Ultimately thin metasurface wave plates

Optical properties of a metasurface which can be considered a monolayer of uniaxial metamaterials ‐ parallel‐plate and nanorod arrays – are investigated. It is shown that such metasurface acts as an ultimately thin sub‐100 nm wave plate. This is achieved via an interplay of epsilon‐near‐zero and epsilon‐near‐pole behavior along different axes in the plane of the metasurface allowing for extremely rapid phase difference accumulation in very thin metasurface layers. These effects are shown to not be disrupted by non‐locality and can be applied to the design of ultrathin wave plates, Pancharatnam‐Berry phase optical elements and plasmon‐carrying optical torque wrench devices.

     

多功能太赫兹超表面偏振控制器

本文提出了一种“金属栅-开口环/硅环-金属栅”结构的透射式超表面偏振控制器, 研究了入射角度和抽运光对该器件传输及偏振态控制性能的影响. 研究结果表明, 当线偏振太赫兹波垂直入射时, 可对0.39-1.11 THz频段的太赫兹波实现偏振方向90°旋转, 偏振旋转效率为99%, 损耗为1 dB. 对于斜入射的情况, 偏振转换性能在0-60°范围内基本保持不变, 且透过率达到90%以上. 同时, 通过调控抽运光强度的方式, 该器件能够实现对透射与反射太赫兹光束的强度调制, 调制深度均达到90%, 且可以实现太赫兹波偏振分束功能. 该器件可以作为未来太赫兹空间光通信和信息处理的宽带、角度不敏感、可调谐的偏振转换器和分束器.     

Note on Periodic Complementary Sets of Binary Sequences

Denote by $PCS_p^n $ resp. $ACS_p^n $ thecollection consisting of ordered p-tuples of binary sequences(i.e., sequences whose elements are $ \pm 1$ ), each having length n, such that the sum of their periodic resp. aperiodicauto-correlation functions is a delta function. We fill many open cases inthe Bömer and Antweiler diagram [3] of the known cases where $PCS_p^n $ exist for $p \leqslant 12$ and $n \leqslant 50$ . In particular we show that $PCS_2^{34} $ exist, whileit is well known [1] that $ACS_2^{34} $ do not.     

Full Manipulation of the Power Intensity Pattern in a Large Space-Time Digital Metasurface: From Arbitrary Multibeam Generation to Harmonic Beam Steering Scheme

Beyond the scope of space-coding metasurfaces, space-time digital metasurfaces can substantially expand the application scope of digital metamaterials. In this paper, by adopting a superposition operation of terms with unequal coefficients, Huygens' principle, and a proper time-varying biasing mechanism, some useful closed-form formulas in the class of large digital metasurfaces are presented for predicting the absolute directivity of scatted beams. Moreover, in the harmonic beam steering scheme, by applying several suitable assumptions, two separate expressions are derived for calculating the exact total radiated power at harmonic frequencies and total radiated power for scattered beams located at the end-fire direction. Despite the simplifying assumptions applied, it is proved that the provided formulas can still be a good and fast estimate for developing a large digital metasurface with a predetermined power intensity pattern. The effect of quantization level and metasurface dimensions as well as the limitation on the maximum scan angle in harmonic beam steering are addressed. Several demonstrative examples numerically demonstrated through MATLAB software and the good agreement between simulations and theoretical predictions are observed. The author believes that the proposed straightforward approach discloses a new opportunity for various applications such as multiple-target radar systems and communication.     

Planar Spoof Surface Plasmon Polariton Antenna by Using Transmissive Phase Gradient Metasurface

Spoof surface plasmon polariton (SSPP) antennas are of particular importance in communication and radar systems. Currently available SSPP radiation devices are limited to low performance with high side-lobes because it is extremely challenging to accurately control the wave vector of SSPP and the inherent momentum mismatch between the SSPP and spatial waves. Inspired by the optical principle of reversibility, high-performance radiation control of SSPP is proposed to be achieved with transmissive phase gradient metasurface (TPGM). The TPGM, placed a meticulously optimized distance above the SSPP propagation structure, can provide an additional opposite wave vector to match the momentum between the SSPP and spatial waves. When the propagating SSPP transmits on the TPGM, it can be decoupled into the free space accurately and flexibly. Numerical results coincide well with the measurements, indicating that the radiation control of SSPP achieves high-performance and low side-lobe within 9 to 10.5 GHz with the measured radiation efficiency higher than 50%. The measured maximum efficiency appears at 9.8 GHz for 69%. Thanks to the flexible and accurate manipulation of the dispersion relation of SSPP provided by TPGM, the findings may open an avenue in achieving larger angle scanning antenna.     

