*3.1. Principle*

Figure 3a shows the operating principle of MIM-PMAs for incident EM waves. Figure 3b–d shows the calculated electric and magnetic fields, and the power distribution of MIM-PMAs at the absorption wavelength, respectively [41].

**Figure 3.** (**a**) Schematic illustration of the operating principle of MIM-PMAs. E, H, and p represent the electric displacement vector, magnetic field, and current, respectively. Calculated results: (**b**) magnetic field; (**c**) electric field; and (**d**) power distribution. The color maps represents the amplitude of each distribution. (**b**–**d**) are reprinted from Reference [41] with the permission of AIP Publishing.

As shown in Figure 3a, a pair of anti-parallel oscillating currents is induced in both the bottom layer and the top micropatches, and significant magnetic resonance is produced. Dipole electric resonance is formed accordingly between the edge of the micropatches and the near bottom layer. LSPPs are induced by the incident light at the absorption wavelength. This principle is confirmed by the calculated electromagnetic field distribution, as shown in Figure 3b–d [41]. The electric displacement vectors in the bottom layer and the micropatches are opposite to each other, which generates a strong magnetic response [80] (Figure 3b). Strong electric dipole resonances are observed at the sides of the micropatches (Figure 3c). The reflectance can be completely cancelled in the far field by the interference of these two dipoles due to the π shift phase [65]. Strong absorption is thus attributed to these localized magnetic and electric dipole resonances, which provide sufficient time to consume light energy by the ohmic losses in the metals (Figure 3d).

## *3.2. Wavelength Selectivity*

Figure 4a,b shows the calculated and measured optical properties of MIM-PMAs in IR wavelengths [38]. Wavelength selective absorption is clearly obtained at 6 μm, which is a typical wavelength-selective absorption property of MIM-PMAs. The main absorption wavelength is always longer than the period of the micropatches because wavelengths smaller than the period are diffracted. Figures 4c [41] and 4d [81] show the calculated absorbance as a function of the wavelength and the micropatch size (w) in the near-IR wavelength region, as well as the measured relation between the micropatch size and the absorption wavelength in the IR wavelength region.

**Figure 4.** Calculated spectra for (**a**) absorption, reflection, and transmission; (**b**) Comparison of the measured and calculated absorption spectra; (**c**) Absorbance as a function of the wavelength and the micropatch size (w) in the near-IR wavelength region; (**d**) Relation between the micropatch size and the absorption wavelength in the IR wavelength region. (**<sup>a</sup>**,**b**) are adapted with permission from Reference [38]. © 2010 American Physical Society. (**c**) is reprinted from Reference [41] with the permission of AIP Publishing.

The absorption wavelength is almost proportional to the micropatch size in the near-IR wavelength region. In contrast, the relation between the micropatch size and the absorption wavelength is non-linear in the IR wavelength region, which is attributed to the loss of the middle dielectric layer [40]. Most oxides become lossy in the vicinity of 10 μm, where no absorption occurs, and this causes the non-linearity between the micropatch size and the absorption wavelength, as shown in Figure 4d. This is an important point for the design of MIM-PMAs for use at IR wavelengths. The thickness of the middle dielectric layer has less impact on the absorbance and the absorption wavelength, and can thus be optimized for the operating wavelength [41].

#### *3.3. Incidence Angle Dependence*

Figure 5a,b shows the calculated incident angle dependence of the absorbance as a function of the wavelength for the transverse-electric (TE) and transverse-magnetic (TM) modes, respectively [22]. The calculated model is for an MIM-PMA with 2D circle-shaped micropatches.

Figure 5 shows that the absorption can be realized at almost the same wavelength for a wide range of incidence angle up to approximately 70◦ for both TE and TM modes. This property is attributed to the strong LSPPs, as shown in Figure 3. The incident angle independence is an important advantage for device applications such as solar cells, IR image sensors, and biological sensors.

**Figure 5.** Calculated absorption for the (**a**) transverse-electric (TE) and (**b**) transverse-magnetic (TM) modes. Figures are adapted with permission from Reference [22]. © 2010 American Chemical Society.

## *3.4. Polarization Dependence*

In this section, the coordinate system is set as shown in Figure 3c,d. When the electric field of the incident light is in the *x* or *y* direction, the absorption wavelength is defined by the side-length of the micropatches in the *x* or *y* direction, respectively [39]. Each side-length of the square-shaped micropatches in the *x* and *y* direction is the same. Thus, the absorption wavelength is also the same for each polarization. MIM-PMAs with this configuration are polarization insensitive.

