We present a new derivation of the Fresnel-Fizeau formula for the drag of light by a moving medium using a simple perturbation approach. We focus particulary on the physical origin of the phenomenon and we show that it is very similar to the Doppler-Fizeau effect. We prove that this effect is, in its essential part, independent of the theory of relativity. The possibility of applications in other domains of physics is considered.
At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the macroscopic Maxwell equations. However, equations of motion for macroscopic fields in a transparent linear medium can be written using Ampere {E,B}, Chu {E,H}, Lorentz, Minkowski, Peierls, Einstein-Laub, and other formulations of continuum electrodynamics. We present a representation-independent derivation of electromagnetic boundary conditions and Fresnel relations …
A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of travelling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actu…
It was recently shown [Halimeh et al. arXiv:1510.06144 (to appear in Phys. Rev. A)] that as a result of the Doppler effect, inherently dispersive single-frequency ideal free-space invisibility cloaks in relative motion to an observer can only cloak light whose frequency in the cloak frame coincides with the operational frequency of the cloak, although an infinite number of such rays exist for any cloak motion. In this article, we show analytically and through ray-tracing simulations that even though this relationship can be relaxed by simplifying the ideal invisibility cloak into a broadband a…
Electromagnetic wave is reflected and refracted at interfaces, satisfying Fresnel-Snell law which is required by conservations of energy and momentum. If the incident angle is lower than the critical angle, we can use this Fresnel-Snell law, but the Fresnel-Snell law is modified in the case of existence of dissipation ($\tilde{n} = n + iκ, κ> 0$) or in the condition of total internal reflection. In the cases, we have to extend the angle of refraction from real number to complex number ($θ\rightarrow \tildeθ = θ+ iψ, ψ\neq 0$). In this paper, by using complex-angle approach, we analyse the beha…
A moving dielectric medium can displace the optical path of light passing through it, a phenomenon known as the Fresnel-Fizeau optical drag effect. The resulting displacement is proportional to the medium's velocity. In this article, we report on an anomalous optical drag effect, where the displacement is still proportional to the medium's speed but along the direction opposite to the medium's movement. We conduct an optical drag experiment under conditions of electromagnetically-induced transparency and observe the transition from normal, to null, to anomalous optical drag by modification of …
The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the scattering properties of the pulse mimics that found from the Fresnel jump conditions for a plane wave - except that the transmission to incident amplitudes are augmented by a factor of $\sqrt{n_2/n_1}$. As the boundary layer becomes thicker one finds deviations away from the Fresnel conditions and eventually one approaches WKB propagation. However there is found …
The Fresnel-Fizeau effect of transverse drag, in which the trajectory of a light beam changes due to transverse motion of the optical medium, is usually extremely small and hard to detect. We observe transverse drag in a moving hot-vapor cell, utilizing slow light due to electromagnetically induced transparency (EIT). The drag effect is enhanced by a factor 360,000, corresponding to the ratio between the light speed in vacuum and the group velocity under EIT conditions. We study the contribution of the thermal atomic motion, which is much faster than the mean medium velocity, and identify the …
The repulsion between free electrons inside a metal makes its optical response spatially dispersive, so that it is not described by Drude's model but by a hydrodynamic model. We give here fully analytic results for a metallic slab in this framework, thanks to a two-modes cavity formalism leading to a Fabry-Perot formula, and show that a simplification can be made that preserves the accuracy of the results while allowing much simpler analytic expressions. For metallic layers thicker than 2.7 nm modified Fresnel coefficients can actually be used to accurately predict the response of any multilay…
When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Haenchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted…
Trace formula for chaotic dielectric resonators tested with microwave experiments
我们测量了两个体育场形介质微波谐振器的谐振谱，并测试了Bogomolny等人提出的混沌介质谐振器的半经典迹公式[Phys.Rev.E78，056202（2008）]。我们发现实验数据和痕量公式的预测之间有很好的定性一致性。偏差可归因于根据先前实验[Phys. Rev. E 81，066215（2010）]测得的光谱中缺少共振。数值长度谱的研究表明，与迹线公式有良好的定性和定量一致性。然而，它表明需要对迹线公式进行高阶修正。曲率修正的应用程序的菲涅尔反射系数进入跟踪公式产生了更好的协议，但偏差仍然存在，表明进一步调查的必要性。
Experiments on light dragging in a moving medium laid the cornerstones of modern physics more than a century ago, and they still are in the focus of current research. When linearly polarized light is transmitted through a rotating dielectric, the polarization plane is slightly rotated -- a phenomenon first studied by Fermi in 1923. For typical non-resonant dielectric materials, the measured polarization drag angle does not surpass several microradians. Here we show that this effect may be dramatically enhanced if the light is sent to a gas of fast unidirectionally spinning molecular superrotor…
When a monochromatic electromagnetic plane-wave arrives at the flat interface between its transparent host (i.e., the incidence medium) and an amplifying (or gainy) second medium, the incident beam splits into a reflected wave and a transmitted wave. In general, there is a sign ambiguity in connection with the k-vector of the transmitted beam, which requires at the outset that one decide whether the transmitted beam should grow or decay as it recedes from the interface. The question has been posed and addressed most prominently in the context of incidence at large angles from a dielectric medi…
When a monochromatic electromagnetic plane-wave arrives at the flat interface between its transparent host (i.e., the incidence medium) and an amplifying (or gainy) second medium, the incident beam splits into a reflected wave and a transmitted wave. In general, there is a sign ambiguity in connection with the k-vector of the transmitted beam, which requires at the outset that one decide whether the transmitted beam should grow or decay as it recedes from the interface. The question has been posed and addressed most prominently in the context of incidence at large angles from a dielectric medi…
The Fresnel-Snell law, which is one of the fundamental laws in optics and gives insights on the behaviour of light at interfaces, is violated if there exists dissipation in the transmitting media. In order to overcome this problem, we extend the angle of refraction from a real number to a complex number. We use this complex-angle approach to analyse the behaviour of light at interfaces between lossy media and lossless media. We reveal that dissipation makes the wavenumber of the light exceed the maximum allowed at lossless interfaces. This is surprising because, in general, dielectric loss onl…
We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster's law. An astonishing consequence of this effect is that the reflected field's Cartesian components acquire local phase singularities at Brewster's angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states …
Here, we show that isorefractive spacetime crystals with a travelling-wave modulation may mimic rigorously the response of moving material systems. While generic spacetime crystals are characterized by a bi-anisotropic coupling in the co-moving frame, isorefractive crystals have a response that is observer independent, which leads to isotropic constitutive relations free of bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, w…
