The dependence of macroscopic radiation pressure on the velocity of the object being pushed is commonly attributed to the Doppler effect. This need not be the case, and here we highlight velocity dependent radiation pressure terms that have their origins in the mixing of s and p polarizations brought about by the Lorentz transformation between the lab and the material rest frame, rather than in the corresponding transformation of frequency and wavevector. The theory we develop is relevant to the nano-optomechanics of moving bodies.
This is a Reply to a Comment by V.P. Torchigin and A.V. Torchigin, published in Physical Review A 92, 017803 (2015). The paper which is commented upon is titled "Deducing radiation pressure on a submerged mirror from the Doppler shift," originally published in Physical Review A 85, 023807 (2012).
We consider the spectral response of moving diffraction gratings, in which the incident light extends over a broad angular range and where the diffracted light is observed from a specific angle. We show that the dispersion relation between the frequency perceived by an observer who is looking at a moving grating and the incident frequency can exhibit some unique features, such as a flat band (i.e., a local minimum). An observer can see the light diffracted into a non-specular diffraction order from a multitude of incident light rays and the angle of incidence of each ray is frequency-dependent…
When a light pulse is reflected from a mirror, energy and momentum are exchanged between the electromagnetic field and the material medium. The resulting change in the energy of the reflected photons is directly related to their Doppler shift arising from the change in the state of motion of the mirror. Similarly, the Doppler shift of photons that enter an absorber is intimately tied to the kinetic energy and momentum acquired by the absorber in its interaction with the incident light. The argument from the Doppler shift yields expressions for the exchanged energy and momentum that are identic…
The formula for the frequency shift of a plane-polarized light wave reflected from a uniformly moving mirror is derived directly from the constant light speed postulate and the basic principles of wave optics. Unlike the original derivation by Einstein, our derivation does not involve Lorentz transformations. As such, it lies within the scope of a first course in special relativity.
The energy extinction cross section of a concentrically layered sphere varies with velocity as the Doppler shift moves the spectral content of the incident signal in the sphere's co-moving inertial reference frame toward or away from resonances of the sphere. Computations for hollow gold nanospheres show that the energy extinction cross section is high when the Doppler shift moves the incident signal's spectral content in the co-moving frame near the wavelength of the sphere's localized surface plasmon resonance. The energy extinction cross section of a three-layer sphere consisting of an oliv…
The Doppler effect of light was implemented by interference with a reference wave to infer linear velocities in early manifestations, and more recently lateral and angular velocities with scalar phase structured light. A consequence of the scalar wave approach is that it is impossible to deduce the motion direction and position of moving targets directly. Here we overcome this limitation with vectorially structured light, exhibiting spatially variant polarization, allowing both the position and velocity of a particle to be robustly determined by a new vectorial Doppler effect. We use this to s…
Phenomena of wave propagation in dynamically varying structures have reemerged as the temporal variations of the medium's properties can extend the possibilities for electromagnetic wave manipulation. While the dynamical change of the electromagnetic medium's properties is a difficult task, the movement of scatterers is not. In this paper, we analyze the electromagnetic fields trapped inside two smoothly moving mirrors. We employ the method of characteristics and take into account the relativistic phenomena to show that the temporally and spatially local Doppler effects can filter and amplify …
An inverse Doppler shift occurs in a photonic crystal (PC) bounded by a moving wall. The interpretation of this result has stirred some controversy. In this paper, we address the problem using a diagrammatic approach. This visual representation provides immediate insight into the phenomenon, and is a powerful tool for the design of time-varying PCs.
We derive the formula of the complex Doppler shift in a two-dimensional, dispersive metamaterial and we show that a moving, monochromatic radiation source generates multiple frequency modes. The role of the group velocity is stressed and the Doppler shifted radiation field exhibits features of the Cherenkov effect. The presented theory is also applicable to the case of a moving, nonoscillating charge and explains many peculiar characteristics of the Cherenkov radiation in lefthanded metamaterials such as the backward direction of power emission, the constant radiation angle and the lack of vel…
The well-known linear Doppler effect arises from the linear motion between source and observer, while the less well-known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments illustrating the relationship between the rotational and linear Doppler effects. A spiral phaseplate is used to generate a light beam carrying orbital angular momentum and the frequency shift is measured arising from its rotational and/or linear motion. By considering either the motion-induced time-evolving phase or the momentum and energy conservation in light-matter…
The Doppler effects for the reflected wave from a moving media are systemically analyzed in this paper. The theoretical formula for the Doppler shift in the left-handed material, which is described by Drude's dispersion model, is presented. This formula is examined by first-principles numerical experiments, which are in agreement with the theoretical results.
