Lasha Tkeshelashvili

Solid State Theory Meets Photonics:The Curious Optical Properties of Photonic Crystals

The past decades have seen dramatic advances in microstructuring technology. Today, a wide variety of structures with feature sizes ranging from a couple of micrometers all the way down to a few tens of nanometers are routinely fabricated with precision better than ten nanometers. In addition to these improvements in fabrication quality, the variety of materials that can be processed is growing continuously. These advances in materials science are paralleled by the development of novel and improvement of existing laser sources that allows one to generate electromagnetic fields with previously unattainable energy densities as well as temporal and spatial coherences. Bringing together advanced microfabrication technologies with sophisticated laser systems lies at the heart of Nano-Photonics: The control over the flow of light on length scales of the wavelength of light itself through microstructured optical materials (“photonic metamaterials”) with carefully designed properties.

Chaotic scattering of solitons on point defects in fiber Bragg gratings

We present detailed studies on the interaction between solitons and defects in nonlinear Fiber Bragg gratings. The numerical simulations demonstrate that in the case of strong defects the scattering process of slow gap solitons exhibits so-called n-bounce resonance and becomes chaotic. Our results provide a quantitative guideline to experiments on the dynamics of soliton-defect interactions in these systems.

Improving the Impedance Matching in Photonic Crystal Waveguides

Summary form only given: We demonstrate that the dispersion of guided propagating modes in certain photonic crystal waveguides (PCWGs) can be kept constant when the waveguides structure changes with distance. This suggests that the principle of constant group velocity may be utilized to improve impedance matching between different types of PCWGs while at the same time providing significant design flexibility. We illustrate this principle through the design of several efficient coupling structures between two different PCWGs via a local density of state (LDOS) and Fourier transform analysis of the associate electromagnetic fields. The couplers consist of heterostructures whose individual sections exhibit rather distinct structural parameters. Furthermore, we compare these structures to an adiabatic coupler

Nonlinear photonic crystals

In this paper, we describe a theoretical approach by which we can qualitatively and quantitatively determine the nonlinear optical properties of a photonic crystals. We start by accurately characterizing the linear properties of the structure, using a recently developed multigrid method to efficiently compute the photonic bandstructure and Bloch functions of the PC. This results in a generalization of the slowly varying envelope approximation to the case of nonlinear PCs.

Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with

Interaction of noncollinear spatial solitons in a nonlinear optical medium

{\ensuremath{\chi}}^{(2)}

Photonic Crystals: Optical Materials for the 21st Century

nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective

General theory of nonresonant wave interaction: Giant soliton shift in photonic band gap materials

{\ensuremath{\chi}}^{(3)}

A krylov-subspace based solver for the linear and nonlinear maxwell equations

nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.

A solid state theoretical approach to the optical properties of photonic crystals

The effects caused by nonresonant nonlinear interaction between noncollinear self-focusing beams are considered in two-dimensional optical samples by use of multiscale analysis. An analytical expression for beam trajectory shifts that are due to mutual interaction is derived, and the range of parameters is given, beyond which the mentioned consideration fails. We compare our results with the naive geometrical-optics model. It is shown that these two approaches give the same results. This justifies use of the geometrical-optics approach to describe elastic and almost-elastic collision processes both in Kerr and saturable nonlinear media. The results we obtained could be useful for the design of phase independent nonlinear photonic switches and all-optical logic elements.