## Monday, June 12, 2017

### Abstract-A metasurface-based prism analogue for terahertz rainbow spectrum manipulation

Shen Zheng, Chao Lia), Shichao Li, Xiaojuan Zhang, Guangyou Fang,

http://aip.scitation.org/doi/10.1063/1.4984749

Optical prisms can spread compound light spatially into a rainbow and have widespread applications in spectroscopy and imaging. Limited by the natural materials as well as technologies, there has been no natural counterpart of the optical prism that works in the Terahertz (THz) band so far. In this letter, a THz prism analogue based on metasurfaces working in the transmission diffraction mechanism is first proposed to generate the THz rainbow spectrum. The physics of different modes excited by the interaction between the incident wave and the metasurface is investigated in theory and simulation. A coherent enhancement method was developed to improve the mode competition of the rainbow spectrum over other unwanted leaky modes to guarantee the high transfer efficiency of the wavelength dependent transmission diffraction. The experimental results show that the prism analogue can spread the incident spectrum from 0.15 to 0.22 THz in an angular scope of about 30.8° with comparatively high transferring efficiency.
An optical dispersive prism allows the separation of white light into its constituent spectrum as a rainbow. Consequently, different wavelengths are steered toward different directions and thus are discriminated with each other. This characteristic enables widespread applications in communication, instrumentation, and ultrafast signal processing, such as in spectroscopy,imaging, wavelength multiplexing, and demultiplexing.
In the visible band, the optical rainbow can be achieved based on a shaped glass prism with the frequency dependent refractive index. As shown in Fig. 1(a), the optical prism divides the compound light into the rainbow light with spectrum separated spatially. With the development of artificial materials, new concepts have also been reported for the manipulation of light polarization, phase, and deflection in the visible and ultraviolet frequency band.
The terahertz (THz) wave has unique properties due to its special position in the electromagnetic spectrum, which lies in the gap between the electronics and photonics. In recent years, spectroscopy, imaging, and sensing with EM radiation in the THz band have aroused considerable interest and promising applications but are still greatly limited by the lack of functional devices. In the THz band, due to the natural materials as well as the design and fabrication difficulties, there is no natural counterpart of the optical prism so far to spatially separate the THz spectrum.
In this letter, a THz prism analogue with the artificial metamaterial is proposed to generate a THz rainbow spectrum as shown in Fig. 1(b). The proposed device is based on metasurfaces with the planar structure, which are 2D equivalents of volumetric metamaterials and have been recently explored to arouse new concepts in physics and produce exotic functionalities, including high-efficiency THz modulators, low-loss polarization conversions, and the abnormal reflections and transmissions of THz waves.
The metasurface-based prism analogue discriminates THz wavelengths in the transmission diffraction mode. It has a planar periodical structure with a unit cell as shown in Fig. 2. The unit cells are formed by the dielectric substrate with metal strips of special geometries on the topside. The incident plane is the XOZ plane. Dx is the length of the unit in the X direction, while Dy is the length of the unit in the Y direction. The THz incident wave illuminates the bottom of the periodical structure, shown as the green dashed line in Fig. 2. The incident angle between the incident direction and the Z direction is defined as θ0. The metasurface is fabricated on a Rogers 5880 substrate of thickness 0.254 mm. The incident wave frequency band is chosen from 0.15 THz to 0.22 THz, and θ0 is 45°. The electric field is polarized along the Y direction.
To generate a rainbow spectrum, the unit structure and the periodical structure should be carefully optimized to realize the wavelength dependent diffraction in the chosen THz band. The diffraction angle between the diffraction wave and the Z direction is indicated as θm in Fig. 2. In this work, two H shaped metal strips with specific dimension are designed in each unit cell to enhance the coupling efficiency from the incident wave to the frequency-dependent diffraction as shown in Fig. 2. The optimized unit cell sizes are Dx = 1.4 mm and Dy = 0.6 mm, and Table I shows the detail dimension of each strip at the unit cell.