Radiation pressure and photon momentum in negative-index media are no different than their counterparts in ordinary (positive-index) materials. This is because the parameters responsible for these properties are the admittance, sqrt(epsilon/mu), and the group refractive index n_g of the material (both positive entities), and not the phase refractive index, n=sqrt(epsilon*mu), which is negative in negative-index media. One approach to investigating the exchange of momentum between electromagnetic waves and material media is via the Doppler shift phenomenon. In this paper we use the Doppler shif…
Radiation pressure on a flat mirror submerged in a transparent liquid, depends not only on the refractive index n of the liquid, but also on the phase angle psi_0 of the Fresnel reflection coefficient of the mirror, which could be anywhere between 0^{\circ} and 180^{\circ}. Depending on the value of psi_0, the momentum per incident photon picked up by the mirror covers the range between the Abraham and Minkowski values, i.e., the interval (2\hbarw_0/nc,2n\hbarw_0/c). Here \hbar is the reduced Planck constant, w_0 is the frequency of the incident photon, and c is the speed of light in vacuum. W…
The Doppler shift is investigated in one-dimensional system with moving source. Theoretical findings are confirmed in numerical simulations of optical and acoustical waves propagation in simple metamaterial model, showing the reversed shift and the existence of multiple frequency modes. The properties of these waves are discussed. The effect of absorption on the phenomenon is outlined.
Nowadays, there is considerable interest in metamaterials which realize the electromagnetically induced transparency in a classical system. We consider the frequency shifts of particle moving in metamaterials exhibiting electromagnetically induced transparency effect. The dramatic change of the material dispersion due to the EIT influences the conditions for signal propagation in the medium and has a significant impact on the Doppler effect, possibly leading to the optical control over this phenomenon. The dependence of the Doppler shift to the source frequency and velocity and radiation spect…
We present Doppler-corrected position and velocity measurement with a fiber-coupled COFDR system based on the FMCW radar principle for high precision localization applications. A high measurement accuracy and the ability to track targets are demonstrated.
Fizeau demonstrated in 1850 that the speed of light can be modified when it is propagating in moving media. Can we achieve such control of the light speed efficiently with a fast-moving electron media by passing electrical current? Because the strong electromagnetic coupling between the electron and light leads to the collective excitation of plasmon polaritons, it will manifest as the plasmonic Doppler effect. Experimental observation of the plasmonic Doppler effect in electronic system has been challenge because the plasmon propagation speed is much faster than the electron drift velocity in…
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.
A general theory of optical forces on moving bodies is here developed in terms of generalized/4x4 transfer and scattering matrices. Results are presented for a planar dielectric multilayer of arbitrary refractive index placed in an otherwise empty space and moving parallel and perpendicular to the slab-vacuum interface. In both regimes of motion the resulting force comprises lateral and normal velocity-dependent components which may depend in a subtle way on the Doppler effect and TE-TM polarization mixing. For lateral displacements in particular, polarization mixing, which is here interpreted…
A moving pellicle superconducting mirror, which is driven by radiation pressure on its one side, and by the Coulomb force on its other side, can become a parametric oscillator that can generate microwaves when placed within a high-Q superconducting Fabry-Perot resonator system. A paraxial-wave analysis shows that the fundamental resonator eigenmode needed for parametric oscillation is the TM011 mode. A double Fabry-Perot structure is introduced to resonate the pump and the idler modes, but to reject the parasitic anti-Stokes mode. The threshold for oscillation is estimated based on the radiati…
Metasurfaces consisting of electrically thin and densely packed planar arrays of subwavelength elements enable an unprecedented control of the impinging electromagnetic fields. Spatially modulated metasurfaces can efficiently tailor the spatial distribution of these fields with great flexibility. Similarly, time modulated metasurfaces can be successfully used to manipulate the frequency content and time variations of the impinging field. In this paper, we present time-modulated reflective metasurfaces that cause a frequency shift to the impinging radiation, thus realizing an artificial Doppler…
We report here the first observation of electromagnetically induced transparency (EIT) in $^{20}$Ne. The power broadening of the EIT linewidth is measured as a function of neon pressure and RF excitation power. Doppler effects on the EIT broadening are found even at low pressures and low intensities, where the linewidth should be governed only by homogeneous effects.
