Multifunctional phase modulated metasurface based on a thermally tunable InSb-based terahertz meta-atom

Wenxuan Wu; Rong Lin; Na Ma; Ping Jiang; Xiaoyong Hu

doi:10.1364/OME.444019

1. Introduction

THz radiation has gained tremendous interest due to its specific characteristics. Therefore, various THz devices have been proposed to control the properties of THz waves, including intensity [1–8], phase [9–13] and polarization [14–18]. Among various THz wave manipulation designs, PB metasurfaces which can introduce extra geometric phase by rotating the orientation of the meta-atoms play important roles in manipulating THz CP wave. Therefore, they exhibit widely applications in drug delivery, biological sensing, THz imaging and communication [19,20]. A tremendous of PB metasrufaces have been designed to realize varieties of THz wavefront manipulation functions [21–24]. Wang et al. proposed a PB metasurface which consists of a Z-shaped gold layer to obtain multi-foci metalens in THz range [25]. Jia et al. designed a PB metasurface composed of U-shaped metallic structures to realize photonic spin Hall effect [26]. Li et al. demonstrated a PB metasurface with aluminum double rings to generate vortex beam [27]. However, the applications of these THz PB metasurfaces are still limited due to their fixed electromagnetic responses. Therefore, it is urgently needed to develop functional-material-based THz PB metasurfaces whose electromagnetic responses can be dynamically manipulate [28]. Deng et al. applied graphene into THz PB metasurface to realize tunbale THz wide-band CP reflection by adjusting the extra voltage [29]. Zhang et al. designed a THz PB metasurface adopted with graphene which can generate tunable orbital angular momentum (OAM) beam by changing the chemical level of the graphene [30]. Lately, Tan et al. introduced magneto-optic material into THz PB metasurface, which can switch the state of Bessel beams by changing the external magnetic field [31]. Even though great efforts have been made in recent years, seldom reports have been found in tunable multifunctional THz metasurfaces.

Here, we propose a thermally tunable reflection-type InSb-based THz PB meta-atom, which can not only convert the incident CP wave into cross-polarized components but also adjust the reflection efficiency by tuning the temperature of InSb. Besides, the full 2π phase coverage can be achieved on the metasurface constructed by the proposed meta-atom based on the PB phase principle. Investigated with FDTD method, various functional devices, including anomalous reflector, reflection-type metalens, and reflection-type OAM beams generators, are realized by using the proposed meta-atom. The working state of these functional devices can be switched from “ON” to “OFF” at the frequency of 1 THz successfully by changing the temperature of InSb from 220 K to 360 K. This work offers a high-quality thermally tunable PB meta-atom. Moreover, it provides new ideas for tunable THz PB metasurface designs which have great potential for terahertz imaging, detection, and communication.

2. Structure design and theoretical analysis

Figure 1(a) shows a schematic diagram of a metasurface constructed by the proposed thermally tunable InSb-based THz PB meta-atom. Details of the proposed meta-atom are shown in Fig. 1(c-d). The meta-atom consists of a polyimide substrate sandwiched between the top layer of a copper split-ring with the gap filled with InSb and the bottom layer of a copper plate. The bottom copper plate is thick enough to guarantee the complete reflection for the incident THz wave. The metasurface is constructed by a periodic lattice of arrays of meta-atoms. The period of the meta-atom is p, the outer radius of the copper ring is r0, the inner radius of the copper ring is r1 and the width of the InSb gap is w. The thickness of the copper ring and InSb is ti, the thickness of the polyimide layer is ts, and the thickness of the copper plate is tm. The normally incident CP wave can be reflected and converted into the cross-polarized components by the metasurface at 220 K, while most of the incident CP wave will be absorbed by the metasurface at 360 K.

Fig. 1. (a) Schematic of a metasurface constructed by the proposed thermally tunable InSb-based THz PB meta-atom, (b) The proposed meta-atom, (c) The top view of the proposed meta-atom, (d) The lateral view of the proposed meta-atom.

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With the normally incident CP THz wave, the general reflection matrix RCP of the meta-atom can be written as Eq. (1).

