Transverse Wave Vector Research Articles

Experimental retrieval of metaholographic images via evanescent wave using a single-layer nanostructure for encryption.

Metasurfaces have demonstrated significant potential in optical encryption and anti-counterfeiting due to their incredible capability of manipulating various light properties. However, previous metasurface-encryption methods did not sufficiently explore the spatial frequency aspect, particularly regarding evanescent waves. Here, we propose an encryption scheme by introducing evanescent waves into the encoding and decoding processes. Different parts of the target image are individually encoded at distinct spatial frequencies within the evanescent-wave region. Only when an evanescent wave with a specific transverse wave vector (TWV) serves as the key can the complete target image be retrieved. Our work exemplifies a thorough exploration of the mathematical framework underlying metasurface-based holography. It enables the feasibility of a single metasurface in concealing and retrieving information in the evanescent-wave region, thus opening up a new, to our knowledge, methodology for high-security optical information encryption.

Fano resonances in gated phosphorene junctions

Fano resonances appear in plenty of physical phenomena due to the interference phenomena of a continuum spectrum and discrete states. In gated bilayer graphene junctions, the chiral matching at oblique incidence between the spectrum of electron states outside the electrostatic barrier and hole bound states inside it gives rise to an asymmetric line shape in the transmission as a function of the energy or Fano resonance. Here, we show that Fano resonances are also possible in gated phosphorene junctions along the zigzag direction. The special pseudospin texture of the charge carriers in the zigzag direction allows at oblique incidence the interference phenomena of the spectrum of electron states outside the electrostatic barrier with hole bound states inside it, giving rise to an asymmetric Fano line shape in the transmission. Due to the energy scale of the electrostatic barriers in phosphorene ultra thin barriers are required to observe the Fano resonance phenomenon. The preservation of the pseudospin texture with the closing of the phosphorene band gap opens the possibility to observe Fano resonances in smaller and wider electrostatic barriers. The asymmetric Fano line shape is susceptible to the transverse wave vector, the strength and width of the electrostatic barrier. Additionally, the conductance shows a characteristic mark in the position where the Fano resonances take place. The similarities and differences with respect to Fano resonances in bilayer graphene are also addressed.

Transmission in graphene through a double laser barrier

We study the tunneling behavior of Dirac fermions in graphene subjected to a double barrier potential profile created by spatially overlapping laser fields. By modulating the graphene sheet with an oscillating structure formed from two laser barriers, we aim to understand how the transmission of Dirac fermions is influenced by such a light-induced electric potential landscape. Using the Floquet method, we determine the eigenspinors of the five regions defined by the barriers applied to the graphene sheet. Applying the continuity of the eigenspinors at barrier edges and using the transfer matrix method, we establish the transmission coefficients. These allow us to show that oscillating laser fields generate multiple transmission modes, including zero-photon transmission aligned with the central band ε and photon-assisted transmission at sidebands ε + l ϖ, with l = 0, ± 1, ⋯ and frequency ϖ. For numerical purposes, our attention is specifically directed towards transmissions related to zero-photon processes (l = 0), along with processes involving photon emission (l = 1) and absorption (l = − 1). We find that transmission occurs only when the incident energy is above the threshold energy ε > k y + 2ϖ, with transverse wave vector k y . We find that the variation in distance d 1 separating two barriers of widths d 2 − d 1 suppresses one transmission mode. Additionally, we show that an increase in laser intensity modifies transmission sharpness and amplitude.

Momentum-dependent Pancharatnam-Berry phase enabled in- and out-of-plane photonic spin-Hall shifts

