Cascaded Quadratic Nonlinear Interactions In One Dimensional Photonic Structures

Parametric interactions are one of the oldest studied phenomenon in nonlinear optics. The nonlinear light-matter-light interaction allows one to generate light at any wavelength within the transmission band of a nonlinear crystal. It is known that the efficiency of the harmonic generation process strongly depends on the phase mismatch between interacting waves and, in order to observe harmonic generation, some technique has to be implemented. The spatially periodic modulation of the sign of nonlinearity is one of the solutions to this phase mismatch problem. Such structures, called nonlinear photonic crystals, are nowadays widely realized. Proper design of the nonlinearity modulation gives one a great control over the properties of a newly generated harmonic. The purpose of this thesis is the theoretical analysis of possible phase matching schemes and the experimental investigation of nonlinear scattering processes. The nonlinear structures under consideration in this work are periodic and strongly disordered 1D nonlinear gratings; 2D random nonlinear photonic crystals; and a single boundary between two regions of different nonlinearity. Chapter 1 provides a general introduction to aspects of frequency conversion relevant to the topic of this thesis. Basic terms used in quadratic parametric processes are defined. The fundamental theory of harmonic generation in nonlinear crystals is presented. Phase matching techniques in homogeneous and periodic structures are reviewed followed by an introduction to nonlinear diffraction mechanisms in one and two dimensional nonlinear gratings. Chapter 2 contains a theoretical study of parametric wave interaction in nonlinear optical media with a randomized distribution of quadratic nonlinearity. In particular, it shows how the transition from an ideal periodic structure to a fully random structure affects properties of the second and cascaded third harmonic generation. Analytical formulas describing properties of such harmonics in the presence of nonlinearity disorder are derived. In chapter 3 we study theoretically and numerically the second harmonic generation in a two dimensional nonlinear crystal with a random distribution of ferroelectric domains. We numerically generate a disordered structure composed of semi-circular ferroelectric domains of random size and random position. Aside from presenting numerical simulations, we show that the strict model presented in chapter 2 can be successfully applied to 2D random structures. We show that the specific features of disordered domain structures greatly affect the emission pattern of the generated harmonics. In chapter 4 and chapter 5 we study, experimentally and theoretically, the Cerenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vectors of the crystal can be used to compensate for the phase mismatch in the transverse direction. We also experimentally investigate the Cerenkov second harmonic tuning response to a wavelength and the position of the incident beam. We reveal that, in contrast to the classic second harmonic generation whose tuning response is determined by the superlattice itself, the sensitivity of the Cerenkov harmonic intensity depends strongly on the width of the incident beam.

The aim of the work is give an overview of the activity in the field of Photonic Crystal developed in the frame of COST P11 action . The main objective of the COST P11 action was to unify and coordinate national efforts aimed at studying linear and nonlinear optical interactions with Photonic Crystals (PCs), without neglecting an important aspect related to the material research as idea and methods of realizations of 3D PC, together with the development and implementation of measurement techniques for the experimental evaluation of their potential applications in different area, as for example telecommunication with novel optical fibers, lasers, nonlinear multi-functionality, display devices, opto-electronics, sensors. The book contains contributions from authors who gave their lecture at the Cost P11 Training School.

This volume contains papers presented at the NATO Advanced Study Institute (ASI) Photonic Crystals and Light Localization held at the Creta Maris Hotel in Limin Hersonissou, Crete, June 18-30, 2000. Photonic crystals offer unique ways to tailor light and the propagation of electromagnetic waves (EM). In analogy to electrons in a crystal, EM waves propagating in a structure with a periodically modulated dielectric constant are organized into photonic bands, separated by gaps where propagating states are forbidden. There have been proposals for novel applications ofthese photonic band gap (PBG) crystals, with operating frequencies ranging from microwave to the optical regime, that include zero threshold lasers, low-loss resonators and cavities, and efficient microwave antennas. Spontaneous emission, suppressed for photons in the photonic band gap, offers novel approaches to manipulate the EM field and create high-efficiency light-emitting structures. Innovative ways to manipulate light can have a profound iofluence on science and technology.

