Dynamically Tunable Perfect Absorbers Utilizing Hexagonal Aluminum Nano-Disk Array Cooperated with Vanadium Dioxide

Peng Zhou(周鹏)$^{1}$, Gai-Ge Zheng(郑改革)$^{1,2\hyperlink{s}{**}}$, Yun-Yun Chen(陈云云)$^{1,2}$,\\ Feng-Lin Xian(咸冯林)$^{1}$, Lin-Hua Xu(徐林华)$^{1}$

doi:10.1088/0256-307X/36/1/014202

⇦Chinese Physics Letters, 2019, Vol. 36, No. 1, Article code 014202⇨ Dynamically Tunable Perfect Absorbers Utilizing Hexagonal Aluminum Nano-Disk Array Cooperated with Vanadium Dioxide * Peng Zhou (周鹏)1, Gai-Ge Zheng (郑改革)1,2**, Yun-Yun Chen (陈云云)1,2, Feng-Lin Xian (咸冯林)1, Lin-Hua Xu (徐林华)1 Affiliations 1Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 2Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044 Received 10 August 2018, online 25 December 2018 ^*Supported by the National Natural Science Foundation of China under Grant No 41675154, the Six Major Talent Peak Expert of Jiangsu Province under Grant Nos 2015-XXRJ-014 and R2016L01, the Jiangsu 333 High-Level Talent Cultivation Program under Grant No BRA2016425, and the Research Innovation Program for College Graduates of Jiangsu Province under Grant No KYCX18_1022.
^**Corresponding author. Email: 002382@nuist.edu.cn Citation Text: Zhou P, Zheng G G, Chen Y Y, Xian F L and Xu L H et al 2019 Chin. Phys. Lett. 36 014202 Abstract A tunable perfect absorber composed of hexagonal-arranged aluminum nano-disk array embedded in the vanadium dioxide (VO$_{2}$) film is proposed. The aim is to achieve the tunability of resonance absorption peak in the visible and near-infrared regimes. Numerical results reveal that the absorption peak achieves a large tunability of 76.6% while VO$_{2}$ undergoes a structural transition from insulator phase to metallic phase. By optimizing the structural parameters, an average absorption of 95% is achieved from 1242 to 1815 nm at the metallic phase state. In addition, the near unity absorption can be fulfilled in a wide range of incident angle (0$^{\circ}$–60$^{\circ}$) and under all polarization conditions. The method and results presented here would be beneficial for the design of active optoelectronic devices. DOI:10.1088/0256-307X/36/1/014202 PACS:42.25.Bs, 78.66.Bz, 78.40.-q © 2019 Chinese Physics Society Article Text Recently, metamaterial absorbers (MMAs) have attracted considerable attention due to their prospects in many aspects, such as sensors,[1] optical detectors,[2] photovoltaic cells,[3] and emitters.[4] Various MMAs have been designed and fabricated over visible, infrared, microwave and terahertz bands of electromagnetic (EM) spectrum.[5] However, due to resonant nature in MM structures, a high absorption rate is achieved only near the specific resonance frequencies, which greatly hampers their practical applications.[6] MMA with a wavelength-tunable property is beneficial for the development of tunable sensors, switches and biological detectors. Integrating active material can further control the resonant response in plasmonic structures through electrical,[7] thermal,[8] optical[9] and mechanical[10,11] tuning methods. The thermal method exploits the effect of temperature on the phase of special materials such as vanadium dioxide (VO$_{2}$) and germanium antimony telluride (GST). VO$_{2}$ is a representative of phase change materials (PCMs) and it is a promising candidate due to its potential applications in both electronic and optical devices.[12-18] It undergoes an insulator-to-metal transition (IMT) at a temperature around 68$^{\circ}\!$C. The change of refractive index (RI) upon the phase transition can change the surrounding dielectric environment of plasmonic structures to tune the resonance frequency. Motivated by these fundamental studies, we propose a VO$_{2}$-based thermally-tunable perfect absorber (PA) that works in the visible (Vis) and near-infrared (NIR) ranges. The characteristics and the absorption mechanisms of the proposed PA are comprehensively investigated. Numerical simulation based on the finite-difference time-domain (FDTD) method shows broadband near-unity absorption at the wavelength range from 1242 to 1815 nm, when VO$_{2}$ is a dielectric phase. However, the resonance peak shifts to 795.2 nm when VO$_{2}$ changes to metal phase below its phase transition temperature of 20$^{\circ}\!$C. Furthermore, the near-unity absorption capability remains high with the incident angle varying from 0 to 60$^{\circ}$ for both transverse magnetic (TM) and transverse electric (TE) polarizations.

