Wavelength de-multiplexing metasurface hologram

A wavelength de-multiplexing metasurface hologram composed of subwavelength metallic antennas is designed and demonstrated experimentally in the terahertz (THz) regime. Different character patterns are generated at the separated working frequencies 0.50 THz and 0.63 THz which determine a narrow frequency bandwidth of 130 GHz. The two working frequencies are around the central resonance frequency of the antennas where antennas behave strong wavefront modulation. Each antenna is fully utilized to control the wavefront of the metasurface at different frequencies by an optimization algorithm. The results demonstrate a candidate way to design multi-colors optical display elements.


Principle
The basic ideal for multi-color metasurface hologram is presented in Fig. 1. The metasurface device is composed of predesigned antennas. When the device is illuminated with desired multi-wavelength light, the light with different frequency will be modulated by each antenna. On the preset plane, the light with same frequency will interfere and generate the desired pattern. The pattern generated by different frequency can overlap with each other, thus a colorful image can be generated on the preset plane. In order to demonstrate this concept, a metasurface device in the THz range is designed, fabricated, and characterized. The device is composed of 128*128 metallic (gold) antennas deposited on a high resistive silicon substrate. Each antenna contributs to the wavefront modulation of metasurface at the preset working frequencies. When the metasurface is illuminated by the linearly polarized plane wave from the substrate side, the image can be reconstructed by the transmitted cross-polarized light. The observation plane for 0.50 THz and 0.63 THz is the same which locates at a distance 5.0 mm from the structure plane of metasurface. The character image "C" and "N" will be reconstructed for 0.50 THz and 0.63 THz, respectively. Two character images overlap at the observation plane for their working frequency simultaneously.
The same C-shaped subwavelength metallic antennas proposed by Zhang et al. in the THz regime 18 , as shown in Fig. 2(a), are adopted as dual-color wavefront modulator units. The period of C-shaped antennas is 80 μ m, which is about 1/5 smaller than the working wavelength. At 0.63 THz, the antennas from No. 1 to No. 8 provide pure phase modulation with total phase range of 2π and a phase step of π /4, as shown by green dot curve in Fig. 2(b). But for 0.50 THz, the biggest deviation of amplitude modulation of antennas (red solid curve) is about 20% and phase step is not always π /4 for two neighbor antennas, especially for No. 4 and No. 5 (red dot curve). Thus it's better to consider both amplitude and phase modulation of the hologram for achieving a good reconstruction quality.

Results
The dual-color THz metasurface hologram is designed by the simulated annealing (SA) algorithm (see Methods) and fabricated by the ultraviolet lithography. The antenna arrays are transferred to the gold film which is deposited on the high resistive silicon substrate. The thickness of gold film and silicon substrate is 100 nm and 350 μ m, respectively. The metasurface is composed of 128 × 128 pixels with total size of 10.240 mm × 10.240 mm, as shown in Fig. 3(a). The propagation distance between the observation plane and exit plane of metasurface device is 5.0 mm.
The rebuilt character patterns of THz metasurface hologram at the observation plane are recorded using a THz focal plane imaging system 21,22 based on electro-optics sampling method, see Fig. 3(b). The THz pulse is generated by a femtosecond laser beam with the central wavelength of 800 nm exciting on a ZnTe crystal. The parabolic mirror (PM) collects and collimates the THz radiation. Another ZnTe crystal is used to detect the transmitted cross-polarization wave located on the observation plane (see Methods).
The recorded hologram patterns at 0.50 THz and 0.63 THz are shown in Fig. 4(c,f), respectively. The desired objective images Fig. 4(a,d) and the design results Fig. 4(b,e) obtained by the simulated annealing algorithm are also displayed for comparison. The x-and y-axis are corresponding to the horizontal and perpendicular polarization directions of light. The optical axis is located at (x = 0, y = 0) which centered at the detection area. From the designed results shown in Fig. 4(b,e), it can be seen that the rebuilt character patterns are overlapped around the optical axis with slight cross-talks for each working frequencies. The measured "C" and "N" patterns in Fig. 4(c,f) agree well with the desired patterns about the character shape, location and size at 0.50 THz and 0.63 THz. Efficiency is always an important issue for practical applications 28 . The cross-polarization conversion efficiency of the device is above 10%, measured with a THz time domain spectroscopy at the working frequencies.
In Fig. 5, the intensities of object images, design results, and recorded images along the straight line y = 0 are presented for comparison. In Fig. 5(a), one peak between x = − 2.5 mm and x = 0 mm indicates the character "C" rebuilt at working frequency 0.50 THz. In Fig. 5(b), three peaks are observed due to the character "N" rebuilt at 0.63 THz. The measured results behave lower signal noise ration than the design results obtained by the simulated annealing algorithm at both working frequencies while the main features can be distinguished by bare eyes.

