Encoding metasurfaces based on tunable materials can achieve dynamic control of terahertz beams with reconfigurability under the action of external control and are the main solutions to the design of encoding metasurfaces in terahertz bands. The liquid crystal (LC) is a more practical solution than other tunable materials because of its mature processing technology, low manufacturing cost, and simple driving scheme. However, most of the relevantly reported LC-coded metasurfaces employ one-bit encoding, inevitably producing symmetric beams and limiting the beam deflection efficiency to only 50%. Increasing the LC layer number and exploiting the resonance switching mechanism of LCs in different regions are two options to achieve multi-bit encoding, but will increase the complexity of the external voltage manipulation system. Meanwhile, since the corresponding rate of LC integrated devices is mainly related to the thickness of LCs, the design of thin LC multi-bit-coded metasurface cells with low voltage control based on simplifying the external voltage control has certain research significance and good application prospects. Additionally, for the encoding sequence design, under plane wave excitation, the traditional method is to adopt gradient phase encoding and complex encoding to independently regulate single and multiple beams. Meanwhile, there will be some limitations on the initiative, flexibility, and deflection accuracy of the design of the beam regulation encoding. Thus, we employ the genetic algorithm for the reverse design of the encoding sequence, which can overcome the shortcomings of traditional methods.

Compared to the optimization of the underlying shape and structural parameters, topological optimization by dividing the surface pattern into equal-sized pixel units is generally combined with optimization algorithms to increase the design freedom and yield better performance and has been widely applied to the design of various functional devices for metasurfaces. First, we aim at the achievable 2 bit encoding and thin LC for the reverse design of LC-coded metasurface cells based on topology optimization. The surface topological pattern and structural parameters are 2 bit encoded by adopting ABRR as the objective function, and they are optimized several times using a genetic algorithm. For the encoding sequence design, based on the far-field scattering principle of digital encoding and designed LC-coded metasurface unit, the different array encoding sequences obtained by reverse design according to the scattering principle of digital encoding, and the beam assignment and vortex beam functions are simulated in a full-wave simulation using the simulation software CST.

By employing the genetic algorithm to optimize the design several times, the designed single-layer LC metasurface structure is shown in Fig. 3. The LC thickness is only 14 μm, the amplitude and phase response curves of the metasurface unit in reflection mode are shown in Fig. 4, and the αABRR,minn of the encoding metasurface is 8.92 at 0.394 THz, which means that the designed metasurface unit can achieve 2 bit encoding. Then, based on the designed LC-coded metasurface units, the full-wave simulations of beam assignment and vortex beam functions are simulated with different array coding sequences obtained by reverse design. For beam shaping, flexible control of a single beam (Fig. 6) and a specified number of multiple beams within a pitch angle θ of 0°-30° and an azimuth angle φ of 0°-360° is achieved. In particular, for multiple beams (Figs. 7 and 8), independent control of the main flap of each target is realized. Compared to the method of reverse design by complex encoding and the addition law, it is advantageous to achieve independent multi-beam modulation of each target main flap under plane wave excitation with only 2 bit encoding rules, with improved design initiative. For vortex beams, single vortex beams with topological charges l=±1, ±2, and ±3 and mode purity above 70% are achieved at 0.394 THz (Figs. 10 and 11). By conducting vortex phase convolution, double vortex beams to quintuple vortex beams with pitch angles θ within 30° and an azimuthal angle φ within 360° are generated and flexibly regulated (Fig. 12).

We design a thin-thickness reflective LC-coded metasurface unit based on topological optimization with a LC thickness of only 14 μm, which simplifies the complexity of the LC multi-bit-coded external feed control system, with a fast response rate. The reverse design of the array encoding sequence using the genetic algorithm can realize the flexible regulation of beam assignment and vortex beams, which improves the design efficiency and the diversity of encoding functions. The results show that for beam assignment, not only the flexible control of a single beam at 0.394 THz with pitch angle θ within 30° and azimuth angle φ within 360° is achieved, but also the independent control of pitch angle θ and azimuth angle φ of a single beam from triple vortex beams to quintuple vortex beams is realized. For vortex beams, single-vortex beams with topological charges l=±1, ±2, and ±3 and mode purity above 70% are achieved at 0.394 THz. Meanwhile, by adopting vortex-phase convolution, double vortex beams to quintuple vortex beams are generated and flexibly tuned within a pitch angle θ of 30° and an azimuthal angle of φ in the range of 360° are achieved. The proposed topology-optimized metasurface cell structure and reversely designed array encoding sequences have potential applications in terahertz beam manipulation devices.