(1)$${R_{CP}} = \left( {\begin{array}{*{20}{l}} {{R_{LL}}}&{{R_{LR}}}\\ {{R_{RL}}}&{{R_{RR}}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {\frac{{{r_{xx}} + {r_{yy}} + i({{r_{xy}} - {r_{yx}}} )}}{2}}&{\frac{{{r_{xx}} - {r_{yy}} - i({{r_{xy}} + {r_{yx}}} )}}{2}}\\ {\frac{{{r_{xx}} - {r_{yy}} + i({{r_{{x_y}}} + {r_{yx}}} )}}{2}}&{\frac{{{r_{xx}} + {r_{yy}} - i({{r_{xy}} - {r_{yx}}} )}}{2}} \end{array}} \right)$$

Here, R_LL, R_LR, R_RL, and R_RR represent the complex reflection coefficients of the CP wave, while r_xx, r_xy, r_yx and r_yy represent the complex reflection coefficients of the linear polarized component. The first subscript denotes the polarization state of the output wave, and the second subscript indicates the polarization of the input wave.

When the split-ring on the meta-atom is rotated by angle θ in the anticlockwise direction, the reflection matrix R_cp* can be expressed as Eq. (2).

(2)$$R_{CP}^\ast{=} \left[ {\begin{array}{ll} {\frac{{{r_{xx}} + {r_{yy}} - ({{r_{xx}} - {r_{yy}}} )\sin 2\theta + i({{r_{xy}} - {r_{yx}}} )\cos 2\theta }}{2}}&{\frac{{({{r_{xx}} - {r_{yy}}} )\cos 2\theta - i({{r_{xy}} + {r_{ys}}} )+ i({{r_{xy}} - {r_{yc}}} )\sin 2\theta }}{2}}\\ {\frac{{({{r_{xx}} - {r_{yy}}} )\cos 2\theta + i({{r_{xy}} + {r_{yx}}} )+ i({{r_{Xy}} - {r_{yx}}} )\sin 2\theta }}{2}}&{\frac{{{r_{xx}} + {r_{yy}} + ({{r_{xx}} - {r_{yy}}} )\sin 2\theta - i({{r_{xy}} - {r_{yx}}} )\cos 2\theta }}{2}} \end{array}} \right]$$

In our study, the right-handed circularly polarized (RCP) wave is used as the input THz wave, the electric field vector of which can be demonstrated as E_in= (1, i)^T. Then the electric field vector of the output wave can be described as Eq. (3).

(3)$$\begin{aligned} {E_{\textrm{out }}} &= R_{CP}^\ast{\cdot} {E_{\textrm{in }}}\\ &= \frac{1}{2}({{\textrm{r}_{xx}} + {r_{yy}} + {r_{xy}} + {r_{yx}}} )\left( {\begin{array}{*{20}{c}} 1\\ i \end{array}} \right) + \frac{1}{2}({{r_{xx}} - {r_{yy}} - {r_{yx}}} ){e^{i2\theta }}\left( {\begin{array}{*{20}{c}} i\\ 1 \end{array}} \right) \end{aligned}$$

where the first term demonstrates the co-polarization component RCP, and the second term corresponds to the cross-polarization component left-handed circularly polarized (LCP) with an additional phase shift 2θ.

In summary, while the split ring on the proposed meta-atom rotates an angle θ, the corresponding meta-atom can convert the input RCP wave into the output LCP wave with a phase shift 2θ. According to the PB phase principle [32,33], a metasurface constructed by the proposed meta-atom can obtain the full 2π phase coverage, which is an essential step to realize varieties of wavefront manipulation functions. Next FDTD method is used for numerical simulations. Optimized parameters of the metasurface structure are listed as follow:

p = 100 μm, r₀ = 40 μm, r₁ = 35 μm, w = 15 μm, t_i= 10 μm, t_s= 25 μm, and t_m= 2 μm. The conductivity of the copper is σ=5.8 × 10⁷ S/m, and the complex relative permittivity of the polyimide is 3.5 + 0.0027i. Besides, the complex relative permittivity of InSb can be obtained through the Drude model as shown in Eq. (4) [34–36].

(4)$$\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2}}{{{\omega ^2} + i\gamma \omega }}$$

Here ω is the resonance frequency. And ε_∞=15.68 represents high-frequency permittivity. The damping constant γ is set as 0.1π THz. Besides, the plasma frequency ω_p can be obtained by Eq. (5).

(5)$${\omega _p} = \sqrt {\frac{{N{e^2}}}{{{\varepsilon _0}m}}}$$

where e is the electronic charge, m is the effective mass of free carriers, ε₀ is the vacuum permittivity, and the intrinsic carrier density N is defined as Eq. (6).

(6)$$N = 5.76 \times {10^{14}}\sqrt {{T^3}} {e^{\frac{{ - 0.13}}{{kT}}}}$$

in which k is the Boltzmann constant and T is the temperature of InSb.

