Finite difference time domain calculation of transients in antennas with nonlinear loads

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials

Applications of microstructured fibers : supercontinua and novel components

Microstructured fibers are a special class of pure-silica optical fibers. They consist of a silica core, surrounded by a periodic array of air-holes running along the entire length of the fiber. These air-holes permit guidance of light through total-internal reflection. Diameter and spacing of the air-holes determines the optical properties of the fiber, therefore allowing for tailoring of the fiber according to the intended application. This thesis contains novel results on supercontinuum generation in microstructured fibers. Several critical advances have been made in tailoring of the fiber properties in order to further reduce power requirements hindering miniaturization of supercontinuum sources. In particular, the influence of a second zero-dispersion wavelength of the fiber and the input polarization of highly-birefringent fibers have been studied. Furthermore, a novel two-pump scheme allows for efficient generation of broadband blue-light. The generated supercontinua are applied to characterization of absorption and transmission spectra of novel optical components. The high spectral power density of supercontinuum allows for observation of several new excited-state absorption lines of Erbium-doped fibers and characterization of optical components with strong variations in the transmission spectrum. The second part of the thesis deals with applications developed for microstructured fibers. A tapered microstructured fiber is designed for coupling between standard fibers and photonic-crystal waveguides. An elliptical-core microstructured fiber is proposed as an efficient adapter between standard fibers and highly asymmetric waveguides. In addition, a microstructured fiber based optically bistable fiber cavity is applied to all-optical switching. In particular, an optical flip-flop is numerically studied.reviewe

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. Their basic property is the photonic gap, a frequency range in which wave propagation is not allowed in any direction, in a close analogy with the electronic energy band gap in semiconductors;In this dissertation we study two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material. Such systems have been shown to exhibit bistability, an essential feature for an all-optical switching mechanism. Here, we will study an approximate structure model, in which the nonlinear material is concentrated in very thin, or delta-function, layers. We will derive analytical solutions, and compare with the finite-width nonlinear layer case, in order to find it\u27s limitations and the physical mechanisms behind them. Also, by using numerical simulations, we will study the dynamics of an externally-controlled switching mechanism for such systems, which is pulse injection while they are illuminated by a constant wave. Finally, we will develop a model for the nonlinear response of colloidal crystals, which will reveal a light-lattice coupling similar to the electron-phonon in semiconductors;The second area of study is focused on the mechanisms responsible for the gap formation, as well as other properties of two-dimensional PBG materials. We will show that in one case, the dominant gap-forming mechanism is the excitation of single scatterer Mie resonances and not Bragg-like multiple scattering, and that the photonic states are analogous to the localized atomic orbitals in semiconductors. We will develop a tight-binding model based on a linear combination of Mie resonances, that will successfully reproduce the photonic band structure of any lattice arrangement, with and without defects, thus proving the validity of a strongly localized photon picture. Then, using ab initio numerical techniques, we will study the effects of disorder for various realizations of two-dimensional photonic band gap materials, and identify the cases for which the strongly localized photon picture applies, and those for which a nearly free photon picture is a more proper one

A Seismic Channel Model: The San Ramon Fault

Although seismic waves have been studied for many years, their soliton structure has only recently studied. Deformation solitons propagate along earthquake faults and can induce large earthquakes. Rotation solitons are generated in earthquake sources and propagate throughout the Earth. The conclusion to be reached from our paper is that the research on seismic solitons is essential for investigating the propagation of seismic waves and helps understand mechanisms triggering earthquakes. This paper discusses the development of elastodynamics equations similar to Maxwell's equations in a chiral -mode which is applied to a seismic channel, which is dispersive and nonlinear. The chirality is described in terms of the formalism proposed by Born-Fedorov. The nonlinearity is Kerr-type, and dispersion of the medium is taken into account explicitly through the Taylor series expansion. Through numerical calculations these theoretical results allow us analyze the soliton propagation of S-seismic pulses which can induce strong earthquakes. The numerical calculation is applied to the San Ramon Fault localized in Santiago City, Chile which is a seismically active fault that is a main element to be considered in any study on seismic hazard assessment for this city