The photonic spin-Hall effect (PSHE) is a result of the interaction of spin and orbital angular momentum (OAM). However, previous research on the PSHE has primarily focused on out-of-plane (transverse) shifts. In fact, it encompasses both out-of-plane shifts and relatively weaker in-plane shifts, and the latter of which plays a crucial role in controlling the direction of spin separation. Here, we investigate the in- and out-of-plane shifts of the PSHE based on a full-wave theory, revealing that they have the same physical mechanism. The in- and out-of-plane displacements of the PSHE are determined by a momentum-dependent Pancharatnam-Berry (PB) phase, where the in-plane wavevector kx-dependent phase gradient determines the in-plane shift, and the transverse wavevector ky-dependent phase gradient dictates the out-of-plane shift. We discover that the intrinsic OAM (IOAM) and extrinsic OAM (EOAM) carried by incident off-axis vortex beams can respectively convert into the EOAM and IOAM of abnormal modes in the transmitted beam. The OAM generated during the spin-reversal process, together with the OAM carried by the incident beam, collectively determines the in- and out-of-plane displacements. When off-axis vortex beams are incident, the competition between the IOAM and EOAM is more complex than in those without OAM. Our study unifies in- and out-of-plane shifts into a single theoretical framework, which offers an alternative perspective on the spin–orbit interaction of light.

Multi-dimensional tunable arbitrary shape beams with engineered axial profile

Bessel beams, as one type of special light field, would significantly do benefit to several applications such as light-sheet microscopy, particle manipulation and free-space optical communications. In this paper, we investigate the generation of multi-dimensional tunable arbitrary shape beams with engineered axial profile based on the superposition of zero-order Bessel beams by designing the angular spectrum, providing a universal method to manipulate arbitrary shape beams in terms of longitudinal intensity, transverse wavevector distribution and transverse field shape. Through angular spectral analysis, we demonstrate the shape-invariant axial engineering of circle, ellipse, parabolic, and epicycloid-shaped beams, as well as shape-variant axial engineering such as self-acceleration, self-rotation, and self-mode conversion, from both theoretical and experimental perspectives. Our work provides a deep insight into the fundamental properties of arbitrary shape light with engineered axial profile and paves new way toward exploiting more dimensions for its future applications.

Refractive index sensing of spoof surface plasmon polaritons excited on graphene strips based on cylindrical dielectric metasurface coupling

In this paper, we present a novel terahertz plasmonic sensing concept that utilizes a metasurface coupler to excite spoof surface plasmon polaritons (SSPs) modes on graphene strips. The dielectric metasurface unit cell consists of two silicon cylindrical rods with different radii on a quartz substrate. Vertically incident terahertz waves are deflected by the metasurface, resulting in a transverse wave-vector within the substrate that matches the SSPs wave-vector supported by the graphene strips. This enables efficient excitation of SSPs modes on the graphene strips surface, leading to absorption resonances in the range of 0.420–0.430 THz with a high quality (Q) factor of 152. We then applied this device for refractive index sensing, and the investigation results indicate that the high Q resonances in the absorption spectrum experience shifts with changes in the refractive index of the target substance, with a sensitivity of 110 GHz/RIU. The designed structure in this study exhibits significant potential for applications in trace substance absorption spectrum detection.

Shaping the angular spectrum of a Bessel beam to enhance light transfer through dynamic strongly scattering media

We prepare a quasi-non-diffracting Bessel beam defined within an annular angular spectrum with a spatial light modulator. The beam propagates through a strongly scattering media, and the transmitted speckle pattern is measured at one point with a Hadamard Walsh basis that divides the ring into N segments (N = 16, 64, 256, 1024). The phase of the transmitted beam is reconstructed with 3-step interferometry, and the intensity of the transmitted beam is optimized by projecting the conjugate phase at the SLM. We find that the optimum intensity is attained for the condition that the transverse wave vector k⊥ (of the Bessel beam) matches the spatial azimuthal frequencies of the segmented ring k ϕ . Furthermore, compared with beams defined on a 2d grid (i.e., Gaussian) a reasonable enhancement is achieved for all the k⊥ sampled with only 64 elements. Finally, the measurements can be done while the scatterer is moving as long as the total displacement during the measurement is smaller than the speckle correlation distance.

