Evanescent Regime Research Articles

Observation of parity-time symmetry for evanescent waves

Parity-time (PT) symmetry has enabled the demonstration of fascinating wave phenomena in non-Hermitian systems characterized by precisely balanced gain and loss. Until now, the exploration and observation of PT symmetry in scattering settings have largely been limited to propagating waves. Here, we demonstrate a versatile coupled-resonator acoustic waveguide (CRAW) system that enables the observation of PT-symmetric scattering responses for evanescent waves within a bandgap. By examining the generalized scattering matrix in the evanescent wave regime, we observe hallmark PT-symmetric phenomena—including phase transitions at an exceptional point, anisotropic transmission resonances, and laser-absorber modes—in systems that do not require balanced distributions of gain and loss. Owing to the peculiar energy transfer features of evanescent waves, our results not only demonstrate a distinct pathway for observing PT symmetry, but also enable strategies for exotic energy tunneling mechanisms, paving fresh directions for wave engineering grounded in non-Hermitian physics.

Experimental observation of parabolic wakes in thin plates

Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90∘. We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations. Published by the American Physical Society 2024

Tailoring spatiotemporal dynamics of plasmonic vortices

Plasmonic vortices confining orbital angular momentums to surface have aroused wide research interest in the last decade. Recent advances of near-field microscopes have enabled the study on the spatiotemporal dynamics of plasmonic vortices, providing a better understanding of optical orbital angular momentums in the evanescent wave regime. However, these works only focused on the objective characterization of plasmonic vortex and have not achieved subjectively tailoring of its spatiotemporal dynamics for specific applications. Herein, it is demonstrated that the plasmonic vortices with the same topological charge can be endowed with distinct spatiotemporal dynamics by simply changing the coupler design. Based on a near-field scanning terahertz microscopy, the surface plasmon fields are directly obtained with ultrahigh spatiotemporal resolution, experimentally exhibiting the generation and evolution divergences during the whole lifetime of plasmonic vortices. The proposed strategy is straightforward and universal, which can be readily applied into visible or infrared frequencies, facilitating the development of plasmonic vortex related researches and applications.

Self-induced backaction in optical waveguides.

In this paper, we study the backaction effect on the force exerted upon Rayleigh particles in guided structures. We show that the backaction becomes stronger as the group velocity of the guided modes is decreased, which is not unexpected since the fall of group velocity increases the interaction time between the particle and the electromagnetic field. Interestingly, the sign of the group velocity affects the pushing and pulling nature of the exerted electromagnetic force. We specifically investigate the case of a single mode optical waveguide both in the propagating and evanescent regimes, and show that the backaction enables us to enhance the ratio of the potential depth to the trapping intensity, and thereby can be a beneficial tool for nondestructive trapping of small nanoparticles. We further show that backaction can induce some resonances in the optical force in the evanescent regime. These resonances can be employed for sorting of nanoparticles.

Scattering of low-frequency acoustic waves from a moving source by the sea surface.

This paper examines the scattering of a monochromatic acoustic wave by sea-surface gravity waves in the 1-200 Hz frequency range. The source is moving in a straight line at a constant speed, and the acoustic waves are traveling upward in a refractive channel. Considering the scales of the problem, the small perturbation method coupled with the normal-mode theory and an asymptotic analysis are used to derive the first-order scattered pressure field p1. This method, established by Labianca and Harper [J. Acoust. Soc. Am. 61(2), 378-389 (1977)], allows p1 to be expressed with normal-mode functions, which are computed numerically using the in-house modal propagation code MOCTESUMA for any sound-speed profile. The pressure field is calculated in a deep-water configuration with a moving source inside a summer thermocline. First, the spatial distribution of p1 is found to follow the diffraction grating formula. Particular attention is drawn to the border between the propagative and evanescent regimes in which singularities in the theory lead to computational difficulties. Subsequently, the power spectral density of the pressure field is computed and the Doppler sidebands, asymmetrically shifted from the carrier frequency, are examined.