TABLE I. The detail dimension of each strip at the unit cell.
TABLE I.The detail dimension of each strip at the unit cell.
L1L2L3L4d
0.2 mm0.4 mm0.08 mm0.5 mm0.5 mm
Due to the response of the periodical unit cells, the Floquet mode can be excited along the metasurface under the illumination of the THz incident wave. The metasurface can couple the incident waves into diffraction waves and surface waves. The surface waves are confined near the metasurface, with phase velocity slower than the speed of light in free space and cannot be radiated toward the free space. The diffraction waves are leaky toward the half space opposite to the incident wave, with the phase velocity faster than the speed of light in free space. As long as the phase velocity of a diffraction mode is dependent on the wavelength, the mode can contribute to the rainbow spectrum generation and realize the function of the prism in THz rainbow manipulation.
Based on the EM simulation, the amplitude and phase distributions of the Ey component along the metasurface can be obtained numerically. Then, the phase change in the nth-order mode along the X direction in a unit cell, which is referred to as ${\Delta \phi }_{n}$, can be derived using the Floquet theorem for periodical structures. The phase velocity of each mode can be obtained by the formula
 Vpn=ωDxΔφn,${V}_{pn}=\frac{{\omega D}_{x}}{{\Delta \phi }_{n}},$ (1)
where $\omega$ is the angular frequency.
Figure 3 shows the full wave simulation results of the phase distribution of the Ey component on the top surface of a unit cell under the excitation of THz incident waves at different frequencies from 0.15 THz to 0.22 THz.
Figure 4 shows the phase velocity of the zero-order mode, the 1st order mode, and the 2nd order mode derived based on the field distribution shown in Fig. 3. It can be seen that only the phase velocities of the zero-order mode and 1st order mode are faster than the speed of light and hence radiate into the free space as the diffraction modes. All the other modes have phase velocities slower than the speed of light and hence being confined near the metasurface as the surface wave modes. Additionally, for the diffraction modes, only the 1st order mode has the phase velocity varying with the frequency, while the phase velocity of the zero-order mode remains unchanged with varying frequencies. This means, only the 1st order mode can contribute to the generation of the rainbow spectrum.
To improve the coupling efficiency of the incident THz wave to the 1st order diffraction mode, two well-designed H shaped subcells are incorporated into each unit cell to achieve the coherent diffraction enhancement. Here, different subcells generate different transfer phases from the incident wave to the diffraction mode, which are referred to as abrupt phase shifts in this letter. Supposing ${\phi }_{1}$ and ${\phi }_{2}$ are the abrupt phase shifts corresponding to the subcells 1 and 2. As the distance d and the abrupt phase shifts satisfy following condition:
 φ12=−2πDxd+(φ2−φ1)=2nπ, n=0,±1,±2,…${\phi }_{12}=\frac{-2\pi }{{D}_{x}}d+{\left(\phi }_{2}-{\phi }_{1}\right)=2n\pi , \mathrm{n}=0,±1,±2,\dots$ (2)
the total phase difference ${\phi }_{12}$ of the two subcells in the diffraction direction would be 2nπ. Namely, the phase difference caused by the path difference in the first term of Eq. (2) is compensated by the difference of the abrupt phase shifts in the second term of Eq. (2), which leads to the coherent enhancement of the diffraction beam and the suppression of the unwanted zero-order mode.
Based on Eq. (2), an optimization process combined with full wave electromagnetic simulation is developed. The goal of the optimization is to keep the phase difference of the abrupt phase shifts to be constant over the whole band from 0.15 THz to 0.22 THz, with values satisfying Eq. (2), by tuning the sizes of the two subcells. In our optimization process, d is set to be from 0.3 mm to 1.1 mm, with 0.1 mm interval. For each individual d, the abrupt phase for the two subcells is optimized using the software HFSS. Finally, comprehensively considering the unit cell length and the fabrication difficulty, the optimization result with d = 0.5 mm is chosen for the sample fabrication and experiments. Figure 5 shows the corresponding results of the abrupt phase shifts for the two subcells, with the phase difference remaining almost unchanged over the comparatively broad bandwidth.
