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Abstract
Metasurface antennas scatter traveling guided waves into spatial waves, which act as extendable subsources to overcome the size limitation on emission sources. With the use of a Pancharatnam–Berry phase metasurface stimulated by a circularly polarized wave in a waveguide, the local phase distributions of scattered spatial waves can be made consistent with those of an Airy beam, thereby allowing the generation of high-quality Airy beams. In a slab waveguide, circularly polarized waves are synthesized through superposition of in-plane transverse electric modes. Simulations demonstrate that a 20 mm × 20 mm footprint all-dielectric guided wave-driven metasurface generates a 2D Airy beam at a frequency of 0.6 THz. Furthermore, we employ a metasurface deposited on a strip waveguide to generate a 1D Airy beam under direct stimulation by the fundamental transverse electric mode. Our work not only provides a large-scale emitter, but it also suggests promising potential applications in on-chip imaging and holography.
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1. Introduction
The Airy function occurs as a solution of the Schrödinger equation describing a free particle in quantum mechanics [1]. The Helmholtz equation in the paraxial approximation has a similar form to the Schrödinger equation [2–4], and so an Airy beam can also be represented in terms of the Airy function. The application of an exponential decay factor enables experimental generation of truncated Airy beams [5], which propagate along parabolic trajectories and exhibit nondiffracting [6], self-healing [7] and self-accelerating [8]. Due to these unique properties, Airy beams have been intensively studied, and they have been widely applied in fields including micromanipulation [9], light sheet microscopy [10–12], and light bullets [13,14]. Metasurfaces, with their ability to control the amplitude [15–20], phase [21–33], and polarization [34–40] of incident electromagnetic waves, have been proposed for the generation of Airy beams [41–44], with the aim of replacing the conventional technology based on a spatial light modulator and a Fourier lens [7,45–47]. With appropriate optimization of the metasurface arrangement, selection of the material type, and structural design, metasurface-based devices can regulate the amplitude and polarization of incident electromagnetic waves, with simultaneous cubic [48–50] and $0$–$\pi$ [8,16,51,52] binary phases. They are therefore suitable for the engineering of incident electromagnetic waves that is required for Airy-beam generation. The use of metasurfaces has enabled the generation of Airy beams with a range of interesting properties, such as orbital angular momentum mode-loaded [53], polarization-dependent [42], spin-dependent [54,55], autofocusing [56,57] and achromatic [58] beams.
Although impressive progresses have been made in generating Airy beams using metasurfaces, most of these works have been conducted in the optical band [42,50,52,55,59–61], and the sublobes of an Airy beam cannot be clearly distinguished in the low-frequency range from the terahertz [58] to microwave [44,51,62,63] regimes. The underlying reason for this is that the experimental realization of microwave and terahertz Airy beams requires large-scale metasurfaces [41,64], which increases the complexities of fabrication and measurement, as well as cost, especially in the two-dimensional (2D) case. In the optical band, it is easy to fabricate metasurfaces with a size of more than 40 times the wavelength [50], thereby enabling the generation of high-quality Airy beams. In the low-frequency range, by keeping the high-gain horn antenna away from the metasurface (with a spacing of up to 13 m) [63], folding the propagation path of spatial waves to reduce the distance from the horn antenna aperture to the metasurface plane [65], or selecting a small enough decay factor $\alpha$ in the exponential truncation factor [16], it is possible to generate Airy beams with clearly distinguishable sublobes. However, devices based on these methods take up a large amount of space and provide almost-vertical emission rather than self-accelerating propagation. Nonetheless, experimental results have shown that Airy beams at low frequencies have considerable prospects for application to long-distance, high-efficiency wireless power transfer [66] and secure communications [62,67]. It is thus of great importance to find methods to generate high-quality Airy beams in the low-frequency range.
