An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane

We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole formalism into a linear eigenvalue problem, for which fast and accurate methods are available. Observing that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family, we present a numerical algorithm to compute a range of multiple-disk resonances and field distributions using only two diagonalizations. This method can be applied to photonic molecules, photonic crystals, photonic crystal fibers, and random lasers. © 2009 Optical Society of America

Polarization-selective out-coupling of whispering gallery modes

Whispering gallery mode (WGM) resonators are an important platform for linear, nonlinear and quantum optical experiments. In such experiments, independent control of in- and out-coupling rates to different modes can lead to higher conversion efficiencies and greater flexibility in the generation of non-classical states based on parametric down conversion. In this work, we introduce a scheme that enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and the coupler such that a negative (positive) birefringence allows for polarization-selective coupling to TE (TM) WGMs. We formulate a new coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive a criterion for polarization-selective coupling. Finally, we experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a \SI{22}{dB} suppression of coupling to TM modes relative to TE modes

Numerically efficient multipole method for photonic molecules

A novel and numerically efficient multipole formulation for the calculation of resonances of photonic molecules is presented. Photonic molecules are often modeled as two dimensional coupled dielectric disks. We use the multipole expansion of the individual fields and formulate the boundary conditions in terms of a generalized eigenvalue problem. The complex root search is simplified by studying the flow of the eigenvalues, where we argue that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family. Based on this analytic behavior we present a numerical algorithm to compute a range of photonic molecule resonances and field distributions using only two diagonalizations. ©2008 IEEE

Dielectric perturbations: anomalous resonance frequency shifts in optical resonators

Small perturbations in the dielectric environment around resonant dielectric structures usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can oppose and even exceed the contribution of the perturbations’ polarizability. We show in particular how the mode frequencies of a lithium niobate whispering-gallery-mode resonator are shifted by planar substrates—of refractive indices ranging from 1.50 to 4.22—contacting the resonator rim. Both blue- and redshifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. [J. Opt. Soc. Am. B 33, 2177 (2016) [CrossRef] ] and provide an additional intuitive explanation based on the Goos–Hänchen shift for the optical domain, with applications to dielectric structures ranging from meta-surfaces to photonic crystal cavities