Field Deformation on a Bent Step Index Fibre

Abstract

We consider the problem of propagation of light in a bent step index circular core optical fibre. We first derive the exact equations in toroidal coordinates and give an analytic solution at first order with respect to the parameter λ/(curvature radius), neglecting radiation losses.     

Self-phase Modulation in Quadratically Nonlinear Media

Abstract

We discuss self-phase modulations and related transverse effects accompanying interaction of a light beam with a second harmonic radiation generated by it. Some experimental observations are explained by a simple perturbative approach. Numerical simulations provide a further insight into the nature of transverse self-effects in quadratically nonlinear media. An effective x ⁽³⁾-like behaviour of dispersive quadratically nonlinear media is discussed. Such feature may lead to important consequences for measurements of the x ⁽³⁾ tensor in complex nonlinear media.     

Waveguide confinement of cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization

Abstract

The feasibility of making a frequency doubler for integrated optics is studied with the electromagnetic theory of gratings and graded-index waveguides as a tool. The device consists of a first waveguide filled with a sol-gel nonlinear material doped or grafted with a nonlinear chromophore whose thickness is chosen to generate a second-harmonic Cerenkov radiation in a dispersive glass substrate. The Cerenkov radiation is coupled into a second waveguide through a graded-index layer produced by ion exchange into glass, lying on top of an ion-etched grating coupler. The aim of the study is to optimize the optogeometrical parameters of the device in order to obtain a resonance line of the second waveguide modes that has an angular width large enough to match the experimental constraints, and which leads to a good enough coupling coefficient. The electromagnetic theory of grating couplers is developed into an S-matrix propagation algorithm form in order to be combined with the electromagnetic analysis of the thick graded-index waveguide with a view to analysing the device.     

Solitary Waves of Maxwell's Equations in Nonlinear Anisotropic Media

Abstract

The (1 + 1)-D solitary wave solutions of Maxwell's equations in nonlinearity induced anisotropic media (in liquids such as carbon disulphide, and in crystals, etc.) are investigated. We find that there is no arbitrarily linearly polarized (in the x-y plane perpendicular to the propagation direction z) soliton solution from Maxwell's equations except that with linear polarization either in alignment with or orthogonal to the geometric axis of the light induced refractive index change. This contradicts the prediction of the vector nonlinear Schroedinger equation (an approximation of Maxwell's equations) which yields soliton solutions with an arbitrary linear polarization. However, Maxwell's equations are found to admit stable elliptically polarized solitary wave solutions which reduce to the stable circularly polarized solitary wave solutions of the vector nonlinear Schroedinger equation when the induced refractive index change approaches zero.     

Broad Tunable Two-photon-resonant Parametric Oscillators for Vacuum Ultraviolet

Abstract

We derive the condition for broad tunability of optical parametric oscillators (OPOs) based on two-photon-resonant four-wave mixing in media with a centre of inversion. Our theory takes into account both depletion of the pump due to two-photon absorption (TPA) and the effect of population saturation. We show that to achieve a broad tunable range in a four-wave two-photon resonant OPO, it is necessary to provide significant TPA of the pump over the length of the nonlinear medium without any intermediate resonances. We make estimates for OPOs based on electronic transitions in rare gases, organic solutions, and glasses with wide transparent bands, and show that such media may be very promising for constructing broadly tunable coherent sources. In particular, we demonstrate the feasibility of constructing an OPO using neon pumped by an argon excimer laser with a tuning range from 70 nm to 1000 nm spanning the vacuum ultraviolet, visible and infrared regions.     

Kerr nonlinear coupler with varying linear coupling coefficient

Abstract

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.     

Slow light in moving media

Abstract

We review the theory of light propagation in moving media with extremely low group velocity. We intend to clarify the most elementary features of monochromatic slow light in a moving medium and, whenever possible, to give an instructive simplified picture.     

Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.     

The Theory of Spiral Laser Beams in Nonlinear Media

Abstract

The analytical theory governing the propagation of spiral laser beams in nonlinear media is developed. It is shown that, taking into account the saturation effect in a Kerr medium, spiral beams have a tube-like structure with a periodicity along the axis of a nonlinear autoguide. In the case of the absence of saturation mechanism the collapse of spiral beams is described. It is found that critical autoguide power depends on the topological charge of the spiral beam. The stability of a circular symmetry structure of the beam is investigated. The analytical results are in good agreement with the numerical experiment.     

Transfer characteristics and propagation effects of a multi-resonance ring resonator-based optical device

Abstract

We describe the linear and nonlinear optical transfer characteristics of a multi-resonance device consisting of two optical ring resonators coupled one to the other and to an optical waveguide. The propagation effects displayed by the device are compared with those of a sequence of fundamental ring resonators coupled to a waveguide.     

Trends in optical biomedical imaging

Abstract

Recent progress in the development of optical techniques for non-invasive imaging in biology and medicine is reviewed. We start with some fundamental considerations of light propagation in random media. We then discuss imaging using coherent unscattered light and diffuse light. Microscopic techniques based on one- and two-photon fluorescence are described and several types of nonlinear and time-resolved microscopy are explained. We conclude with some application examples and an outlook.     

