Lorenz-Mie theory for 2D scattering and resonance calculations

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.Comment: 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 i

Aperiodic nano-photonic design

The photon scattering properties of aperiodic nano-scale dielectric structures can be tailored to closely match a desired response by using adaptive algorithms for device design. We show that broken symmetry of aperiodic designs provides access to device functions not available to conventional periodic photonic crystal structures.Comment: 23 pages, LaTex, 8 postscript figure

Rigorous Approach to Analysis of Two-Dimensional Potential Problems, Wave Propagation and Scattering for Multi-conductor Systems

The research described in this chapter analyses two-dimensional potential problems for the multi-body systems, transverse electromagnetic wave propagation along multi-conductor transmission lines and two-dimensional plane wave scattering by various arrays. All conductors may be of arbitrary cross-sections; the only restriction on the system geometry is a smooth parameterization. These problems are mathematically modelled by Dirichlet boundary value problems for either the Laplace or the Helmholtz equation, with the classical integral representation of the solutions in the form of single-layer potential. The analytical-numerical algorithm presented here is based on the method of analytical regularization. The key idea behind this technique is an analytical transformation of the initial ill-posed integral equations to a well-conditioned Fredholm second kind matrix equation. The resulting system of infinite linear algebraic equations is effectively solved using the truncation method: the solution of the truncated system converges to the solution of the infinite system with the guaranteed accuracy that only depends on the truncation number and thus may be pre-specified. The solution obtained is applied to the accurate analysis of 2-D electrostatic- and electrodynamic-field problems for multi-conductor systems with arbitrary profiled conductors. Examples of some conceptual shielded transmission lines incorporating various configurations of conductors and scattering problems for the arrays of thick strips establish the utility of our method and its reliability in various situation

Synthesis of Electromagnetic Metasurfaces: Principles and Illustrations

The paper presents partial overview of the mathematical synthesis and the physical realization of metasurfaces, and related illustrative examples. The synthesis consists in determining the exact tensorial surface susceptibility functions of the metasurface, based on generalized sheet transition conditions, while the realization deals with both metallic and dielectric scattering particle structures. The examples demonstrate the capabilities of the synthesis and realization techniques, thereby showing the plethora of possible metasurface field transmission and subsequent applications. The first example is the design of two diffraction engineering birefringent metasurfaces performing polarization beam splitting and orbital angular momentum multiplexing, respectively. Next, we discuss the concept of the "transistor" metasurface, which is an electromagnetic linear switch based on destructive interferences. Then, we introduce a non-reciprocal non-gyrotropic metasurface using a pick-up circuit radiator (PCR) architecture. Finally, the implementation of all-dielectric metasurfaces for spatial dispersion engineering is discussed

Generalized Lorenz-Mie theory : application to scattering and resonances of photonic complexes

Les structures photoniques complexes permettent de façonner la propagation lumineuse à l’échelle de la longueur d’onde au moyen de processus de diffusion et d’interférence. Cette fonctionnalité à l’échelle nanoscopique ouvre la voie à de multiples applications, allant des communications optiques aux biosenseurs. Cette thèse porte principalement sur la modélisation numérique de structures photoniques complexes constituées d’arrangements bidimensionnels de cylindres diélectriques. Deux applications sont privilégiées, soit la conception de dispositifs basés sur des cristaux photoniques pour la manipulation de faisceaux, de même que la réalisation de sources lasers compactes basées sur des molécules photoniques. Ces structures optiques peuvent être analysées au moyen de la théorie de Lorenz-Mie généralisée, une méthode numérique permettant d’exploiter la symétrie cylindrique des diffuseurs sous-jacents. Cette dissertation débute par une description de la théorie de Lorenz-Mie généralisée, obtenue des équations de Maxwell de l’électromagnétisme. D’autres outils théoriques utiles sont également présentés, soit une nouvelle formulation des équations de Maxwell-Bloch pour la modélisation de milieux actifs appelée SALT (steady state ab initio laser theory). Une description sommaire des algorithmes d’optimisation dits métaheuristiques conclut le matériel introductif de la thèse. Nous présentons ensuite la conception et l’optimisation de dispositifs intégrés permettant la génération de faisceaux d’amplitude, de phase et de degré de polarisation contrôlés. Le problème d’optimisation combinatoire associé est solutionné numériquement au moyen de deux métaheuristiques, l’algorithme génétique et la recherche tabou. Une étude théorique des propriétés de micro-lasers basés sur des molécules photoniques – constituées d’un arrangement simple de cylindres actifs – est finalement présentée. En combinant la théorie de Lorenz-Mie et SALT, nous démontrons que les propriétés physiques de ces lasers, plus spécifiquement leur seuil, leur spectre et leur profil d’émission, peuvent être affectés de façon nontriviale par les paramètres du milieu actif sous-jacent. Cette conclusion est hors d’atteinte de l’approche établie qui consiste à calculer les étatsméta-stables de l’équation de Helmholtz et leur facteur de qualité. Une perspective sur la modélisation de milieux photoniques désordonnés conclut cette dissertation.Complex photonic media mold the flow of light at the wavelength scale using multiple scattering and interference effects. This functionality at the nano-scale level paves the way for various applications, ranging from optical communications to biosensing. This thesis is mainly concerned with the numerical modeling of photonic complexes based on twodimensional arrays of cylindrical scatterers. Two applications are considered, namely the use of photonic-crystal-like devices for the design of integrated beam shaping elements, as well as active photonic molecules for the realization of compact laser sources. These photonic structures can be readily analyzed using the 2D Generalized Lorenz-Mie theory (2D-GLMT), a numerical scheme which exploits the symmetry of the underlying cylindrical structures. We begin this thesis by presenting the electromagnetic theory behind 2D-GLMT.Other useful frameworks are also presented, including a recently formulated stationary version of theMaxwell-Bloch equations called steady-state ab initio laser theory (SALT).Metaheuristics, optimization algorithms based on empirical rules for exploring large solution spaces, are also discussed. After laying down the theoretical content, we proceed to the design and optimization of beam shaping devices based on engineered photonic-crystal-like structures. The combinatorial optimization problem associated to beam shaping is tackled using the genetic algorithm (GA) as well as tabu search (TS). Our results show the possibility to design integrated beam shapers tailored for the control of the amplitude, phase and polarization profile of the output beam. A theoretical and numerical study of the lasing characteristics of photonic molecules – composed of a few coupled optically active cylinders – is also presented. Using a combination of 2D-GLMT and SALT, it is shown that the physical properties of photonic molecule lasers, specifically their threshold, spectrum and emission profile, can be significantly affected by the underlying gain medium parameters. These findings are out of reach of the established approach of computing the meta-stable states of the Helmholtz equation and their quality factor. This dissertation is concluded with a research outlook concerning themodeling of disordered photonicmedia

