The nontrivial dispersion relation of a periodic medium affects both the spectral and the spatial distribution of Cherenkov radiation. We present a theory of the spatial distribution of Cherenkov radiation in the far-field zone inside arbitrary three- and two-dimensional dielectric media. Simple analytical expressions for the far-field are obtained in terms of the Bloch mode expansion. Numerical examples of the Cherenkov radiation in a two-dimensional photonic crystal is presented. The developed analytical theory demonstrates good agreement with numerically rigorous finite-difference time-domain calculations.
Time- and frequency-domain study for electron beams penetrating dielectric nanospheres: fingerprints of Cherenkov and transition radiation
Max-Born-Institut（马克斯·玻恩研究所）；Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik and Photonik（柏林洪堡大学物理学院理论光学与光子学组）；POLIMA—Center for Polariton-driven Light-Matter Interactions, University of Southern Denmark（南丹麦大学极化激元驱动光物质相互作用中心）；Danish Institute for Advanced Study, University of Southern Denmark（南丹麦大学丹麦高等研究院）
Modern trends in beam-driven radiation sources involve interaction of Cherenkov wakefields with open-ended circular waveguide structures having complicated dielectric lining, with a three-layer dielectric capillary recently offered for reducing the radiation divergency being a representative example \cite{Jiang2020}. This paper presents rigorous approach allowing analytical description of electromagnetic processes occuring when the described structure is excited by single waveguide mode. In other words, corresponding canonical waveguide diffraction problem is considered in rigorous formulation…
We consider radiation generated by an electron travelling parallel to a planar rectangular silicon grating: Smith-Purcell radiation to the vacuum side, internal Smith-Purcell radiation into the dielectric, and Cherenkov radiation into the dielectric. Internal Smith-Purcell radiation dominates over the other two radiation mechanisms in the range where conventional Smith-Purcell radiation is forbidden. This observation may lead to improved design of contactless particle beam monitors.
Recent advances in engineered material technologies (e.g., photonic crystals, metamaterials, plasmonics, etc) provide valuable tools to control Cherenkov radiation. In all these approaches, however, the designed materials interact only with the particle velocity to affect Cherenkov radiation, while the influence of the particle trajectory is generally negligible. Here, we report on surface Dyakonov-Cherenkov radiation, i.e. the emission of directional Dyakonov surface waves from a swift charged particle moving atop a birefringent crystal. This new type of Cherenkov radiation is highly suscepti…
We investigate optical (transverse gradient) forces between two high-index dielectric planar waveguides immersed in low-index dielectric fluid media. Complimentary to previous studies, we extend optical forces calculations, in order to take into account a non-vacuum (and non-air) background medium, by using the Minkowski stress tensor formulation; we derived a very simple set of equations in terms of the effective refractive indexes of the waveguide eigenmodes. We also used a normalized version of the dispersion relation method to calculate the optical forces, in order to validate our results …
Dielectric photonics platform provides unique possibilities to control light scattering via utilizing high-index dielectric nanoantennas with peculiar optical signatures. Despite the intensively growing field of all-dielectric nanophotonics, it is still unclear how surrounding media affect scattering properties of a nanoantenna with complex multipole response. Here we report on light scattering by a silicon cubic nanoparticles embedded in lossless media, supporting optical resonant response. We show that significant changes in the scattering process are governed by the electro-magnetic multipo…
Electromagnetic Momentum in Dispersive Dielectric Media
当考虑色散效应时，亚伯拉罕和闵可夫斯基关于电介质中电磁动量的表达式都不能给出辐射的吸收体或发射体的正确反冲动量。与电介质中的场相关的总动量密度有三个贡献：（i）场的亚伯拉罕动量密度，（ii）与亚伯拉罕力相关的动量密度，以及（iii）由介质对场的响应的色散部分产生的动量密度，后者显然具有由D.F. Nelson [Phys.Rev.A44，3985（1991）]。所有这三个贡献都需要在电介质中的吸收体或发射体的反冲动量守恒。我们考虑交换的动量和作用在可极化粒子上的力（例如，当光脉冲入射到宿主电介质上时，宿主电介质中的原子或小电介质球），包括电介质的色散以及粒子对场的响应中的色散分量。在慢光介质中，这种力可以大大增加。
