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Register a new userTheory of unconventional Smith-Purcell radiation in finite-size photonic crystals
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Unusual emission of light, called the unconventional Smith-Purcell radiation (uSPR) in this paper, was demonstrated from an electron traveling near a finite photonic crystal (PhC) at an ultra-relativistic velocity. This phenomenon is not related to the accepted mechanism of the conventional SPR and arises because the evanescent light from the electron has such a small decay constant in the ultra-relativistic regime that it works practically as a plane-wave probe entering the PhC from one end. We analyze the dependence of the SPR spectrum on the velocity of electron and on the parity of excited photonic bands and show, for PhCs made up of a finite number of cylinders, that uSPR probes the photonic band structure very faithfully.
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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.
We investigate parametric X-ray radiation (PXR) under condition of the extremely asymmetric diffraction, when the ultra-relativistic electron bunch is moving in textit{vacuum} parallel to the crystal-vacuum interface, close to the crystal surface. This type of geometry coincides with the well known mechanism of generation of radiation, when the self-field of the particle beam interacts with the reflecting metal grating, namely the Smith-Purcell effect. We demonstrate that in this geometry the main contribution is given via a tail region of the beam distribution, which penetrates the crystal and X-rays are radiated along the normal to the crystal surface. We determine the electron beam characteristics, when this phenomenon can be observed. It is essential that in this geometry the majority of electrons does not undergo multiple scattering and consequently the characteristics of the particle beam are not changed, thus allowing the usage of the emitted X-rays for the purpose of non-destructive beam diagnostics, which can complement the traditional knife-edge method.
Doped semiconductors are intrinsically homogeneous media. However, by applying an external magnetic field that has a spatially periodic variation, doped semiconductors can behave extrinsically like conventional photonic crystals. We show this possibility theoretically by calculating the photonic band structures of a doped semiconductor under an external, spatially periodic magnetic field. Homogeneous media, behaving like conventional photonic crystals under some external, spatially periodic fields, define a new kind of photonic crystals: extrinsic photonic crystals. The proposed extrinsic photonic crystals could not only extend the concept of photonic crystals but also lead to the control of the dispersion and propagation of electromagnetic waves in a unique way: simply manipulating the externally applied fields.
The complete symmetry characterization of eigenstates in bare opal systems is obtained by means of group theory. This symmetry assignment has allowed us to identify several bands that cannot couple with an incident external plane wave. Our prediction is supported by layer-KKR calculations, which are also performed: the coupling coefficients between bulk modes and externally excited field tend to zero when symmetry properties mismatch.
We study wave propagation and diffraction in a bidimensional photonic crystal with finite height, in case where the wavelength is large with respect to the period of the structure. The device is made of materials with anisotropic permittivity and permeability tensors. We derive rigorously the homogenized system, using the concept of two-scale convergence. The effective permittivity and permeability tensors turn out to be that of a two-dimensional photonic crystal with infinite height.
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