2.1.

Effect of the Micropatch Shape

Figure 1 shows schematic illustrations of the structure investigated in this study. The micropatches are arrayed and connected to the bottom plate with posts. This structure is referred to as a mushroom metamaterial.^26,27 In this work, all of the components were assumed to be made of Au. The dielectric constant of Au used in our calculations was taken from Ref. 28. The minimum thickness of all components is approximately twice the skin depth to prevent light penetration and achieve ultrathin absorbers with low-thermal mass. The structural parameters of the period, the width (diameter) and thickness of the micropatch, the thickness of the bottom plate, and the width (diameter) and height of the posts are defined as $p$, $w_{\mathrm{m}}$; $t_{\mathrm{m}}$, $t_{\mathrm{b}}$; $w_{\mathrm{p}}$; and $h_{\mathrm{p}}$, respectively. The gap between the micropatches and the bottom plate is equal to $h_{\mathrm{p}}$. The thickness $t_{\mathrm{b}}$ has no impact on the absorption, as long as it is sufficiently thick to reflect incident IR radiation. Thus, $t_{\mathrm{b}}$ is considered to be at least $>50\mathrm{nm}$ in the IR wavelength region for practical applications²⁹ and was set as a semi-infinite thickness for the simulation. The parameters $t_{\mathrm{m}}$, $w_{\mathrm{p}}$, and $h_{\mathrm{p}}$ were fixed at 50, 200, and 150 nm, respectively. The incident angle is set to normal incidence for the fundamental evaluation of MPMAs conducted in this study. The polarization direction used is defined as that parallel to the basic lattice vector of the square lattice structure, which corresponds to the $x$- and $y$-directions, as shown in Fig. 1(b). The results obtained represent the averaged total absorption for all polarizations due to the symmetry of the MPMAs.

Fig. 1

Schematic illustrations of the mushroom plasmonic metamaterial absorber (MPMA) proposed in this study: (a) surface view and (b) cross-section of one unit cell with the incident light and the electric field directions are shown.

We first investigated the absorption properties of a circular-shaped micropatch using rigorous coupled-wave analysis (RCWA). The period $p$ was fixed at $4.0\mu \mathrm{m}$ and $w_{\mathrm{m}}$ was varied. Figures 2(a) and 2(b) show the absorption for the MPMAs with $w_{\mathrm{m}}$ at 2.0, 2.5, 3.0, and $3.5\mu \mathrm{m}$, and the absorption for $w_{\mathrm{m}}$ from 1.0 to $4.0\mu \mathrm{m}$ as a function of the wavelength. Figure 2 indicates that sufficient absorption of over 90% was obtained for the MPMAs with most of the $w_{\mathrm{m}}$ values, and the absorption wavelength could be controlled primarily by $w_{\mathrm{m}}$, regardless of $p$. The absorption wavelength is almost proportional to $w_{\mathrm{m}}$; however, a forbidden band where the absorption is suppressed appears for some $w_{\mathrm{m}}$ values, such as 1.8, 2.5, 2.8, and $3.2\mu \mathrm{m}$. The full width at half maximum (FWHM) also increases with $w_{\mathrm{m}}$. As the absorption wavelength approaches the period, the FWHM is improved due to the reduction of the gap resonance between the micropatches.

Fig. 2

Calculated absorption spectra for the MPMA with circular-shaped micropatches. (a) Spectra for $w_{\mathrm{m}}=2.0$, 2.5, 3.0, and $3.5\mu \mathrm{m}$, and (b) spectra as a function of wavelength and $w_{\mathrm{m}}$. The colormap on the right side defines the absorption scale.

