Lithography-free tunable absorber at visible region via one-dimensional photonic crystals consisting of an &#x03B1;-MoO<sub>3</sub> layer

Tian Sang; Tian Sang; Yao Pei; Yao Pei; Qing Mi; Qing Mi; Shi Li; Shi Li; Chaoyu Yang; Chaoyu Yang; Yueke Wang; Yueke Wang; Guoyang Cao; Guoyang Cao

doi:10.1364/OE.457528

1. Introduction

Anisotropic optical materials offer a platform to manipulate and control diverse polarization-dependent devices at the nanoscale [1]. Numerous distinctive and non-intuitive optical phenomena such as negative refraction [2,3], resonant transmission or reflection [4,5], ultrabroadband absorption [6,7] and hyperlensing [8,9], which have been demonstrated typically with artificial metamaterials. However, to achieve these anisotropic optical phenomena, one needs to design specific patterned nanostructures capable of manipulating these unconventional wavefronts, which strongly relies on complex and high-precision fabrication techniques.

In recent years, van der Waals (vdW) layered materials such as hexagonal boron nitride (hBN) and α-phase molybdenum trioxide (α-MoO₃), have attracted significant attention due to their unique optical anisotropy [10,11]. In particular, unlike the hBN which behaves only out-of-plane optical anisotropy, α-MoO₃ provides new degrees of freedom for controlling light in two-dimensions due to the in-plane anisotropic nature [12,13]. The in-plane anisotropy of α-MoO₃, originating from lattice anisotropy, has revolutionized optical systems and has triggered many exciting physical properties such as subwavelength focusing [14,15], edge-oriented hyperbolic polaritons [16], configurable field localizations [17], diffraction-less propagation [18], and tunable plasmon-phonon hybridization [19]. In addition, for various optoelectronic devices such as polarization converters [20,21] and light absorbers [22,23], the optical performances of these devices can be enhanced by tailoring the anisotropic absorption efficiency of α-MoO₃ in the systems. However, all the researches on α-MoO₃ mentioned above were focused on infrared frequencies where α-MoO₃ exhibits three distinct reststrahlen bands, while the features and applications of α-MoO₃ at visible region were seldom studied. It was not until recently that α-MoO₃ was engineered for creating optical devices with enhanced or novel functionalities in the visible region. In 2020, Wei et al. [24] demonstrates that the triple-layer metal/α-MoO₃/metal device exhibits multiple functions based on the optical anisotropy of α-MoO₃ in the visible frequency, and dual-functions including polarization reflectors and polarization color filters can be realized by constructing the Au/α-MoO₃/Au cavities. In 2021, Tang et al. [25] shows that multi-band anisotropic perfect absorbers can be realized at visible region by integrating the α-MoO₃ nanoribbons into the unit cell of the metamaterials, and the absorption channels can be increased to three as triple α-MoO₃ nanoribbons are cascaded. However, highly efficient light absorption enhancement of α-MoO₃ in the visible wavelength region is still rare. In particular, to our knowledge, flexible control of light absorption of α-MoO₃ based on its in-plane anisotropy within a lithography-free architecture has not been reported yet at visible region. Our effort in this work is to extend the versatile absorption performances of a lithography-free α-MoO₃ to the visible region, which has significant importance for many applications such as photodetectors, light modulation, color filtering, and so on.

In this work, a lithography-free tunable absorber (LTA) at visible region is presented based on the in-plane optical anisotropy of α-MoO₃. The proposed absorber consists of two one dimensional (1D) photonic crystals (PCs) with different bulk band properties, and the topological interface state-induced light absorption enhancement of α-MoO₃ can be realized as an α-MoO₃ thin film is introduced into the system. An anisotropic nanocavity model is proposed to estimate the locations of the resonant absorption peak of the LTA for two orthogonal polarization states along the two orthogonal crystal directions, and the results are in good agreement with those of the transfer matrix method (TMM). The absorption efficiency of LTA is associated with the electric-field enhancement described by the field enhancement factor (FEF) within the α-MoO₃ layer. By merely increasing the number of the period of the bottom PC, near perfect absorption of α-MoO₃ can be realized at the over-coupled resonance. By varying the polarization angle, the absorption and reflection responses of the LTA can be dynamically tuned due to the excellent in-plane anisotropy of α-MoO₃.

