110”, where “1” represents a 140 nm wide nanostrip filled with gold while “0” represents a 140 nm wide nanostrip filled with air. Accordingly, the top antenna layer consists of seven gold nanostrips with widths of 1120 nm, 840 nm, 420 nm, 980 nm, 140 nm, 1260 nm, and 980 nm, respectively. The air gaps between adjacent nanostrips are 140 nm, 140 nm, 140 nm, 140 nm, 140 nm, 140 nm, and 280 nm, respectively. The simulated absorption spectrum of the optimized structure contains five spectral peaks: λ₁ = 8.36 µm, λ₂ = 9.23 µm, λ₃ = 9.48 µm, λ₄ = 10.45 µm, and λ₅ = 11.47 µm, and the average absorption coefficient of TM mode in the 8 µm – 12 µm band is 0.773.

3. Discussion

To further understand the details about the broadband absorption of the GA optimized structure, we plot in Figs. 3(a)–3(j) the local distribution of magnetic field intensity of the TM polarization at each resonant wavelength of the two absorption spectra shown in Figs. 2(c) and 2(d). In the MWIR absorber case, the 5 resonant wavelengths: λ₁ = 3.06 µm, λ₂ = 3.31 µm, λ₃ = 3.69 µm, λ₄ = 4.05 µm, and λ₅ = 4.61 µm correspond to the nanostrip #3 (w₃ = 255 nm), nanostrip #1 (w₁ = 255 nm), nanostrip #5 (w₅ = 340 nm), nanostrip #2 (w₂ = 340 nm), and nanostrip #4 (w₄ = 425 nm), respectively. In the LWIR absorber case, the 5 resonant wavelengths: λ₁ = 8.36 µm, λ₂ = 9.23 µm, λ₃ = 9.48 µm, λ₄ = 10.45 µm, and λ₅ = 11.47 µm correspond to the nanostrip #2 (w₂ = 840 nm), nanostrip #7 (w₇ = 980 nm), nanostrip #4 (w₄= 980 nm), nanostrip #1 (w₁ = 1120 nm), and nanostrip #6 (w₆ = 1260 nm), respectively. It is worth noting that in a MIM structure based on the periodic single-sized nanostrip antenna, a wider nanostrip corresponds to a longer resonant wavelength. However, when multiple nanostrip antennas with different widths are arranged in one unit cell, there could be two or more nanostrips having the same width. For example, in the MWIR absorber case, the widths of nanostrip #1 and nanostrip #3 are both 255 nm. Correspondingly, at the resonant wavelengths of λ₁ = 3.09 µm and λ₂ = 3.31 µm, the local magnetic fields are enhanced under both nanostrip #1 and nanostrip #3. Similarly, at the resonant wavelengths of λ₃ = 3.69 µm and λ₄ = 4.05 µm, the local magnetic fields are mainly enhanced under both nanostrip #2 and nanostrip #5 because their widths are both 340 nm, though there are also slight field enhancement under #3 and #4, respectively.

 

Fig. 3. The distribution of magnetic field intensity |H| at each absorption peak. (a) ∼ (e) The distribution of magnetic field intensity |H| at each absorption peak of the MWIR absorber designed for 3 µm – 5 µm. (f) ∼ (j) The distribution of magnetic field intensity |H| at each absorption peak of the LWIR absorber.

