Jiří Petráček

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.

Determination of leaky modes in planar multilayer waveguides

In this letter, we present a numerically exact and simple novel technique for the determination of leaky modes in planar multilayer waveguides. The technique uses a dispersion equation provided by the thin-film transfer matrix method. Complex roots, that correspond to leaky modes, are searched on the basis of a smooth transition between the bound modes of a closed waveguide and the leaky modes of an open waveguide. The technique does not use any approximation.

Optical Response of Plasmonic Nanohole Arrays: Comparison of Square and Hexagonal Lattices

Nanohole arrays in metal films allow extraordinary optical transmission (EOT); the phenomenon is highly advantageous for biosensing applications. In this article, we theoretically investigate the performance of refractive index sensors, utilizing square and hexagonal arrays of nanoholes, that can monitor the spectral position of EOT signals. We present near- and far-field characteristics of the aperture arrays and investigate the influence of geometrical device parameters in detail. We numerically compare the refractive index sensitivities of the two lattice geometries and show that the hexagonal array supports larger figure-of-merit values due to its sharper EOT response. Furthermore, the presence of a thin dielectric film that covers the gold surface and mimics a biomolecular layer causes larger spectral shifts within the EOT resonance for the hexagonal array. We also investigate the dependence of the transmission responses on hole radius and demonstrate that hexagonal lattice is highly promising for applications demanding strong light transmission.

Second-harmonic generation at periodic second-order susceptibility gratings with self-phase and cross-phase modulation

Quasi-phase-matched second-harmonic generation at periodic quadratic susceptibility gratings with self-phase and cross-phase modulation owing to Kerr nonlinearities is investigated. A model of interaction of monochromatic plane travelling waves is considered. The solution assumes a nondepleted pump and results for a numerical computation of second-harmonic conversion efficiency for a highly efficient process are presented. It is shown that for high spatial-frequency gratings the efficiency of second-harmonic generation depends on the reduced detuning δ and the Kerr-nonlinearity coefficient κ only. In some cases, if the signs of δ and κ are opposite, the Kerr nonlinearity can enhance the second-harmonic conversion efficiency due to the compensation of the phase mismatch attained in the below-half-conversion stage by the reversed phase mismatch in the above-half-conversion stage of the process. The computed maximum conversion efficiencies for various values of δ and κ are plotted in a contour map on the δ-κ plane.

On the puzzling phase of second-harmonic light generated in self-prepared frequency doubling fibres

The evolution of mutual phase shift between the second-harmonic seeding light and the second-harmonic light produced by the photo-induced non-linearity in optical fibre in the course of the fibre preparation process is computed using the data of Lambelet–Feinbergs experiment. It is shown that this mutual phase shift monotonously decreases from its initial value, which depends upon the light intensities of the fundamental pump and second-harmonic seeding radiations, and approaches −π/2 in the saturation state. A simple phenomenological model is proposed that describes the formation of a photo-induced χ(2) grating by means of a complex rate coefficient β, which is dependent upon the light intensities of shaping radiation and varies in the course of the χ(2) writing process. The self-organized parametric down-conversion with strong second-harmonic seeding being above the saturation value is proposed for an effective χ(2) grating formation.

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.

Comments on directional photoionization model of second-harmonic generation in doped glass fibers

Abstract The multiphoton-ionization-interference model of self-organized second-harmonic generation by Anderson et al. (Optics Lett. 16 (1991) 796; SPIE Proc. 1516 (1992) 154) is discussed in the view of recent experiments. It is shown that the inconsistency of the directional photoionization model with some experimental results is a consequence of the fact that the model is based on the instantaneous response of the medium. A new phenomenological model including memory is proposed which removes the difficulties of the Anderson et al. model. The saturation of second-order susceptibility predicted by either model is found to be in a good agreement with all experimental results.

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.

Extraordinary Transmission Characteristics of Subwavelength Nanoholes with Rectangular Lattice

We investigate the extraordinary optical transmission (EOT) properties of nanohole arrays with a rectangular lattice for label-free refractive index sensing applications. We show that the deviation within the periodicities along the two axes at the nanohole plane leads to more advantageous spectral quality of EOT signal compared to the conventional square lattice geometries. We introduce a way to further improve the sensitivity of the aperture system by carefully choosing the periodicities. We introduce nanohole arrays with a rectangular lattice supporting EOT signals with larger figure-of-merit values as well as enabling much stronger light transmission. We also model a nanohole system covered with a thin dielectric layer, mimicking biomolecules captured on the gold surface, in order to show its biosensing capability. We also show that certain deviation amounts between periodicities create spectral splitting within the EOT signal leading to larger spectral shifts in the presence of a thin dielectric film.

Nonlinear switching in plasmonic directional couplers

We present a numerical study of all-optical switching in Kerr-nonlinear plasmonic directional couplers. We consider planar couplers that consist of two identical plasmonic slot waveguides and demonstrate the influence of geometrical and optical parameters on switching characteristics. Underlying physical mechanisms that affect the coupler performance are briefly discussed, too.