Design and analysis of quad-band polarization-insensitive infrared perfect metamaterial absorber with a wide-incident angle

doi:10.21203/rs.3.rs-2612091/v1

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Design and analysis of quad-band polarization-insensitive infrared perfect metamaterial absorber with a wide-incident angle

https://doi.org/10.21203/rs.3.rs-2612091/v1

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published 21 Sep, 2023

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A novel quad-band infrared perfect metamaterial absorber (QPMA) is proposed and numerically investigated. The structure of the QPMA is composed of coaxial multi-layer dielectric (SiO₂) disks of circular shape with different diameters where each disk is surrounded by a gold ring. All disks are placed on a SiO₂ dielectric spacer and an impermeable gold ground layer. Simulation results reveal that the proposed absorber has four absorption peaks around wavelengths of 1064 nm, 1550 nm, 2080 nm, and 3000 nm. Additionally, the QPMA structure enjoys a good absorption performance for a wide range of incident angles for both TE and TM waves. It achieves absorption greater than 85% at incident angles up to 40^o at 1064 nm, and absorption greater than 90% for the other bands at incident angles up to 50^o. Moreover, due to the symmetrical shape of the structure, the absorption is insensitive to wave polarization changes. The structure under investigation will help in laser stealth, infrared photodetection, and medical applications due to perfect absorption performance and multi-band capability.

metamaterial

plasmonic waves

absorber

laser stealth

quad-band absorption

Metamaterials are artificial materials that are composed of periodic sub-wavelength structures (Pendry 2000; Islam et al. 2016; Wang et al. 2022). Owing to their unique properties, they attracted extensive interest in many applications such as polarization conversion, cloaking, and absorbance (Xiao et al. 2022; Cheng et al. 2019; Zhao et al. 2018a; Zhao et al. 2018b). One of the most important applications is the perfect metamaterial absorber (PMA) with near-unity absorption, which is proposed for the first time by Landy et al. (2008) to operate in the microwave band. Using the appropriate design technique, the intrinsic loss can be controlled, and several types of perfect metamaterial absorbent can be produced at specific wavelengths ranging from the microwave band to the visible and infrared bands (Chai et al. 2022; Khatami et al. 2022; Shen et al. 2011; Bai et al. 2015; Pan et al. 2021). For the infrared and visible bands, the perfect absorption of the PMA is mainly due to the excitation of localized surface plasmon resonance modes at normal/oblique incidents of light waves (Zhang et al. 2011; Liu and Lan 2017; Lei et al. 2018; Cao et al. 2021). When the light waves interact with the metallic nanoparticles, the collective electron oscillations excite the localized surface plasmon resonance (Pu et al. 2011). Based on the requirements of the desired application, the PMA can be classified as PMA with broadband, single-band, and multiband in terms of the bandwidth of the maximum absorption (Dubey et al. 2022; Liao et al. 2017). Applications such as energy harvesting and photovoltaic require PMAs with broadband absorption capability (Che et al. 2018; Bendelala et al. 2018; Ehsanikachosang et al. 2022; Lakshmiprabha et al. 2022) while sensing and photo-detection applications require PMAs with ultra-narrow single or multi-band absorption capability (Korkmaz et al. 2022; Liao et al. 2022; Shi et al. 2020). The typical metamaterial absorber is a three-part structure called metal-dielectric-metal (MDM); a dielectric substrate part sandwiched between the bottom part which is bulk metal acts as a back reflector and a top geometrical metal pattern part. In addition, many other PMAs are based on dielectric-dielectric-metal (Liao et al. 2017) or all-metal structures (Zhao et al. 2018b; Zhang et al. 2021).