In this paper, using the Pancharatnam—Berry (PB) phase triggered by an all-dielectric guided wave-driven metasurface [68–70], a high-quality Airy beam with distinguished sublobes was generated and simulated at 0.6 THz. Metasurfaces composed of an array of silicon pillars on top of a silicon waveguide are considered as subsources scattering guided waves, with the initial phase realizing the generation of an Airy beam. Our proposed method overcomes the previous limitation, according to which Airy-beam generation in the low-frequency range is hindered by the size of the emission source. Under excitation by transverse electric (TE) guided waves from two different ports, we were able to synthesize circularly polarized (CP) guided waves in the waveguide so that we could employ the PB phase in the metasurface. The desired phase of the flipped CP spatial waves can then be manipulated by altering the structural locations and rotating the unit cells. This novel strategy for generating a high-quality 2D Airy beam with distinguishable sublobes was verified by our simulation results. Furthermore, to address the large footprint of the 2D design, a compact scheme based on metasurfaces deposited on a strip waveguide is proposed. This provides an integrated method to generate one-dimensional (1D) Airy beams by locally modulating phases and locations. The proposed generation and modulation approaches have great potential for application as large-scale light sources.
2. 2D Airy-beam generation by PB metasurfaces in a slab waveguide
The arbitrary acceleration trajectory is defined as a curve $f(x,y,z)$, and we wish to determine the corresponding spatial phase function $\varphi (x,y)$ at the plane $z = 0$ that will generate the curve as a caustic [46]. The caustic curve is an envelope of tangent lines that, at each point on the curve, can be functionally related to a corresponding point in the plane $z = 0$ via a tangent of a given slope. Therefore, we determine the phase functions for three representative accelerating trajectories (parabolic, quartic, and logarithmic curves) by using a generalized geometric argument [42,46]. In particular, the intensity peak of the Airy beams propagates along the parabolic curve. In the paraxial approximation, we obtain the spatial phase function of an Airy beam [58], expressed as $\varphi (x,y)=-\frac {4}{3}a^{1/2}{k_0}(x^{3/2}+y^{3/2})$, where $a$ is the acceleration coefficient determining the bending trajectory of the beam, and ${k_0}$ is the wavevector in free space. Once the generalized principle for obtaining the desired $\varphi (x,y)$ of Airy and other self-accelerating beams has been clarified, the next step is to design appropriate metasurfaces to implement such phase distributions. To generate a high-quality Airy beam, we apply the PB phase in a guided wave-driven metasurface to engineer the wavefront of scattered spatial waves to conform to the 3/2 spatial phase profile.
2.1 Working principle
Generally, a PB phase metasurface only works efficiently in the case of CP incident light, and so we first need to construct a CP light-excitation field. A quarter-wave plate is usually employed to produce CP light in free space, but it is difficult to construct the corresponding functional element in a waveguide. Instead, we synthesize CP light by superposition of the in-plane fields of guided waves. To clarify the steps involved in this synthesis, we first study two fundamental TE modes independently propagating along the $+x$ and $+y$ directions in a slab waveguide. The phase difference between the two TE modes at any coordinates $(x,y)$ in the waveguide can be expressed as $\Delta \varphi = {\varphi _x} - {\varphi _y}$, where $\varphi _x = {\varphi _0} + \beta x$ and $\varphi _y = \beta y$ are the propagation phases of the two TE modes, $\varphi _0$ is the initial phase difference between the excited modes, $\beta$ is the propagation constant, and $x$ and $y$ are the propagation distances of each mode.
Here, the principal electric components of each TE mode ($E_x$ for propagation along the $y$ direction and $E_y$ for propagation along the $x$ direction) are orthogonal to each other, and so we construct a series of in-plane polarization states based on the synthetic field with respect to different phase retardations ($\Delta \varphi$). We acquire the desired left circularly polarized (LCP, $-$) or right circularly polarized (RCP, $+$) light in the waveguide in terms of the phase differences $\Delta \varphi = \pm \pi /2 + 2m\pi$ (where $m$ is an integer). Following these steps for synthesizing CP light, we obtain the relation between $x$ and $y$ in general form as $x-y= \beta ^{-1}( \pm \frac {1}{2}\pi +2m\pi -{{\varphi }_{0}} )$. In other words, the two TE modes at different coordinates $(x, y)$ on the line family synthesize CP light, but this light has different phases of $\varphi _x$ (or $\varphi _y$). To achieve the analogous plane waves in the guided wave-driven metasurface, it is sufficient to spatially arrange the metasurface along the $x$ and $y$ directions with an effective wavelength (equal to $2\pi /\beta$) of the fundamental TE mode.