Saturable Absorption Dynamics of Highly Stacked 2D Materials for Ultrafast Pulsed Laser Production

This review summarizes recent developments of saturable absorbers (SAs) based on 2D materials for nonlinear optical absorption and ultrafast pulsed laser generation. Apart from graphene, various 2D materials such as topological insulators and transition metal dichalcogenides are investigated for SA applications and their important potential as passive mode-lockers for femtosecond laser production are extensively investigated. By selecting appropriate 2D materials, a wide spectral range of passively mode-locked pulsed lasers are obtained, covering visible, midinfrared and a terahertz region. A set of different approaches is used for fabricating SA modules of fiber laser photonics, which include sandwiching, side-polishing and tapering methods. Noticeably, through systematic studies, it is demonstrated that layer-stacking seldom deteriorates the SA performance of 2D materials in the evanescent regime, although their ultrathin nature may improve the efficiency in a transmission mode like sandwich-type SAs. The direction for designing new SAs is presented based on material characterization.

Scattering of electromagnetic waves by cylinder inside uniaxial hyperbolic medium.

We study electromagnetic wave scattering inside a hyperbolic medium by a circular cylinder. The hyperbolic medium's unique properties result in scattering behaviors that differ greatly from scattering by the same cylinder inside a positive isotropic medium. Incident wave polarization is preserved for all angles of incidence and the scattered waves have the same polarization in the far-field region. TM-polarized plane wave scattering is highly anisotropic. At any given frequency, the dielectric cylinder's scattering properties can vary from the Rayleigh regime, to the resonant regime, to the evanescent regime, by simply changing the angle of incidence. At a given angle, as a function of frequency, the scattering efficiency exhibits narrow resonant features associated with Fano interference. We also show that a magnetic cylinder's scattering can be suppressed. All of these effects stem from the hyperbolic medium's properties, as well as point to the interesting opportunities of tailoring scattering properties by controlling the surrounding medium.

Stationary Schr\xf6dinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions

This paper is concerned with a 1D Schrödinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid “turning points”. We derive a non-overlapping domain decomposition method to split the original problem into sub-problems on these regions, both for the continuous and afterwards for the discrete problem. Further, a hybrid WKB-based numerical method is designed for its efficient and accurate solution in the semi-classical limit: a WKB-marching method for the oscillatory regions and a FEM with WKB-basis functions in the evanescent regions. We provide a complete error analysis of this hybrid method and illustrate our convergence results by numerical tests.

Experiments with mixing in stratified flow over a topographic ridge

AbstractThe interaction of quasi‐steady abyssal ocean flow with submarine topography is expected to generate turbulent mixing in the ocean. This mixing may occur locally, close to topography, or via breaking quasi‐steady lee waves that can carry energy into the ocean interior. There is currently no theoretical, or empirically derived, prediction for the relative amounts of local and interior mixing. We report measurements of the mixing rate in laboratory experiments with a topographic ridge towed through a density stratification. The experiments span three parameter regimes including linear lee waves, nonlinear flow and an evanescent regime in which wave radiation is weak. Full field density measurements provide the depth‐dependence of energy loss to turbulent mixing, allowing separation of the local mixing in the turbulent wake and remote mixing by wave radiation. Remote mixing is significant only for a narrow band of forcing parameters where the flow speed is resonant with internal waves; in all other parameter regimes local mixing close to the topography is dominant. The results suggest that mixing by local nonlinear mechanisms close to abyssal ocean topography may be much greater than the remote mixing by quasi‐steady lee waves.

Scattering of the evanescent components in the angular spectrum of a tightly focused electromagnetic beam by a spherical particle

In many previous studies where a tightly focused beam is scattered by a spherical particle, either the experimental conditions were such that evanescent components were absent from the angular spectrum of the incident beam, or if they were present, it was assumed that their contribution to scattering was small with respect to that of the oscillatory components, and could safely be ignored. In this paper the contribution of the evanescent components is explicitly calculated and the validity of their neglect in various situations is assessed. It is demonstrated that when a particle whose size is comparable to the wavelength is located near the plane in which the strength of the evanescent components is maximized, the angular spectrum components just inside the evanescent regime, when added to the contribution of the oscillatory components, can possibly make a significant contribution to the shape coefficients of the incident beam.

Effect of d-wave pair coupling on evanescent type of Andreev reflection

In this paper, we investigate the current resulted from virtual Andreev process, passing through a N/S gapped graphene-based junction, where superconductivity in the S-region is induced by depositing unconventional d-wave superconductor. It is shown that the evanescent type of Andreev reflections occurs above the critical electron incident angle, and needs to take into account its effect when calculating the tunneling conductance in the both conventional and unconventional superconductor junctions. In the evanescent wave regime, the new pure imaginary wavevector of hole-like quasiparticle is obtained, and consequently, the tunneling conductance formalism is modified. We show that due to the nature of pair interaction in d-wave superconductivity, considering the virtual Andreev process affects significantly the behavior of charge carriers in the structure. In particular, the conductance in the virtual regime is more sensitive to the superconductor gap characterized by orbital rotated angle, so that with increasing α the width of zero conductance versus bias energy decreases and above α=0.1π the current in junction is supplied just by virtual Andreev process.

