Realization of Terahertz Wavefront Manipulation Using Transmission-Type Dielectric Metasurfaces

Introduction

The traditional electromagnetic (EM) devices are designed to realize the control functionalities by adjusting the physical geometrical shape and the component material [1]. Recently, metasurfaces, made of a large number of subwavelength structures, have performed very well to locally manipulate the wavefront of EM waves. Many EM controls have achieved by metasurfaces, including ultrathin planar lenses [2–4], multi-focal devices [5–9], vortex beam [10–12], and various holography [13, 14]. With the development of terahertz (THz) technology, highly efficient, compact functional devices are required, which can be provided by dielectric metasurfaces.

In this paper, we propose a transmission-type, fused silica metasurface to manipulate THz wavefront. Different from previous dielectric pillars on substrate [10, 11, 15] or cross shaped restorers [16–19], the metasurface unit cell consists of a cross net shaped structure with a rectangular pillar placed in the center. The weak coupling of each basic unit is formed by the high refractive index difference between the fused silica and the surrounding air, which concentrates the confined energy within the central structure. Compared with dielectric pillars, the proposed metasurface have more adjustable unit structural parameters. Moreover, the metasurface reduces the difficulty in fabricating because each of the basic unit is reciprocally freestanding by cross shaped restorers without substrates. Through this work, on-axis and off-axis focusing, generation of a non-diffracting Bessel beam, and multi-spot focusing are demonstrated. The total control efficiency could be as high as 62% in numerical simulation. These advantages of the proposed metasurface will enrich THz functional devices, and provide a novel way for the design of multifunctional miniaturized devices.

Results and Discussion

Figure 1A schematically shows the metasurface structure and the inset shows the details of geometry basic unit cell. Both the width a and length b are in the range of 0.3–1.9 mm, respectively. The width of the cross net shaped structure w is set to 0.3 mm. The period T and thickness h are 2 mm and 3.6 mm, respectively. The amplitude transmission and corresponding phase delay for x-polarized incident waves are calculated using a commercially available software package COMSOL Multiphysics (Figures 1B,C). The phase shift can cover the range of 0–360°, which facilitates the wave control. Eight unit cells are selected as (a, b) = (0.8, 1.6 mm), (0.58, 1.5 mm), (0.54, 1 mm), (0.35, 0.35 mm), (1.9, 1.86 mm), (1.65, 1.75 mm), (1.25, 1.7 mm), (0.95, 1.65 mm) for fully covering the phase range with an interval of 45°, as shown in Figure 1D. The average amplitude transmittance of the unit cells is ~93%. To demonstrate modulation ability of the proposed metasurface, several THz functional devices are designed based on the eight unit cells.

Figure 1. Proposed dielectric metasurface and the control characteristics of metasurface unit cells. (A) Schematic of the proposed metasurface. The inset shows a basic unit cell of the metasurface. (B,C) Amplitude transmission and corresponding phase shift, respectively, of x-polarized wave with a frequency of 0.14 THz. (D) Phase shift and amplitude transmission for the selected eight unit cells.

We first demonstrate on-axis and off-axis focusings achieved using the proposed metasurface. The phase distribution on the metasurface for realizing this focusing can be described as: $\phi (x)=\frac{2\pi }{{\lambda }_0}(\sqrt{{(x-x_0)}^2+L^2}-L)$, where λ₀ for free space, and x and x₀ are the position coordinates of basic units and the focal spot, respectively, and L is the focal length. The obtained phase profiles are quantized into eight values, ranging from 0 to 360°. The eight basic units are placed on the corresponding positions. When x-polarized THz waves are normally incident on the designed metasurface device, the metasurface modifies the wavefront. The transmitted waves are then focused into an on-axis spot with the propagation distance L = 5 cm, as shown in Figure 2A. The control efficiency is defined as the ratio of the power of E_x component on the focal plane to that of the incident wave. The on-axis focusing efficiency is 60%, which is much higher than the single-layer plasmonic metasurfaces [20]. Furthermore, an off-axis focus lens with the same focal length (L = 5 cm) is designed. The off-axis distance is 8 mm, as shown by the simulated results in Figure 2B. The simulated control efficiency is 62%.