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4. Experiments

For experimental verification, a 100 nm thick gold backplate with 10 nm chrome adhesion layer was deposited onto a silicon substrate via electron beam evaporation(EBE), followed by a 120 nm (for 3 µm – 5 µm) / 200 nm (for 8 µm – 12 µm) thick silicon spacer by EBE, too. The 50 nm thick gold antenna layer is patterned by electron beam lithography (EBL) and metal lift-off. Figures 4(a) and 4(b) show the scanning electron microscope (SEM) images of the antenna layers of the fabricated MWIR absorber and LWIR absorber, respectively. The reflectance spectra of the fabricated samples were characterized from the wavelength of 2.5 µm to 25 µm using a Fourier transform infrared (FTIR) spectrometer (NICOLET 5700 from Thermo Electron) combined with an IR microscope (Continu-µm). The area of each nanoantenna array on top of the absorber is 150 µm × 150 µm, and the aperture size of the FTIR is 100 µm × 100 µm. The measured reflection spectra are normalized with respect to a gold mirror (Thorlabs, PF05-03-M01), while the transmission spectrum is considered to be zero. The FTIR is not installed with a polarizer, so the infrared beam incident on the sample is un-polarized. In this case, the measured spectral absorption should be the average of the absorption of TE polarized light and the absorption of TM polarized light, i.e., A_measured = (A_TE + A_TM)/2. Figures 4(c) and 4(d) plot the simulated spectral absorption of the TE polarized light (dotted line) and TM polarized light (dash line). It is seen that the spectral absorption of the TE polarized light is almost zero (A_TE = 0). Thus the measured spectral absorption should be half of the spectral absorption of TM polarized light, i.e., A_measured = A_TM/2). We then plot the measured spectral absorption times 2 using solid red lines in Fig. 4(c) and (d) and compare them with the simulated spectral absorption of the TM polarized light. In Fig. 4(c), the measured spectral absorption well reproduces the simulated spectral absorption. The measured average absorption in the target band for the two fabricated metasurfaces is 0.821 and 0.801, respectively. The minor discrepancy is attributed to the fact that the infrared beam from the FTIR is focused onto the sample by a reflective objective (Spectra-Tech Reflachromat 15x, NA = 0.58). Thus the absorber is not excited a normally incident plane wave as assumed in the simulation. Another possible reason is that the fabrication error in the nanostrips size during the experiment slightly broadens the absorption band.

 

Fig. 4. The SEM images of the fabricated (a) MWIR absorber, and (b) LWIR absorber that are inversely designed by the GA program. The measured and simulated absorption spectra of (a) MWIR absorber in 3 µm – 5 µm, and (d) LWIR absorber in 8 µm – 12 µm.

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To find out the appropriate values of the antenna thickness h₁ and spacer thickness h₂, we studied the average spectral absorption coefficient in 3 µm – 5 µm band (MWIR absorber) and 8 µm – 12 µm (LWIR absorber) as a function of h₁ and h₂, and the results are shown in Figs. 5(a) and 5(b). It is seen that the average absorption coefficients change rapidly as a function of h₂ but are less sensitive to h₁. To keep the electron beam lithography and subsequent metal lift-off process convenient and maintain high average absorption coefficients, we chose h₁ = 50 nm and h₂ = 120 nm for the MWIR absorber, and h₁ = 50 nm and h₂ = 200 nm for the LWIR absorber to conduct the nanofabrication. Note that if both the MWIR absorber and the LWIR absorber are built into the same focal plane array for dual-band operation, one can choose h₁ = 50 nm and h₂ = 150 nm to keep a same thickness h₂ of the spacer, as labeled by the white filled circles in Figs. 5(a) and 5(b).

 

Fig. 5. The average spectral absorption coefficient of (a) MWIR absorber in 3 µm – 5 µm and (b) LWIR absorber in 8 µm – 12 µm, as a function of the thicknesses of the antenna layer and the spacer. The spectral absorption of (c) the MWIR absorber and (d) the LWIR absorber as a function of the incident angle. The average absorption coefficient of the TM mode and the polarization extinction ratio in (e) the MWIR absorber in 3 µm – 5 µm and (f) the LWIR absorber in 8 µm – 12 µm, as a function of the incident angle.

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Figures 5(c) and 5(d) show the spectral absorption of the TM mode as a function of the incident angle θ for MWIR absorber and LWIR absorber, respectively. The white dash line, λ = P×(1+sin θ), represents the resonant wavelength of the Surface Plasmon Polariton (SPP) excited in the structure as a function of the incident angle θ. The excited SPPs will disrupt the spectral absorption resulted from LSPR, and the simulation results are consistent with the theory. The polarization extinction ratio is defined as the ratio of the average absorption coefficient of TM mode to that of TE mode in the 3 µm – 5 µm band for the MWIR absorber and 8 µm – 12 µm band for the LWIR absorber. In Figs. 5(e) and 5(f), the red line represents the average absorption coefficient of TM mode, and the blue line shows the polarization extinction ratio. The polarization extinction ratio is defined as the ratio of the average absorption coefficient of TM polarization to the average absorption coefficient of TE polarization in the target waveband. As the incident angle θ increases, both the average absorption coefficient of the TM mode and the polarization extinction ratio decrease. Within the range of θ < 30°, the MWIR absorber can maintain an average absorption coefficient of TM mode of over 61% and a polarization extinction ratio of over 16. While for LWIR absorber, the average absorption coefficient of TM maintains at above 68%, and the polarization extinction ratio is above 26.