The absorption properties of square-shaped micropatches were also investigated by RCWA; a schematic illustration of an MPMA with square-shaped micropatches is provided in Fig. 3. As with the circular-shaped micropatch, the period $p$ was again fixed at $4.0\mu \mathrm{m}$ and $w_{\mathrm{m}}$ was varied. Figure 4 shows the wavelength absorption for this MPMA for various values of $w_{\mathrm{m}}$ from 1.0 to $4.0\mu \mathrm{m}$. Sufficient absorption of over 90% was obtained for the MPMA with all of the $w_{\mathrm{m}}$ values, and the absorption wavelength could be controlled according to $w_{\mathrm{m}}$, regardless of $p$. The absorption wavelength is almost proportional to $w_{\mathrm{m}}$, and a uniform absorption peak is maintained over a wide range of MWIR and LWIR wavelengths compared with that for the MPMA with circular-shaped micropatches. Each circular-shaped micropatch forms an unequal gap with the adjacent micropatches, which produces broader resonance. In contrast, the square-shaped micropatches maintain a parallel gap with the adjacent micropatches, which produces narrower resonance. When the absorption wavelength is smaller than $p$, diffraction starts to occur for both the circular- and square-shaped micropatches. Therefore, the absorption abruptly decreases for wavelengths $<4\mu \mathrm{m}$.

Fig. 3

Schematic illustration of an MPMA with square-shaped micropatches. (a) Surface view and (b) cross-section of one unit cell with the incident light and the electric field directions are shown.

Fig. 4

Calculated absorption spectra for the MPMA with square-shaped micropatches. (a) Spectra for $w_{\mathrm{m}}=2.0$, 2.5, 3.0, and $3.5\mu \mathrm{m}$, and (b) spectra as a function of wavelength and $w_{\mathrm{m}}$.

The time-averaged electromagnetic field amplitude distribution was calculated at the resonance using the 2-D finite-difference time-domain (FDTD) method. Here, $w_{\mathrm{m}}$ was fixed at $2.0\mu \mathrm{m}$, whereas the values of the other parameters were the same as in the RCWA calculation. Figures 5(a)–5(c) show the normalized amplitude of the electric field and the magnetic field distribution, and the power, respectively. $X$, $Y$, and $Z$ are defined as parallel to $w_{\mathrm{m}}$, vertical to the $x$-direction, and parallel to $h_{\mathrm{p}}$, respectively. Figure 5 clearly demonstrates that plasmonic resonance occurs only at the perimeter of the micropatch. These results confirm that localized plasmonic resonance rather than propagating plasmonic resonance occurs in the MPMAs. The absorption wavelength is defined only by the size of the micropatch beyond the pattern period due to this strong confinement of such localized plasmonic resonance, and thus contributes to a smaller pixel size.

Fig. 5

Simulated time-averaged normalized amplitude of the (a) electric field distribution in the $x$-direction, (b) magnetic field distribution in the $y$-direction, and (c) power for a unit cell.

2.2.

Effect of the Post Height

The effect of $h_{\mathrm{p}}$ was investigated for an MPMA with square-shaped micropatches. Figure 6 shows the wavelength absorption for the MPMA as a function of $h_{\mathrm{p}}$ from 0 to 500 nm with a fixed $w_{\mathrm{m}}$ and $p$ of 2.0 and $4.0\mu \mathrm{m}$, respectively. Sufficient absorption of over 90% was obtained for $h_{\mathrm{p}}$ ranging from $\sim 80$ to 200 nm, where the shift of the absorption wavelength was small. This result indicates that the narrow-gap resonance between the micropatches and the bottom plate is especially important to obtain sufficient absorption.

Fig. 6

Absorption spectrum for an MPMA with square-shaped micropatches as a function of the post height ($h_{\mathrm{p}}$).

2.3.

Effect of the Post Width

The effect of $w_{\mathrm{p}}$ was also investigated for an MPMA with square-shaped micropatches. Figure 7 shows the wavelength absorption for the MPMA as a function of $w_{\mathrm{p}}$ from 100 nm to $1.0\mu \mathrm{m}$ with a fixed $w_{\mathrm{m}}$ and $p$ of 2.0 and $4.0\mu \mathrm{m}$, respectively. Sufficient absorption of over 90% was obtained, and a single absorption mode was achieved over a wide range of $w_{\mathrm{p}}$ values from 100 nm to $1.0\mu \mathrm{m}$, which is half that of $w_{\mathrm{m}}$ at $2.0\mu \mathrm{m}$. This result is attributed to the strongly localized plasmonic resonance at the edge of the micropatches. The post width has less impact on the absorption properties, and single-mode operation can be maintained, in contrast to the 2-D PLA with Si-post structures, which produces a gap resonant mode inside the Si post.

Fig. 7

Absorption spectrum for an MPMA as a function of the post width ($w_{\mathrm{p}}$).