Fig. 1. (a) Schematic diagram and (b) cross-section view of the VO$_{2}$ with Al cylinder arrays sitting on the Al substrate. The heights of the Al arrays and the VO$_{2}$ layer are $h$ and $t$, respectively, and $r$ represents the radius of Al cylinder arrays. The period of array along $x$ is marked as $p_{x}$.

The schematic diagrams of the initial structure and the cross-section view in the $x$–$z$ plane are shown in Fig. 1. The MMA consists of hexagonally arrayed Al nano-disks embedded in the VO$_{2}$ layer and the Al layer used as a reflector to block the transmission, and these two layers are separated by a VO$_{2}$ spacer layer whose thickness is expressed as $t$. The height and radius of Al disk are denoted as $h$ and $r$, respectively. The period of arrays along the $x$ direction is marked as $p_{x}$, and $p_{y}=\sqrt 3 p_{x}$ is the period of array along the $y$ direction. The perfectly matched layer (PML) absorbing boundary conditions are utilized at the top and bottom of computational space, and the periodic boundary conditions are employed along $x$ and $y$ directions, respectively. The plane wave is defined as the light source and normally incidents to the array, while the electrical vector of plane wave is parallel to the $x$-direction in simulation unless clarified. The mesh size is chosen as $\Delta x=\Delta y=\Delta z=2$ nm to minimize any numerical errors. The optical properties of the VO$_{2}$ in the metallic state are described by the Lorentz–Drude dispersion relation model[19] $$\begin{align} \varepsilon(\omega)=\,&\varepsilon_{\infty}+\frac{\Delta \varepsilon_{1}}{-a_{1}\omega^{2}-ib_{1}\omega}\\ &+\sum\limits_{k=2}^6 \frac{\Delta \varepsilon_{k}}{-a_{k}\omega^{2}-ib_{k}\omega +c_{k}},~~ \tag {1} \end{align} $$ and the optical properties of the VO$_{2}$ in insulation state can be followed by the Lorentz dispersion relation model,[19] $$\begin{align} \varepsilon(\omega)=\,&\varepsilon_{\infty}\sum\limits_{k=1}^6 \frac{\Delta \varepsilon_{k}}{-a_{k}\omega^{2}-ib_{k}\omega +c_{k}},~~ \tag {2} \end{align} $$ where $\Delta \varepsilon_{k}$, $a_{k}$, $b_{k}$ and $c_{k}$ are constants and the values in metallic state are $\varepsilon_{\infty}=3.95$, $\Delta \varepsilon_{k}=284.783$, 34.493, 195.708, 323.458, 570.599 and 0, $k=(1, 2,\ldots, 6)$, $a_{1}=a_{2}=a_{3}=a_{4}=a_{5}=1$, $a_{6}=0$, $b_{k}=3.344$, 7.914, 13.792, 18.341, 24.477 and 0, $k=(1,2,\ldots,6)$, $c_{k}=0$, 18.994, 201.345, 311.017, 543.428 and 0, $k=(1,2,\ldots, 6)$. In the insulation state, the values of $\Delta \varepsilon_{k}$, $a_{k}$, $b_{k}$ and $c_{k}$ are $\varepsilon_{\infty}=4.26$, $\Delta \varepsilon_{k}=21.108$, 20.572, 27.909, 104.101, 411.654, 384.864, $k=(1, 2,\ldots, 6)$, $a_{1}=a_{2}=a_{3}=a_{4}=a_{5}=a_{6}=1$, $b_{k}=4.083$, 3.122, 3.671, 7.469, 23.275, 20.197, $k=(1, 2,\ldots, 6)$, $c_{k}=26.719$, 43.402, 57.784, 194.219, 312.807, 363.079, $k=(1, 2,\ldots, 6)$.[20] The material property of Al is adopted from Palik's optical constants handbook.[21] The absorbance $A(\omega)$ can be calculated by $A(\omega)=1-R(\omega)-T(\omega)$, where $R(\omega)$ represents the reflectivity which is obtained from the numerical simulation, while $T(\omega)$ is the transmittance which reduces to be zero due to the block of the reflective Al substrate. To design and develop MMAs, one of the most inspiring aspects is to achieve desired optical properties by configuring structures beyond their intrinsic properties. Metal-insulator-metal (MIM) structure-based PAs typically have a thick bottom metallic film as the back reflector and one or several pairs of insulator-metal structures.