According to Eqs. (4–6), it is clearly noted that the permittivity of InSb can be changed by modifying the temperature where the InSb located. Therefore, InSb can achieve a corresponding temperature response [37,38]. Figure 2(a) and (b) show the real and imaginary parts of InSb permittivity at 220 K and 360 K respectively. InSb is in the insulation state at 220 K, that the real part and the imaginary part of its permittivity always equal to zero. Therefore, the top layer of the proposed PB meta-atom can be served as a split- ring. Rotating the top layer varying different angles can introduce different levels of phase shifts, which is helpful to achieve phase distributions that different wavefront manipulation functions required. Furthermore, InSb is in the metallic state at 360 K. The real part and the imaginary part of its permittivity varying with the frequency, which means the top layer of the proposed PB meta-atom can be identified as a closed ring. Therefore, rotating the top layer with varying different angles cannot introduce different phase shifts, which cannot satisfy the phase distributions of metasurfaces required by wavefront manipulation functions.

Fig. 2. (a) Real part of InSb permittivity at 220 K and 360 K, (b) Imaginary part of InSb permittivity at 220 K and 360 K.

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To further study the characteristics of meta-atom under different temperature conditions, the top layer of the proposed meta-atom is rotated with different angles. The rotation angle is designed in steps of π/8, which corresponding to the phase gradient π/4. Thus eight meta-atoms are obtained. The reflection coefficients of these meta-atoms at 220 K and 360 K are demonstrated in Fig. 3(a). The reflection coefficients of eight meta-atoms are over 0.82 ranging from 0.8 THz to 1.2 THz at 220 K. And their reflection coefficients are lower than 0.17 in the same frequency range at 360 K. By combining eight meta-atom, full 2π phase coverage can be achieved at 220 K and 360 K as shown in Fig. 3(b).

Fig. 3. (a) The reflection coefficients of the proposed meta-atom structure with different rotation angle at 220 K and 360 K. (b) The phase shift of the proposed structure with different rotation angle at 220 K and 360 K.

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In summary, switching the state of InSb by changing the temperature can influence the reflection coefficient of the proposed InSb-based PB meta-atom. Although all the results are achieved from simulations, it is feasible in experiment. A heater board can be used as the device holder to manipulate the temperature. For the fabrication method and experimental setup, some reported works [39,40] could give some references.

3. Multifunctional wavefront manipulation

Based on the above analysis, the eight proposed meta-atoms can convert the incident CP wave into cross-polarized component and adjust the reflection efficiency by tuning temperature. Then full 2π phase coverage can be achieved by combing these meta-atoms. In order to verify the working state of the wavefront manipulation function generated by the metasurface made of the proposed meta-atom can be switched by changing the temperature condition, anomalous reflector, reflective focusing metalens, and reflection-type OAM beam generators constructed by the proposed meta-atom are studied respectively under temperatures of 220 K and 360 K at the frequency of 1 THz.

3.1 Anomalous reflector

For achieving a linear phase coverage from 0 to 2π, the metasurface is periodically composed by three supercells with eight meta-atoms along x-axis with spatial discrete rotation step θ = 22.5°. Figure 4. (a) shows the schematic diagram of the supercell. The rotation angles θ of the top layer of these meta-atoms are set as 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, and 157.5° respectively, which can introduce a corresponding phase shift 2θ. The RCP THz wave was normally incident from the top of the metasurface. The anomalous reflection can be expressed by the generalized Snell’s law as shown in Eq. (7).

(7)$${n_t}\sin ({{\theta_r}} )- {n_i}\sin ({{\theta_i}} )= \frac{{{\lambda _0}}}{{2\pi {n_i}}}\frac{{d\Phi }}{{dx}}$$

where n_t and n_i are the refractive indexes of the media. θ_i and θ_r represent the angle of the input wave and output wave. λ₀ denotes the incident wavelength in vacuum. And $d\varPhi /dx$ is the phase gradient along the interface. In simulation, n_t and n_i are defined as 1, the incident angle θ_i is zero. Then the angle of anomalous reflection can be calculated by Eq. (8).

(8)$${\theta _r} = {\sin ^{ - 1}}\left( {\frac{{{\lambda_0}}}{{pN}}} \right)$$

where p is set as 10 μm, which is the period of the meta-atom. N is set as 8 which is the number of different meta-atoms used here. λ₀ equals to 300 μm, corresponding to the 1 THz frequency of the incident wave.