Calculation of Nonlinear Waves Guided by Optical Fibres Using the Resonance Technique

Abstract

A recently developed, simple, and easily programmable method based on a resonance technique for the analysis of nonlinear guided modes for planar geometry has been extended to include fibre configurations. We consider here nonlinear media of the general type (non-Kerr media) including the more complicated but realistic case of saturable media. In the present paper, as an example of the proposed methodology, the following configuration is treated: a circular optical fibre consisting of a linear core bounded by a nonlinear cladding medium. The numerical results obtained by the method, correspond to the ‘weak guidance’ approximation, including both field distribution and power calculations.     

High-order dark solitons in nonlocal nonlinear media

Abstract

The high-order dark solitons in nonlocal nonlinear media are found up to fifth-order. The stability of high-order dark solitons is investigated numerically. The stability relation graphs of negative imaginary eigenvalues versus propagation constant are obtained. The propagation graphs of the input signal with noise added prove the result of the stability analysis to be correct.     

Optically induced non-radiative fast pulses in metals

Abstract

We describe new experiments in which the signals induced inside a solid conductor by external excitation using nanosecond long pulsed laser radiation are detected using a pyro-electric material. From the data obtained, it is shown that there is a previously unreported ‘early’ or ‘fast’ signal which propagates inside the solid at a speed greater than that reported for sound in the same media. This signal is observed in addition to the usually observed thermal and acoustic waves that travel at the speed of sound in the same media. We demonstrate that this signal cannot be adequately accounted for by existing theories of thermo-elastic wave propagation in solids.     

Mixed-type solitons for the coupled higher-order nonlinear Schrödinger equations in multi-mode and birefringent fibers

Abstract

In this paper, coupled higher-order nonlinear Schrödinger equations are studied for the ultrashort pulse propagation in such optical media as the multi-mode fibers and birefringent fibers. Through the Hirota method and symbolic computation, analytic mixed-type one- and two-soliton solutions are derived, and three sets of conditions for the non-singular solutions are given as well. Via the one-soliton solutions obtained, critical condition for the black and gray solitons is obtained analytically. Asymptotic analysis is carried out on the two-soliton solutions to derive the condition for the inelastic interaction. Evolution of the bound vector solitons, elastic and inelastic interactions between the two vector solitons are also investigated graphically. Moreover, after the inelastic interaction, the two bright solitons are observed to disappear, while the two dark ones form the new bound soliton.     

Enhanced third-order nonlinear optical response of photonic bandgap materials

Abstract

We calculate the nonlinear phase shift acquired by a laser beam in propagating through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the direction of propagation. We find that the nonlinear phase shift shows resonances for laser frequencies close to the edge of the stop band of the photonic bandgap structure. Enhancements of the nonlinear phase shift compared with that of a homogeneous nonlinear optical material by a factor of approximately five are predicted under realistic laboratory conditions. We find that similar enhancements of the two-photon absorption rate can occur for a material with an imaginary nonlinear susceptibility. We also treat the case of a photonic bandgap material containing a ′defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approximately thirty.     

Quantum statistics and dynamics of nonlinear couplers

Abstract

We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.     

Propagation of (2 + 1)-dimensional solitary waves in dissipative/active saturable nonlinear media

Abstract

We investigate the propagation of (2 + 1)D bright solitary waves in a saturable nonlinear medium perturbed with gain or loss. We find that in the presence of loss (gain) the amplitude and width of the (2 + 1)D bright solitary waves may both increase (decrease) with their product varying adiabatically during evolution. This is in contrast to the (1 + 1)D Kerr bright (dark) solitons or (2 + 1)D vortex solitons whose amplitude decreases (increases) at the same rate as the width increases (decreases), keeping their product unchanged with the propagation distance. For a very weak nonlinear saturation approaching Kerr nonlinearity, it is found that the amplitude and the width change at a rate faster than the (1 + 1)D Kerr bright and dark solitons, whereas their variation in highly saturable media is slower than the (1 + 1) or (2 + 1)D Kerr dark solitons. In a medium of moderate nonlinear saturation, the beam width and amplitude may vary in the way following that of high nonlinear saturation or weak nonlinear saturation or a combination of the two, depending on loss or gain and propagation distance.     

Propagation of a Gaussian Beam in Planar and Cylindrically Inhomogeneous Media: Comparison of Modal Analysis and Approximate Approaches

This work presents a study on the propagation of electromagnetic waves in media, characterized by k = k₀ m k₂ y ² and k = k₀ m k₂ r². A vector theory based on Maxwell's equations is used to derive linear homogeneous second-order equations satisfied by the transverse electric and magnetic field components. The various modes of propagation and the corresponding propagation constants have been determined. These are used to study the propagation and focusing of waves which have an intensity distribution along their wavefront. An alternative method for the study of the propagation and focusing of electromagnetic waves has been discussed. This is based on an approximate solution of the wave equation given in previous communications. For parameters of interest, the results obtained from the approximate solution are in excellent agreement with the solution obtained from the modal analysis of the problem. The present study should be of relevance in tropospheric communication and focusing of laser beams in selfoc fibres, gas lenses, etc.