[22,23] The dielectric constants of VO$_{2}$ can change dramatically once the phase transition is initiated by the external thermal field, and then the active tunability of the absorption can be realized. Geometrical parameters are originally assumed to be $t=20$ nm, $h=80$ nm, $r=60$ nm, and $p_{x}=500$ nm. Figure 2 shows the absorption spectra of the sample at 20$^{\circ}\!$C and 80$^{\circ}\!$C under normal incidence. At 80$^{\circ}\!$C, VO$_{2}$ is at the metallic phase state (m-VO$_{2}$), there is one absorption peak at 795.2 nm. There are also two absorption peaks at 20$^{\circ}\!$C when VO$_{2}$ is at the dielectric phase state (i-VO$_{2}$). The two peaks are located at 1396 and 1712 nm, respectively. It is worth noting that the absorption bandwidth with the 90% absorption can be maintained when wavelength ranges from 1245 to 1820 nm. In the metallic phase of VO$_{2}$, the imaginary part of the dielectric permittivity is so high that field penetration is minimal. Therefore, incident light is mostly absorbed. The VO$_{2}$ spacer layer acts as a tunable dielectric environment for the resonant PA due to the unique phase changing merits. The optical constant of VO$_{2}$ thin film would be altered during the phase transition. Because the Al arrays are embedded in the VO$_{2}$ film, the surrounding dielectric environment of Al arrays will be changed accordingly. Then quantifiable shifts in the LSPR extinction wavelength maximum ($\lambda_{\max}$) will be met, as demonstrated by[24] $$\begin{align} \Delta \lambda_{\max}=m\Delta n\Big[1-\exp\Big(-\frac{2t}{l_{\rm d}}\Big)\Big],~~ \tag {3} \end{align} $$ where $m$ is the bulk refractive index response of the Al arrays, $\Delta n$ is the change in refractive index induced by the phase transition, $t$ is the VO$_{2}$ film thickness, and $l_{\rm d}$ is the characteristic electromagnetic field decay length, modeled as an exponential decay.[25] The dielectric constant of the VO$_{2}$ film decreases upon a phases transition from insulator phase to metallic phase, and $\Delta n$ would be less than zero, resulting in $\Delta \lambda_{\max} < 0$ and showing a blue shift.

Fig. 2. Absorption spectra of the sample for VO$_{2}$ in the dielectric state (at 20$^{\circ}\!$C) and the metallic state (at 80$^{\circ}\!$C) under normal incidence.

To understand the modulation in the absorption spectra under the TM polarized incidence, we analyze the electric-field distributions at these three resonance wavelengths, as shown in Fig. 3. Figures 3(a) and 3(d) show the electric-field distributions for VO$_{2}$ in the metallic state at 795.2 nm in the $x$–$z$ and $x$–$y$ planes, respectively. It is observed that the electric fields are mainly focused on the edges of the Al pillars owing to the LSP.[26,27] The field localization leads to a dip in the reflection spectrum and a peak in the absorption spectrum. More interestingly, the strong near-field intensities extend into the surrounding VO$_{2}$. Figures 3(b) and 3(c) show the electric-field distributions for VO$_{2}$ in the dielectric state at 1396 and 1712 nm in the $x$–$z$ planes, respectively. The electric-field is mainly confined within the Al pillar and the underneath VO$_{2}$. The corresponding electric-field distribution at 1396 and 1712 nm in the $x$–$y$ planes are presented in Figs. 3(e) and 3(f), respectively. All the intensity distributions are symmetric, and the maximum resonance intensity is at the edges of the Al nano-pillars (NPs), indicating that oscillating charges accumulate there.