Fig. 4. (a) Schematic diagram of the supercell with eight meta-atoms, (b) Phases and reflection coefficients of LCP for the eight elements at frequency of 1 THz with temperature of 220 K.

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Figure 4. (b) shows that the reflection coefficients of these meta-atoms are higher than 0.9 at 1 THz. Besides, the phase gradient of these meta-atoms is in steps of π/4, which means the metasurface constructed by these meta-atoms can realize 2π phase coverage.

To characterize the anomalous reflector as shown in Fig. 5(a), electric fields of the LCP component at the frequency of 1 THz under temperature of 220 K and 360 K are shown in Fig. 5(b) and (c) respectively. Figure 5(b) shows that the normally incident RCP THz wave propagated along the z-axis is converted to LCP THz wave with an anomalous reflection angle θ_r=21° which closes to the theoretical result 22° calculated by Eq. (8) at 220 K. As raising the temperature into 360 K, the intensity of the electric field of the LCP component is close to zero as shown in Fig. 5(c), which means the working state of anomalous reflector is switched from “ON” to “OFF”. Furthermore, the above results can also be observed in far-field as shown in Fig. 5(d). It can be simply noted that the intensity with the temperature of 360 K is always lower than 0.1, while the peak value of the intensity with the temperature of 220 K reaches one at the reflection angle 21°. All these results illustrate that working state of the high-efficiency anomalous reflection introduced by the metasurface can be switched by changing temperature of InSb.

Fig. 5. (a) Schematic diagram of the proposed anomalous reflector. Electric field distribution of LCP wave at the frequency of 1 THz with temperatures of (b) 220 K (c) 360 K, (d) The intensity of the far-field with temperatures of 220 K and 360 K.

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3.2 Reflection-type metalens

Besides of the study on anomalous reflector, metalens also attracts scientists’ interests due to its potential applications. To achieve a focused beam with a spherical wavefront through metalens, an extra phase should be introduced by every meta-atom on the metasurface to compensate the propagation phase between the source and the focal point, ensuring the reflection waves from every meta-atom can reach at the focal point at the same time. To further illustrate the principle of metalens, the required phase distribution of the corresponding metasurface is shown as Eq. (9).

(9)$$\varphi (R,r) ={-} \frac{1}{\lambda }\left[ {2\pi \left( {\sqrt {{R^2} + {f^2}} - f} \right)} \right]$$

here, R=(x²+y²)^1/2 represents the distance from any point (x, y) on the metasurface to the center of the metasurface. And f represents the focal length.

In this section, we propose a 21 × 21 array constructed by the proposed thermally tunable InSb-based THz PB meta-atom to obtain metalens, as shown in Fig. 6(a). The focal length of it is set as 1500 μm. The periodic boundary conditions are applied on the x-axis and y-axis. And open boundary condition is applied on the z-axis. Figure 6(d) shows the phase distribution of the proposed metalens. It can be noted that the full 2π phase coverage is realized. Figure 6(b) and (e) shows the electric field of the LCP component in X-O-Z plane with temperatures of 220 K and 360 K respectively. It is obvious that the normal incident RCP THz waves propagating along the z-axis are reflected and transformed into LCP THz waves, then converged around 1500 μm at 220 K. On the contrary, the intensity of LCP component is closed to zero at 360 K, which means the output waves do not converge since the metasurface do not satisfy the requirement of phase distribution of the metalens. To further verify whether the value of the focal point is satisfied with the default value, Fig. 6(c) demonstrates the electric field intensity of x component at z = 1500 μm under different temperature conditions. The full width at half maximum (FWHM) of the curves is 314.38 μm. The peak value of the intensity curve equals to 1 at x = -2.2 μm with temperature of 220 K, which proves that the real focal point hardly deviates from the central axis. Moreover, the intensity is always lower than 0.15 at 360 K. Figure 6(f) shows the electric field intensity of z component at x = 0 μm with temperature of 220 K and 360 K. The peak value of the intensity curve equals to 1 at z = 1479 μm at 220 K, while the intensity is always lower than 0.15 with the temperature of 360 K. The simulated focal length is identified with the theoretical calculation result. These results demonstrate that the working state of the reflective focusing metalens can be controlled by adjusting the temperature of InSb.

Fig. 6. (a) Schematic of the proposed metalens. (b) Distribution of the reflected LCP electric field intensity at 220 K. (c) The intensity of electric field of the x component along x-axis. (d) Phase distribution of the proposed metalens. (e) Distribution of the reflected LCP electric field intensity at 360 K. (f) Intensity of electric field of the z component along z-axis.

