arXiv subjects
Publications and source records attributed to G. V. Morozov.
Exact analytical results (in terms of Bessel functions) for the bandgaps, reflectance, and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the period are derived for the first time. This extends a group of exactly solvable models of periodic refractive indices. The asymptotic approximations of the above exact results have been also obtained.
Circular microresonators are micron sized dielectric disks embedded in material of lower refractive index. They possess modes of extremely high Q-factors (low lasing thresholds) which makes them ideal candidates for the realization of miniature laser sources. They have, however, the disadvantage of isotropic light emission caused by the rotational symmetry of the system. In order to obtain high directivity of the emission while retaining high Q-factors, we consider a microdisk with a pointlike scatterer placed off-center inside of the disk. We calculate the resulting resonant modes and show that some of them possess both of the desired characteristics. The emission is predominantly in the direction opposite to the scatterer. We show that classical ray optics is a useful guide to optimizing the design parameters of this system. We further find that exceptional points in the resonance spectrum influence how complex resonance wavenumbers change if system parameters are varied.
Circular microresonators (microdisks) are micron sized dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analysed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wavenumber plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well defined azimuthal and radial modal indices.
We present a new design of dielectric microcavities supporting modes with large quality factors and highly directional light emission. The key idea is to place a point scatterer inside a dielectric circular microdisk. We show that, depending on the position and strength of the scatterer, this leads to strongly directional modes in various frequency regions while preserving the high Q-factors reminiscent of the whispering gallery modes of the microdisk without scatterer. The design is very appealing due to its simplicity, promising a cleaner experimental realisation than previously studied microcavity designs on the one hand and analytic tractability based on Green's function techniques and self-adjoint extension theory on the other.
We study surface states of 1D photonic crystals using a semiclassical coupled wave theory. Both TE and TM modes are treated. We derive analytic approximations that clarify the systematics of the dispersion relations, and the roles of the various parameters defining the crystal.
Accurate analytic approximations are developed for the band gap boundaries and surface waves of a 1D photonic crystal, making use of the semiclassical theory recently developed by the authors: [Phys. Rev. E {69} (2004) 016612 and {70} (2004) 016606]. These analytic results provide useful insight on systematics of surface states.