Discussion
A narrow-band wavelength de-multiplexing metasurface hologram is proposed. A THz dual-color synthesis device based on the wavefront modulation of metallic subwavelength C-shaped antennas is demonstrated. The character patterns are rebuilt by the transmited cross-polarization light at the same observation plane. The metasurface is designed by the SA algorithm to fully utilize the spatial bandwidth product in the limited total size while each antenna performs strong amplitude and phase modulations at the two nearby working frequencies. It is expected this method can be extended to visible range to achieve RGB hologram.

Methods
The amplitude and phase modulations of the metallic antennas at different frequency are calculated by a commercial software package FDTD Solution based on the finite-difference time-domain method. The metasurface consisted of antenna arrays is optimized by the SA algorithm. The SA algorithm 29 is not parallelized and the computation cost becomes huge when the number of total pixel increases. We adopted two ways to accelerate the convergence speed. One is the optimized annealing temperature curve. An exponential temperature curve is selected as t(k) = t 0 × α k , where t 0 is the initial temperature, k is iteration number and α is the temperature ratio which is set to 0.98 in the optimization. The other is difference calculation method of Fresnel diffraction. In the iterations, we evaluate each pixel one by one. The discrete form of Fresnel diffraction integral to compute the observation-plane optical field U 2 (r, c) from knowledge of the source-plane optical field U 1 (j, k) is expressed as: where G x (r, j) and G y (c, k) are the Fresnel transform matrix, Scientific RepoRts | 6:35657 | DOI: 10.1038/srep35657 x ik z In each iteration, a pixel of source-plane optical field U 1 (j, k) is changed from one antenna to another antenna with the increment Δ U ξ,η , x y 2 2 , Noted only at one pixel Δ U ξ,η is nonzero, thus the computation is reduced from calculation of product of three matrix in Eq. (1) to the product of two one-dimensional vectors G x (r, ξ) and G y (c, η) in Eq. (5). Compared with other methods to calculate the wave propagation, this approach is faster at the cost of accuracy. However, experiment results demonstrate this approach is acceptable.

Measurement method.
A THz focal plane imaging system is adopted to character the performances of the device 30 . A laser beam with central wavelength 800 nm, repeated frequency 1 kHz, pulse width 100 fs and average power 800 mW is divided to pump beam and probe beam by a beam splitter. The pump beam is incident on a < 110> ZnTe crystal with 3 mm thickness to generate THz radiation. Then the THz radiation is collected and collimated by a 90 degree off-axis metallic parabolic mirror with 150 mm focal length. Thus the THz beam is converted to a linearly polarized plane wave and illuminates on the sample normally. The probe beam is expanded to about 15 mm diameter by a combination of concave and convex lens. Then a 50/50 beam splitter is used to reflect the probe beam to electro-optical detecting crystal (the other < 110> ZnTe with 3 mm thickness). Finally, the probe beam modulated by the THz radiation in the crystal is reflected by the back surface of ZnTe crystal and recorded by an imaging module including a quarter wave plate, two lenses, a Wollaston prism and a CY-DB1300A CCD. The CCD is synchronized with the chopper in the pump beam to acquire the THz image with the dynamics subtraction technique. The mechanics delay line is adopted to scan a total 10 ps THz temporal images with a step of 20 μ m. To enhance the signal to noise ratio, 100 frames are recorded and averaged at each scan position.
In the experimental, the co-polarization component is filtered out by the polarization dependent detection method 30 . In the THz focal plane imaging system used in this work, a < 110> ZnTe is used to detect THz wave. The horizontal component of the THz electric field can be measured when the probe polarization is parallel to the < 001> axis of the crystal, and the half of the vertical component can be measured when the angle between the probe polarization and the < 001> axis is 45°. The probe laser beam is linearly polarized and the polarization state can be rotated by a half wave plate (HWP), thus two components of the THz wave can be achieved.