Decidability of Hierarchies of Regular Aperiodic Languages

A new, logical approach is propounded to resolve the decidability problem for the hierarchies of Straubing and Brzozowski based on preservation theorems in model theory, a theorem of Higman, and the Rabin tree theorem. We thus manage to obtain purely logical, short proofs of some known decidability facts, which definitely may be of methodological interest. The given approach also applies in some other similar situations, for instance, to the hierarchies of formulas modulo a theory of linear orderings with finitely many unary predicates.     

Near-Zero-Sidelobe Optical Subwavelength Asymmetric Focusing Lens with Dual-Layer Metasurfaces

Existing metasurfaces with ultrathin volume for asymmetric transmission are often constructed from metal with low efficiency in optical frequencies, and cannot realize optical asymmetric transmission and focusing simultaneously. Although acoustic asymmetric focusing in asymmetric focusing lenses (AFL) has been realized, the obtained focal point is accompanied by a large sidelobe. To solve these problems, an AFL with dual-layer metasurfaces designed by using impedance matching materials can realize optical asymmetric transmission and focusing simultaneously in this paper. Furthermore, through optimizing the design theory of AFL, near-zero-sidelobe (NZS) focusing can be realized on the subwavelength scale. NZS asymmetric focusing of the optimized AFL is effective in broadband, which is expected to show tremendous potential in optical micro-nanoprocessing, quantum communication, optical micromanipulation, etc.     

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

A spectral classification of general one‐dimensional binary aperiodic crystals (BACs) based on both their diffraction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth‐order energy spectrum main features for BACs belonging to different spectral classes, including Fibonacci‐class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed‐type Hamiltonians which include both diagonal and off‐diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation effects present in the underlying lattice is introduced. Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which defines the basic anatomy of the zeroth‐order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci‐class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for specific particular choices of the corresponding model parameters only. The transmission coefficient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.     

Freeform Metagratings Based on Complex Light Scattering Dynamics for Extreme,High Efficiency Beam Steering

Conventional phased‐array metasurfaces utilize subwavelength‐scale nanoparticles or nanowaveguides to specify spatially‐dependent amplitude and phase responses to light. An alternative design strategy is based on freeform inverse optimization, in which wavelength‐scale elements are designed to produce devices that possess exceptionally high efficiencies. In this report, we theoretically analyze the physical mechanisms enabling high efficiency in freeform‐based periodic metasurfaces, i.e., metagratings. An in‐depth coupled mode analysis of ultra‐wide‐angle beam deflectors and wavelength splitters shows that the extraordinary performance of these designs originates from the large number of propagating modes supported by the metagrating, in combination with complex multiple scattering dynamics exhibited by these modes. We also apply our coupled mode analysis to conventional nanowaveguide‐based metagratings to understand and quantify the factors limiting the efficiencies of these devices. We envision that freeform metasurface design methods will open new avenues towards high‐performance, multi‐functional optics by utilizing strongly coupled nanophotonic modes and elements.     

A new numerical technique for the analysis of parametrically excited nonlinear systems

A new computational scheme using Chebyshev polynomials is proposed for the numerical solution of parametrically excited nonlinear systems. The state vector and the periodic coefficients are expanded in Chebyshev polynomials and an integral equation suitable for a Picard-type iteration is formulated. A Chebyshev collocation is applied to the integral with the nonlinearities reducing the problem to the solution of a set of linear algebraic equations in each iteration. The method is equally applicable for nonlinear systems which are represented in state-space form or by a set of second-order differential equations. The proposed technique is found to duplicate the periodic, multi-periodic and chaotic solutions of a parametrically excited system obtained previously using the conventional numerical integration schemes with comparable CPU times. The technique does not require the inversion of the mass matrix in the case of multi degree-of-freedom systems. The present method is also shown to offer significant computational conveniences over the conventional numerical integration routines when used in a scheme for the direct determination of periodic solutions. Of course, the technique is also applicable to non-parametrically excited nonlinear systems as well.