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3.3 Orbital angular momentum (OAM) beam generators

OAM becomes an important topic, as it has unbounded quantum states theoretically to increase the capacity of optical communication systems. Furthermore, OAM-carrying beams also play important roles in wavefront manipulation, detection and THz imaging due to their unique energy distributions. In this section, metasurface generated vortex beams with different topological charges are accomplished by the proposed meta-atom. The phase of each position (x,y) on the metasurface should satisfy the following equation.

(10)$${\varphi _l}(x,y) = l \cdot {\tan ^{ - 1}}(y/x)$$

To describe OAM comprehensively, topological charge of the OAM generator l is set as 1 and 2 respectively. Therefore, the corresponding metasurfaces should be divided into 8 and 16 triangular regions as shown in Fig. 7(a) and (b), in which the adjacent regions maintain a phase gradient of π/4. The digitized phase in each region can be defined as (Eq. (11)).

(11)$${\varphi _i}(x,y) = \frac{{2\pi }}{N} \cdot \left[ {\frac{{{l_i} \cdot {{\tan }^{ - 1}}(y/x)}}{{2\pi /N}} + 1} \right]$$

where N represents the number of triangular regions.

Fig. 7. Digitized phase gradient distribution for the vortex beam generator with topological charges of (a) l=1, (b) l=2. Schematic diagrams of the vortex beam generator with topological charges of (c) l=1, (d) l=2.

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In simulation, the InSb-based PB metasurface consists 12 × 14 meta-atoms in the X-O-Y plane as shown in Fig. 7(c) and (d). A RCP Gaussian beam is applied as the incident wave along z-axis as it can eliminate the truncation effect produced by the metasurface. Figure 8(a1) and (b1) show the phase distributions of the reflection THz output wave at 220 K with different topological charges. It can be seen that the RCP input wave totally transform to the LCP output wave. Figure 8(a2) and (b2) show the intensity distributions of the LCP component at 220 K and 360 K with different topological charges. It should be noticed that the intensity of the LCP component always equal to zero at 360 K as shown in the insert diagrams. This means that the working states of OAM beams generators are turned to “OFF”. Besides, it can be observed that the intensity distribution showing the null points at 220 K, the number of which relates to the value of topological charge. This phenomenon is caused by phase singularity. The corresponding points can be found in Fig. 8(a1) and (b1). In addition, the purity of OAM mode with different topological charges are shown in Fig. 8(a3) and (b3). When the topological charge is set as 1, the purity of OAM beams with other modes are lower than 0.1. And the purity of the desired OAM beam is close to 0.9 when the topological charge is set as 2, while the purity under other mode are lower than 0.1. These results illustrate that the InSb-based OAM beams generators not only have a high quality, but the working state also can be manipulated by adjusting temperature.

Fig. 8. Phase distributions of the LCP at 220 K with (a1) l = 1 and (b1) l = 2. Intensity distributions of the LCP at 220 K (main figure) and 360 K (insert figure) with (a2) l = 1 and (b2) l = 2. Purity of OAM modes at 220 K with (a3) l = 1 and (b3) l = 2.

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4. Conclusion

In summary, we demonstrate a reflective InSb-based thermally tunable THz PB meta-atom, which can adjust the reflection efficiency of CP wave by tuning temperature and convert the polarization statement of CP wave. A full 2π phase coverage can be obtained on the metasurface conmposed by the proposed meta-atom through introducing geometric phase. To explore the charcteristcs of the proposed meta-atom, several functional metasurfaces like anomalous reflection generator, reflective focusing metalens and OAM beam generators are proposed. The states of these functions can be switched from “ON” to “OFF” by raising the temperature from 220 K to 360 K. All the simulation results are in great agreement with theoretical calculation results. The proposed reflective InSb-based thermally tunable THz PB meta-atom in this paper exhibits the ability of thermal tuning in reflective CP wave, which is expected to expand the application ranges of THz wavefront manipulation.

Funding

Central University Basic Research Fund of China (19CX02056A).

Acknowledgments

This research was funded by Central University Basic Research Fund, grant number 19CX02056A.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

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Multifunctional phase modulated metasurface based on a thermally tunable InSb-based terahertz meta-atom

Abstract

1. Introduction

2. Structure design and theoretical analysis

3. Multifunctional wavefront manipulation

3.1 Anomalous reflector

3.2 Reflection-type metalens

3.3 Orbital angular momentum (OAM) beam generators

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (11)

Optical Materials Express