In the quest for visible and infrared multi-band PMA absorbers, several designs have been investigated numerically or experimentally. Bai et al. (2015) proposed a polarization-insensitive dual-band infrared PMA with a wide-incident-angle. The PMA was made of double L-shaped gold pieces on a SiC dielectric spacer and gold ground layer. In (Liao et al. 2022), a dual-band guided-laser absorber at wavelengths of 1064 nm and 1550 nm was investigated. This absorber consists of periodic silicon squares on a silicon film and a nickel layer (i.e., dielectric-dielectric-metal structure). In (Shi et al. 2020), a PMA was proposed to make ultra-narrow triple absorption bands in the near-infrared for sensing applications. This PMA is composed of a periodic arrangement of metallic nanodisks etched with regular prismatic holes on the dielectric-metal bi-layer films. Based on a periodic array of silicon nanorod resonator and metal substrate, a quad-band perfect absorber for visible light is investigated in (Cao and Cheng 2018). In this design, the proposed absorber achieved absorbance greater than 90% at wavelengths around 0.69 µm, 0.657 µm, 0.622 µm, and 0.594 µm. Zhang et al. (2021) introduced a quad-band perfect absorber that is based on an all-metal nanostructure metasurface for refractive index applications in the infrared band. Based on numerical analysis, the proposed absorber achieved absorbance greater than 99% at wavelengths around 3.48 µm, 1.25 µm, 1 µm, and 0.87 µm. In (Korkmaz et al. 2022), the authors presented an experimental study on quad-band PMA for biosensing applications. The design is based on an MDM structure where MgF₂ dielectric spacer was inserted between an optically thick gold layer and a patterned gold shape. The four peak absorption of the proposed design covers a spectral range from 1.8 µm to 10 µm.

In this work, we introduce a novel design of a quad-band infrared perfect metamaterial absorber (QPMA). The proposed absorber achieves quad-band perfect absorption around specific wavelengths. These wavelengths are tuned to be corresponding to Nd: YAG laser (1064 nm), the most important laser wavelength in communication systems (1550 nm), Ho: YAG laser (2080 nm), and mid-infrared laser for medical applications (3000 nm). Thus, the proposed absorber structure is useful for different practical applications such as laser stealth, photodetection, and medical applications. The design is based on an improved MDM structure where its top pattern consists of coaxial multi-layer dielectric (SiO2) disks of circular shape with different diameters. Each disc is surrounded by a gold (Au) metal ring. Each Au ring is responsible, effectively, for one resonance wavelength and is optimized with its neighbor to achieve perfect absorption at the desired wavelength. Each resonance of the QPMA structure is a good consequence of the related geometrical parameters (mainly the radius and height of the Au ring), therefore, good tunability for each resonant wavelength can be achieved. Owing to the simplicity and symmetry of the proposed structure, it enjoys several benefits, such as polarization insensitivity and coverage of wide-incident angles.

The rest of the paper is organized as follows. Section 2 introduces the proposed structure in which the shape, dimensions, and materials are explained. The effect of incident angles and the polarization angles in both TE and TM are presented in section 3. Finally, we conclude the obtained results in section 4.

The proposed QPMA structure is consisting of periodic cells. The schematic of the unit cell structure is illustrated in Fig. 1 (a) and (b); each unit cell is composed of a coaxial multilayer of SiO2 dielectric disks each disk surrounded by an Au metal ring. The dielectric disks are labeled, from bottom to top, by D1, D2, D3, and D4. On the other hand, the metal rings are labeled, from bottom to top, by M1, M2, M3, and M4. The structure is built on a substrate of SiO2. This substrate is built over a continuous layer of Au which acts as a back reflector. The unit cell period along the x and y directions equals ${P}$. The Au back reflector has a thickness ${T}{m}$ while the SiO2 substrate layer has a thickness ${T}{d}$. The radii of the four gold rings from bottom to top are ${R}{g}1$, ${R}{g}2$, ${R}{g}3$, and ${R}{g}4$, respectively, while their thicknesses are labeled ${T}{r}1$, ${T}{r}2$, ${T}{r}3$, and ${T}{r}4$. The golden rings have widths of ${W}{g}1$, ${W}{g}2$, ${W}{g}3$, and ${W}{g}4$. The proposed structure ends with a golden disk with a diameter ${D}$ and thickness ${T}{r}5$.

We numerically study the electromagnetic behavior of the proposed QPMA by frequency domain solver in the commercial CST Microwave Studio which is based on the finite element method. Here, the complex refractive index data of Au metal is extracted from (Ciesielski et al. 2018). Furthermore, the refractive index of the SiO₂ dielectric layers is assumed to be 1.45.