2. Design and theoretical model

Figure 1 shows the structure of the LTA and the optical characteristics of α-MoO₃. As shown in Fig. 1(a), the proposed LTA consists of an α-MoO₃ thin film with thickness h sandwiched by PC 1 and PC 2. PC 1 and PC 2 are the high-low refractive index stacks with the same thickness of 2d_A+2d_B in a unit cell, but the unit cell of PC 1 is translated by half the lattice constant along the z direction comparing with that of PC 2. Since half lattice constant is translated in the unit cell between PC1 and PC 2, two identical common gaps with different Zak phases at each photonic band can be created, and the topological interface state can be excited as the two PCs are cascaded with each [26]. The unit cell of PC 1 and PC 2 are indicated by the green and orange dash lines, respectively. N₁ and N₂ are the number of the period of PC 1 and PC 2, respectively. The high (Ta₂O₅) and low (SiO₂) refractive indexes of the two PCs are 2.1 and 1.47, respectively. Figure 1(b) shows schematic diagram of atomic orientation of α-MoO₃ in the bulk structure along three crystallographic directions. The layered α-MoO₃ crystal with orthorhombic lattice composed of bilayer distorted MoO₆ octahedra is a highly anisotropic structure [12,27–29]. The distorted MoO₆ octahedra contain corner-sharing rows along the [100] direction, edge-sharing zigzag rows along the [001] direction, and are weakly bound along the vertical [010] direction via vdW interactions. In simulations, we define three orthogonal crystal directions of [100], [001] and [010] as x, y and z directions, respectively. Figure 1(c) shows the refractive index of α-MoO₃ along x, y and z directions at visible region, and the refractive index data are taken from Lajaunie et al. [30]. As can be seen in Fig. 1(c), the refractive index of α-MoO₃ is highly anisotropic particular in its real part arising from the strong structure anisotropy at visible region. In practice, the LTA can be fabricated by combing the physical vapor deposition (PVD) techniques with the α-MoO₃ fabrication and transfer [20,24]. First, the PC 2 is deposited onto a quartz substrate by using the standard PVD techniques such as the ion beam sputtering [31]. Next, the α-MoO₃ flake is grown on a SiO₂/Si substrate using low pressure PVD, and the α-MoO₃ layer is transferred to the surface of the PC 2 from the SiO₂/Si substrate via the polycarbonate-based process [20,24]. Finally, the LTA can be obtained after the PC 1 is deposited on top of the α-MoO₃ layer by using the ion beam sputtering.

Fig. 1. The structure under study and optical characteristics of α-MoO₃. (a) Schematic diagram of the proposed LTA under normal incidence, where the α-MoO₃ thin film is sandwiched by two 1D PCs. The unit cell of PC 1 and PC 2 are indicated by the green and orange dash lines, respectively. (b) Schematic diagram of atomic orientation of α-MoO₃ along three crystallographic directions, and the three possible positions of oxygen atoms are denoted O₁, O₂ and O₃. (c) Anisotropic refractive index of α-MoO₃ along x, y and z directions at visible region [30].

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For the proposed LTA structure where the multilayer contains vdW crystal with the anisotropic permittivity tensor of $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftrightarrow$}} \over \varepsilon } \textrm{ = }diag({\varepsilon _x},{\varepsilon _y},{\varepsilon _z})$, according to the Maxwell equations, the electric-field inside such a medium can be expressed as:

(1)$${\nabla ^2}{\boldsymbol E} + {k_0}^2\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftrightarrow$}} \over \varepsilon } {\boldsymbol E}\textrm{ = }\nabla (\nabla \cdot {\boldsymbol E})$$

where E is the electric field, and k₀=2π/λ is the free-space wave vector.

In order to obtain nontrivial plane-wave solutions of Eq. (1), the 4×4 TMM is used to calculate the absorption performances of the LTA [32,33], and the transfer matrix equation of the entire device can be written as:

(2)$$\left( \begin{array}{l} {A_s}\\ {B_s}\\ {A_p}\\ {B_p} \end{array} \right) = {\mathbf T}\left( \begin{array}{l} {C_s}\\ 0\\ {C_p}\\ 0 \end{array} \right) = \left( \begin{array}{llll} {T_{11}}&{T_{12}}&{T_{13}}&{T_{14}}\\ {T_{21}}&{T_{22}}&{T_{23}}&{T_{24}}\\ {T_{31}}&{T_{32}}&{T_{33}}&{T_{34}}\\ {T_{41}}&{T_{42}}&{T_{43}}&{T_{44}} \end{array} \right)\left( \begin{array}{l} {C_s}\\ 0\\ {C_p}\\ 0 \end{array} \right)$$

Where T is the transfer matrix of the system, (A_s,A_p), (B_s,B_p), and (C_s,C_p) are the amplitudes of incident light, reflected light, and transmitted light, respectively. The reflection and transmission coefficients in terms of the matrix elements can be expressed as:

(3)$${r_{ps}} \equiv {\left( {\frac{{{B_s}}}{{{A_p}}}} \right)_{{A_s} = 0}} = \frac{{{T_{11}}{T_{23}} - {T_{21}}{T_{13}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}},\quad{r_{pp}} \equiv {\left( {\frac{{{B_p}}}{{{A_p}}}} \right)_{{A_s} = 0}} = \frac{{{T_{11}}{T_{43}} - {T_{41}}{T_{13}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}}$$

(4)$${r_{sp}} \equiv {\left( {\frac{{{B_p}}}{{{A_s}}}} \right)_{{A_p} = 0}} = \frac{{{T_{41}}{T_{33}} - {T_{43}}{T_{31}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}},\quad{r_{ss}} \equiv {\left( {\frac{{{B_s}}}{{{A_s}}}} \right)_{{A_p} = 0}} = \frac{{{T_{21}}{T_{33}} - {T_{23}}{T_{31}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}}$$

(5)$${t_{ps}} \equiv {\left( {\frac{{{C_s}}}{{{A_p}}}} \right)_{{A_s} = 0}} = \frac{{ - {T_{13}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}},\quad{t_{pp}} \equiv {\left( {\frac{{{C_p}}}{{{A_p}}}} \right)_{{A_s} = 0}} = \frac{{{T_{11}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}}$$

