1. Introduction

Recently, metasurfaces emerge as a rapidly growing research frontier due to their extraordinary abilities in high efficient light manipulations in ultrathin structures [1–4]. In particular, by tuning the phase change of the reflected or transmitted electromagnetic wave, the metasurfaces are of great importance in the applications of the light-matter interactions and the beam deflection. Besides, the terahertz spectrum has attracted enormous attention due to its unique properties such as low photon energy, spectral fingerprints of molecular vibrations and rotations, and good penetration ability [5]. The terahertz (THz) metasurfaces are desirably for imaging, identify unknown materials, and sensing [6]. The latest researches and applications of the THz metasurfaces include the high modulation depth THz metamodulator [7], using THz plasmonic for biological detection and sensing [8], electromagnetically induced transparency by electrical control [9], and perfect absorbers in THz band [10].

Regarding the surface electric field enhancement, a typical example is the magnetic mirror metasurfaces (or simply as magnetic mirrors) [11]. The magnetic mirrors can keep the phase change between the reflected and the incident electromagnetic waves in the range of $|{\mathrm \vartriangle }\phi _{\mathrm E}|<\pi /{2}$ (i.e., reducing the half-wave loss of reflection). Especially, the perfect magnetic mirrors, which possess both the zero-phase change (${\mathrm \vartriangle }\phi _{\mathrm E}={\mathrm 0}$) and a unity (or close to unity) reflectivity, can generate a constructive interference between the reflected and the incident electromagnetic fields, and hence significantly enhance the electric field near the interface [12]. Therefore, the magnetic mirrors attract great interest in the interface light-matter interaction enhancement, including perfect absorbers [13] and reflectors [14], subwavelength imaging [15], molecular fluorescence [16], photocurrent generation [17], etc. However, it is difficult for a magnetic mirror with fixed structures, such as a fixed grating period [18,19] or a fixed phase gradient [20–24] to behave as a perfect magnetic mirror with varying incidence angle over a certain frequency range.

In this work, we propose a functional reflective metasurface, operating in the terahertz band due to the rapid development in terahertz technology and applications [25], simply constructed by a one-dimensional periodic micro cylindrical dielectric rod array on a Teflon substrate with a metal-coated bottom. By real-time changing the incident direction and frequency of illumination wave, the reflected metasurface can maintain zero-phase change between the incident and reflected waves with high reflectivity at different incident angles and corresponding frequencies, meaning that the metasurface performs as a tunable perfect magnetic mirror. Furthermore, even in the case of oblique incidence, the perfect magnetic mirror can work as a retroreflector to reflect wave returning by the way of the incident wave.

2. Metasurface structure

The model of the reflective metasurface is depicted in Fig. 1(a). The micro cylindrical rods are parallel to the $z$-direction and possess a cross-section with a radius of $r={\mathrm 60.56\,\mu } {\mathrm m}$ in the $x$-$y$ plane. The period of the micro cylindrical rod array is $d={\mathrm 823.60}\,\mu {\mathrm m}$ along the $x$-direction. Besides, the thickness of the Teflon substrate is $h={\mathrm 191.57}\,\mu {\mathrm m}$. The material of the micro cylindrical rods is chosen as lithium tantalate (${\mathrm {LiTaO_3}}$), whose electric permittivity is determined as

 

Fig. 1. Schematics of (a) reflective metasurface and (b) computational simulation model applied in the finite element method.

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3. Results and discussion

Figure 2(a) shows the calculated reflectivity (R) and phase change (${\mathrm \Delta }\phi _{\mathrm E}$) of the reflected wave to a normal incident TE mode wave in the frequency range of 0.2 to 0.35 THz through the finite element method. We see that at 0.286 THz (point A), the reflected wave possesses ${\mathrm R=0.98}$ and ${\mathrm \Delta }\phi _{\mathrm E}={\mathrm 0}$, indicating that the metasurface performs as a perfect magnetic mirror. Figure 2(b) indicates the corresponding distribution of electric field $|{\mathrm {E_z}}|$ at frequency point A. A constructive interference on the metasurface implies the zero-phase difference between the incident and reflected waves. Besides, Fig. 2(c) exhibits the electric field ${\mathrm {E_z}}$ distribution of the dip indicated in Fig. 2(a). The distribution of the $z$-component of the current density ${\mathrm {J_z}}$ in Fig. 2(d) illustrates the induced magnetic resonance of the rod excited. According to the Electrodynamics formula ${\mathrm {Q_e=Re(\mathbf {J}^\ast \cdot \mathbf {E})/{2}}}$, we can compute the electromagnetic power loss density ${\mathrm {Q_e}}$ distribution of the dip in Fig. 2(e). It demonstrated that the strong resonant electromagnetic power loss of the rod is the origin of the dip in Fig. 2(a). Moreover, Fig. 2(f) illustrates that the metasurface also meets the condition of a magnetic mirror with $|{\mathrm \vartriangle }\phi _{\mathrm E}|<\pi /{2}$ and a reflectivity great than 0.75 as the incident angle of illumination wave is in the range of ${\mathrm 0^\circ }$ to ${\mathrm 4.6^\circ }$ and ${\mathrm 11.0^\circ }$ to ${\mathrm 15.5^\circ }$ at 0.286 THz, respectively. From the figure, we see that the reflected wave displays a Fano-like dip at ${\mathrm 5.7^\circ }$ with ${\mathrm R=0.11}$ and a near-zero phase change. The highly localized electromagnetic energy into the micro cylindrical rod [inset of Fig. 2(f)] indicates that the dip [including the dip shown in Fig. 2(a)] may be originated from the interference of the broad Mie resonances of each rod and the narrow resonance of the rod array [30].