PB metasurfaces are based on uniformly shaped pillars with rotational orientations under CP stimulation. They are uniform in height, with cross sections having two perpendicular mirror-symmetry axes. Any arbitrary ${{E}^\mathrm {in}}$ can be scattered to any desired ${{E}^\mathrm {out}}$, implementing a local Jones matrix of the following form in a Cartesian coordinate system:
in which $s_x$ and $s_y$ denote the complex scattering coefficients along the long and short axes, respectively, of the pillars. Here, the Jones matrix is different from that in free space because the scattering coefficients $s_x$ and $s_y$ depend on the contribution of the scattering guided wave to the spatial waves. From the properties of the PB phase in free space, the Jones matrix describing a dielectric guided wave-driven metasurface with an orientation angle of $\theta$ is given by2.2 Device structure
Finding a material that is highly transparent in the terahertz regime is the most crucial part of dielectric waveguide design. In Refs. [71,72], it was shown that high-resistivity silicon (HR-Si) is among the best available choices owing to its low absorption coefficient of less than 0.087 dB/cm (0.01 cm$^{-1}$) over the entire range 0.1–1.0 THz. Hence, we chose HR-Si as the material in our design.
Figure 1 schematically depicts the structure of the guided wave-driven metasurface for 2D terahertz Airy-beam generation. This consists of an array of rectangular HR-Si antennas on top of a HR-Si slab waveguide, with a 400-$\mathrm {\mu }$m-thick silicon dioxide (SiO$_2$) layer as the substrate. The heights of the HR-Si pillars and HR-Si waveguide are set to be $H = 650~\mathrm {\mu }$m and $H_\mathrm {wg} = 200~\mathrm {\mu }$m, respectively. With our chosen parameters, the fundamental TE mode is excited from the two vertical ports and propagates along the $+x$ and $+y$ directions, respectively, and the RCP light is synthesized by the two fundamental TE modes in the slab waveguide. The propagation constants of the two fundamental TE mode are the same value $3.295k_0$, the optimized periods of the metasurfaces are $P_x = P_y = 151.64~\mathrm {\mu }$m, and the overall metasurface footprint is 400 mm$^2$ (20 mm $\times$ 20 mm). The metasurface scatters the synthesized RCP guide waves within the waveguide into LCP spatial waves, carrying the PB phase conferred by the rotation angle $\theta$, thereby generating a 2D Airy beam from the scattered spatial waves. As the inset of Fig. 1 shows, the rectangular antenna has an arm length $L$ and arm width $W$, the design of which will be described in detail in the next section. The proposed structure can be fabricated by using photolithography and an inductively coupled plasma etching processes [73], and the excitation of TE modes can be achieved using grating couplers.
Fig. 1. Schematic of the guided wave-driven PB metasurface for 2D terahertz Airy-beam generation. The inset shows the details of a single pillar on the slab waveguide.