Relativistic electron transport through an oscillating barrier: Wave-packet generation and Fano-type resonances

Transport properties of massive Dirac particles are investigated through an oscillating barrier. The Floquet quasienergies related to the time-dependent potential appear both in transmission and reflection as sidebands around the incoming electron's energy. We take all relevant sidebands into account and present time averaged transmission and reflection probabilities in a wide energy range. Most qualitative features of scattering on a static barrier---like Klein paradox---are still visible, but the transmission probability in the evanescent regime observably increases due to the oscillation of the potential. The strongly inelastic scattering process is shown to lead to multiple Fano-type resonances and temporal trapping of the particles inside the oscillating potential. We also present a detailed study of the time evolution of the wave packets generated in the scattering process. Our results can be relevant for graphene with an induced energy gap.

Plasmonic nanowires arranged in Fibonacci number chain: Excitation angle-dependent optical properties

Herein we numerically study the excitation angle-dependant far-field and near-field optical properties of vertical plasmonic nanowires arranged in an unconventional linear geometry: Fibonacci number chain. The first five numbers in the Fibonacci series (1, 1, 2, 3, 5) were mapped to the size of gold nanowires, and arranged in a linear chain to study their optical interactions, and compared them to conventional chain of vertical gold nanowires. By harnessing the radiative and evanescent coupling regimes in the geometry, we found a systematic variation in the far-field extinction and near-field confinement in the geometries. Our simulation studies revealed enhanced backscattered intensity in the far-field radiation pattern at excitation angles along the chain-length of Fibonacci geometry, which was otherwise absent for conventional chain of plasmonic nanowires. Such angular reconfiguration of optical fields in unconventional linear geometries can be harnessed for tunable on-chip plasmonics.

Longitudinally polarized electric and magnetic optical nano-needles of ultra high lengths

We demonstrate a method to generate longitudinally polarized electric and magnetic light spots over ultra-long distances. The method proposed here relies on the generation of radially and azimuthally polarized Bessel beams at the limit between propagating and evanescent regimes, by projecting radially and azimuthally polarized doughnut beams onto an axicon-based system of numerical aperture (NA) equal to 1. Tight electric and magnetic light spots (0.36λ) can be produced over distances reaching 50λ and with longitudinal intensities about 3.5×104 times above the transverse intensities. Same confinement abilities over distances larger than 335 λ is also predicted with longitudinal intensities 883 fold above the transverse ones. Experimental characterization of these tiny optical needles with polarization-resolved heterodyne SNOM reveals electric and magnetic light spots smaller than 0.4 λ whose longitudinal intensities are about 200-fold larger than the transverse ones.

Effects of edge potential on an armchair-graphene open boundary and nanoribbons

Pseudospin flipping is found to be the key process leading to the formation of an edge-potential-induced edge state at an armchair-graphene open boundary and nanoribbons. At an open boundary, the edge potential ${U}_{0}$ is shown to turn on pseudospin-flipped (intravalley) scattering even though ${U}_{0}$ does not post an apparent breaking of the $AB$ site (basis atoms) symmetry. For a valley-polarized incident beam, the interference between the pseudospin-conserving (intervalley) and -nonconserving (intravalley) processes in the scattering state leads to a finite out-of-plane pseudospin density. This two-wave feature in the evanescent regime leads to the formation of the edge state. The physical origin of the edge state is different from that for the Tamm states in semiconductors. For an armchair-graphene nanoribbon with a gapless energy spectrum, applying ${U}_{0}$ to both edges opens up an energy gap. Both edge states and energy gap opening exhibit distinct features in nanoribbon conductance.