 

Fig. 2. The reflectivity (blue curve) and the phase change (red dashed curve) of the reflected wave from a reflective metasurface to the normal incident TE electromagnetic wave. (b) The electric field distribution of an incident wave in one period of the metasurface at 0.286 THz (point A). (c)-(e) The electric field ${\mathrm {E_z}}$ distribution, $z$-component of the current density (${\mathrm {J_z}}$, ${\mathrm {A/m^3}}$), and electromagnetic power loss density (${\mathrm {Q_e}}$, ${\mathrm {W/m^3}}$) of the dip indicated in (a), respectively. (f) The reflectivity (blue curve) and the phase change (red dashed curve) of the reflected wave at 0.286 THz versus the angle of incidence from ${\mathrm 0^\circ }$ to ${\mathrm 15.5^\circ }$. The inset exhibits the electric field distribution of wave in one period of the metasurface at the angle of incidence of ${\mathrm 5.7^\circ }$. (g) The reflectivity (blue solid curve, ${\mathrm R_0}$), the transmissivity (blue dashed curve, ${\mathrm T_0}$), and the phase change (red curve, ${\mathrm \vartriangle }\phi$) of the reflected wave from periodic micro cylindrical rod array to the normal incident TE electromagnetic wave. (h)-(i) The energy density distribution of a normal incident Gaussian beam at 0.286 THz with an amplitude of 1 V/m in the metasurface and periodic micro cylindrical rod array (without substrate), respectively. The incident wave marked by a red arrow, the reflected wave marked by a blue arrow and ${\mathrm R_0}$, the transmission wave marked by a white arrow and ${\mathrm T_0}$.

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Figure 2(g) displays the reflectivity, the transmissivity, and the phase change of the 0th order reflected wave of the periodic micro cylindrical rod array (without the Teflon and PEC substrate) to a normal incident TE electromagnetic wave. We see that at 0.286 THz, the reflectivity is ${\mathrm R_0=0.95}$ while the transmissivity ${\mathrm T_0}$ is near zero, and the phase change is ${\mathrm \vartriangle }\phi _{\mathrm E}=-0.05\pi$, meaning that only a periodic micro cylindrical rod array can perform as a near-perfect magnetic mirror. Figures 2(h) and 2(i) show the numerically simulated energy density distribution of a normal incident Gaussian beam at 0.286 THz to the metasurface and the cylindrical rod array (without substrate), respectively. We see that the two structures possess almost complete back-reflected (${\mathrm R_0}$) without any higher-order reflections. Furthermore, approaching zero transmission (${\mathrm T_0}$) of the cylindrical rod array (without substrate) [Fig. 2(i)] demonstrates that the dielectric rod array itself can behave as a perfect magnetic mirror under the condition of point A of Fig. 2(a).

To reveal the physical mechanism of the perfect magnetic mirror effect of the metasurface, we calculate the multipolar scattering of a single micro cylindrical rod to the normal incident TE mode electromagnetic wave. According to Mie theory [31], the scattering coefficient can be expressed as

 

Fig. 3. (a) Multipolar scattering coefficients of the electric dipole (ED) moment and the magnetic dipole (MD) moment in one micro cylindrical rod according to Mie theory. The inset displays the distribution of the electric field at 0.286 THz in the micro cylindrical rods, which coincides with the MD resonance. (b) The scattering efficiencies of multiple cylindrical rods. N denotes the number of the cylindrical rods.