2D-smoothing of laser beam fluctuations in optical compressor

We propose a modification of the four diffraction gratings Treacy compressor (TC)—a double-smoothing grating compressor (DSGC)—which enables smoothing of spatial fluctuations of a laser beam in two directions. Smoothing along the groves is due to oblique incidence on the gratings or tilted grooves. Smoothing in the direction normal to the grooves is achieved due to the use of nonidentical pairs of gratings. It is shown that the far-field fluence and the focal beam intensity after the DSGC are like those after the TC. Smoothing is a consequence of spatial harmonics lagging behind or overtaking the main pulse in proportion to the transverse wave vector. Analytical expressions are obtained for the spectrum of fluence fluctuations and fluence rms at the DSGC output. The efficiency of suppressing small-scale self-focusing in transmissive optical elements after the DSGC, for example, in the case of post-pulse compression is assessed.

Long-range polaritonic heat conduction in asymmetric surrounding media

Surface Phonon Polaritons (SPhPs) as an evanescent electromagnetic surface wave supports long propagation which readily surpasses the mean free path of classical heat carriers, e.g., phonons and electrons in solids. SPhPs have emerged as a promising candidate to dominate heat transfer in thin films. Polaritonic heat transfer has two distinct advantages: superior thermal conduction and a wide range of manipulation. Here, we study the upper limit of the thermal conductivity mediated by long-range polaritons in asymmetric surrounding media, where its surface effect overwhelms the volumetric one. The thin film structure strengthens the interactions of two surface waves at the top and bottom surfaces, and the asymmetric surrounding media makes an evanescent surface wave to further penetrate the free space with a higher refractive index, but it requires a fine tuning of asymmetric permittivity of the surrounding media to reach the upper limit of energy transmission efficiency near to the modal cut-off, where the transverse wavevector becomes zero. Both analytical and numerical simulations were introduced to investigate dispersion in asymmetric surrounding media and to model the thermal conductivity of glass thin films. Anomalously high thermal conductivity of 248 W/m-K was achieved with a 50 nm thick SiO2 film in asymmetric surrounding media, yet subtly dissimilar.

Robust propagation of a steady optical beam through turbulence with extended depth of focus based on spatial light modulator

Finding appropriate strategies to increase the robustness through turbulence with extended depth of focus (DOF) is a common requirement in developing high-resolution imaging through air or water media. However, conventional lenses with a specially designed structure require high manufacturing costs and are limited by a lack of dynamic modulation characteristics. Spatial light modulators (SLMs) are unique flat-panel optical devices which can overcome the distance limitation of beam propagation for the dynamic modulation property. In this work, we address the dynamic generation of a steady optical beam (STOB) based on the mechanism of transverse wave vector elimination. STOBs generated by the SLM have significant advantages over Gaussian beams for the characteristics of peak intensity, robust propagation, extended-DOF beam profile, and dynamic wavefront modulation over a long distance under strong turbulent media. Our versatile, extensible, and flexible method has promising application scenarios for the realization of turbulence-resistant circumstances.

Strain-Modulated Perfect Valley Precession and Valley Transistor in Graphene

We propose the realization of perfect valley precession by use of strain, which gives rise to an effective vector potential and moves two valleys in opposite directions in momentum space. It is shown that the spatial precession period is independent of both the Fermi energy and the transverse wave vector. This is crucial to perfect precession in a practical device with multiple transverse wave vectors or modes. To theoretically demonstrate the perfect valley precession, we investigate the conductivity of a Kekul\'e graphene superlattice/graphene/Kekul\'e graphene superlattice junction that acts as a valley transistor. Due to the valley precession, the conductivity exhibits perfect oscillations with the strain and the conductivity minima are very close to zero. Our finding provides a strategy to design ideal valleytronics and straintronics devices.

