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Register a new userTheory of Cherenkov radiation in periodic dielectric media: Emission spectrum
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The Cherenkov radiation is substantially modified in the presence of a medium with a nontrivial dispersion relation. We consider Cherenkov emission spectra of a point charge moving in general three- (3D) and two-dimensional (2D) photonic crystals. Exact analytical expressions for the spectral distribution of the radiated power are obtained in terms of the Bloch mode expansion. The resulting expression reduces to a simple contour integral (3D case) or a one-dimensional sum (2D case) over a small fraction of the reciprocal space, which is defined by the generalized Cherenkov condition. We apply our method to a specific case of an electron moving with different velocities in a 2D square-lattice photonic crystal. Our method demonstrates an excellent agreement with numerically rigorous finite-difference time-domain calculations while being less demanding on computational resources.
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Using the Finite-Difference-Time-Domain (FDTD) method, we compute the electromagnetic field distribution in and around dielectric media of various shapes and optical properties. With the aid of the constitutive relations, we proceed to compute the bound charge and bound current densities, then employ the Lorentz law of force to determine the distribution of force-density within the regions of interest. For a few simple cases where analytical solutions exist, these solutions are found to be in complete agreement with our numerical results. We also analyze the distribution of fields and forces in more complex systems, and discuss the relevance of our findings to experimental observations. In particular, we demonstrate the single-beam trapping of a dielectric micro-sphere immersed in a liquid under conditions that are typical of optical tweezers.
We propose a new type of axisymmetric dielectric target which effectively concentrates Cherenkov radiation (CR) generated in the bulk of the material into a small vicinity of focus point. It can be called the axicon-based concentrator for CR. A theoretical investigation of radiation field produced by a charge moving through the discussed radiator is performed for the general case where a charge trajectory is shifted with respect to the structure axis. The idea of dielectric target with specific profile of the outer surface was presented and developed in our preceeding papers. However, contrary to the previous configuration of such a target (which was investigated for both centered and shifted charge trajectory), the current version allows efficient concentration of CR energy from relativistic particles, making this device extremely prospective for various applications.
It is shown that in some special cases the Cherenkov radiation from a charged particle moving along the axis of cylindrical waveguide filled with a semi-infinite material consisting of dielectric plates alternated with vacuum gaps is many times stronger than that in the waveguide filled with semi-infinite solid dielectric without vacuum gaps.
We investigate the radiation from a charged particle moving outside a dielectric cylinder parallel to its axis. It is assumed that the cylinder is immersed into a homogeneous medium. The expressions are given for the vector potential and for the electric and magnetic fields. The spectral distributions are studied for three types of the radiations: (i) Cherenkov radiation (CR) in the exterior medium, (ii) radiation on the guided modes of the dielectric cylinder, and (iii) emission of surface polaritons. Unlike the first two types of radiations, there is no velocity threshold for the generation of surface polaritons. The corresponding radiation is present in the spectral range where the dielectric permittivities of the cylinder and surrounding medium have opposite signs. The spectral range of the emitted surface polaritons becomes narrower with decreasing energy of the particle. The general results are illustrated for a special case of the Drude model for dispersion of the dielectric permittivity of the cylinder. We show that the presence of the cylinder may lead to the appearance of strong narrow peaks in the spectral distribution of the CR in the exterior medium. The conditions are specified for the appearance of those peaks and the corresponding heights and widths are analytically estimated. The collective effects of particles in bunches are discussed.
The force of electromagnetic radiation on a dielectric medium may be derived by a direct application of the Lorentz law of classical electrodynamics. While the lights electric field acts upon the (induced) bound charges in the medium, its magnetic field exerts a force on the bound currents. We use the example of a wedge-shaped solid dielectric, immersed in a transparent liquid and illuminated at Brewsters angle, to demonstrate that the linear momentum of the electromagnetic field within dielectrics has neither the Minkowski nor the Abraham form; rather, the correct expression for momentum density has equal contributions from both. The time rate of change of the incident momentum thus expressed is equal to the force exerted on the wedge plus that experienced by the surrounding liquid.
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