2.3 Design process
To maximize the polarization conversion rate (PCR) of the PB metasurface, we optimize the structures to behave as much like a half-wave plate as possible, satisfying $| \text {arg}(s_x) - \text {arg}(s_y) | = \pi$ and $\text {abs}(s_x)=\text {abs}(s_y)$. Here, the PCR is defined as $|s_\mathrm {cross}|^2/(|s_\mathrm {cross}|^2+|s_\mathrm {co}|^2)$, where $s_\mathrm {cross}$ and $s_\mathrm {co}$ represent the cross- and co-polarized complex scattering coefficients under a normally incident synthesized CP wave. The phases $\text {arg}(s_x)$ and $\text {arg}(s_y)$, and the scattered amplitude coefficients $\text {abs}(s_x)$ and $\text {abs}(s_y)$ imposed by the array in $E_x$ are functions of $L$ and $W$ of the Si pillars, where the excitation field is a TE mode propagating along the $+y$ direction. The phases and scattered amplitude coefficients are first determined via simulations, as shown in Figs. 2(a) and 2(b), respectively. Owing to the twofold ($C_2$) rotational symmetry of our rectangular design, rotating the Si pillar by $90^\circ$ will give the same simulation results for the $y$-polarized TE mode propagating along the $+x$ direction. From these simulations, the required parameters $L$ and $W$ to achieve all combinations of $\arg (s_x)$ and $\arg (s_y)$ while maintaining high scattering efficiency are derived from Figs. 2(a) and 2(b). We then calculate the PCR for each pillar as shown in Fig. 2(c) and determine the structural parameters taking account of PCR, with PCR $= 94.25\%$ for $L = 115~\mathrm {\mu }$m and $W = 80~\mathrm {\mu }$m. To further confirm that the PB phase driven by the synthesized CP light in the waveguide works as well as in free space, we excite the square-arranged metasurfaces with multiple wavelengths on the waveguide. As shown in Fig. 2(d), the phases of the RCP scattered spatial waves with the same excitation polarization do not depend on the rotation angle $\theta$ (indicated by the red dots), whereas the phases of the LCP scattered light obtained by polarization conversion are given by $2 \theta$ (indicated by the blue dots). These results confirm that the PB phase still works in guided wave-driven metasurfaces. The PB phase in guided wave-driven metasurfaces can be used as a reliable way to employ the phase profiles of an Airy beam. It should be pointed out that our designed metasurfaces have a weak affect on the modes propagating in the waveguide, and this is manifested as a scattering efficiency of only 0.25$\%$ in Fig. 2(d). Fortunately, the generation of high-quality Airy beams relies on the enhanced scattering efficiency of as many metasurfaces as possible, and the low scattering efficiency ensures that the waveguide modes are scattered into spatial waves by more metasurfaces. Therefore, by increasing the number of metasurfaces interacting with the guided waves, it is possible to generate terahertz or low-frequency microwave Airy beams with distinguishable sublobes. This avoids the problems of complicated light-path design and the large physical volume of the system caused by beam expansion of the emission source.
Fig. 2. Design of silicon pillars for controlling the phase and amplitude of scattered spatial waves. (a,b) Simulated phase shifts and intensity of scattering coefficients of pillars with different values of $L$ and $W$ excited by the fundamental TE mode propagating along the $+y$ direction. (c) Calculated polarization conversion rate of each pillar for RCP to LCP. (d) Numerically simulated phase shifts and up-scattering efficiency as functions of rotation angle $\varphi$ of a selected pillar ($L = 115~\mathrm {\mu }$m, $W = 80~\mathrm {\mu }$m, $\mathrm {PCR} = 94.25\%$).
2.4 Results and analysis
Based on the required 3/2 phase profile of Airy-beam generation with an acceleration coefficient $a = 4$ m$^{-1}$, we construct a 2D Airy beam device with PB phase on guided wave-driven metasurfaces. With the required phases for all our metasurfaces known, we can retrieve their rotation angles $\theta$ from the equation $\theta = \frac {1}{2}\varphi ( {x,y} ) = - \frac {2}{3}{a^{1/2}}{k_0}( {{x^{3/2}} + {y^{3/2}}} )$ and finally design the metasurface by putting them in appropriate locations. The fundamental TE mode is excited separately from the two vertical ports, with an initial phase difference ${{\varphi }_{0}} = 0.5\pi$. Figure 3(a) shows the phase profile of the LCP spatial wave on the $x$–$y$ near-field plane at a spacing of $200~\mathrm {\mu }$m from the metasurface. This wave is scattered from the synthetic RCP guided wave by the metasurface. To clearly compare the phases of the scattered spatial waves with the phases of the Airy beam, Fig. 3(b) extracts the phases of the scattered spatial waves along the diagonal direction [the black dashed line in Fig. 3(a), $x=y$], and it can be seen that there is good agreement with the phases required for Airy-beam generation.