The metasurface-based Prism Analogue was fabricated by the laser fine etching technology. Figure 6 shows the 1/8 graphics of the fabricated device. To characterize the rainbow manipulation property, a THz quasi-optical measurement setup was developed. Figure 7(a) is the schematic diagram of the setup.
A microwave Vector Network Analyzer (VNA) is employed to drive the THz transmitter to generate signals in the band 0.15–0.22 THz as shown in Fig. 7(a). The signal was the output from a transmitting horn and then collimated by a polyethylene lens to illuminate the fabricated prism sample, with an incident angle of 45°. The diffraction wave leaking from the sample from the other side was received by a probe at the front end of a THz receiver. The measured intermediate signal of the THz receiver was sent back to the VNA for signal processing to obtain the amplitude and phase of the THz field for each frequency point by a frequency sweeping measurement. In the experiment, the THz receiver is set on a motorized platform to perform a raster scanning measurement of the diffraction field distribution along the x direction. The scanning scope of the platform is 600 mm. Figure 7(b) shows the experimental setup.
With the transmission S parameter measured at different frequency points and different receiver locations along the X axis, the frequency (or wavelength)-dependent beam scanning properties can be verified. Figure 8 shows the measured field density distribution for different frequencies along the x direction. Different colors from red to purple represent different frequencies in the range of 0.15 THz–0.22 THz, and the brightness of the same color means the value of the field which is greater if the brightness is greater. It can be seen that the peak density occurs at different locations for different frequencies, which means that the spectrum of the incident THz beam was separated along the x direction, and one can obtain a rainbow THz spectrum with the proposed device in this letter. The spectrum from 0.15 to 0.22 THz was spread in about 31.1 cm scope along the x direction at the distance of 56.5 cm. To characterize the far field characteristics, the field extrapolation method was employed to deal with the measured amplitude and phase information to get the radiation pattern of the metasurface under the excitation of the incident THz wave. From the results shown in Fig. 9, it is found that the THz prism analogue achieves beam scanning from −46.2° to −15.4° over the frequency range of 0.15 THz–0.22 THz with the scanning angle scope as wide as 30.8°. To investigate the transfer efficiency from the incident THz wave to the wavelength dependent diffraction mode, the field patterns for the direct transmission beam without the metasurface are also measured for the whole frequency band. Figure 10 shows the ratio of the amplitudes between the diffraction mode and the direct transmission beam, with the comparison between the measurement and the simulation. It can be seen that the measured ratio is slightly lower than the simulated one but is still higher than 0.5 almost for the whole bands with the maximum value of 0.625, in spite of the unavoidable dielectric loss, unwanted reflection, and mode competition from the zero-order mode. This verifies the effectiveness of the coherent enhancement of the rainbow spectrum in our design.
In this letter, a prism analogue, which works in the transmission diffraction mechanism, is first proposed to generate the THz rainbow spectrum based on THz metasurfaces. The physics of different modes excited by the metasurface and the mechanism of the prism are investigated in theory with numerical simulation. To improve the transfer efficiency from the incident THz wave to the rainbow spectrum, a coherent enhancement method with multiple unit cells was proposed to optimize the metasurface. The experimental results show that the prism analogue can spread the incident spectrum from 0.15 to 0.22 THz in an angular scope of about 30.8° with comparatively high transferring efficiency. The convenience of the transmission diffraction topology, comparatively simple fabrication process, and low cost may bring a lot of potential applications of the proposed device, such as THz spectroscopy, imaging, and target detections with high frame rates.
This work was supported by the National Natural Science Foundation of China (Nos. 11174280 and 61671432).
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