In this volume, six review articles which cover a broad range of topics of current interest in modern optics are included. The first article by S. Saltiel, A.A. Sukhorukov and Y.S. Kivshar presents an overview of various types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic non-linear media, the so-called multi-step parametric interactions. The second article by H.E. Tureci, H.G.L. Schwefel, Ph. Jacquod and A.D. Stone reviews the progress that has been made in recent years in the understanding of modes in wave-chaotic systems. The next article by C.P. Search and P. Meystre reviews some important recent developments in non-linear optics and in quantum optics. The fourth article by E. Hasman, G. Biener, A. Niv and V. Kleiner discusses space-variant polarization manipulation. The article reviews both theoretical analysis and experimental techniques. The article which follows, by A.S. Desyatnikov, L. Torner and Y.S. Kivshar presents an overview of recent researches on optical vortices and phase singularities of electromagnetic waves in different types of non-linear media, with emphasis on the properties of vortex solitons. The concluding article by K. Iwata presents a review of imaging techniques with X-rays and visible light in which phase of the radiation that penetrates through a transparent object plays an important part.

The aim of the work, is to study nonlinear parametric interactions, such as nonlinear frequency conversion and all-optical switching, in miniaturized photonic band gap materials. In particular, we wish to address highly efficient chi(sup 2) and chi(sup 3) processes in the short- wavelength range (less than 0.4 micrometers) to far (8-12 micrometers) IR regions of the electromagnetic spectrum near the photonic band edge of one-dimensional photonic crystals. The work is performed in collaboration with the group of Dr. C. Bowden, Weapons Science Directorate, Missile Research Development & Engineering Center, U.S. Army Aviation and Missile Command, Redstone Arsenal, AL 35898-5000. According to the previous reports related to the first 9 months of the contract, the work has been performed and continued following different activities, as described in technical report.

Ultrafast photonics has become an interdisciplinary topic of high international research interest because of the spectacular development of compact and efficient lasers producing optical pulses with durations in the femtosecond time domain. Present day long-haul telecommunications systems are almost entirely based on the transmission of short burst

Nonlinear optical phenomena can be exploited in advanced devices for transport, processing, and storage of information. These are needed as the present-day approach - mainly using on electron-based technology - faces the challenges of increasing demand on bandwidth and processing speed. A key role in the development of nonlinear devices is the availability of novel materials with the required nonlinear optical properties. With such materials, scientific creativity and careful design, promising concepts have been developed resulting in the demonstration of devices. This book contains the proceedings of NOIS 2000 (Nonlinear Optics for the Information Society) Annual Meeting of the COST Action P2, held at the University of Twente, in Enschede, The Netherlands, on 26-27 October, 2000. It comprises a selection of the presentations at the meeting, reporting state-of-the-art research and developments in the field of applications of nonlinear phenomena in information technology.

The current research into solitons and their use in fiber optic communications is very important to the future of communications. Since the advent of computer networking and high speed data transmission technology people have been striving to develop faster and more reliable communications media. Optical pulses tend to broaden over relatively short distances due to dispersion, but solitons on the other hand are not as susceptible to the effects of dispersion, and although they are subject to losses due to attenuation they can be amplified without being received and re-transmitted. This book is the first to provide a thorough overview of optical solitons. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping. It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including their stability and dynamics. Also, it will summarize a number of important experimental verification of the basic theoretical predictions and concepts covering the observation of self-focusing in the earlier days of nonlinear optics and the most recent experimental results on spatial solitons, vortex solitons, and soliton interaction & spiraling. * Introduces the fundamental concepts of the theory of nonlinear waves and solitons through realistic models * Material is based on authors' years of experience actively working in and researching the field * Summarizes the most important experimental verification of the basic theories, predictions and concepts of this ever evolving field from the earliest studies to the most recent

Nonlinear optical studies of periodic dielectric structures have blossomed in the past two decades. New fabrication techniques are producing fiber grating and multidimensional photonic crystals in materials where the refractive index can be varied by light pulses and beams. Gap solitons that can propagate at any velocity from zero to the speed of light and spatial solitons that prevent the diffractive spread of light in waveguide arrays are two examples of the new phenomena described in this book. Many new materials and structures are being developed that will impact new optical devices with applications in optical communications and optical data processing. All the above topics are addressed in detail in this book.