Figure 2. Simulated intensity distributions of (A) on-axis and (B) off-axis focusings with a focal length L = 5 cm.

Furthermore, we demonstrate generation of a non-diffracting Bessel beam using the dielectric metasurface. The phase distribution on the metasurface for generating a Bessel beam can be described as: $\phi (x)=C\frac{2\pi }{{\lambda }_0}\left|x\right|$, where C is a coefficient. When x-polarized waves are normally incident on the metasurface with a width of 52 mm, the arranged unit cells transform the wavefront into an axisymmetrical slope shape, so that a Bessel beam can be formed by the wave interference [21]. The simulated intensity distribution of a one-dimensional Bessel beam is shown in Figure 3. The control efficiency is 45%. Compared with the focusing in Figure 2A, the focal depth of the Bessel beam is much longer and the beam width changes much more slowly along the long propagation direction, which are consistent with the typical characteristics of the non-diffractive Bessel beam.

Figure 3. Simulated intensity distribution of generation of a non-diffracting Bessel beam.

To demonstrate the versatile control of the proposed metasurface, a one-dimensional multi-spot focusing lens (MSFL) is designed. The phase distributions for obtaining one-dimensional double-spot and tri-spot focusing are calculated, respectively, using the Gerchberg-Saxton (GS) retrieval algorithm [22] on the basis of Fresnel diffraction. In the simulations using the COMSOL Multiphysics, the required phase distributions can be obtained by arranging the aforementioned unit cells in the one-dimensional metasurface with a width of 52 mm. Then the double-spot and tri-spot focusing are formed by the wave interference, respectively. The simulated intensity distribution of one-dimensional double-spot focusing is shown in Figure 4A (off-axis ± 11 mm). The control efficiencies for the two spots are 25 and 24% respectively. Thus, the total control efficiency is 49%. Tri-spot focusing with the same focal length is also demonstrated, as shown in Figure 4B (on-axis and off-axis ± 17 mm). The efficiency for each is 19, 18, and 18%, and thus the total control efficiency is 55%. The simulated field distributions on the focal plane are consistent with the predesigned results.

Figure 4. Simulated intensity distributions of (A,B) double-spot and tri-spot focusing, respectively, with a focal length of 5 cm.

Conclusion

In summary, a dielectric metasurface based on a fused silica resonator, consisting of a cross net shaped structure with a rectangular pillar placed in the center, is proposed to manipulate THz waves. As a proof of concept, several transmission-type devices for THz spatial modulation are designed, including on-axis and off-axis focusing, generation of a non-diffracting Bessel beam, and multi-spot focusing. The simulated control efficiencies range from 45 to 62%. The versatile control with high efficiency makes the metasurface valuable for the practical applications in THz communications and imaging.

Method Section

All simulations were using a commercial finite element simulation software COMSOL multiphysics. The refractive index of fused silica at the target frequency of 0.14 THz is 1.95. The perfect matching layers (PML) with a thickness of 3 mm were used along z-direction. The periodic boundary conditions were used in both x- and y-directions to simulate the control characteristics of basic unit cells. In the simulations of functional devices, the scattering and periodic boundary conditions were used along the x- and y-directions, respectively.

Data Availability Statement

The original contributions presented in the study are included in the article/supplementary materials, further inquiries can be directed to the corresponding author/s.

Author Contributions

JL and HL proposed the idea and conceived and performed the simulations. TN designed the TMFL. MZ designed the Bessel beam. IL and HS guided the theoretical work. All authors analyzed and discussed the results.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant No. 11874270, the Fund Project for Shenzhen Fundamental Research Programme under Grant Nos. JCYJ20190808143409787 and JCYJ20180305125000525, and the China Scholarship Council under Grant No. 201908440615.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References