Lorenz-Mie theory for 2D scattering and resonance calculations

Abstract

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers.

This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

References in corpus (11)

• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Strong Interactions in Multimode Random Lasers
• Supporting Online Material for "Strong Interactions in Multimode Random Lasers"
• Self-consistent multi-mode lasing theory for complex or random lasing media
• Spectrally-engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis
• Theory of the spatial structure of non-linear lasing modes
• Ab initio self-consistent laser theory and random lasers
• Efficient analysis and design of low-loss whispering-gallery-mode coupled resonator optical waveguide bends
• Steady-state ab initio laser theory for complex gain media
• Beam shaping using genetically optimized two-dimensional photonic crystals
• Optimization of integrated polarization filters

Cited by in corpus (6)

• Inverse design of functional photonic patches by adjoint optimization coupled to the generalized Mie theory
• Aperiodic bandgap structures for enhanced quantum two-photon sources
• A framework to compute resonances arising from multiple scattering
• Structural entropy and spatial decay of quasimodes in Vogel spirals
• Mie Scattering in the Macroscopic Response and the Photonic Bands of Metamaterials
• Non-orientable Exceptional Points in Twisted Boundary Systems