Different side lengths, such as ellipse [47] or asymmetric-cross-shaped [52] micropatches, produce dual band absorption, as discussed in the next section. The 1D periodic configuration shown in Figure 3b also produces two absorption modes. However, when one side-length is much longer than the other, the other absorbance is outside the operation wavelength region, which results in polarization-selective absorbers. Polarization-selective absorbers can be applied to IR polarimetric imaging [82,83] to enhance object recognition ability such as distinct human trace in a natural environment and human facial recognition [84].

#### *3.5. Inductor-capacitor (LC) Circuit Model*

The operation principle of MIM-PMAs is sometimes explained using the LC equivalent circuit model. This may be due to the influence of CA absorbers mentioned in the introduction section. Figure 6 shows a schematic illustration of the LC equivalent circuit for MIM-PMAs [40,63]. Two models are considered, with or without the loss of the insulator layer. The frequency that gives a total impedance of zero is the absorption frequency.

**Figure 6.** Schematic illustration of the LC equivalent circuit for MIM-PMAs. Figures were adapted with permission from Reference [40]. © 2013 Optical Society of America.

#### **4. Multi-Band and Broadband Operation**

The strategies of multi-band and broadband absorption are classified into three groups: asymmetrically-shaped [47,52,85–89] or multi-size [42,65,66,90–94] micropatches, multi-layers of MIM structure [95–100], and embedded in dielectric materials [57,101,102]. The first two are based on multi-resonance that produces multi-mode absorption. Each absorption mode becomes close, which results in broadband absorption [103]. Figure 7a–d shows MIM-PMAs with two-types of asymmetrically shaped micropatches, such as cross [52] and elliptical shapes [47], for dual-band operation. This dual-band absorption is designed in consideration of the polarization dependence for the two orthogonal directions.

**Figure 7.** *Cont.*

**Figure 7.** Schematic illustration of an MIM-PMA with asymmetric cross-shaped micropatches for dual-band operation. (**a**) Electric field distribution for modes I and II; and (**b**) the corresponding reflectance spectrum. (**c**) Schematic illustration and (**d**) SEM image of an MIM-PMA with an elliptical nanodisk array. Calculated absorbance for (**e**) TE and (**f**) TM modes. (**<sup>a</sup>**,**b**) are adapted with permission from Reference [52]. © 2012 American Chemical Society. (**<sup>c</sup>**–**f**) are adapted with permission from Reference [47]. © 2011 Optical Society of America.

Figure 8a,b shows oblique and the cross-sectional schematic illustrations of an MIM-PMA with 1D stripe-shaped multi-size-micropatches (w1 to w4), respectively [65]. Figure 8c,d shows a schematic illustration and magnetic field distribution of an MIM-PMA with 2D multi-size micropatches and the corresponding absorption spectrum, respectively [66]. The absorption spectrum is the summation of the absorption wavelengths generated by each micropatch resonator. Figure 8d shows that the distance between each resonant wavelength becomes close, which results in broadband absorption.

Figure 9a,b shows a schematic illustration of a multi-layer MIM-PMA and the calculated absorption spectrum, respectively [95]. Each MIM layer produces multi-plasmonic-resonances at different wavelengths and each resonance is coupled, so that broadband absorption occurs [103].

Broadband absorption is also achieved by MIM-PMAs with single or multi-layers embedded in lossy dielectrics such as amorphous Si [57] and SiN [101]. The resonances of MIM-PMAs can be broadened by lossy materials, which results in broad absorption. However, these structures increase the thickness and volume of the absorbers, and cause difficulties for fabrication. Care should be taken in applying them to practical devices by comparison with other convenient structures such as simple multi-flat-layer structures [77–79] or gold black [104,105] in terms of their thickness, ease of fabrication, and cost.

**Figure 8.** Schematic illustrations of MIM-PMAs with multi-size micropatches having (**<sup>a</sup>**,**b**) 1D and (**c**) 2D periodic configurations. (**d**) Calculated and measured absorption spectra for the 2D periodic configuration. (**<sup>a</sup>**,**b**) are reprinted from Reference [65] with the permission of AIP Publishing. (**<sup>c</sup>**,**d**) are adapted with permission from Reference [66]. © 2012 Optical Society of America.