Theory of optical rectification in a travelling wave structure

This thesis is concerned with the interaction of an optical wave with a microwave in a waveguiding structure coupled by a second order nonlinearity. Emphasis is laid upon the generation of ultrashort electrical transients via optical rectification (OR) as well as cascading effects due to the interplay of OR and the linear electro-optic effect. A simple transmission line model is introduced to explain qualitatively the basic physical mechanisms of an externally induced polarisation in a travelling wave structure. For a quantitative description, evolution equations for the overall interaction between the microwave and the optical wave based on a coupled mode formalism are developed. The basic properties of the structure under consideration are discussion and techniques for their evaluation are introduced. A set of corresponding parameters for typical structures is estimated and used for calculations throughout the thesis. The generation of electrical signals from optical waves via OR is discussed in detail for the cases of single and mixed polarization optical modes in the structure. The self phase modulation due to cascading of OR and the electro-optic effect is elucidated. It is shown that continuous wave solutions of the conservative system are modulationally unstable in a large range of relevant system parameters. The possibility of formation of solitary waves due to the mutual interaction of optical wave and microwave is considered in the context of long wave short wave interaction. Basic properties of bright stationary solutions and their excitation are discussed. The possibility of formation of solitons due to microwave self-interaction is illuminated. The linear stability of bright solitary waves is investigated. The observed oscillations and radiation of perturbed propagated bound states are explained by the existence of discrete, quasi-bond internal modes of the stationary solutions. Collision scenarios are addressed

A preconditioned Newton-Krylov method for computing steady-state pulse solutions of mode-locked lasers

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008.Includes bibliographical references (p. 47-48).We solve the periodic boundary value problem for a mode-locked laser cavity using a specially preconditioned matrix-implicit Newton-Krylov solver. Solutions are obtained at least an order of magnitude faster than with dynamic simulation, the standard method. Our method is demonstrated experimentally on a one-dimensional temporal model of an eight femtosecond mode-locked laser operating in the dispersion-managed soliton regime. Our solver is applicable to finding the steady-state solution of any nonlinear optical cavity with moderate self phase modulation, such as those of solid state lasers, and requires only a model for the round-trip action of the cavity. We conclude by proposing avenues of future work to improve the method's convergence and expand its applicability to lasers with higher degrees of cavity nonlinearity. Our approach can be extended to spatio-temporal cavity models, potentially allowing for the first feasible simulation of the full dynamics of Kerr-lens mode locking.by Jonathan R. Birge.S.M

Modelling of photonic components based on ÷(3)nonlinear photonic crystals

En esta tesis se llevó a cabo un estudio de diversas propiedades de los cristales fotónicos 1D y 2D no lineales de tercer orden y de cómo se pueden aplicar dichas propiedades al desarrollo de dispositivos totalmente ópticos (por ejemplo, limitadores y conmutadores, compuertas lógicas, transistores ópticos, etc.). Se propuso una aproximación numérica para calcular las características básicas de los cristales fotónicos no lineales como, por ejemplo, el diagrama de bandas o la transmisión. La aproximación numérica presentada en la tesis tiene ciertas ventajas útiles para cualquiera que diseñe dispositivos ópticos basados en cristales fotónicos no lineales. El sofware desarrollado a base de esta aproximación numérica ha permitido diseñar y simular numéricamente un conmutador totalmente óptico cuyas prestaciones son superiores a las de dispositivos optoelectrónicos convencionales.This dissertation represents a summary of a study of different properties of 1D and 2D third-order nonlinear photonic crystals. It is shown how these properties can be utilized to develop various all-optical devices (e.g. optical limiters and switches, logical gates, optical transistors, etc.) In the dissertation, a novel numerical approximation has been proposed for analyzing the basic characteristics of the nonlinear photonic crystals like dispersion characteristics or transmittance curves. This numerical approximation possesses some important advantages useful in designing all-optical devices based on nonlinear photonic crystals. The software based on its algorithm has allowed to design and simulate a high-production all-optical switching device

Lagrangian modelling of nonlinear waves in optical fibres

The Lagrangian perturbation method for the NLS is revisited in the form of an equivalent direct problem. The analogy can be extended to arbitrarily perturbed systems. It is then possible to provide first order perturbation expansions for the fundamental soliton. The case of the damped NLS is considered and shown to fully comply with IST predictions. Subsequently the problem of NLS initial condition not corresponding to an exact soliton is examined. There are two issues that need to be considered: the location of the soliton solution and the modelling of the continuum. The location of the soliton solution is handled by considering the integrals of motion of the NLS. The improvement arises by the inclusion of the contributions due to the continuum. The results are compared with numerical calculations and are proved to be satisfactory provided that the initial pulse shape does not depart greatly from the Asech(z) functional form. The propagation problem is handled by considering the evolution of the soliton and the continuum separately and recombining them at the required time. Two cases are considered: the far field pattern and the position where the peak of the soliton lies. For the former the recombination of continuum with the soliton is achieved with the help of the inverse part of the IST. For the peak position a Bäcklund transform is considered. Results from both regimes are compared with numerical results and shown to agree satisfactorily