Spatial Self-Phase Modulation in Graphene-Oxide Monolayer

The spatial self-phase modulation (SSPM) of the optical field revealed the magnitude and polarity of nonlinear refraction coefficients of the graphene-oxide (GO) atomic layers in an aqueous base solution with a resonant excitation using a chopped quasi-static laser at 532 nm. The SSPM of the optical field as a result of the intrinsic nonlinear refraction coefficient of GO atomic layers and the spatial distribution of intensity displayed the concentric diffraction rings at the far field due to the coherent superposition of transverse wave vectors. The number of concentric rings as a function of the applied intensity revealed the nonlinear refraction coefficient of GO which was estimated to be ~–6.65 × 10−12 m2/W for the laser-excitation duration of ~0.32 s, where the negative polarity of nonlinear refraction coefficient was confirmed with the interference image profile of SSPM. The upper and vertical distortion of concentric rings at the far field at the longer laser-excitation duration of ~0.8 s indicates the distortion of the coherent superposition of transverse wave vectors due to the localized thermal vortex of GO in the aqueous solution that offers novel platforms of thermal metrology based on localized optical nonlinearity and temperature-sensitive all-optical switching.

Reducing laser beam fluence and intensity fluctuations in symmetric and asymmetric compressors

AbstractAll space–time coupling effects arising in an asymmetric optical compressor consisting of two non-identical pairs of diffraction gratings are described analytically. In each pair, the gratings are identical and parallel to each other, whereas the distance between the gratings, the groove density and the angle of incidence are different in different pairs. It is shown that the compressor asymmetry does not affect the far-field fluence and on-axis focal intensity. The main distinctive feature of the asymmetric compressor is spatial noise lagging behind or overtaking the main pulse in proportion to the transverse wave vector. This results in a degraded contrast but reduces beam fluence fluctuations at the compressor output. Exact expressions are obtained for the spectrum of fluence fluctuations and fluence root mean square that depends only on one parameter characterizing compressor asymmetry. The efficiency of small-scale self-focusing suppression at subsequent pulse post-compression is estimated.

Electron wave-vector filtering in a magnetoelectric nanostructure consisting of a δ-magnetic-barrier and a δ-electric-barrier

Based on a δ-magnetic-barrier and a δ-electric-barrier, we propose a magnetoelectric nanostructure, which can be constructed by patterning a half-infinitely wide ferromagnetic (FM) stripe and a narrow Schottky-metal (SM) stripe in a parallel configuration on the surface of GaAs/AlxGa1-xAs heterostructure. An obvious wave-vector filtering (WVF) effect occurs thanks to an essentially two-dimensional process for electron across the magnetoelectric nanostructure. WVF efficiency is associated with electronic energy, transverse wave vector and magnetic field; especially it can be modulated by rationally fabricating the SM stripe. These interesting features are helpful for developing electron-momentum filter (EMF) in nanoelectronics.

Anomalous Reflection with Omnidirectional Active Metasurfaces Operating in Free Space

Metasurfaces that manipulate the reflection of impinging sound have recently received significant attention, but virtually all past designs are passive structures with high temporal and spatial dispersion and thus have narrow bandwidths and are unidirectional. In this work, we introduce a method to design omnidirectional and broadband anomalous acoustic reflectors composed of nonresonant active scatterers arranged in a periodic lattice of subwavelength periodicity. The method relies on the manipulation of the wave-vector component parallel to the reflector's surface (i.e., transverse component) in a broadband manner and for arbitrary impinging sound directions. To illustrate our method experimentally, we design and measure an anomalous reflecting metasurface operating in free space for which the transverse wave-vector components of the incident and reflected waves differ by a prescribed constant. We show that the effect does not depend on the direction of incidence and has a bandwidth an order of magnitude larger than passive anomalous reflectors. This work shows that the active scatterers behave similarly to the atoms of a natural material rather than the unit cells of gratings or phononic crystals in that rearranging the active scatterers changes the metasurface geometry while preserving the device's desired functionality.

Dependence of evanescent wave polarization on the losses of guided optical modes

Spin-momentum locking of evanescent waves describes the relationship between the propagation constant of an evanescent mode and the polarization of its electromagnetic field, giving rise to applications in light nano-routing and polarimetry among many others. The use of complex numbers in physics is a powerful representation in areas such as quantum mechanics or electromagnetism; it is well known that a lossy waveguide can be modelled with the addition of an imaginary part to the propagation constant. Here we explore how these losses are entangled with the polarization of the associated evanescent tails for the waveguide, revealing a well-defined mapping between waveguide losses and the Poincar\'e sphere of polarizations, in what could be understood as a "polarization-loss locking" of evanescent waves. We analyse the implications for near-field directional coupling of sources to waveguides, as optimized dipoles must take into account the losses for a perfectly unidirectional excitation. We also reveal the potential advantage of calculating the angular spectrum of a source defined in a complex, rather than the traditionally purely real, transverse wavevector space formalism.