Fig. 3. Results from simulation of 2D Airy-beam generation. (a) Simulated near-field phase profile of the LCP spatial waves scattered by the metasurface structures. (b) Phase profile along the black dashed line in (a) compared with the theoretical ideal result. (c) Normalized intensities of LCP light in the $x$–$y$ plane along propagation trajectories at different $z$ positions. The black solid line corresponds to the theoretical trajectory $x = y = - a{z^2}$. (d) Field intensity distributions along the $x$ direction (three black dashed lines) in (c). (e) Comparison of the simulated trajectory of the main lobe and the theoretical parabolic trajectory $x=-az^2$.
To reduce the requirements for computational resources, we employ the phase profile extracted from the near-field plane to calculate the evolution of scattered space waves using the Fresnel-diffraction method. Figure 3(c) shows the evolution of the generated 2D Airy beam, including the normalized LCP spatial waves at three different $z$ coordinates ($z = 2.0$, $2.5$, and $3.0$ cm). The generated beam bends in both the $-x$ and $-y$ directions during its evolution, indicating the self-bending property of the Airy beam. From the simulated results, the main lobe and multiple sublobes of the 2D Airy beam are clearly distinguished. We further calculate the theoretical curving trajectory (the black solid curve), as well as the coordinates of the main lobe at the three $z$ positions; these coordinates are $(-0.16, -0.16, 2)$, $(-0.25, -0.25, 2.5)$, and $(-0.36, -0.36, 3)$, respectively (all in cm). The simulated positions of the main lobe at the peak electric field intensity are close to the ideal ones. To further analyze the simulated intensity distribution of the main lobe and sublobes at different $z$-axis positions, we pick the field intensity distributions along the $x$ direction (the black dashed line) on the $x$–$y$ plane in Fig. 3(c) and present them in Fig. 3(d). It can be clearly seen in Fig. 3(d) that the position of the main lobe shifts from $-0.084$ mm to $-0.314$ mm along the $-x$ direction when the propagation length is increased by 1 cm along the $z$ direction. It can also be shown that there are multiple distinguishable sublobes close to the main lobe, and the spatial width of the main lobe remains nearly unchanged at different spatial positions, which is typical of nondiffracting beams. For further comparison, Fig. 3(e) shows the curving trajectory of the main lobe mapped from the simulation results. The simulated trajectory matches well with the ideal caustics given by the parabolic function $x=-az^2$ within the range of 0–5 cm.
