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 call 'the spectral curvature'. Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X-wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.
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…
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, nor…
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…
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…
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.
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 clarify the claims and errors in the paper "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality" by Mark Stockman. Contrary to the central assertion in that paper, simple examples consistent with the basic inequality which Stockman discovered show that it is possible to have negative refraction and low loss in an arbitrarily large frequency window. Further examination of the paper reveals additional errors that invalidate his argument that active materials cannot have low loss and negative refraction in a frequency window. Also, we point out t…
The general reflection and refraction laws at the metasurface with the abrupt phase shift were derived by two different methods of Fermat's principle and the boundary conditions respectively. It is found that one or two critical angles for total internal reflection exist when a light hits on the optical sparse material from the optical denser material, and one such a critical angle exists when light spreads from the optical sparse material to the optical denser material. Anomalous reflection and refraction, such as, negative reflection and negative refraction may occur when a light passes thro…
Focal-plane imaging with microwave and millimeter wave has many potential applications. The bad resolution is a main shortcoming of this technique at present. In this paper, influence of frequency of electromagnetic wave on the refractive energy is analyzed. According to the refractive mechanism of electromagnetic induction, the principle for designing artificial materials with enough refractive ability is proposed. The material of artificial molecules is fabricated with cage-shaped granules of conductor (CGC). The refractive index of CGC material to microwave was measured by assembling CGC pr…
A new look at the so-called effect of an accelerating matter is presented. It was previously stated that the effect is optical in nature and consists in changing the frequency of the wave passing through a refractive sample moving with acceleration. However, from a simple consideration based on the principle of equivalence, it follows that the idea of the connection of the effect only with the refraction phenomenon is unreasonably narrow, and a change in the wave frequency should inevitably occur during scattering by any object moving with acceleration. Such an object can be either an elementa…
Although a plethora of techniques are now available for controlling the group velocity of an optical wave packet, there are very few options for creating accelerating or decelerating wave packets whose group velocity varies controllably along the propagation axis. Here we show that `space-time' wave packets in which each wavelength is associated with a prescribed spatial bandwidth enable the realization of optical acceleration and deceleration in free space. Endowing the field with precise spatio-temporal structure leads to group-velocity changes as high as $\sim c$ observed over a distance of…
Within the Franck-Condon approximation, the single ionization of H$_2$ leaves H$_2^+$ in a coherent superposition of 19 nuclear vibrational states. We numerically design an optimal laser pulse train to transfer such a coherent nuclear wave packet to the ground vibrational state of H$_2^+$. The simulation results show that the population of the ground state after the transfer is more than 91%. Frequency analysis of the designed optimal pulse reveals that the transfer principle is mainly an anti-Stokes transition, i.e., the H$_2^+$ in $1sσ_g$ with excited nuclear vibrational states is first pump…
Realistic attosecond wave packets have complex profiles that, in dispersive conditions, rapidly broaden or split into multiple components. Such behaviors are encoded in sharp features of the wave packet spectral phase. Here, we exploit the quantum beating between one- and two-photon transitions in an attosecond photoionization experiment to measure the photoelectron spectral phase continuously across a broad energy range. Supported by numerical simulations, we demonstrate that this experimental technique is able to reconstruct sharp fine-scale features of the spectral phase, continuously as a …
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…
Doppler-induced tunable and shape-preserving frequency conversion of microwave wave packets
Fondazione Bruno Kessler (FBK)（布鲁诺·克塞勒基金会）；Department of Physics, University of Milano-Bicocca（米兰比可卡大学物理系）；University of Milano-Bicocca（米兰比可卡大学）；Department of Physics, University of Trento（特伦托大学物理系）；University of Trento（特伦托大学）；TIFPA - INFN（INFN理论物理、粒子物理和天体物理研究所）；INFN（意大利国家核物理研究所）；CNR-IFN（意大利国家研究委员会光纤与光子学研究所）；CNR（意大利国家研究委员会）；INFN - Milano Bicocca（INFN米兰比可卡分部）；Pitaevskii BEC Center（皮塔耶夫斯基玻色-爱因斯坦凝聚中心）；CNR-INO（意大利国家研究委员会光学研究所）
Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can be related to global topological invariants such as those classifying quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a wave packet. Here, we experimentally demonstrate for the first time that wave packet dynamics …
The universal theory of weakly nonlinear wave packets given by the nonlinear Schrödinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple scale analysis carried out beyond all orders reveals that a single soliton, bright or dark, can travel at a different speed than the group velocity. In an exponentially small but finite range of parameters, the envelope of the soliton is locked to the rapid oscillations of the carrier wave. Eventually, the dynamics is governed by an equation anologous to that of a pendulum, in which the center of ma…