In the above discussions, the pattern of the multi-sized nanostrip antennas is assumed to be periodic in the x-direction and infinitely long in the z-direction, which implies that the MIM absorbers are infinitely large. However, the designed absorbers will eventually be built into the pixels of the focal plane array detectors. In this scenario, the sizes of the absorbers are limited by the dimensions of the detector pixels in the focal plane array, and there is an air gap between two finite-sized MIM absorbers. For simplicity, we assume that the size of the absorber equals the size of the detector pixel. Figure 6(a) shows the 2D unit cell used by the FDTD solver to evaluate the influence of the finite absorber size and the air gap on the spectral absorption of the absorbers. The pixel spacing equals the size of the air gap, and the pixel pitch, or the period P of the unit cell, equals the size of the absorber plus the size of the air gap. The spectral absorption coefficient A is now calculated as A = 1 – R – T, because the transmission T is no longer zero due to the air gap. Note that in the 2D simulation, the whole structure is still assumed to be infinite in the z-direction. Although a full 3D simulation can account for the finite-size effect in both x-direction and z-direction, the required computational resource has exceeded our capability. Figures 6(b) to 6(g) plot the spectral absorption of the TM mode in both the MWIR absorber and the LWIR absorber as a function of the pixel spacing assuming the pixel pitch P of the detector are 7 µm, 14 µm, and 21 µm, respectively. It is seen that when the pixel pitch P is 7 µm, the spectral absorption rapidly deteriorates as the pixel spacing increases. When the pixel spacing is 2.8 µm, the average absorption coefficients of the MWIR absorber and LWIR absorber drop to 0.457 and 0.555, respectively. As the pixel size is increased to 21 µm, the line shape of the spectral absorption is more immune to the influence of the air gap. At a pixel spacing of 2.8 um, the average spectral absorption coefficients are as high as 0.612 and 0.648, respectively. This study indicates that for the current absorber design, large pixel size and small air gap size can help avoid the negative impact on the spectral absorption caused by the inter-pixel air gap.

 

Fig. 6. (a) Configuration of the 2D unit cell used to simulate the finite-sized absorber with air gaps added to the two sides of the absorber in the x-direction. (b) - (d) The spectral absorption of the TM mode in the MWIR absorber as a function of the pixel spacing assuming the pixel pitch P is 7 µm, 14 µm, and 21 µm, respectively. (e) - (g) The spectral absorption of the TM mode in the LWIR absorber as a function of the pixel spacing assuming the pixel pitch P is 7 µm, 14 µm, and 21 µm, respectively.

