G. V. Morozov

Floquet-Bloch waves in one-dimensional photonic crystals

Using binary photonic crystals as an example, it is shown in a physically transparent manner how to construct two independent Floquet-Bloch waves in lossless one-dimensional periodic structures. Particular attention is given to those special cases where only one Bloch wave develops inside the structure.

One-dimensional photonic crystals with a sawtooth refractive index: another exactly solvable potential

Exact analytical results expressed 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, to our knowledge for the first time. This extends the set of exactly solvable models with periodic refractive indices. Asymptotic approximations to the above exact results have been also obtained.

Transverse-magnetic-polarized Floquet–Bloch waves in one-dimensional photonic crystals

Using binary and sinusoidal photonic crystals as examples, it is shown how to construct two independent Floquet–Bloch waves for TM-polarized light in a lossless one-dimensional periodic structure. Particular attention is given to those special situations where either one Bloch wave and a hybrid Floquet mode develop inside the structure (instead of two Bloch waves) or both developed Bloch waves become periodic functions.

Band structure analysis of an analytically solvable Hill equation with continuous potential

This paper concerns analytically solvable cases of Hill’s equation containing a continuously differentiable periodic potential. We outline a procedure for constructing the Floquet–Bloch fundamental system, and analyze the band structure of the system. The similarities to, and differences from, the cases of a piecewise constant periodic potential and the Mathieu potential, are illuminated.

Floquet–Bloch analysis of analytically solvable Hill equations with continuous potentials

Exact analytical solutions of two Hill’s equations that have continuously differentiable coefficients are obtained in terms of the Floquet–Bloch fundamental system. New features of the band structures of those equations are reported and investigated.

High-order bandgaps in one-dimensional photonic crystals

Bandgaps, including high-order ones, of one-dimensional photonic crystals are analysed. Accurate analytical expressions for band edges for both s and p polarized light are derived. As a consequence, the conditions for bandgap closing are obtained in a simple analytical form. The derivation is based on a perturbative expansion of the dispersion equation using a new parameter which remains small around the band edges of all physically feasible one-dimensional photonic crystals.

Disappearance of allowed bands in light scattering from a binary photonic crystal beyond the second critical angle

We consider light scattering from a binary (two-layered) photonic crystal. When the index of refraction of the incident medium exceeds that of either layer, total internal reflection may occur, which is a type of phase transition. At band edges (similar to the case where the index of refraction of the incident medium is less than those of the layers), the two Bloch waves describing propagation become degenerate and a hybrid Floquet mode is required to understand the response. For angles of incidence exceeding the second critical angle (when total internal reflection occurs in both layers), the allowed bands disappear entirely.

Floquet-Bloch solutions in a sawtooth photonic crystal

Band structure of a sawtooth photonic crystal for optical wave propagation along the axis of periodicity is investigated. Floquet–Bloch solutions are found and illustrated for the bandgaps, allowed bands, and bandedges of the crystal. Special attention is given to the cases where Floquet–Bloch solutions become periodic functions.

Light scattering from one-dimensional photonic crystals under total internal reflection

We consider light scattering from a 1D photonic crystal when total internal reflection occurs inside the crystal. This can occur if the refractive index of the incident medium exceeds that encountered somewhere in the crystal. Examples include binary, sawtooth, and rugate crystals. Both TE (s) and TM (p) polarized light are treated.

Microdisk resonators with two point scatterers

Optical microdisk resonators exhibit modes with extremely high Q-factors. Their low lasing thresholds make circular microresonators good candidates for the realization of miniature laser sources. They have, however, the serious drawback that their light emission is isotropic, which is inconvenient for many applications. In our previous work, we showed that the presence of a point scatterer inside the disk can lead to highly directional modes in various frequency ranges while preserving the high Q-factors. In the present paper we generalize this idea to two point scatterers. The motivation for this work is that the strength of a point scatterer is difficult to control in experiments, and the presence of a second scatterer leads to a higher dimensional parameter space which permits to compensate this deficiency. Similar to the case of a single scatterer in a circular disk, the problem of finding the resonance modes in the presence of two scatterers is to a large extent analytically tractable.