(6)$${t_{sp}} \equiv {\left( {\frac{{{C_p}}}{{{A_s}}}} \right)_{{A_p} = 0}} = \frac{{ - {T_{31}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}},\quad{t_{ss}} \equiv {\left( {\frac{{{C_s}}}{{{A_s}}}} \right)_{{A_p} = 0}} = \frac{{{T_{33}}}}{{{T_{11}}{T_{33}} - {T_{13}}{T_{31}}}}$$

According to the model of Schubert [34], the transfer matrix T for the multilayer system consisting of anisotropic materials can be expressed as:

(7)$${\mathbf T} = {\mathbf L}_a^{ - 1}\mathop \prod \limits_{n = 1}^N {[{{\mathbf T}_{np}}({d_n})]^{ - 1}}{{\mathbf L}_f} = {\mathbf L}_a^{ - 1}\mathop \prod \limits_{n = 1}^N {{\mathbf T}_{np}}( - {d_n}){{\mathbf L}_f}$$

where L_a and L_f are the incident and exit matrices, respectively. d_n is the thickness of the nth layer, and T_np is the partial transfer matrix that connects the in-plane wave components at the top and bottom interfaces of the nth layer. By using the matrix elements of T, the absorption of the LTA for the x-polarized (p polarization) and y-polarized (s polarization) waves can be calculated as:

(8)$${A_p} = 1 - |{r_{ps}}{|^2} - |{r_{pp}}{|^2} - |{t_{ps}}{|^2} - |{t_{pp}}{|^2}$$

(9)$${A_s} = 1 - |{r_{sp}}{|^2} - |{r_{ss}}{|^2} - |{t_{sp}}{|^2} - |{t_{ss}}{|^2}$$

At normal incidence, there is no polarization conversion between the x- and y-polarized waves with |r_ps|²=|t_ps|²=|r_sp|²=|t_sp|²=0, thus the absorption of the total device can be simplified as:

(10)$${A_p} = 1 - |{r_{pp}}{|^2} - |{t_{pp}}{|^2},\begin{array}{ccc} {}&{}&{} \end{array}{A_s} = 1 - |{r_{ss}}{|^2} - |{t_{ss}}{|^2}$$

In simulations, we employ the 4×4 TMM to study the anisotropic optical performances of the proposed LTA by using Matlab codes. To verify the numerical results of the TMM for the LTA, simulations were also performed by using the finite-difference time-domain (FDTD) software Lumerical. According to our investigations not completely shown in this paper, the results of the TMM are in line with those of the FDTD. In FDTD simulation, the reflection and transmission of the LTA are defined as the ratios of the reflected and transmitted power to the launched power, respectively. Periodic boundary conditions are set in the x and y directions, and perfectly matched layers are used in the z direction. The grid size is chosen as 5 nm in all directions to ensure the accuracy of the calculation results.

3. Results and discussion

Figure 2 shows optical characteristics of the LTA in the cases of without (h=0) and with (h=5 nm) α-MoO₃ thin film. The thickness of Ta₂O₅ and SiO₂ are in quarter-wavelength optical thickness in a unit cell for both the two PCs, 2d_A=102 nm and 2d_B=71 nm for the design wavelength of 600 nm. As can be seen in Fig. 2(a), a reflection dip (transmission peak) is occurred at λ=610.6 nm in the wavelength region of interest, indicating the excitation of an interface state in the band gap of the two PCs. In general, two PCs with the unit cell translated by half lattice constant have the same photonic band gap with different topological properties of bulk dispersion, that is, if the Zak phase equals 0(π) relative to one inversion center, it must be π(0) relative to the other, and the topological interface state can be realized in the band gap as the two PCs are cascaded [26]. For the 1D PCs, their Zak phases are tightly related to the surface impedance of the corresponding PCs, and the topological interface state can be excited as the sum of the surface impedances of two semi-infinite PCs are equal to 0 [35,36]; here it can be simplified as Z_PC1+Z_PC2=0, where Z_PC1(Z_PC2) is the surface impedance of the semi-infinite PC with N₁=∞(N₂=∞) on the upward(downward) side of the interface. The existence condition of a topological interface state can be equivalent to φ_PC1+φ_PC2=0, where φ_PC1 and φ_PC2 are the reflection phases PC 1 and PC 2, respectively. Figure 2(b) shows the reflection phases of the two PCs, note the reflection phase of PC 2 is displayed as the negative value (-φ_PC2) to show the crossing point where φ_PC1=-φ_PC2. As shown in Fig. 2(b), the location of the crossing point can be calculated as 619.2 nm, which is slightly deviated from the location of the topological interface state in Fig. 2(a) due to the finite value of the N₁ and N₂. Figures 2(c) and 2(d) shows optical responses of the LTA with h=5 nm under the illuminations of x polarization, and y polarization, respectively. As can be seen in Fig. 2(c), the topological interface state-induced absorption enhancement with the peak value of 12.2% can be obtained as the ultrathin α-MoO₃ film is inserted at the interface of the two PCs. In addition, comparing with the location of the topological interface state with h=0 shown in Fig. 2(a), the location of the absorption peak in Fig. 2(c) is slightly red-shifted to 617.8 nm from 610.6 nm due to the increased optical thickness. In Fig. 2(d), the absorption performances of y polarization such as the location of the absorption peak (619.5 nm) and its peak value (25.5%) are slightly altered comparing with those of Fig. 2(c), and the proposed absorber shows low-efficient and insignificant polarization-dependent absorption features due to the weak optical anisotropy as h is small.