Engineering aperiodic spiral order for photonic-plasmonic device applications

Thesis (Ph.D.)--Boston UniversityDeterministic arrays of metal (i.e., Au) nanoparticles and dielectric nanopillars (i.e., Si and SiN) arranged in aperiodic spiral geometries (Vogel's spirals) are proposed as a novel platform for engineering enhanced photonic-plasmonic coupling and increased light-matter interaction over broad frequency and angular spectra for planar optical devices. Vogel's spirals lack both translational and orientational symmetry in real space, while displaying continuous circular symmetry (i.e., rotational symmetry of infinite order) in reciprocal Fourier space. The novel regime of "circular multiple light scattering" in finite-size deterministic structures will be investigated. The distinctive geometrical structure of Vogel spirals will be studied by a multifractal analysis, Fourier-Bessel decomposition, and Delaunay tessellation methods, leading to spiral structure optimization for novel localized optical states with broadband fluctuations in their photonic mode density. Experimentally, a number of designed passive and active spiral structures will be fabricated and characterized using dark-field optical spectroscopy, ellipsometry, and Fourier space imaging. Polarization-insensitive planar omnidirectional diffraction will be demonstrated and engineered over a large and controllable range of frequencies. Device applications to enhanced LEDs, novel lasers, and thin-film solar cells with enhanced absorption will be specifically targeted. Additionally, using Vogel spirals we investigate the direct (i.e. free space) generation of optical vortices, with well-defined and controllable values of orbital angular momentum, paving the way to the engineering and control of novel types of phase discontinuities (i.e., phase dislocation loops) in compact, chip-scale optical devices. Finally, we report on the design, modeling, and experimental demonstration of array-enhanced nanoantennas for polarization-controlled multispectral nanofocusing, nanoantennas for resonant near-field optical concentration of radiation to individual nanowires, and aperiodic double resonance surface enhanced Raman scattering substrates

Engineering photonic and plasmonic light emission enhancement

Thesis (Ph.D.)--Boston UniversitySemiconductor photonic devices are a rapidly maturing technology which currently occupy multi-billion dollar markets in the areas of LED lighting and optical data communication. LEDs currently demonstrate the highest luminous efficiency of any light source for general lighting. Long-haul optical data communication currently forms the backbone of the global communication network. Proper design of light management is required for photonic devices, which can increase the overall efficiency or add new device functionality. In this thesis, novel methods for the control of light propagation and confinement are developed for the use in integrated photonic devices. The first part of this work focuses on the engineering of field confinement within deep subwavelength plasmonic resonators for the enhancement of light-matter interaction. In this section, plasmonic ring nanocavities are shown to form gap plasmon modes confined to the dielectric region between two metal layers. The scattering properties, near-field enhancement and photonic density of states of nanocavity devices are studied using analytic theory and 3D finite difference time domain simulations. Plasmonic ring nanocavities are fabricated and characterized using photoluminescence intensity and decay rate measurements. A 25 times increase in the radiative decay rate of Er:Si02 is demonstrated in nanocavities where light is confined to volumes as small as 0.01(λ/n)^3 . The potential to achieve lasing, due to the enhancement of stimulated emission rate in ring nanocavities, is studied as a route to Si-compatible plasmon-enhanced nanolasers. The second part of this work focuses on the manipulation of light generated in planar semiconductor devices using arrays of dielectric nanopillars. In particular, aperiodic arrays of nanopillars are engineered for omnidirectional light extraction enhancement. Arrays of Er:SiNx nanopillars are fabricated and a ten times increase in light extraction is experimentally demonstrated, while simultaneously controlling far-field radiation patterns in ways not possible with periodic arrays. Additionally, analytical scalar diffraction theory is used to study light propagation from Vogel spiral arrays and demonstrate generation of OAM. Using phase shifting interferometry, the presence of OAM is experimentally verified. The use of Vogel spirals presents a new method for the generation of OAM with applications for secure optical communications