The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In paper (I) of this sequence, we described theoretically the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two non-dispersive, homogeneous, isotropic dielectrics. Here, in paper (II) of this sequence, we present experimental verification of the novel refractive phenomena predicted for `baseband' ST wave packets upon normal incidence on a planar interface. Specifically, we observe group-velocity invariance, normal and anomalous refraction, and group-velocity inversion leading to group-delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF$_2$, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light-cone.
The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibit fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In paper (III) of this sequence, we prese…
Space-time (ST) wave packets are a class of pulsed optical beams whose spatio-temporal spectral structure results in propagation invariance, tunable group velocity, and fascinating refractive phenomena. Here, we investigate the refraction of ST wave packets at a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface. We verify this new refraction law in ZnSe and CdSe, both of which man…
Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics, such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we cal…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian light beams. These formulas show the presence of anomalous refraction phenomena at any slab thickness, including negative refraction and flat lensing effects, induced by the reflection on the rear face.
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in general case from ones derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by Onoda et al. [Phys. Rev. Lett. 93, 083901 (2004)]. We a…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an optical field is the tacit presumption of the separability of its spatial and temporal degrees-of-freedom. We show here that endowing a pulsed beam with precise spatio-temporal spectral correlations unveils remarkable refractory phenomena, such as group-velocity invariance with respect to the refractive index, group-delay cancellation, anomalous group-veloci…
Refraction of obliquely incident plane waves due to the interface of a vacuous half-space and a half-space occupied by a simply moving, nondissipative, isotropic dielectric-magnetic medium is considered, when the medium's velocity lies parallel to the interface and in the plane of incidence. Counterposition of the refracted wavevector and time-averaged Poynting vector occurs when the medium's velocity is sufficiently large in magnitude and makes an obtuse angle with the incident wavevector. The counterposition induced by relative motion occurs whether the refraction is negative or positive whe…
The group delay incurred by an optical wave packet depends on its path length. Therefore, when a wave packet is obliquely incident on a planar homogeneous slab, the group delay upon traversing it inevitably increases with the angle of incidence. Here we confirm the existence of isochronous `space-time' (ST) wave packets: pulsed beams whose spatio-temporal structure enables them to traverse the layer with a fixed group delay over a wide span of incident angles. This unique behavior stems from the dependence of the group velocity of a refracted ST wave packet on its angle of incidence. Isochrono…
The refraction of linearly polarized plane waves into a half-space occupied by a material moving at constant velocity was studied by directly implementing the Lorentz transformations of electric and magnetic fields. From the perspective of a co-moving observer, the moving material was a spatially local, pseudochiral omega material. Numerical studies revealed that whether or not negative refraction occurrs in the moving material depends upon the speed of movement as well as the angle of incidence and the polarization state of the incident plane wave. Furthermore, the phenomenons of negative pha…
We theoretically propose that Weyl semimetals may exhibit negative refraction at some frequencies close to the plasmon frequency, allowing transverse magnetic (TM) electromagnetic waves with frequencies smaller than the plasmon frequency to propagate in the Weyl semimetals. The idea is justified by the calculation of reflection spectra, in which \textit{negative} refractive index at such frequencies gives physically correct spectra. In this case, a TM electromagnetic wave incident to the surface of the Weyl semimetal will be bent with a negative angle of refraction. We argue that the negative …
We report narrowband transmission filtering based on zero-contrast grating (ZCG) reflectors at normal incidence. Computational results show that the filtering is realized through symmetry-protected modes coupling. The guided modes introduced by the slab layer make the filter frequencies flexible to modify. The rectangular structure of the filter allows simple fabrication and integration into optical systems. The quality factor of the filters could exceed 106. Owing to the low refraction index dispersion of the semiconductor and their scale-invariant operations, these filters can be applied in …
We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, however, in general, do not satisfy the conservation laws for individual photons in consequence of the lack of the ``which path'' information in a two-channel wave scattering. The field structure for the reflected/refracted beam is analyzed. In the scattering of a linearly-polarized beam, photons of opposite helic…
Reflection and Refraction at Nonlinear Temporal Boundaries in Synthetic Lattices
Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（安徽量子网络重点实验室，中国科学技术大学）；CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学院量子信息与量子物理学卓越创新中心，中国科学技术大学）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）；Anhui Center for Fundamental Sciences in Theoretical Physics, University of Science and Technology of China（安徽理论物理基础科学中心，中国科学技术大学）
Space-time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio-temporal correlation. Here it is proved that the space-time wave packets are stable in dispersive media as well and free from the spread in time caused by material dispersion. Furthermore, the law of anomalous refraction for space-time wave packets is generalized to the weakly dispersive situation. These results reveal new potential of space-time wave packets for the applications in real dispersive media.