The optimized parameters of the proposed structure used in the simulation are as follows (units in nm): ${P}=$634, ${T}{m}=$100, ${T}{d}=$50, ${T}{r}1=$65, ${T}{r}2=$65, ${T}{r}1=$41, ${T}{r}4=$22, ${T}{r}5=$30, ${R}{g}1=$264, ${W}{g}1=$61, ${R}{g}2=$163, ${W}{g}2=$25, ${R}{g}3=$101, ${W}{g}3=$20, ${R}{g}4=$62, ${W}{g}3=$24, ${D}=$76.

Due to the periodicity of the structure, we simulate only one unit cell. Therefore, the boundary conditions in the x and y directions are set as a unit cell while the perfectly matched layer boundary condition is used in the positive z-direction.

The structure under investigation has a symmetrical behavior in the x and y-directions. As indicated in Fig. 1(c), the transverse electric (TE) or transverse magnetic (TM) incident waves are propagated in the negative z-direction. The TE/TM wave is incident on the structure in the x-z incidence plane with an incident angle θ relative to the z-direction. The polarization angle, φ, (i.e., azimuthal angle) is defined as the angle between the projection of the incident light wave on the x-y plane and the x-direction. The spectral absorptivity ${A}\left({\omega }\right)$ can be calculated by ${A}\left({\omega }\right)=1-{R}\left({\omega }\right)-{T}\left({\omega }\right)$, where ${R}\left({\omega }\right)={\left|{{S}}_{11}\right|}^{2}$ and ${T}\left({\omega }\right)={\left|{{S}}_{21}\right|}^{2}$ are the spectral reflection and transmission, respectively. ${{S}}_{11}$ and ${{S}}_{21}$ denotes the S-parameters. Since the thickness of the Au back reflector is much higher than its skin depth in the infrared, the spectral transmission can be neglected, i.e. ${T}\left({\omega }\right)$ = 0.

Figure 1(d) displays the absorption spectra in the band from 0.9 µm to 4 µm for normal incidence electromagnetic waves. It can be noted that under the optimized structure parameters, which were introduced in the previous section, we obtained four maximum absorption peaks around the wavelengths of 1064 nm, 1550 nm, 2080 nm, and 3000 nm with absorption values of 99.9%, 99.9%, 99.1%, and 99.9%, respectively. These values of absorptivity indicate perfect absorption at the four wavelengths.

To explain the nature of these four absorption peaks, absorption spectra are simulated for the sequential steps of construction growth direction (i.e., the effect of adding each Au ring to the structure). This process is depicted in Fig. 2. Figure 2(a) introduces the absorption spectra for the first Au ring, which has a radius of $Rg1$. It can be noted that the structure with this ring has a single absorption peak at a wavelength of 2965.5 nm with an absorptivity of 97.3%. As shown in Fig. 2(b), after adding the second ring, which has a radius of $Rg2$, another absorption peak appears at a wavelength of 1982 nm with an absorptivity of 94%. Also, it can be noted that the addition of the second ring causes a red shift to the first peak from 2965.5 nm to 3000 nm and enhance the value of its absorption to be equal to 99.9%. Figure 2(c) illustrates the effect of adding the third ring, which has a radius of $Rg2$, on the absorption spectra. Another absorption peak appears at a wavelength of 1428 nm with an absorptivity of 90.85%. Also, the addition of the third ring leads to a red shift to the second peak to a wavelength around 2080 nm with enhanced absorptivity to become 99.1% while it does not affect the first peak. Figure 2(d) shows the effect of adding the fourth ring to the structure. This addition results in the appearance of the fourth peak at the wavelength of 1010 nm with an absorptivity of 96.5% and a red shift to the third peak to a wavelength around 1550 nm with an absorptivity of 99.9% while it does not affect the first and second peaks. Finally, to adjust the fourth peak to be at a wavelength of 1064 nm with absorptivity of 99.9%, a golden disk of radius $Rg5$ is added on the top of the fourth ring as shown in Fig. 2(e). From the description of Fig. 2, we can conclude that adding a new ring adds a new resonance and adjust the previous resonance to a desired wavelength with perfect absorbability.