Fig. 2. Optical characteristics of the LTA without (h=0) and with (h=5 nm) α-MoO₃ thin film. Other parameters are: 2d_A=102 nm, 2d_B=71 nm, and N₁=N₂=8. (a) Optical responses of the LTA without α-MoO₃ thin film (h=0). (b) Reflection phases of the two PCs, note the red line indicates the negative value of the reflection phase of PC 2, and the red dash line indicates the crossing point of the two curves. (c) Optical responses of the LTA with h=5 nm under the illumination of x polarization. (d) Optical responses of the LTA with h=5 nm under the illumination of y polarization.

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According to the Fabry-Pérot theory, the α-MoO₃ thin film in the LTA can be treated as an optically anisotropic cavity surrounded by two PCs, and high-efficient absorption of α-MoO₃ can be realized as the resonance condition is satisfied:

(11)$$2{k_{z,i}}h + {\varphi _{1,i}} + {\varphi _{2,i}} = m\pi ,\begin{array}{c} {} \end{array}m = 1,2,3,\ldots $$

where the subscript i indicates the x or y polarization, k_z,i=2πn_i/λ is the wave vector along the wave propagation direction in the α-MoO₃ layer; φ_1,i and φ_2,i are the phase retardations on the upper and lower interfaces of the α-MoO₃ layer, respectively.

Figures 3(a) and 3(c) show absorption two dimensional (2D) map of the LTA as functions of the thickness of the α-MoO₃ layer for the x and y polarizations, respectively. As can be seen in Figs. 3(a) and 3(c), highly efficient absorption with multiple channels can be achieved with the increase of the thickness of α-MoO₃, and the absorption responses of the structure show distinct polarization-dependent features due to the strong optical anisotropy of α-MoO₃. Figure 3(b) and 3(d) show the locations of absorption peak of the LTA as functions of h at the resonance condition for the x and y polarizations, respectively. As shown in Figs. 3(b) and 3(d), the estimated locations of the absorption peak based on the anisotropic cavity model are in good agreement with those of the TMM shown in Figs. 3(a) and 3(c), validating the physical basis for the robust light absorption with anisotropic features of the LTA.

Fig. 3. Absorption characteristics of the LTA as functions of the thickness of the α-MoO₃ layer. Other parameters are the same as Fig. 2. (a) and (c) are the absorption 2D map of the LTA as functions of h for the x and y polarizations, respectively. (b) and (d) show the locations of the absorption peak of the LTA as functions of h based on the anisotropic cavity model for the x and y polarizations, respectively.

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Figure 4 shows optical performances of the LTA as functions of the number of the period of the two PCs with h=100 nm. As shown in Figs. 4(a) and 4(b), the absorption efficiency of the LTA is decreased with the increase of N₁, and the locations of the absorption peak for the x and y polarizations are 562.3 nm and 581.1 nm, respectively; which are different due to the optical anisotropy of the α-MoO₃ layer. Interestingly, the locations of the absorption peaks of the LTA can be kept the same for both the x and y polarizations as N₁ is varied. This is because that the resonance condition for the anisotropic absorption of α-MoO₃ is irrelevant to N₁ according to Eq. (11). Note the dip value of reflection is increased while the peak value of transmission is decreased with the increase of N₁ for both the x and y polarizations. Figures 4(c) and 4(d) show spectral responses of the LTA as functions of the number of the period of PC 2 for the x and y polarizations, respectively. As can be seen in Figs. 4(c) and 4(d), the absorption responses of the LTA also show polarization-dependent feature and the location of the absorption peak can also be kept the same as N₂ is varied. However, unlike the influences of N₁, although the absorption efficiency of the LTA can also be significantly affected by the number of the period of the multilayer stacks, the absorption efficiency of the LTA is increased with the increase of N₂. In addition, the dip value of reflection and the peak value of transmission are decreased with the increased N₂ for both the x and y polarizations.

Fig. 4. Spectral responses of the LTA as functions of the number of the period of the two PCs with h=100 nm. Other structure parameters are the same as Fig. 2. (a) and (b) are responses as functions of N₁ for the x and y polarizations, respectively. (c) and (d) are responses as functions of N₂ for the x and y polarizations, respectively.

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To distinguish the different influences of the number of the period of the two PCs on the absorption efficiency of the LTA, the electric-field distributions of the LTA at absorption peak wavelengths as functions of N₁ and N₂ are investigated. Figure 5 shows the electric-field distributions of the LTA for the x and y polarizations as functions of N₁ and N₂, and the field distributions around α-MoO₃ are enlarged so as to clearly show the field spatial distributions in the α-MoO₃ layer, which is associated with the anisotropic absorption performances of the LTA. As can be seen in Figs. 5(a) and 5(b), the increase of N₁ will decrease the peak value of the normalized electric-field intensity confined in the α-MoO₃ layer, and less light energy will be dissipated due to the reduced loss, thus the absorption efficiency of the LTA is decreased with the increase of N₁. On the contrary, as can be seen in Figs. 5(c) and 5(d), the increased N₂ will increase the peak value of the normalized electric-field intensity in the α-MoO₃ layer, thus the absorption efficiency of the LTA is increased with the increase of N₂. Therefore, as the variation of N₁ and N₂ will change the electric-field spatial distributions particularly the peak value of the normalized electric-field intensity in the α-MoO₃ layer, the absorption efficiency of the LTA can be tailored by the number of the period of the two PCs.