We have investigated that the Goos-Hänchen (GH) shifts in frustrated total internal reflection (FTIR) studied with wave packet propagation. In the first-order approximation of the transmission coefficient, the GH shift is exactly the expression given by stationary phase method, thus saturates an asymptotic constant in two different ways depending on the angle of incidence. Taking account into the second-order approximation, the GH shift always depends on the width of the air gap due to the modification of the beam width. It is further shown that the GH shift with second-order correction increa…
We have experimentally studied the impact of an initially planar axisymmetric vortex ring, incident at an oblique angle, upon a gravity-induced interface separating two fluids of differing densities. After impact, the vortex ring was found to exhibit a variety of subsequent trajectories, which we organize according to both the incidence angle, $θ_i$, and the interface strength, defined as the ratio of the Atwood and Froude numbers, $A/F$. For grazing incidence angles ($θ_i \gtrsim 70$ deg.) vortices either penetrate or reflect from the interface, depending on whether the interface is weak or s…
Theoretical and computational study of reflection and refraction of electromagnetic waves with $p$-polarized and normal incidence electric wave amplitude vector on anisotropic, inhomogeneous and linear medium has been done. The medium used in this study is a model of susceptibility in the form of rank-2 tensor which its value depends on the frequency, position and time. Theoretical and computational formulation of transmittance and reflectance are then tested using vacuum and FeF$_2$ magnetic material.
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane electromagnetic waves in ordinary dielectrics, the kinematical and dynamical aspects of these phenomena are studied, such as the intensity of the various wave components and the change in the polarization of the wave as it crosses the boundary. As a prerequisite of this, we show that the plane wave solution must be written as a suitable superposition of the cir…
Spatiotemporal Co-reflection with Spacetime Discontinuities at Moving Interfaces
School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Heilongjiang Provincial Key Laboratory of Plasma Physics and Application Technology（黑龙江省等离子体物理及应用技术重点实验室）
Topological notions in physics have become a powerful perspective that leads to the discoveries of topological interface states (TISs). In this work, we present a scheme to achieve negative refraction by leveraging the properties of TISs in a valley photonic crystal (VPC). Due to the chiral characteristics, one type of the TISs deterministically possesses negative dispersion relation, which can cause an obliquely incident wave to undergo a negative lateral shift. By stacking multiple VPC interfaces, the TIS-induced lateral shifts can relay in the transmitted wave towards the far side of incide…
An exact closed-form representation is derived of a vector elegant Laguerre-Gaussian wave packet. Its space-time representation consists of three mutually orthogonal field components - of a common azimuthal index and different radial indices - uniquely distinguished by first three powers of the paraxial parameter. The transverse components are of tm-radial and te-azimuthal polarization and appear, under their normal incidence, to be eigenmodes of any horizontally planar, homogeneous and isotropic structure, with eigenvalues given by the reflection and transmission coefficients. In this context…
We consider an oblique incidence on a uniform dielectric layer of the plane monochromatic TE- and TM-waves, as well as TE- and TM-polarized wave packets consisting of waves with the same angle of incidence. For each polarization the stationary model is presented, which allows one to uniquely restore the dynamics of the transmitted and reflected components of the incident wave packet at all stages of scattering. On this basis we introduce the concepts of ``true group-delay time"\/ and ``false group-delay time"\/ (the corresponding quantities for transmission and reflection are the same). The fo…
We present here the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Based on the theory of finite periodic systems, we show that besides the strong influence of the incidence angle, the low transmission characteristic of a single conductor slab, for frequencies $ω$ below the plasma frequency $ω_p$, becomes in this domain highly oscillating. Similarly, the well-established transmission coefficient of a single left-handed slab becomes highly resonant with superluminal effects in superlattices with more than one unit cell. We determine the space…
Selective avoidance of multiple line-of-sight obstacles at 130~m using locally bending space-time wave packets
CREOL, The College of Optics & Photonics, University of Central Florida（中佛罗里达大学光学与光子学院）；Materials Physics and Applications - Quantum Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室材料物理与应用部量子部门）；Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）
Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S- and P-polarized electromagnetic (EM) waves are examined by means of exactly solvable models. We present generalized Fresnel formulae, describing the influence of the non-local dispersion on reflectance and transmittance of single- and double-layer gradient photonic barriers for S- and P- waves and arbitrary angles of incidence. The non-local dispersion of such layers, arising due to a concave spatial profile of dielectric susceptibility across the plane film, is sho…
Realization of the anomalous refraction effects predicted by Huygens' metasurfaces (HMS) have required tedious and time-consuming trial-and-error numerical full-wave computations. It is shown herein that these requirements can be alleviated for transverse magnetic (TM) propagation by a periodic dielectric-based HMS consisting of an electrically thick array of cascaded Fabry-Pérot etalons. This "Fabry-Pérot HMS" (FP-HMS) is easily designed to mimic the local scattering coefficients of a standard zero-thickness HMS (ZT-HMS) which, according to homogenization theory, should result in the desired …
An explicit time-domain finite-difference technique for modelling zero-thickness Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modelled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens' metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time-domain…