Radiation of charged particles moving in the presence of dielectric targets is of significant interest for various applications in the accelerator and beam physics. The size of these targets is typically much larger than the wavelengths under consideration. This fact gives us an obvious small parameter of the problem and allows developing approximate methods for analysis. We develop two methods, which are called the "ray optics method" and the "aperture method". In the present paper, we apply these methods to analysis of Cherenkov radiation from a charge moving through a vacuum channel in a so…
According to the scientific literature, the momentum of a photon in a simple linear dielectric is either $\hbarω/(nc)$ or $n\hbarω/c$ with a unit vector ${\bf \hat e}_k$ in the direction of propagation. These momentums are typically used to argue the century-old Abraham--Minkowski controversy in which the momentum density of the electromagnetic field in a dielectric is either the Abraham momentum density, ${\bf g}_A={\bf E}\times{\bf H}/c$, or the Minkowski momentum density, ${\bf g}_M={\bf D}\times{\bf B}/c$. The elementary optical excitations, photons, are typically known as polaritions in t…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell's equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decreas…
The classical problem of three-wave mixing in a nonlinear optical medium is investigated using the homotopy analysis method (HAM). We show that the power series basis builds a generic polynomial expression that can be used to study three-wave mixing for arbitrary input parameters. The phase-mismatched and perfectly phase matched cases are investigated. Parameters that result in generalized sum- and difference-frequency generation are studied using HAM with a power series basis and compared to an explicit finite-difference approximation. The convergence region is extended by increasing the auxi…
We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic, absorbing or non-absorbing materials and is free of discontinous solutions. We calculate the reflection and transmission coefficients and derive equations for the electric field distribution for any number of layers. The algorithm is easily comprehensible and can be straight forwardly implemented in a computer program. To demonstrate the capabilities of the appro…
Until recently, the interaction of electromagnetic waves with crystals built from parallel metallic wires (wire media) was analyzed in the approximation of isotropic scattering of the electromagnetic wave by a single wire. However, if the wires are thick (kR~1), electromagnetic wave scattering by a wire is anisotropic, i.e., the scattering amplitude depends on the scattering angle. In this work, we derive the equations that describe diffraction of electromagnetic waves and spontaneous emission of charged particles in wire media, and take into account the angular dependence of scattering amplit…
We propose to use Vavilov-Cherenkov (VC) and transition radiations as a source of twisted photons in a wide range of energies. The experimental setup to observe the orbital angular momentum of photons constituting those radiations is described. The radiation produced by relativistic electrons and ions in passing dielectric plates is considered. The experimental verification of the addition rule for the total angular momentum in the radiation of twisted photons by helically microbunched beams is proposed for VC and transition radiations. The parameters of the experiments are presented.
The intensity of Smith-Purcell radiation from metallic and dielectric gratings (silicon, silica) is compared in a frequency-domain simulation. The numerical model is discussed and verified with the Frank-Tamm formula for Cherenkov radiation. For 30 keV electrons, rectangular dielectric gratings are less efficient than their metallic counterpart, by an order of magnitude for silicon, and two orders of magnitude for silica. For all gratings studied, radiation intensity oscillates with grating tooth height due to electromagnetic resonances in the grating. 3D and 2D numerical models are compared.