Fig. 5. Normalized electric-field distributions of the LTA for the x and y polarizations as functions of N₁ and N₂ at absorption peak wavelengths. Other structure parameters are the same as Fig. 4. The schematic diagrams of the LTA are indicated on the top of the figures, and the regions of the electric-field along the z direction are denoted by the green line in the schematic diagrams of the LTA. (a) and (b) are the electric-field distributions around the α-MoO₃ layer as functions of N₁ for the x and y polarizations, respectively. (c) and (d) are the electric-field distributions around the α-MoO₃ layer as functions of N₂ for the x and y polarizations, respectively.

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To quantitatively corroborate the correlation between the absorption efficiency of the LTA and the electric-filed enhancement in the α-MoO₃ layer, here we define the field enhancement factor (FEF) in the α-MoO₃ layer as:

(12)$$FEF = \frac{{\int_{\alpha - Mo{O_3}} {|{\boldsymbol E}/{{\boldsymbol E}_{\mathbf 0}}{|^2}dV} }}{{\int_{\alpha - Mo{O_3}} {dV} }}$$

where E denotes the electric field, E₀ is the incident electric field amplitude, dV is infinitesimal volume of the α-MoO₃ layer.

Figure 6 shows the peak absorption and the field properties of the LTA as functions of the number of the period of the two PCs. As can be seen in Figs. 6(a) and 6(b), the FEF in the α-MoO₃ layer will achieve the maximal value of 18 as N₁=7, and deviation from it will decrease the FEF for the x polarization; while the FEF in the α-MoO₃ layer will decrease monotonously with the increase of N₁ for the y polarization. In both two cases, the variation of the peak absorption of the LTA shows the same tendency as that of the FEF in the α-MoO₃ layer. In Figs. 6(c) and 6(d), it can be seen that the FEF in the α-MoO₃ layer is increased with the increase of the N₂ for both the x and y polarizations, and the tendency for the peak absorption as function of N₂ is also in line with that of the FEF in the α-MoO₃ layer. Therefore, the larger peak absorption of the LTA is the direct consequence of the larger FEF within the α-MoO₃ layer.

Fig. 6. Peak absorption and field properties of the LTA as functions of the number of the period of the two PCs. Other structure parameters are the same as Fig. 4. (a) and (b) are peak absorption and FEF in the α-MoO₃ layer as functions of N₁ for the x and y polarizations, respectively. (c) and (d) are peak absorption and FEF in the α-MoO₃ layer as functions of N₂ for the x and y polarizations, respectively.

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As the absorption efficiency of the LTA can be controlled by the number of the period of the two PCs, specifically, the peak absorption can be improved with the increase of N₂ according to Fig. 6, it is possible to achieve high-efficient absorption by merely increasing the number of the period of PC 2. According to the coupled mode theory (CMT) [37,38], the resonant absorption of the LTA can be expressed as:

(13)$$A = \frac{{4\delta \gamma }}{{{{(\omega - {\omega _0})}^2} + {{(\delta + \gamma )}^2}}}$$

where ω is the frequency of the incident wave, ω₀ is the resonant frequency, δ is the intrinsic loss of α-MoO₃, γ is the external leaky rate of the resonator. According to Eq. (13), perfect absorption can be realized at critically coupled resonance with δ=γ.

Figure 7 shows absorption response of the LTA for the x polarization with h=100 nm and N₂=16, other structure parameters are the same as Fig. 2. As can be seen in Fig. 7, near-perfect absorption of the LTA can be obtained at the resonance wavelength of 562.3 nm with the peak absorption of 98.7% and bandwidth of 0.52 nm, and the results of the TMM and FDTD are in good agreement with each other. Note further increasing N₂ cannot improve the peak absorption of the LTA due to slight reflection from the surface of the PC 1. In the calculation of the CMT, we extracted the total quality factor Q_t of the LTA as Q_t=ω₀/Δω₁=ω₀/2(δ+γ), where Δω₁ is the absorption bandwidth at the resonant frequency ω₀, and we got δ+γ=0.246 THz as Q_t=1082. The external leaky rate γ can be extracted from the quality factor as Q_γ=ω₀/Δω₂=ω₀/2γ, where Δω₂ is the transmission bandwidth of the LTA without the α-MoO₃ layer (h=0), and γ=0.135 THz as Q_γ=1974. Therefore, δ can be obtained as δ=0.111 THz. Note as the rate of radiative energy coupling from the incident wave to the resonance mode is larger than the internal damping rate due to the material dissipation, i.e., γ>δ, the LTA is operated at over-coupled resonance instead of at critically coupled resonance [39]. As can be seen in Fig. 7, the results of the CMT are in good agreement with those of the TMM, validating that highly efficient absorption of the LTA can be achieved at over-coupled resonance with δ≈γ. Note the inherent absorption is low for a suspending α-MoO₃ layer with the thickness of 100 nm, the detailed information can be found in Supplement 1, Fig. S1. Additional interest is that the LTA exhibits asymmetrical absorption feature at the resonance wavelength for incident light along the opposite direction, indicating the potential application of the LTA as a high-efficient nonreciprocal absorber [40]. The detailed information can be found in Supplement 1, Fig. S2.