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Generally, the phase of a reflection wave is usually dependent on the incident direction and frequency in the case of the metasurface is fixed. In the following, we explore the effect of incident angle and frequency of the illumination wave on the magnetic mirror function of the metasurface. For simplicity, we first consider the relation of reflection efficiency with the incident angle and frequency, because a magnetic mirror should also hold a relatively high reflectivity. Figures 4(a) and 4(b) display the reflectivity differences between the 0th and ${\mathrm {\pm 1st}}$ orders (${\mathrm {R_1-R_0>0}}$ and ${\mathrm {R_{-1}-R_0>0}}$) in the ranges of the incident angle from ${\mathrm 0^\circ }$ to ${\mathrm 70^\circ }$ and the frequency from 0.35 to 1.5 THz, respectively, where the cases of ${\mathrm {R_1-R_0}}$ and ${\mathrm {R_{-1}-R_0}}$ reaching their maximums will be considered because in the cases the 0th order reflections may be suppressed effectively while the ${\mathrm {\pm 1st}}$ orders can reach their peak efficiency under the condition of oblique incidence. For the ${\mathrm {R_1-R_0}}$, the maximum is 0.57 related to the angle of incidence of ${\mathrm 7^\circ }$ and the frequency of 0.71 THz. In such a case, the reflectivities of the +1st order and the 0th order reflected waves are ${\mathrm {R_1=0.71}}$ and ${\mathrm {R_0=0.14}}$, respectively. Due to a little low reflection efficiency, we will focus our discussion on the case of the -1st order reflection as ${\mathrm {R_{-1}-R_0}}$ possesses a difference of higher than 0.95. In this case, the incident wave can be in the range of angle from ${\mathrm 27^\circ }$ to ${\mathrm 30^\circ }$ and frequency from 0.37 to 0.39 THz or from ${\mathrm 17^\circ }$ to ${\mathrm 19^\circ }$ and from 0.57 to 0.59 THz, respectively. In the latter region, however, the metasurface does not perform as a perfect magnetic mirror (the reflected wave cannot maintain the same phase with the incident wave). Instead, in the former region, we find that a 0.382 THz incident wave at ${\mathrm 28.45^\circ }$ incident angle behaves as a perfect magnetic mirror [Fig. 4(c), point B] with as high as ${\mathrm {R_{-1}=0.99}}$ reflectivity. The electric field distribution of wave on the metasurface at frequency point B demonstrates the constructive interference, indicating the identical phase between the reflected and incident waves [Fig. 4(d)].

 

Fig. 4. The reflectivity differences between the ${\mathrm {\pm 1st}}$ and the 0th orders waves in the range of (a) ${\mathrm {R_1-R_0>0}}$ and (b) ${\mathrm {R_{-1}-R_0>0}}$ as the incident angle changes from ${\mathrm 0^\circ }$ to ${\mathrm 70^\circ }$ and the frequency from 0.35 to 1.5 THz, respectively. (c) The phase change (red solid curve, ${\mathrm \vartriangle }\phi _{-1}$) and the reflectivity (blue solid curve, ${\mathrm R_{-1}}$) of the -1st order reflected waves to the incident wave at ${\mathrm 28.45^\circ }$. (d) The distribution of the electric field in one period of the metasurface at the incident angle of ${\mathrm 28.45^\circ }$ at 0.382 THz (point B). (e) The retroreflection energy density of the -1st order reflected waves when a Gaussian beam at the incident angle of ${\mathrm 28.45^\circ }$ at frequency point B with an amplitude of 1 V/m. The incident wave marked by a red arrow, the -1st order reflected wave marked by a blue arrow and ${\mathrm R_{-1}}$.

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Most interestingly, as a perfect magnetic mirror, we further find that the metasurface can behave as a retroreflector that the reflection wave returns by the way of the incident wave [Fig. 4(e)] as the incident wave is with frequency 0.382 THz and ${\mathrm 28.45^\circ }$ incident angle. Substituting the above frequency and incident angle into the grating equation, we find that the diffraction angle of the order is indeed the same as the angle of the incident wave.

4. Conclusion

To conclude, a tunable perfect magnetic mirror working in the terahertz band is achieved through the simple reflective metasurface constructed by a one-dimensional periodic lithium tantalate micro cylindrical rod array on a Teflon substrate with a metal-coated bottom. The MD resonance of each micro cylindrical rod guarantees to the zero-phase change between the reflected and the incident electric fields and the near-unity reflectivity for the wave at 0.286 THz under normal incidence. Varying the illumination direction and frequency of the incident wave to, for example, ${\mathrm 28.45^\circ }$ and 0.382 THz, respectively, the metasurface can still maintain the property of perfect magnetic mirror with as high as ${\mathrm R_{-1}=0.99}$ reflectivity, and further behaves as a retroreflector that the reflection wave returns by the way of the incident wave. Our results may provide the metasurfaces novel potentials in near-field detection, imaging communication, energy harvesting, and functional photonic devices, etc.