Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which -in frequency domain -is given by a coupled system of equations for the electric field and an additional polarization current of the electron gas modeled analogous to a hydrodynamic flow. Recent attempt to simulate such nonlocal model using the finite difference time domain method encountered difficulties in dealing with the grad-div operator appearing in the governing equation of the hydrodynamic current. Therefore, in these studies the model has been simplified with the curl-free hydrodynamic current approximation; but this causes spurious resonances. In this paper we present a rigorous weak formulation in the Sobolev spaces H(curl) for the electric field and H(div) for the hydrodynamic current, which directly leads to a consistent discretization based on Nédélec's finite element spaces. Comparisons with the Mie theory results agree well. We also demonstrate the capability of the method to handle any arbitrary shaped scatterer.
A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.
A spatially three-dimensional, fully vectorial coupled mode theory model for the interaction between several straight or bent dielectric optical waveguides, each supporting multiple modes, is described. The frequency domain model is applied to the coupler regions of cylindrical microresonators, here considered for applications as integrated optical filters. For simple test cases, comparisons with results of beam propagation calculations and of a rigorous system mode analysis provide some validation of the approach. By combination of two coupler representations one obtains a complete 3-D vectorial microresonator description without any free parameters, that permits a convenient investigation of the influence of geometrical parameters on the spectral response. When applied to a microring resonator with pronouncedly hybrid cavity modes, the model reveals the manifold features that may appear in the spectra of these devices.
The effects of perturbations of whispering gallery modes (WGMs) in cylindrical microcavities by embedded particles are studied by FDTD modeling. The principal effects are: i) spectral shift of the WGM-related peaks caused by the variation of the average index, ii) broadening of the WGM peaks introduced by the scattering, and iii) splitting of the WGM peaks due to formation of symmetric (SSW) and antisymmetric (ASW) standing waves. The focus of this work is on the last effect. We show that it can be maximized by placing the nanoparticle inside the cavity at a position corresponding to the antinode of the radial distribution of intensity of WGM. It is demonstrated that in this case the magnitude of splitting reaches several angstroms for cavities with moderately high quality (Q approximately = 10(5)) WGMs. We show that for relatively small particles with radius <70 nm and index contrasts <0.2 the magnitude of SSW/ASW splitting is linearly dependent on the size and index of the nanoparticle. This allows developing biomolecular sensors based on measuring this splitting in porous cavities. It is predicted that a similar effect of splitting can occur in semiconductor microdisks and pillars where the role of embedded dielectric nanoparticles can be played by self-assembled quantum dots.
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