Fig. 7. Absorption response of the LTA for the x polarization with h=100 nm and N₂=16. Other structure parameters are the same as Fig. 2.

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We further investigate the optical performances of the LTA under the variations of the polarization angle, as shown in Fig. 8. Figure 8(a) shows the absorption responses of the LTA as a function of the polarization angle. As can be seen in Fig. 8(a), tunable absorption enhancement of the LTA can be realized as the polarization angle is varied. In particular, the absorption channel of the LTA can be transferred from 562.3 nm to 581.1 nm as the polarization angle is changed from 0° (x polarization) to 90° (y polarization), and the peak absorption can be dynamically tuned by varying the polarization angle for both the two absorption channels. The double absorption peaks are originated from the in-plane optical anisotropy of α-MoO₃, as the shorter and longer absorption channels can be selectively excited by the x and y polarizations, respectively. Figure 8(b) shows the reflection responses of the LTA under the variation of the polarization angle. As shown in Fig. 8(b), the reflection responses of the LTA can be modulated by the polarization angle due to the strong anisotropic absorption of the α-MoO₃ layer. To quantitatively describe the intensity modulation of the reflection response, here we define the modulation contrast ration (MCR) as (R_max-R_min)/(R_max+R_min)×100%, where R_max and R_min are the maximal and minimal reflections at the resonance wavelengths, respectively; and the MCR are 96.6% and 41.2% for the wavelength of 562.3 nm and 581.1 nm, respectively. Thanks to the advantages of flexible control of the absorption and reflection responses based on the in-plane optical anisotropy of α-MoO₃, the LTA may facilitate many potential applications such as light-intensity detection [41], light modulation [42], polarization control [43], and color filtering [44,45].

Fig. 8. Optical performances of the LTA as functions of the polarization angle, other parameters are the same as Fig. 7. (a) Absorption responses of the LTA under the variation of the polarization angle. (b) Reflection responses of the LTA under the variation of the polarization angle.

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4. Summary

We have proposed and demonstrated a type of LTA at visible region based on two 1D PCs consisting of an α-MoO₃ layer. The two PCs have different bulk band properties, and the topological interface state-induced light absorption enhancement can be achieved as an α-MoO₃ thin film is introduced into the system. The anisotropic cavity model is proposed to estimate the resonant location of the LTA, and the results are in good agreement with those of the TMM for both the x and y polarizations. The absorption efficiency of the LTA can be significantly altered as the number of the period of the two PCs is varied, but the location of the absorption peak can be maintained the same due to the resonance nature of the anisotropic cavity. By studying the electric-filed distributions around the α-MoO₃ layer, it is shown that the variation of the number of the period of the PCs will change the electric-field spatial distributions particularly the normalized electric-field intensity in α-MoO₃, and the larger peak absorption is the direct consequence of the larger FEF within the α-MoO₃ layer, thus the absorption efficiency of the LTA can be tailored by the number of the period of the two PCs. By merely increasing the number of the period of the PC 2, highly efficient absorption with the peak absorption of 98.7% can be realized at the over-coupled resonance with δ≈γ. In addition, by varying the polarization angle, the absorption channels of the LTA can be selected and the reflection response can be effectively modulated due to the excellent in-plane anisotropy of α-MoO₃. The proposed design scheme and approach achieves tunable optical performances within the lithography-free nanostructure, which offers new directions for tuning physical properties and polarization-dependent devices in visible frequencies.

Funding

National Natural Science Foundation of China (62105126); Natural Science Foundation of Jiangsu Province (BK20210454); Fundamental Research Funds for the Central Universities (JUSRP21935).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

References

1. C. Wang, G. Zhang, S. Huang, Y. Xie, and H. Yan, “The optical properties and plasmonics of anisotropic 2D materials,” Adv. Opt. Mater. 8(5), 1900996 (2020). [CrossRef]

2. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008). [CrossRef]

3. H. Cho, Y. Yang, D. Lee, S. So, and J. Rho, “Experimental demonstration of broadband negative refraction at visible frequencies by critical layer thickness analysis in a vertical hyperbolic metamaterial,” Nanophotonics 10(15), 3871–3877 (2021). [CrossRef]

4. Q. Mi, T. Sang, Y. Pei, C. Yang, S. Li, Y. Wang, and B. Ma, “High-quality-factor dual-band Fano resonances induced by dual bound states in the continuum using a planar nanohole slab,” Nanoscale Res. Lett. 16(1), 150 (2021). [CrossRef]

5. N. Razmjooei, Y. H. Ko, F. A. Simlan, and R. Magnusson, “Resonant reflection by microsphere arrays with AR-quenched Mie scattering,” Opt. Express 29(12), 19183–19192 (2021). [CrossRef]