Fig. 3. (a)–(c) Electric field distribution profile at the resonant wavelengths of 795.2, 1396 and 1712 nm in the $x$–$z$ plane, respectively. (d)–(f) Electric field distribution profile at the resonant wavelengths of 795.2, 1396 and 1712 nm in $x$–$y$ plane, respectively.

Fig. 4. (a)–(c) Schematic diagram view of the VO$_{2}$ with Al cylinder arrays sitting on the Al substrate, VO$_{2}$ film sitting on the Al substrate, Al cylinder arrays sitting on the Al substrate, respectively. The corresponding absorption spectra are shown in (d)–(f), respectively.

We further investigate the influences of the structural parameters on the hybrid device performance. Throughout this work, the involved structural parameters are optimized by default as those in Fig. 2 unless otherwise specified. By calculating the corresponding absorption spectra for three different structures as shown in Fig. 4, it can be found that wide-band enhanced absorption can be achieved because of the inherent absorption of the material involved as well as the resonance effect of hybrid structure. In recent years, the optical properties of metal nano-pillar arrays (MNPAs) have been the subject of great interest and intensive research. Even at very low area fill fractions, MNPAs exhibit strong optical absorption due to robust coupling into the waveguide and SP modes of individual pillar. These arrays of essentially independent optical antennas have an optical response which is polarization-independent and angle-insensitive. Active materials can be used to tune the absorption. The absorption peak can achieve a large tunability while VO$_{2}$ undergoes a structural transition from insulator phase to metallic phase.

Fig. 5. Absorption map for various radii of Al arrays at the states of (a) m-VO$_{2}$ and (b) i-VO$_{2}$. Other geometric parameters are the same as those in Fig. 2.

Fig. 6. Absorption spectra for various heights of Al arrays at the states of (a) m-VO$_{2}$ and (b) i-VO$_{2}$, respectively. Other geometric parameters are the same as in Fig. 2.

We find that for the hybrid absorber in the m-VO$_{2}$ state, with increasing the radius of Al pillar, the wavelength of the peak absorbance is nearly stable and the peak intensity is gradually reduced, which can be manifested by Fig. 5(a). Meanwhile, Fig. 5(b) shows the absorption map in the i-VO$_{2}$ state. Clearly, broadband absorption can be maintained. The results of absorbance with the height at the fixed radius and period is shown in Fig. 6 for the states of m-VO$_{2}$ and i-VO$_{2}$, the periods and the radii of the NPAs are fixed at 500 and 60 nm, respectively. It is evident that $h$ strongly influences the optical response when varies from 0 nm to 80 nm. The absorption peak becomes red-shifted and the average absorbance increases with $h$, which is enhanced by the larger surface area of the pillars. Figure 7 shows the absorbance of the MMA depending on the wavelength and the thickness of VO$_{2}$ layer ($t$). It can be found that the absorption intensity reaches its maximum value when $t < 20$ nm for both m-VO$_{2}$ and i-VO$_{2}$ states. The decrease of the absorbance is attributed to the weakened resonance and resonant couplings. The increased electric field intensity within the lossy metallic VO$_{2}$ will lead to enhanced power absorption. Therefore, we can manipulate absorption properties by controlling the electric field localization with proper design of ultra-thin VO$_{2}$ layer.

Fig. 7. Absorption spectra for various thicknesses of VO$_{2}$ layer at the states of (a) m-VO$_{2}$ and (b) i-VO$_{2}$, respectively. The other geometric parameters are the same as in Fig. 2.

