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

Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers

© 2014 Optical Society of America We derive formal selection rules for Stimulated Brillouin Scattering (SBS) in structured waveguides. Using a group-theoretical approach, we show how the waveguide symmetry determines which optical and acoustic modes interact for both forward and backward SBS. We present a general framework for determining this interaction and give important examples for SBS in waveguides with rectangular, triangular and hexagonal symmetry. The important role played by degeneracy of the optical modes is illustrated. These selection rules are important for SBS-based device design and for a full understanding the physics of SBS in structured waveguides

Effective impedance modeling of metamaterial structures

© 2016 Optical Society of America. We present methods for retrieving the effective impedance of metamaterials from the Fresnel reflection coefficients at the interface between two semi-infinite media. The derivation involves the projection of rigorous modal expansions onto the dominant modes of the two semi-infinite media. It is shown that the effective impedance can also be written as a ratio of averaged field quantities. Thus, a number of effective impedance formulas, previously obtained by field averaging techniques, can also be derived from the scattering-based formalism by an appropriate choice of projection. Within the effective medium limit, it is observed that a simple semianalytic modeling technique based on the effective impedance can be used to reliably compute the reflection coefficients of metamaterials over a wide range of incidence angles. We use this technique to model planar metamaterial waveguides or surface modes

On the deviation of metamaterial spheres from effective medium

© 2016 IEEE. We analyse the convergence of the actual properties of finite subwavelength metamaterial samples where all the prerequisites for a reliable effective medium description, except for the finite size, are fulfilled, towards the effective medium predictions. We show that the convergence is rather slow and it is likely that hundreds of thousands of individual meta-atoms must be assembled together before the properties of the resulting structure can be claimed to correspond to those a bulk material. These observations are directly relevant for practical design of metamaterials and their future development

Slow convergence to effective medium in finite discrete metamaterials

© 2016 American Physical Society. It is known that metamaterial properties may differ significantly from the predictions of effective-medium theory. In many cases this is due to the finite size and discrete structure, which cannot be neglected in practical samples with a relatively small amount of elements. We analyze the response of finite discrete metamaterial objects of a spherical shape and demonstrate the role of boundary effects in these structures, pointing out an interplay between the size of the structure and the dissipation. We conclude that the discrepancy between the actual resonance frequency of a sphere and the effective-medium prediction is inversely proportional to the size of the sphere

Acoustic build-up in on-chip stimulated Brillouin scattering

We investigate the role of the spatial evolution of the acoustic field in stimulated Brillouin scattering processes in short high-gain structures. When the gain is strong enough that the gain length becomes comparable to the acoustic wave decay length of order 100 microns, standard approximations treating the acoustic field as a local response no longer apply. Treating the acoustic evolution more accurately, we find that the backward SBS gain of sub-millimetre long waveguides is significantly reduced from the value obtained by the conventional treatment because the acoustic mode requires several decay lengths to build up to its nominal value. In addition, the corresponding resonance line is broadened with the development of side bands. In contrast, we argue that intra-mode forward SBS is not expected to show these effects. Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides

Germanium as a material for stimulated Brillouin scattering in the mid-infrared

© 2014 Optical Society of America. In a theoretical design study, we propose buried waveguides made of germanium or alloys of germanium and other group-IV elements as a CMOS-compatible platform for robust, high-gain stimulated Brillouin scattering (SBS) applications in the mid-infrared regime. To this end, we present numerical calculations for backward-SBS at 4mm in germanium waveguides that are buried in silicon nitride. Due to the strong photoelastic anisotropy of germanium, we investigate two different orientations of the germanium crystal with respect to the waveguide's propagation direction and find considerable differences. The acoustic wave equation is solved including crystal anisotropy; acoustic losses are computed from the acoustic mode patterns and previously published material parameters

Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis

© 2015 American Physical Society. ©2015 American Physical Society. Recent theoretical studies of stimulated Brillouin scattering (SBS) in nanoscale devices have led to intense research effort dedicated to the demonstration and application of this nonlinearity in on-chip systems. The key feature of SBS in integrated photonic waveguides is that small, high-contrast waveguides are predicted to experience powerful optical forces on the waveguide boundaries, which are predicted to further boost the SBS gain that is already expected to grow dramatically in such structures because of the higher mode confinement alone. In all recent treatments, the effect of radiation pressure is included separately from the scattering action that the acoustic field exerts on the optical field. In contrast to this, we show here that the effects of radiation pressure and motion of the waveguide boundaries are inextricably linked. Central to this insight is a new formulation of the SBS interaction that unifies the treatment of light and sound, incorporating all relevant interaction mechanisms - radiation pressure, waveguide boundary motion, electrostriction, and photoelasticity - from a rigorous thermodynamic perspective. Our approach also clarifies important points of ambiguity in the literature, such as the nature of edge effects with regard to electrostriction and of body forces with respect to radiation pressure. This new perspective on Brillouin processes leads to physical insight with implications for the design and fabrication of SBS-based nanoscale devices

Elastic Purcell Effect

© 2018 American Physical Society. In this work, we introduce an elastic analog of the Purcell effect and show theoretically that spherical nanoparticles can serve as tunable and robust antennas for modifying the emission from localized elastic sources. This effect can be qualitatively described by introducing elastic counterparts of the familiar electromagnetic parameters: local density of elastic states, elastic Purcell factor, and effective volume of elastic modes. To illustrate our framework, we consider the example of a submicron gold sphere as a generic elastic GHz antenna and find that shear and mixed modes of low orders in such systems offer considerable elastic Purcell factors. This formalism opens pathways towards extended control over dissipation of vibrations in various optomechanical systems and contributes to closing the gap between classical and quantum-mechanical treatments of phonons localized in elastic nanoresonators

Stimulated Brillouin scattering in layered media: Nanoscale enhancement of silicon

© 2019 Optical Society of America. We report a theoretical study of stimulated Brillouin scattering (SBS) in general anisotropic media, incorporating the effects of both acoustic strain and local rotation. We apply our general theoretical framework to compute the SBS gain for layered media with periodic length scales smaller than all optical and acoustic wavelengths, where such composites behave like homogeneous anisotropic media. We predict that a layered medium composing nanometer-thin layers of silicon and As 2 S 3 glass has a bulk SBS gain of 1.28 × 10− 9 W −1 m. This is more than 500 times larger than that of silicon and almost double the gain of As 2 S 3 . The enhancement is due to a combination of roto-optic, photoelastic, and artificial photoelastic contributions in the composite structure