For a deep explanation of the concept of perfect absorption at the designed four wavelengths, we introduce in Fig. 3 the real and imaginary components of the relative input impedance which are retrieved from the S-parameters by using the following equation

$$Z\left(\omega \right)=\sqrt{\frac{{\left(1+{S}_{11}\right)}^{2}-{S}_{21}^{2}}{{\left(1-{S}_{11}\right)}^{2}-{S}_{21}^{2}}}$$

It is clear from this figure, the real component of the relative impedance at the four resonances is approximately equal to one (i.e., Re (z) ≈ 1), while the imaginary component is near zero (i.e., Im (z) ≈ 0). These results indicate that the impedance of the QPMA is in a good matching with the free space characteristic impedance (i.e., ${Z}_{0}=120\pi$ Ω) at the four resonance wavelengths, hence, no reflection occurs and perfect absorption is achieved.

To investigate the concept of absorption of QPMA, we introduce the absolute value of the electric field, $\left|E\right|$, and the magnetic field, $\left|H\right|$, distributions of the absorber, at (a) ${\lambda }_{1}$=3000 nm, (b) ${\lambda }_{2}$=2080 nm, (c) ${\lambda }_{3}$=1550 nm, and (d) ${\lambda }_{4}$=1064 nm, in Figs. 4 and 5, respectively. Figure 4 shows the y–z plane cross-section view for $\left|E\right|$ field distribution while Fig. 5 shows x–z plane cross-section view for $\left|H\right|$ field distribution. It is clear from Fig. 4(a) and Fig. 5(a), corresponding to the wavelength of 3000 nm, that $\left|E\right|$ field and $\left|H\right|$ field distributions are mainly concentrated inside the first dielectric disk, D1, between the rings M1 and M2, with some little distribution inside the substrate. The distribution of the electric field between these rings, M1 and M2, indicates an equivalent capacitance while the magnetic distribution indicates an inductance behavior of this region. The interaction between the capacitance and inductance results in resonance at the first band i.e., 3000 nm. This behavior confirms the result shown in Fig. 2(b) in which the resonance at 3000 nm comes mainly due to the ring M1 with fine tuning from ring M2. Similarly, at a wavelength of 2080 nm, it can be noted from Fig. 4(b) and Fig. 5(b) that $\left|E\right|$ field and $\left|H\right|$ field distributions are mainly concentrated at the dielectric D2 between the ring M2 and M3, which results in a peak absorption at that frequency. Also, the same behavior carries out between rings M3 and M4 at the wavelength of 1550 nm as indicated in Fig. 4(c) and Fig. 5(c). Finally, for the peak absorption at a wavelength of 1064 nm, Fig. 4(d) and Fig. 5(d) shows the $\left|E\right|$ field and $\left|H\right|$ field distributions are mainly concentrated inside the top dielectric disk, D4, between the ring M4 and the top metal disk.

In the following subsections, the effects of the variation in polarization angle and incident angle on the performance of the proposed QPMA structure are studied.

3.1. Effect of polarization angle variation

The polarization insensitivity of the proposed QPMA for TE and TM modes is studied. Either TE or TM waves are incident vertically on the proposed absorber surface. The effect of varying the polarization angle of the TE or TM waves on the absorption of the proposed absorber is presented in Fig. 6. The obtained results reveal that when the polarization angle varies, the peaks of the absorption for the quad bands remain unchanged for both TE and TM modes. Thus, the proposed QPMA is insensitive to polarization angles.

3.2. Effect of incident angle variation

In practical applications, the effect of large-angle absorption plays a significant role in designating the performance of the absorber. In this subsection, we address the effect of incident angle for both TE and TM modes. Owing to the high sensitivity of the proposed absorber at 1064 nm wavelength to the variation of incident angle, as observed from simulation results, the results of this effect for TE and TM modes are introduced in Fig. 7(a) and (b) for 1064 nm wavelength, only, while Fig. 8(a) and (b) present the counterpart results for the remaining triple bands.

At θ = 0 (i.e., normal incidence), due to the symmetrical geometry of the proposed absorber, it can be noted that for both TE and TM, the proposed absorber can trap the incident infrared waves regardless of their polarization.