6. T. Sang, J. Gao, X. Yin, L. Wang, and H. Jiao, “Angle-insensitive broadband absorption enhancement of graphene using a multi-grooved metasurface,” Nanoscale Res. Lett. 14(1), 105 (2019). [CrossRef]

7. X. Wang, T. Sang, G. Li, Q. Mi, Y. Pei, and Y. Wang, “Ultrabroadband and ultrathin absorber based on an encapsulated T-shaped metasurface,” Opt. Express 29(20), 31311–31323 (2021). [CrossRef]

8. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009). [CrossRef]

9. J. Sun, T. Xu, and N. M. Litchinitser, “Experimental demonstration of demagnifying hyperlens,” Nano Lett. 16(12), 7905–7909 (2016). [CrossRef]

10. G. Hu, J. Shen, C.-W. Qiu, A. Alù, and S. Dai, “Phonon polaritons and hyperbolic response in van der Waals materials,” Adv. Opt. Mater. 8(5), 1901393 (2020). [CrossRef]

11. Q. Zhang, G. Hu, W. Ma, P. Li, A. Krasnok, R. Hillenbrand, A. Alù, and C.-W. Qiu, “Interface nano-optics with van der Waals polaritons,” Nature 597(7875), 187–195 (2021). [CrossRef]

12. W. Ma, P. Alonso-González, S. Li, A. Y. Nikitin, J. Yuan, J. Martín-Sánchez, J. taboada-Gutiérrez, I. Amenabar, P. Li, S. Vélez, C. tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S.-T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018). [CrossRef]

13. Z. Zheng, N. Xu, S. L. Oscurato, M. Tamagnone, F. Sun, Y. Jiang, Y. Ke, J. Chen, W. Huang, W. L. Wilson, A. Ambrosio, S. Deng, and H. Chen, “A mid-infrared biaxial hyperbolic van der Waals crystal,” Sci. Adv. 5(5), eaav8690 (2019). [CrossRef]

14. Z. Zheng, J. Jiang, N. Xu, X. Wang, W. Huang, Y. Ke, S. Zhang, H. Chen, and S. Deng, “Controlling and focusing in-plane hyperbolic phonon polaritons in α-MoO₃ with a curved plasmonic antenna,” Adv. Mater. 34(6), 2104164 (2022). [CrossRef]

15. F. Sun, W. Huang, Z. Zheng, N. Xu, Y. Ke, R. Zhan, H. Chen, and S. Deng, “Polariton waveguide modes in two-dimensional van der Waals crystals: an analytical model and correlative nano-imaging,” Nanoscale 13(9), 4845–4854 (2021). [CrossRef]

16. Z. Dai, G. Hu, G. Si, Q. Ou, Q. Zhang, S. Balendhran, F. Rahman, B. Y. Zhang, J. Z. Ou, G. Li, A. Alù, C.-W. Qiu, and Q. Bao, “Edge-oriented and steerable hyperbolic polaritons in anisotropic van der Waals nanocavities,” Nat. Commun. 11(1), 6086 (2020). [CrossRef]

17. W. Huang, F. Sun, Z. Zheng, T. G. Folland, X. Chen, H. Liao, N. Xu, J. D. Caldwell, H. Chen, and S. Deng, “Van der Waals phonon polariton mcrostructures for configurable infrared electromagnetic field localizations,” Adv. Sci. 8(13), 2004872 (2021). [CrossRef]

18. J. Duan, N. Capote-Robayna, J. Taboada-Gutiérrez, G. Álvarez-Pérez, I. Prieto, J. Martín-Sánchez, A. Y. Nikitin, and P. Alonso-González, “Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs,” Nano Lett. 20(7), 5323–5329 (2020). [CrossRef]

19. A. Yadav, R. Kumari, S. K. Varsheny, and B. Lahiri, “Tunable phonon-plasmon hybridization in α-MoO₃–graphene based van der Waals heterostructures,” Opt. Express 29(21), 33171–33183 (2021). [CrossRef]

20. S. A. Dereshgi, T. G. Folland, A. A. Murthy, X. Song, I. Tanriover, V. P. Dravid, J. D. Caldwell, and K. Aydin, “Lithography-free IR polarization converters via orthogonal in-plane phonons in α-MoO₃ flakes,” Nat. Commun. 11(1), 5771 (2020). [CrossRef]

21. N. R. Sahoo, S. Dixit, A. K. Singh, S. H. Nam, N. X. Fang, and A. Kumar, “High temperature mid-IR polarizer via natural in-plane hyperbolic Van der Waals crystal,” Adv. Opt. Mater. 10(4), 2101919 (2022). [CrossRef]

22. G. Deng, S. A. Dereshgi, X. Song, C. Wei, and K. Aydin, “Phonon-polariton assisted broadband resonant absorption in anisotropic α-phase MoO₃ nanostructures,” Phys. Rev. B 102(3), 035408 (2020). [CrossRef]

23. D. Dong, Y. Liu, and Y. Fu, “Critical coupling and perfect absorption using α-MoO₃ multilayers in the mid-infrared,” Ann. Phys. 533(3), 2000512 (2021). [CrossRef]

24. C. Wei, S. A. Dereshgi, X. Song, A. Murthy, V. P. Dravid, T. Cao, and K. Aydin, “Polarization reflector color filter at visible frequencies via anisotropic α-MoO₃,” Adv. Opt. Mater. 8(11), 2000088 (2020). [CrossRef]