3. 1D Airy-beam generation by PB metasurfaces in a strip waveguide
3.1 Design principle
A 2D Airy beam with distinguishable sublobes was successfully generated using the PB phase in the guided wave-driven metasurface, the special feature of which is that the excited CP waves are synthesized from the fundamental TE mode propagating from the two orthogonal ports. Furthermore, we place the metasurface on a strip waveguide, which is driven by a single fundamental TE mode to generate a compact 1D Airy beam. In contrast to the strategy for a slab waveguide, the synthesis of CP light from the excitation field by an in-plane field will no longer be implemented for a strip waveguide. Fortunately, the fundamental TE mode in the waveguide is analogous to a linearly polarized wave and can thus be regarded as a superposition of RCP and LCP waves. Therefore, rotation of a pillar will induce a PB phase for the RCP in the strip waveguide, which will be followed by an opposite PB phase for the LCP wave. A metasurface whose local Jones matrix is of the form in Eq. (4) may then only exhibit the following polarization behaviors and phase responses in the scattered spatial waves. The practical consequences of which are as follows:
To eliminate the undesired scattering of the CP light without the PB phase, we employ the momentum matching condition to eliminate the scattered CP waves. This is easily achieved by optimizing the period of the pillars. The target CP light with the PB phase can be scattered to the spatial waves, while the target same CP light without the PB phase will continue to propagate in the strip waveguide in the forward and backward forms. We can obtain the corresponding phase evolution for each pillar lattice in the propagation of the excited fundamental TE mode (along the $x$ direction) as $\phi (x)=\beta x+ \phi _{0}+\phi _\mathrm {PB}+2m\pi x/P$, in which $\beta x$ is the propagation phase, $\phi _{0}$ is a constant phase, $\phi _\mathrm {PB}$ arises from the rotational angle step of the pillars, and $m$ is the sequence number of the lattice. A suitable constant gradient of phase discontinuity along the interface ($x$ direction) is $(d/dx)\phi (x)= k_x=\beta +(d/dx)( \phi _\mathrm {PB}+2m\pi x/P )$, and thus the corresponding scattered direction of the spatial waves is $\theta =\sin ^{-1}(k_x/k_0)$. In the above derivation, we have assumed that $P$ is the period of the pillar, and thus the phase gradient can be simplified to
Therefore, the scattered angle of the target CP waves with PB phase isThese periodic and PB-phase gradient degrees of freedom help us to eliminate scattering of the target CP waves without the PB phase. We can conclude from comparing Eqs. (7) and (8) that the scattering direction of the target CP waves without the PB phase is only related to the structural period $P$, while the scattering direction of the target CP waves with the PB phase is determined by both the period $P$ and the PB phase $\phi _\mathrm {PB}(x)$ provided by the rotational angle step. Even for the cases with solutions, the detailed restrictive conditions in our design are
It can be verified that optimizing the period $P$ to satisfy $P<2\pi /(\beta +k_0)$ will ensure that the target CP light without PB phase is unable to scatter into the spatial wave. Note that the structural period $P$ is less than the effective wavelength of the fundamental TE mode in the strip waveguide. In addition, therefore, to address the former condition, we add an additional phase $-\beta x$ to the desired phase employed directly by the PB phase in the metasurface. That is, if this additional phase is introduced to eliminate the fundamental TE-mode propagation phase, then the target CP spatial waves with the PB phase obtained by metasurface scattering of the fundamental TE mode can be used to achieve the desired spatial phase profiles.
3.2 Results and analysis
For the generation of a 1D Airy beam, we place the pillars on a strip waveguide so that the scattered LCP wave has a 3/2 spatial phase profile, as shown in Fig. 4(a). The waveguide is of width 400 $\mathrm {\mu }$m and height 75 $\mathrm {\mu }$m. The pillars are of length $L = 65~\mathrm {\mu }$m, width $W = 45~\mathrm {\mu }$m, and height $H = 475~\mathrm {\mu }$m, and the period of the unit cell is $89.96~\mathrm {\mu }$m. The sample length of the metasurface is 2 cm. The acquired PB phase provided by pillar rotation is $\phi _\mathrm {PB}=-\frac {4}{3}a^{1/2}{k_0}x^{3/2}-\beta x$, and thus the rotation angle can be derived as $\theta =\phi _\mathrm {PB}/2$. In the implementation, the metasurface is directly excited by a fundamental TE mode in the strip waveguide to generate an Airy beam with extraction of an LCP spatial wave at 0.6 THz.
Fig. 4. Generation of 1D terahertz Airy beam in a strip waveguide. (a) Schematic of metasurface directly driven by TE mode in the waveguide. (b) Normalized electric-field intensity distribution of LCP spatial wave in the $x$–$z$ cross-plane, with the main lobe trajectory fitting well with the theoretical ideal parabolic trajectory (black dashed line) $x=-az^2$. (c) Near-field phase distribution along the $x$ direction of the LCP spatial wave above the metasurface, in comparison with the theoretical phase profile. (d) Simulated normalized field intensity distributions (red curves) compared with the theoretical results (blue curves) along the $x$ direction at different propagation distances $z = 0.5$, $1.0$, $1.5$, $2.0$, and $2.5$ cm.