For the 1064 nm wavelength, Fig. 7(a) shows the absorption spectra in the band from 0.9 µm to 1.25 µm for TE mode. As can be observed, as the incident angle increases the peak absorption around 1064 nm tends to make redshift up to 1100 nm at θ = 50^o then the absorption peak drops below 90% at a wavelength of 1120 nm and incident angle of θ = 60^o. Also, other absorption peaks (harmonics) are observed at incident angles greater than θ = 30^o. These harmonics, also, tend to make redshift with the increase of incident angle. The proposed structure can perform an absorption peak of 90% around 1064 nm at an incident angle of θ = 40^o at TE mode. On the other hand, as indicated in Fig. 7(b) for the TM mode, peak absorption around 1064 nm tends to make a redshift with a continuously decreasing in its value. In addition, other absorption peaks can be observed at incident angles greater than θ = 10^o which, also, tend to make redshift with the increase of incident angle. The proposed structure can perform an absorption peak of 85% around 1064 nm at an incident angle of θ = 30^o at TM mode.

Furthermore, we investigate the absorber performances for the triple bands, 1550 nm, 2080 nm, and 3000 nm under several incident angles from 0° to 70° for both TE and TM modes are illustrated in Fig. 8(a) and (b), respectively. As shown in Fig. 8(a), in the case of TE mode, it can be noted that as the incident angle increases the absorption peak values decrease for all bands. Also, with the increase of incident angle value, the absorption peaks around the 3000 nm band tend to make a blue shift while the absorption peaks around the 1550 nm band tend to make a redshift. The proposed absorber can perform absorption greater than 90% for all three bands under consideration at incident angles up to 50^o. For incident angles larger than 50°, the absorption intensity of the triple-band peaks degrades rapidly. This is because the magnetic field component in the x-y plane is ${H}_{x-y}=Hcos\theta$ which is required to excite the magnetic polaritons (Bai et al. 2015; Ye et al. 2010), where $H$ is the incident magnetic field intensity. Because the intensity drops rapidly at θ > 50°, the magnetic resonance becomes weaker, hence, we observed lower absorption. On the other hand, in the case of TM mode, shown in Fig. 8(b), the triple absorption peaks intensity remains above 99%. This is due to the stability in the magnetic incident field component in the direction of magnetic polaritons oscillations. Also, it can be noted the absorption peaks around the center wavelengths of the triple bands tend to make, only, a blue shift with an insignificant decrease in its peak value. Yet, due to the blue shift from the center wavelengths, there is a reduction in the absorption values at the center wavelengths of the triple bands. The proposed absorber can perform absorption greater than 90% at the center wavelength of all three bands under consideration at incident angles up to 50^o. The slight blue shift of the three absorption peaks arises, mainly, due to the off-phase oscillating effect (Ye et al. 2010).

This paper presents a numerical demonstration of the absorption performance of the QPMA in the infrared band. The structure of the absorber is composed of coaxial multi-layer SiO₂ disks of circular shape with different diameters. Each disk is surrounded by a gold ring and all coaxial disks are placed on a SiO₂ dielectric spacer and a thick gold ground layer. At the normal incident, the absorption of the quad-band is greater than 99% at wavelengths of 1064 nm, 1550 nm, 2080 nm, and 3000 nm. Also, the effect of the incident angle and polarization angle variations on the stability of the perfect absorber is examined for both TE and TM. The simulation results show that the QPMA has good performance for both TE and TM modes over a wide range of incident angles. It was observed that the absorption is greater than 85% at incident angles up to 40^o at 1064 nm, and absorption was greater than 90% for the other bands at incident angles up to 50^o. Additionally, due to the symmetry of the proposed shape, the absorber enjoys the polarization-insensitive property. This quad-band polarization-independent and wide-angle infrared absorber can be used in many applications such as laser stealth, infrared photodetection, and medical applications.

Ethical Approval

Fortunately, there are no ethical concerns associated with this work.

Competing interests

We declare that the authors have no competing interests.

Authors' contributions

All authors contributed equally to the study's conception and design. Analysis and simulation were performed by AEA and MNA. The first draft of the manuscript was written by AEA and MNA. All authors read and approved the final manuscript.

Funding

Funding is not applicable to this article (no funds for this research).

Data Availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. The availability of data and material is not applicable as there are no data sets used.

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No competing interests reported.

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Design and analysis of quad-band polarization-insensitive infrared perfect metamaterial absorber with a wide-incident angle

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1. Introduction

2. Structure Design

3. Results And Discussions

3.1. Effect of polarization angle variation

3.2. Effect of incident angle variation

4. Conclusion

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