25. B. Tang, N. Yang, X. Song, G. Jin, and J. Su, “Triple-band anisotropic perfect absorbers based on α-phase MoO₃ metamaterials in visible frequencies,” Nanomaterials 11(8), 2061 (2021). [CrossRef]

26. Y. Yang, T. Xu, Y. F. Xu, and Z. H. Hang, “Zak phase induced multiband waveguide by two-dimensional photonic crystals,” Opt. Lett. 42(16), 3085–3088 (2017). [CrossRef]

27. E. Balendhran, J. Deng, J. Z. Ou, S. Walia, J. Scott, J. Tang, K. L. Wang, M. R. Field, S. Russo, S. Zhuiykov, M. S. Strano, N. Medhekar, S. Sriram, M. Bhaskaran, and K. Kalantar-zadeh, “Enhanced charge carrier mobility in two-dimensional high dielectric molybdenum oxide,” Adv. Mater. 25(1), 109–114 (2013). [CrossRef]

28. W. Xie, M. Su, Z. Zheng, Y. Wang, L. Gong, F. Xie, W. Zhang, Z. Luo, J. Luo, P. Liu, N. Xu, S. Deng, H. Chen, and J. Chen, “Nanoscale insights into the hydrogenation process of layered α-MoO3,” ACS Nano 10(1), 1662–1670 (2016). [CrossRef]

29. I. A. de Castro, R. S. Datta, J. Z. Ou, A. Castellanos-Gomez, S. Sriram, T. Daeneke, and K. Kalantar-zadeh, “Molybdenum oxides–from fundamentals to functionality,” Adv. Mater. 29(40), 1701619 (2017). [CrossRef]

30. L. Lajaunie, F. Boucher, R. Dessapt, and P. Moreau, “Strong anisotropic influence of local-field effects on the dielectric response of α-MoO₃,” Phys. Rev. B 88(11), 115141 (2013). [CrossRef]

31. Y. Zhao, Y. Wang, H. Gong, J. Shao, and Z. Fan, “Annealing effects on structure and laser-induced damage threshold of Ta₂O₅/SiO₂ dielectric mirrors,” Appl. Surf. Sci. 210(3-4), 353–358 (2003). [CrossRef]

32. J. Hao and L. Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: generalized 4×4 transfer-matrix method,” Phys. Rev. B 77(9), 094201 (2008). [CrossRef]

33. P. Yeh, “Optics of anisotropic layered media: a new 4×4 matrix algebra,” Surf. Sci. 96(1-3), 41–53 (1980). [CrossRef]

34. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53(8), 4265–4274 (1996). [CrossRef]

35. M. Xiao, Z. Q. Zhang, and C. T. Chan, “Surface impedance and bulk band geometric phases in one-dimensional systems,” Phys. Rev. X 4(2), 021017 (2014). [CrossRef]

36. Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, “Measurement of the Zak phase of photonic bands through the interface states of a metasurface photonic crystal,” Phys. Rev. B 93(4), 041415 (2016). [CrossRef]

37. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]

38. T. Sang, R. Wang, J. Li, J. Zhou, and Y. Wang, “Approaching total absorption of graphene strips using a c-Si subwavelength periodic membrane,” Opt. Commun. 413, 255–260 (2018). [CrossRef]

39. J. WoongYoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5(1), 18301 (2015). [CrossRef]

40. C. Zhang, Y. Wang, M. Lu, and Z. Yao, “Nonreciprocal absorber of subwavelength metallic gratings,” Jpn. J. Appl. Phys. 57(10), 100305 (2018). [CrossRef]

41. T. Sang, G. Chen, Y. Wang, B. Wang, W. Jiang, T. Zhao, and S. Cai, “Tunable optical reflectance using a monolithic encapsulated grating,” Opt. Laser Technol. 83, 163–167 (2016). [CrossRef]

42. X. Sun, H. Yu, N. Deng, D. Ban, G. Liu, and F. Qiu, “Electro-optic polymer and silicon nitride hybrid spatial light modulators based on a metasurface,” Opt. Express 29(16), 25543–25551 (2021). [CrossRef]

43. D. O. Ignatyeva, D. Karki, A. A. Voronov, M. A. Kozhaev, D. M. Krichevsky, A. I. Chernov, M. Levy, and V. I. Belotelov, “All-dielectric magnetic metasurface for advanced light control in dual polarizations combined with high-Q resonances,” Nat. Commun. 11(1), 5487 (2020). [CrossRef]

44. M. J. Uddin, T. Khaleque, and R. Magnusson, “Guided-mode resonant polarization-controlled tunable color filters,” Opt. Express 22(10), 12307–12315 (2014). [CrossRef]

45. Q. He, N. Youngblood, Z. Cheng, X. Miao, and H. Bhaskaran, “Dynamically tunable transmissive color filters using ultra-thin phase change materials,” Opt. Express 28(26), 39841–39849 (2020). [CrossRef]

Lithography-free tunable absorber at visible region via one-dimensional photonic crystals consisting of an α-MoO₃ layer

Abstract

1. Introduction

2. Design and theoretical model

3. Results and discussion

4. Summary

Funding

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

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Equations (13)

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