Figure 4(b) shows the extracted intensity distribution of the LCP spatial wave in the $x$–$z$ plane. It can be seen that the LCP spatial wave scattered by the metasurface has a clear main lobe and distinguishable sublobes. The theoretical curved trajectory is indicated by the black dashed line, and this fits well with the parabolic trajectory of the Airy beam. The spatial phase of the LCP wave scattered by the metasurface with 100 $\mathrm {\mu }$m pillar spacing matches the 3/2 phase profile, as shown in Fig. 4(c).
To further examine the specific intensity distributions, in Fig. 4(d), the simulated result (red curves) is compared with the theoretical distribution of the Airy beam (blue curves) from $z=0.5$ cm to $z=2.5$ cm in steps of $\Delta z=0.5$ cm. In addition, the self-acceleration and non-diffracting properties are clearly shown by the parabolic nature of the propagation trajectory and the stability of the main lobe width. It can also be seen that the curves of the simulated data deviate slightly from the theoretical results. For more precise intensity modulation, we believe that the generated Airy beams could be improved by carefully tuning the scattering pillars. Thus, our simulations of the evolution of scattered LCP spatial waves with the PB phase have been shown to be valid, and our proposed design provides an effective way to eliminate LCP waves without the PB phase.
It should be noted that 1D and 2D design methods each have advantages and disadvantages. The main advantage of the 2D design is that the synthesis of the in-plane electric field components enables polarization multiplexing; one disadvantage, however, is that the process of finding a high-PCR structure is complicated, as is the precise control of the phase difference between the two ports. In contrast, the advantage of the 1D design is that the appropriate period parameters can suppress the scattering of CP waves without the PB phase. Nonetheless, its shortcomings are clear: the scattering efficiency is low, and there are unused polarization states in the scattered field. In particular, we believe that the 2D design method is more practical for two reasons. First, the waveguide mode can synthesize multiple polarization states, and data can be carried independently by each of these polarization states; second, the phase difference between the two ports provides a way to synthesize multiple polarization states, which makes the design method more powerful, such as polarization multiplexing and dynamic control of wavefront.
4. Conclusion
In summary, guided wave-driven metasurfaces offer an integrated and versatile platform to scatter guided waves into spatial waves. The guided waves are able to interact many times with the metasurfaces, thereby providing an extendable light source for manipulation. We have proposed and designed an all-dielectric PB metasurface to generate high-quality Airy beams driven by guided waves in the terahertz range. By superposition of the in-plane TE modes excited by two different ports, we were able to synthesize an RCP wave in a slab waveguide and reshape it into a 2D Airy beam in free space at a frequency of 0.6 THz. The main lobe and multiple sublobes of the 2D Airy beam were clearly distinguishable, and the propagation trajectory of the main lobe agreed well with the theoretical parabolic trajectory. Furthermore, we demonstrated the generation of a 1D Airy beam by a metasurface deposited on a strip waveguide and directly driven by its TE fundamental mode. The metasurface interacts with the guided wave only weakly, which allows the use of a sufficient number of antennas to engineer the guided wave. The weak scattering process that we have implemented means that the conversion ratio of the Airy beam is not high, but fortunately the large number of metasurfaces allows the generation of high-quality Airy beams. A further step would be to optimize the structural parameters to provide higher scattering efficiency and achieve this experimentally in the low-frequency range from the terahertz to microwave regimes. Potential applications should also be investigated, especially for long-distance high-efficiency wireless power transfer, directional communications, and covert communications.
Funding
National Natural Science Foundation of China (11874266, 12174260); Shanghai 324 Rising-Star Program (21QA1406400); Shanghai Science and Technology Development Foundation (21ZR1443500, 21ZR1443600); Shanghai Pujiang Program (20PJ1403400).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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