**Figure 9.** (**a**) Schematic illustration of a multi-layer MIM-PMA and (**b**) the calculated absorption spectrum. Figures are adapted with permission from Reference [95]. © 2012 Optical Society of America.

#### **5. Advanced Structures and Applications**

In this section, we briefly outline the advanced MIM-PMAs structures and applications other than absorbers to clarify the future research of MIM-PMAs. There has been growing interest in mainly three categories of advanced MIM-PMAs: flexible devices, the combination of graphene and other 2D materials, and metalenses.

One of the advanced structures is the flexible MIM-PMA [86,106,107], as shown in Figure 10 [86]. Flexible substrates such as Kapton film [86], polyethylene terephthalate (PET) [106] or polydimethylsiloxane (PDMS) [107] have enabled flexible MIM structures. MIM-PMAs coated on such flexible substrates can thus realize flexible and stretchable devices such as flexible solar cells, health care systems for the human body, and the cloaking of non-flat objects [108].

**Figure 10.** (**a**) Schematic illustration and (**b**) SEM image of a flexible MIM-PMA. Figures are adapted with permission from Reference [86]. © 2011 American Chemical Society.

The combination of graphene [109] and other 2D atomic layer materials [110] such as MoS2 and WSe2 with MIM-PMAs [55,81,111–115] is also drawing significant interest because these 2D atomic layer materials can strongly interact with plasmonic resonance [116]. Figure 11 shows a schematic illustration of graphene coated on an MIM-PMA (GMIM-PMA).

**Figure 11.** Schematic illustration of a graphene-coated MIM-PMA.

MIM-PMAs serve as a platform to enhance graphene absorption and realize high-performance graphene-based photodetectors [81,111,112,114]. The Fermi level of graphene can be electrically tuned according to the applied voltage; therefore, the absorption wavelength [117], reflection angle [118], and phase [119,120] can be electrically tuned by the applied voltage for graphene.

Metalenses are a new type of flat lens based on geometrical phase control [121–123]. MIM-PMAs are considered as an array of optical resonators that can introduce a desired spatial profile of the optical phase and consequently mold the wavefront [123]. Figure 12 shows a schematic illustration of a metalens or reflector using MIM-PMAs [123]. The MIM-PMA structures control the reflection and their phase by phase gradient surface structures with different sized micropatches on the planar surface. Strong plasmonic resonance can change the phase of the reflection and thereby realize geometrical control of the phase. As a result, a flat metalens can be realized.

**Figure 12.** (**a**) Schematic illustration of a flat metalens using MIM-PMAs. (**b**) Schematic illustration of the unit cell of a reflector array lens. (**c**) SEM image of the metalens surface. Figures are adapted with permission from Reference [123]. © 2016 Optical Society of America.

There are other rapidly growing research fields of MIM-PMAs, such as the non-linear response of second [124,125] and third [126] harmonic generation, and reflection control [127]. As discussed in this section, although MIM-PMAs are simple structures, they have significant potential for novel physics and applications.

## **6. Conclusions**

MIM-PMAs have been reviewed here in terms of their structures, basic principles of absorption, materials used, absorption properties of incident angle and polarization dependence, and strategies of multiband or broadband operation to clarify the design strategies for visible and IR wavelengths. The same principles can be applied for a wide range of wavelength regions such as the ultraviolet [128], terahertz [129–132], and microwave [133–135] regions.

A single MIM structure can be considered as a single optical antenna with strong LSPPs. Therefore, MIM structures are free from the restriction of periodicity and beyond the diffraction limit, making them able to realize strong absorption and geometrical tunability of the absorption wavelength with a much thinner and smaller absorber volume than conventional EM absorbers. Such controllability opens up a new stage of EM absorber research and many novel applications are expected.

In the future research of MIM-PMAs, flexible structures are also important to expand applications, such as health care devices for human sensing. The combination of new materials such as graphene and other 2D atomic materials with MIM-PMAs gives rise to the electrical tunability of the absorption wavelength, the phase, and the reflection angle because their optical constant can be tuned according to the applied voltage. MIM-PMAs can control other wavelengths than the absorption wavelength used. Thus, MIM-PMAs can be used for flat metalenses that can go beyond the diffraction limit.

We hope that this review paper will contribute to the development of advanced MM-PMAs and the expansion of their fields of application.

**Conflicts of Interest:** The authors declare no conflict of interest.