Fabrication of Submicron-Diameter and Taper Fibers Using Chemical Etching

The thin, long length and high smoothness silica photonic nanowires and taper optical fiber were fabricated using a simple and low cost chemical etching method. A two-steps wet etch process were used consisting of etching with 30% HF acid to remove cladding and 24% HF acid to decrease fiber core diameter. An approach for on-line monitoring of etching using 1300 nm light power transmitted in the optical fiber was used to determine the diameter of the remaining core and showed a transition between two different operation regimes of nanofiber from the embedded regime, where the mode was isolated from the environment, to the evanescent regime. The data indicated that the diameter of the silica fiber decreased linearly for both 30% and 24% HF acid with 1.2 and 0.1 μm/min grad diameter, respectively at room temperature, and more than 70% of the mode intensity could propagate outside fiber when the core diameter was less than 1 μm. The results of fiber taper showed that the fiber was tapered by a factor of 20 while retaining a thin core structure and leaving about more than 85% of core structure.

Effect of Virtual Andreev Reflection on Tunneling in Normal/Superconductor Graphene Junction

The Andreev reflection (AR) process and the tunneling conductance in graphene-based normal metal/superconductor junction are studied, where both massless and massive fermions are considered. As a result, the evanescent type of AR or the virtual Andreev reflection (VAR), is found to take place at the interface above the critical angle or in case where AR decays due to massive energy gap. Significantly, current of the junction is found to exist in the evanescent AR regime. In this work, we modify tunneling conductance formalism by including the current induced by the evanescent type of AR process (or VAR), which has not been taken into account in previous studies. In contrast to the previous work, our formula leads to a new result due to the influence of the VAR when the energy of the quasiparticles greater than the superconducting gap.

Metallic phase of disordered graphene superlattices with long-range correlations

Using the transfer matrix method, we study the conductance of the chiral particles through a monolayer graphene superlattice with long-range correlated disorder distributed on the potential of the barriers. Even though the transmission of the particles through graphene superlattice with white noise potentials is suppressed, the transmission is revived in a wide range of angles when the potential heights are long-range correlated with a power spectrum $S(k)\sim1/k^{\beta}$. As a result, the conductance increases with increasing the correlation exponent values gives rise a metallic phase. We obtain a phase transition diagram in which a critical correlation exponent depends strongly on disorder strength and slightly on the energy of the incident particles. The phase transition, on the other hand, appears in all ranges of the energy from propagating to evanescent mode regimes.

Macroscopic Maxwell’s equations and negative index materials

We study the linear phenomenological Maxwell’s equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, nonabsorptive, medium with equal electric and magnetic permeabilities ε(ω) and μ(ω), the latter can assume the value of −1 (+1 is their vacuum value) for a discrete set of frequencies ±ω̂n, i.e., for these frequencies the medium behaves as a negative index material (NIM). We show that such systems have a well-defined time evolution. In particular, the fields remain square integrable (and the electromagnetic energy finite) if this is the case at some initial time. Next we turn to Green’s function G(x,y,z) (a tensor), associated with the electric Helmholtz operator for a set of parallel layers filled with a material. We express it in terms of the well-known scalar s and p ones. For a half space filled with the material and with a single dispersive Lorentz form for ε(ω)=μ(ω), we obtain an explicit form for G. We find the usual behavior for NIMs for ω=±ω̂, there is no refection outside the evanescent regime and the transmission (refraction) shows the usual NIM behavior. We find that G has poles in ±ω̂, which lead to a modulation of the radiative decay probability of an excited atom. The formalism is free from ambiguities in the sign of the refractive index.

Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies

The Fabry-Perot resonance effect is studied in order to achieve subwavelength imaging at a far distance (e.g., about 10 wavelengths) from the source at optical frequencies. Two different structures (with matched and mismatched impedances) of alternative metal and air layers are considered first at a relatively short distance (e.g., about one wavelength) from the source. It is found that the impedance match is not necessary for subwavelength focusing since the Fabry-Perot resonance effect is utilized here. An appropriate period is chosen so that the Fabry-Perot resonance occurs in an evanescent regime, and consequently the evanescent waves near the Fabry-Perot resonance peak are amplified. With such a mechanism, a super lens with a resolution of about ${\ensuremath{\lambda}}_{0}∕30$ (${\ensuremath{\lambda}}_{0}$ is the wavelength in the air), acceptable sidelobes and a larger displacement range (when the thickness of the period is within such a displacement range, subwavelength focusing with acceptable sidelobes can be achieved) is designed. Subwavelength focusing (with a spotsize of ${\ensuremath{\lambda}}_{0}∕12$) at a distance far away from the source is also realized in the presence of some material loss.