Jaroslav Luksch

Simulations of high-Q optical nanocavities with a gradual 1D bandgap

High-quality cavities in hybrid material systems have various interesting applications. We perform a comprehensive modeling comparison on such a design, where confinement in the III-V material is provided by gradual photonic crystal tuning, a recently proposed method offering strong resonances. The III-V cavity couples to an underlying silicon waveguide. We report on the device properties using four simulation methods: finite-difference time-domain (FDTD), finite-element method (FEM), bidirectional eigenmode propagation (BEP) and aperiodic rigorous coupled wave analysis (aRCWA). We explain the major confinement and coupling effects, consistent with the simulation results. E.g. for strong waveguide coupling, we find quantitative discrepancies between the methods, which establishes the proposed high-index-contrast, lossy, 3D structure as a challenging modeling benchmark.

Simulation of high-Q nanocavities with 1D photonic gap

We report on theoretical investigation of a hybrid cavity structure which has been conducted within the European Action COST MP0702. The structure, which can reach ultrahigh Q factors, consists of a size-modulated 1D stack cavity made in a III-V material and coupled to a silicon waveguide. We present results of structure behavior simulations obtained by four independent rigorous numerical techniques. We discuss qualitative physical properties of the simulations results and identify the main physical effects contributing to the total Q factor.

Bidirectional eigenmode propagation algorithm for 3D waveguide structures

We demonstrate a new implementation of bidirectional eigenmode propagation algorithm for modeling of three-dimensional waveguide structures. The algorithm is based upon expansion of unknown field into set of orthogonal eigenmodes which are searched using a full vector finite-difference modesolver. Numerical examples demonstrate convergence behaviour and typical circumstances in which the technique may be useful.

Simulation of self-pulsing and chaos in coupled microring resonators

We investigate stability of frequency-domain solutions for Kerr-nonlinear structures consisting of coupled microring resonators in all-pass filter configuration. We present difference equations that describe time-domain evolution of optical pulses inside the structure. We show numerical examples that demonstrate existence of self-pulsing and chaotic solutions.

Simple numerical scheme for modelling of nonlinear pulse propagation in coupled microring resonators

Nonlinear coupled equations that describe propagation of optical pulses in coupled microring resonators under the slowly varying envelope approximation can be solved by a simple explicit finite-difference scheme. The technique, which is based on upwind differencing, is demonstrated by using an example of Kerr-nonlinear structure consisting of one microring resonator coupled to a waveguide. This enables us to study stability of the

Modal methods for 3D modelling of advanced photonic structures

In this contribution we present the basics of four frequency-domain modal methods for numerical modelling of advanced photonic and plasmonic structures that have been independently developed at three collaborating institutions within a joint project. The rigorous coupled-wave analysis (RCWA) method originally built up for modelling periodic 1D and crossed diffraction grating structures was developed and adapted also for modelling 3D photonic waveguiding structures. A very similar but independently developed bi-directional mode expansion propagation method (BEP) based on Fourier series has been extended for modelling 3D structures, too. Implementation of adaptive spatial resolution technique helps reduce the number of expansion terms and thus dramatically increase the numerical efficiency of the methods. Another two variants of the BEP approach differ in the way how the eigenmodes of the structures are searched for; they exploit the finite-difference and the finite-element methods, respectively. Results of modelling of two simple structures (effective indices of guided modes in a SOI photonic wire and reflections from a gap in the waveguide) are mutually compared and other results of modelling of some other promising photonic and plasmonic nanostructures as subwavelength grating waveguides and hybrid dielectric-plasmonic gap waveguides are finally presented, too.

Modelling of nonlinear pulse propagation in coupled microring resonators

We demonstrate a finite-difference scheme for solution of nonlinear coupled evolution equations that describe propagation of optical pulses under the slowly-varying envelope approximation. The technique is used for modelling of Kerr-nonlinear structures which involve microring resonators and exhibit optical bistability and self-pulsing. The results suggest that the technique may be considered as a useful counterpart of the established methods, such as the transfer matrix method or finite-difference time-domain method.

Towards Three‐Dimensional Bidirectional Eigenmode Propagation Algorithm

A new implementation of bidirectional eigenmode expansion and propagation algorithm for the modeling of three‐dimensional waveguide structures is presented. The eigenmodes, which are used for expansion of unknown field, are searched numerically using a full vector finite‐difference or finite‐element modesolver. Numerical examples demonstrate convergence behavior and typical circumstances in which the technique may be useful.

Analysis of coupled equation scheme for modelling of nonlinear pulse propagation in coupled microring resonators

We demonstrate a finite-difference scheme for solution of nonlinear coupled evolution equations that describe propagation of optical pulses under the slowly-varying envelope approximation. The technique is used for modelling of Kerr-nonlinear structures which involve microring resonators and exhibit optical bistability and self-pulsing. The results suggest that the technique may be considered as a useful counterpart of the established methods, such as the transfer matrix method or finite-difference time-domain method.

Modelling of inline optical reflectors based on microring resonators

We present a numerical design procedure for optimization of spectral response of an inline optical reflector, which consists of two coupled microring resonators both of which are coupled to a bus waveguide. The technique provides the optimal values of the coupling coefficients for obtaining maximally flat reflectivity in the requested bandwidth. The optimized designs are compared with the results of other methods.