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So far, we have examined the optical polarization extinction ratio of the MIM absorber that is defined as the ratio of the average optical absorption of TM mode to that of TE mode. When the absorbers are integrated with the detector pixels, it is more relevant to examine the ratio of the temperature increase of the detector pixel caused by the TM polarized light to that of the TE polarized light, which is referred to as thermal polarization extinction ratio. This is because the temperature increase is directly related to the electrical response of the detector pixel. To elaborate on this concept, we consider a simple pixel structure in which a 20 nm thick layer of vanadium oxide is sandwiched between a 20 nm thick passivation layer of silicon nitride and a 250 nm thick support layer of silicon nitride, as shown in Fig. 7(a). The MIM absorber designed for 3-5 µm is placed above the passivation layer. The side length P of the unit cell (pixel pitch) is 12 um, and the air gap size g = 0.4 µm. The simulated spectral absorption of the absorber on the structure is presented in Fig. 7(b). The average absorption coefficients of TM mode and TE mode in the 3 - 5 µm band are 0.6974 and 0.0329, respectively. Thus the optical polarization extinction ratio is 21.20. We then conduct the thermal analysis at λ = 3.87 µm, which is one of the peak wavelengths in the absorption spectra. Figure 7(c) shows the steady-state distribution of the temperature increase ΔT across the structure that is excited by the TM polarized light with the injected power of 20 nW. For more details, the steady-state distribution of the temperature increase ΔT in the x-z plane (y = 0) and y-z plane (x = 0) are presented in Fig. 7(d), respectively. The steady-state distribution of the temperature increase ΔT_VO averaged along the z side of the vanadium oxide layer is drawn in Fig. 7(e). We can conclude that the whole structure on the bridge floor has a nearly uniform temperature increase of 83mK. Figure 7(f) plots the results of the transient-state study on the temperature increase ΔT_VO averaged across the whole vanadium oxide layer, assuming the structure is excited by the TE polarized light and TM polarized light, respectively. In the transient-state study, the incident optical power changes from 0 to 20 nW at t = 1 µs and keeps at 20 nW until it changes from 20 nW to 0 at t = 1.25 ms. The maximum values of ΔT_VO caused by the TM polarized light and TE polarized light are 73.95mK and 1.881mK, respectively. The corresponding thermal polarization extinction ratio is 39.31, which is 1.5 times of the optical polarization extinction ratio. This finding indicates that when the MIM absorber is built into the infrared detector pixel, the detector response can achieve higher polarization extinction ratios than the optical absorption of the absorber. Moreover, the achieved polarization extinction ratio should be high enough for polarization imaging detection [38].

 

Fig. 7. (a) Configuration of finite-sized detector pixel based on vanadium oxide bolometer with built-in MIM absorber for thermal analysis. (b) Simulated spectral absorption of the TE mode and TM mode, and the corresponding polarization extinction ratio of the MIM absorber on the finite-sized detector pixel. (c) The steady-state distribution of the temperature increase ΔT across the full structure. (d) The steady-state distribution of the temperature increase ΔT in the x-z plane (y = 0) and y-z plane (x = 0), respectively. (e) The steady-state distribution of the temperature increase ΔT_VO averaged along the z side of the vanadium oxide layer. (f) The transient-state temperature increase ΔT_VO averaged across the whole vanadium oxide layer, assuming the structure is excited by the TE polarized light and TM polarized light, respectively.

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5. Conclusion

We have developed an intelligent program based on the genetic algorithm to inversely design the metal-insulator-metal based metamaterial absorber with multi-sized nanostrip antennas as the top layer towards polarization selective and wideband high absorption in the mid-infrared spectral band. The program starts from a randomly generated pattern of the top antenna layer and iteratively optimize the pattern until the desired design target is reached. Specifically, the program found the optimized designs of two polarization selective MIM absorbers with wideband high absorption in the specified 3 - 5 µm (MWIR) band and 8 -12 µm (LWIR) band. For the MWIR absorber, the average absorption coefficient of the TM mode in the 3–5 µm band is 72.8%, and the polarization extinction ratio is 31 under normal incidence. When the incident angle is 30°, the average absorption coefficient and the polarization extinction ratio can still maintain at 61% and 16, respectively. For the LWIR absorber, the average absorption coefficient of the TM mode in the 8-12 µm band is 77.3%, and the polarization extinction ratio is 37 under normal incidence. When the incident angle is 30°, the average absorption coefficient and the polarization extinction ratio can still maintain at 68% and 26, respectively. The two computationally optimized designs were fabricated, and the measured spectral absorption under normal incidence agree well with the simulated results. Numerical studies reveal that when the designed absorbers are integrated with detector pixels, a large pixel size and a small air gap size can help avoid the negative impact on the spectral absorption caused by the finite pixel size and the air gap between the neighboring pixels. We emphasize that the developed program can also find optimized designs to cover other specified spectral bands. When integrated with the pixels of microbolometer based IR FPAs, the inversely designed absorbers can, therefore, replace the bandpass filters and micro-polarizers and enable compact multi-band IR polarimetric imagers.