Applicability of the soft and hard apodization techniques to suppress Bessel beam intensity oscillations

We investigate the applicability of the soft and hard apodization techniques to suppress Bessel beam intensity oscillations through varying several parametric quantities, which include the input pixel pitch, the quantized amplitude gray level number, the transverse wave vector, the incident wavelength and the amplitude smoothing parameter. The Bessel beam propagating intensities are simulated by the complete Rayleigh–Sommerfeld method. Three performance indicators are defined to characterize the stable propagation property of the diffracted Bessel beam, i.e., the longitudinal range with stable axial intensity, the axial intensity percentage deviation and the transverse intensity percentage deviation. Numerical results demonstrate that the intensity oscillations are substantially suppressed by the two apodization techniques within a wide range of parameters, and thus the apodized Bessel beams propagate stably during the whole propagation distance. Numerical simulation also reveals that the apodized Bessel beams process a good self-healing property when encountering a circular obstacle. In addition, the hard apodization technique shows obvious superiority to the soft apodization technique with 256 gray levels, such as a higher accuracy, a lower cost and an easier fabrication process.

Second-order hyperpolarizability and all-optical-switching of intensity-modulated spatial self-phase modulation in CsPbBr1.5I1.5 perovskite quantum dot

The averaged second-order hyperpolarizability of perovskite (CsPbBr1.5I1.5) quantum dots (QDs) was characterized using the intensity-dependent spatial self-phase modulation (SSPM). The radial intensity variation of the Gaussian beam displayed the diffraction profile of concentric rings at the far-field due to the coherent superposition of transverse wave vectors with characteristic spatial nonlinear phases. The number of concentric rings as a function of input-intensity revealed the nonlinear refraction coefficients of the QDs. The nonlinear refraction coefficient or the real part of third-order nonlinear susceptibility as a function of concentration of QDs characterized the averaged second-order hyperpolarizability which is the nonlinear refraction coefficient of a single perovskite QD. The vertically asymmetric diffraction ring of SSPM indicates the phase distortion of the optical field due to the heat convection. All-optical switching characteristics of perovskite QDs is attributable to the intensity-modulated SSPM. The input intensity of optical switching by the SSPM was estimated to be ~1.05 MW/m2.

Wave-Vector-Varying Pancharatnam-Berry Phase Photonic Spin Hall Effect.

The geometric Pancharatnam-Berry (PB) phase not only is of physical interest but also has wide applications ranging from condensed-matter physics to photonics. Space-varying PB phases based on inhomogeneously anisotropic media have previously been used effectively for spin photon manipulation. Here we demonstrate a novel wave-vector-varying PB phase that arises naturally in the transmission and reflection processes in homogeneous media for paraxial beams with small incident angles. The eigenpolarization states of the transmission and reflection processes are determined by the local wave vectors of the incident beam. The small incident angle breaks the rotational symmetry and induces a PB phase that varies linearly with the transverse wave vector, resulting in the photonic spin Hall effect (PSHE). This new PSHE can address the contradiction between spin separation and energy efficiency in the conventional PSHE associated with the Rytov-Vladimirskii-Berry phase, allowing spin photons to be separated completely with a spin separation up to 2.2 times beam waist and a highest energy efficiency of 86%. The spin separation dynamics is visualized by wave coupling equations in a uniaxial crystal, where the centroid positions of the spin photons can be doubled due to the conservation of the angular momentum. Our findings can greatly deepen the understanding in the geometric phase and spin-orbit coupling, paving the way for practical applications of the PSHE.

Angular momentum of optical modes in a silicon channel waveguide

This work studies the behavior of angular momentum of highly confined optical modes in a channel waveguide, in which the influence of transverse confinement is characterized by the average transverse wavevectors