Cherenkov radiation (CR) generated by a charge moving through a hollow conical target made of dielectric material is analyzed. We consider two cases: the charge moves from the base of the cone to its top (``straight'' cone) or from the top to the base (``inverted'' cone). Unlike previous papers, a nonzero shift of the charge trajectory from the symmetry axis is taken into account which leads to generation of asymmetric CR. The most interesting effect is the phenomenon of ``Cherenkov spotlight'' which has been reported earlier for axially symmetric problems. This effect allows essential enhance…
In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric permittivity are related by spatial Kramers-Kronig (KK) relations, are one-way reflectionless, whatever the angle of incidence. Such a fascinating property, besides of extending our comprehension of the fundamental phenomenon of reflection, may offer new ways for the design of antireflection surfaces and thin materials with efficient light absorption. However, KK dielectric media are generally describ…
We report for the first time the theory of optical tweezers of spherical dielectric particles embedded in a chiral medium. We develop a partial-wave (Mie) expansion to calculate the optical force acting on a dielectric microsphere illuminated by a circularly-polarized, highly focused laser beam. When choosing a polarization with the same handedness of the medium, the axial trap stability is improved, thus allowing for tweezing of high-refractive-index particles. When the particle is displaced off-axis by an external force, its equilibrium position is rotated around the optical axis by the mech…
The interaction of magnetic dipole (MD) emitters and common photonic cavities is usually weak, which is partially due to the low magnetic near field enhancements of the cavities. Here, we show that whispering gallery modes (WGMs) of a subwavelength dielectric cavity can not only greatly boost the emission rate of a MD emitter but also bring efficient couplings between coherent MD emitters. In a WGM cavity, the maximal emission rate (γmax) of a single emitter occurs at an antinode of the field pattern. The emission of the MD emitter can also be greatly affected by another coherent one depending…
We present an effective medium description of time-modulated dielectric media. By taking the averaged fields over one modulation period, the relationship between them is derived, defining therefore the different constitutive parameters. In the most general situation, it is found that the effective material is described by means of a spatially and temporally dispersive transverse dielectric function and a constant longitudinal dielectric function. It has been also found that the frequency dependence in the former is weak, in comparison with its wavenumber-dependence (spatial dispersion). Differ…
By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.
Cherenkov radiation which generates by a charge moving in presence of a dielectric prism from the base to the top is analyzed. Unlike our previous works, here we consider the case when the charge trajectory is not parallel to the prism face. We apply a new version of the aperture method which uses the expansion in terms of plane waves in the prism material and on the aperture. The integrals for the radiation field are calculated analytically in the Fraunhofer region where the field components are written as single integrals. The influence of the incline of the charge trajectory on the radiatio…
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.
The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies as well as in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantised electromagnetic fiel…
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and th…
The Quantum Vacuum of Complex Media. A Unified Approach to the Dielectric Constant, the Spontaneous Emission and the Zero-Temperature Electromagnetic Pressure
Near-field radiative heat transfer (NFRHT) between rough surfaces, due to its widespread presence in engineering practice of near-field energy utilization, requires indepth studies, especially from the perspective of physical mechanism. In this paper, an effective multilayer model is built to approach the NFRHT between random rough surfaces of silicon carbide (SiC). Using the effective medium theory (EMT), the effective dielectric function of each layer is obtained, which forms a gradient distribution of dielectric function along the depth of the medium. The influence of the effective dielectr…
A broad class of planar dielectric media with complex permittivity profiles that are fully invisible, for both left and right incidence sides, is introduced. Such optical media are locally isotropic, non-magnetic and belong to the recently discovered class of Kramers-Kronig media [{\it Nature Photon.} 9, 436 (2015)], i.e. the spatial profiles of the real and imaginary parts of the dielectric permittivity are related each other by a Hilbert transform. The transition from unidirectional to bidirectional invisibility, and the possibility to realize sharp reflection above a cut-off incidence angle…
Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime
Princeton Materials Institute, Princeton University（普林斯顿大学材料研究所）；Department of Chemistry, Princeton University（普林斯顿大学化学系）；Department of Physics, Princeton University（普林斯顿大学物理系）；Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院化学与生物分子工程系）；GIST InnoCORE AI-Nano Convergence Institute for Early Detection of Neurodegenerative Diseases, Gwangju Institute of Science and Technology（光州科学技术研究院GIST InnoCORE神经退行性疾病早期检测AI-纳米融合研究所）；Program in Applied and Computational Mathematics, Princeton University（普林斯顿大学应用与计算数学项目）