Fig. 8. Contour plot of the spectral absorption of the proposed absorber as a function of wavelength and polarization angle of incident light under normal incidence under the condition of (a) m-VO$_{2}$ and (b) i-VO$_{2}$ states, respectively. Contour plot of the spectral absorption of the proposed absorber as functions of wavelength and incident angle under the condition of (c) m-VO$_{2}$ and (d) i-VO$_{2}$ states, respectively. The other geometric parameters are fixed as the same as used in Fig. 2.

Fig. 9. Absorption map of the proposed absorber as a function of wavelength and incident angle with Al cylinder arrays sitting on Al substrate (a) without VO$_{2}$ and (b) with VO$_{2}$ at the i-VO$_{2}$ state, respectively.

Finally, the absorption stability of the structure under the changes in the polarization and incident angles has been investigated. At the normal incidence, the electric polarization along the $x$ direction is 0$^{\circ}$, and along the $y$ direction is 90$^{\circ}$. As shown in Figs. 8(a) and 8(b), the influence of polarization angle on the absorption efficiency is studied under the normal incidence. An extremely high absorption of EM radiation can be clearly observed. For a specific wavelength, the absorption does not have any change with the polarization angles changing from 0$^{\circ}$ to 90$^{\circ}$, which indicates the independence of the polarization of the incident light. Obviously, for a specific polarization angle, the electric field can be decomposed into TE and TM polarization lights, and meanwhile the absorption spectra for TM and TE polarization configuration is the same at normal incidence owing to the high symmetrical structure of the absorber.[28,29] In addition, the angular independence of a PA is also important to maximize the energy absorption. Figures 8(c) and 8(d) show the spectral absorption of the absorber with different incident angles at TM polarization. Note that, even with a 60$^{\circ}$ angle of incidence, the absorber can still maintain a high absorption above 95%. As seen from Fig. 4, the Al-VO$_{2}$ hybrid pillar arrays have much broader absorption at both states of VO$_{2}$ especial in the insulator phase (i-VO$_{2}$). To further prove that the large angle absorption is due to the cover layer which is the VO$_{2}$ film, the absorption maps have been calculated with the proposed absorber as functions of wavelength and incident angle with Al cylinder arrays sitting on the Al substrate without VO$_{2}$ and with VO$_{2}$ at the i-VO$_{2}$ state. The result in Fig. 9 has been proved that the VO$_{2}$ film is the reason for the large angle absorption. From the above analyses, the absorption performance of the proposed selective absorber is insensitive to the polarization angle, and high absorption efficiency can be maintained over a large range of incident angle. In summary, a tunable MMA based on VO$_{2}$ phase transition has been proposed and numerically investigated. The bandwidth and position of the absorption resonance can be tuned by controlling the ambient temperature around the phase transition temperature. FDTD numerical simulation shows a broadband near-unity absorption in the NIR range when VO$_{2}$ is a dielectric, but the resonance peak shifts when VO$_{2}$ changes to metal phase below its phase transition temperature. Moreover, the absorption capability remains high with the incident angle varying from 0 to 60$^{\circ}$ for both TM and TE polarizations. We believe that our study will enhance the fundamental understanding of optical materials of VO$_{2}$ and will motivate new potential applications in sensors, optical detectors and thermo-photovoltaic cells. References Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: A comparison with the metasurfacesUltra-thin infrared metamaterial detector for multicolor imaging applicationsDesign of Broadband Metamaterial Absorbers for Permittivity Sensitivity and Solar Cell Application ^*Perfect infrared absorber and emitter based on a large-area metasurfaceMetamaterials: artificial materials beyond natureActive nanoplasmonic metamaterialsElectrically driven optical metamaterialsActive thermal cloakActive and tunable metamaterialsA multi-layer active elastic metamaterial with tuneable and simultaneously negative mass and stiffnessMechanically tunable metamaterials terahertz dual-band bandstop filterMemory MetamaterialsThermal radiative near field transport between vanadium dioxide and silicon oxide across the metal insulator transitionReconfigurable anisotropy and functional transformations with

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