Stability of higher-order bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves (ECW) equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. The first and second Bragg resonances are studied in detail since they are the archetypes for all odd and even resonances. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular not taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback (DFB) lasers.     

Analysis and design of grating couplers

Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The results cover TE_v and TM_v modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric profiles are also discussed.     

Mode launching on a multimode slab-waveguide by a plane wave

Mode launching on a symmetrical multimode slab-waveguide by a plane wave incident onto the front side of the guide is investigated theoretically and experimentally. A single plane wave always excites a whole set of modes. Among these are, in general, three adjacent modesm-1, m, m+1 which are excited most strongly. The relative power launched into these modes is approximately given by the ratio 0.4:1:0.4. The theoretical results are confirmed by qualitative observations of the far-field mode patterns. In the far field the modes are separated by using a wedge-type waveguide.     

TE-TE mode coupling at oblique incidence in a periodic dielectric waveguide

The characteristics of reflection of a TE mode into another TE mode in a planar dielectric waveguide with a sinusoidally modulated index are investigated for the general case in which the wavevectors are not aligned with the grating vector. A singular perturbation procedure is used to deduce the asymptotically exact coupled mode equations which govern the interaction. An analysis of the coupled-mode equations has shown the existence of the Brewster phenomenon at the angle of incidence θ_iB=45°. For angles of incidence sufficiently greater than the Brewster angle, the reflection coefficient can be considerably larger than that for the normal incidence. In the spectral response curves of the reflection coefficient, a higher maximum and a smaller base bandwidth are possible for the oblique incidence as compared to that for the normal incidence. The angular sensitivity of the reflection characteristics increases as the angle of incidence changes from the normal incidence to the grazing incidence.     

Guided-wave methods for optical configurations

Guided-wave methods used in the past to treat electromagnetic problems and applications in the microwave area have recently been extended to cover work in fiber and integrated optics. The basic principles of these methods are reviewed briefly and, in particular, the “open” properties of optical configurations are contrasted to the “closed” characteristics that describe most microwave applications. These aspects are illustrated in the context of beam couplers of uniform and periodic varieties, which are shown to lend themselves to rigorous treatment by microwave guided-wave methods that include both theoretical and experimental facets.     

TM-mode coupling in anisotropic optical waveguides caused by periodic variation optic-axis direction

The problem of mode coupling caused by a small periodic variation of the opticaxis direction in an anisotropic optical waveguide is reduced to a pair of coupled differential equations and an expression for the coupling coefficient is given. For a periodically perturbed section of the waveguide the coupled-mode equations are solved subject to suitable boundary conditions, and the coupling between the forward TM mode and the backward TM mode is analysed. A perturbed section of an anisotropic waveguide acts as a frequency selective reflection filter for TM modes only.     

Impedance of an electric dipole located in a cylindrical cavity in a dissipative medium

The electromagnetic fields of an electric dipole located inside a cylindrical cavity or empty tunnel are formulated. The results are used to deduce an expression for the change of self-impedance due to the presence of the cavity or tunnel walls. A numerical evaluation of the resultant convergent integral and a summation of the angular harmonic series were performed. An important finding is that the input resistance of the dipole is approximately a constant for frequencies less than about 25 MHz for a typical tunnel radius of 2 m. Such results are shown to be in qualitative agreement with an earlier analysis of an electric dipole over a dissipative half-space.     

Waves in an active medium guided by a reactive surface with reactance of gain modulation

The characteristics of surface waves (i) in a passive medium supported by a passive surface with reactance modulation and an active surface with the modulation of either the reactance or the negative resistance, and (ii) in an active medium supported by a passive surface with a reactance modulation are investigated with emphasis on the band regions. The periodic variation is sinusoidal and is in the propagation direction. For a passive medium terminated by a passive surface with a reactance modulation, there are stop bands in frequency for the surface waves and the structure of the first two stop bands is analyzed. For a passive medium terminated by an active surface and for an active medium terminated by a reactance-modulated passive surface, the characteristics of the absolute instabilities occurring in the first-order band are examined. The nature of the convective instability taking place in the second-order band for an active medium terminated by a reactance-modulated surface is discussed. Analytical expressions for the frequency shift of the second-order band are deduced. The Floquet theory is used to obtain the exact dispersion relation in the form of a continued fraction which is analyzed by singular expansions.     

Electromagnetic wave propagation in a rectangular waveguide partially loaded with magnetized planar ferrite

The propagation of electromagnetic waves in a rectangular waveguide containing a slab of transversely magnetized planar ferrite is investigated. Numerical results indicate a large differential phase shift on application of small magnetic fields when the easy plane is oriented normal to the waveguide axis. This suggests the possibility of application in ‘Remanence Operation’ at high frequencies. Work partially supported by CSIR (India).     

Asymmetric first-order Bragg interactions in an active dielectric waveguide

The asymmetric first-order Bragg interactions in an active planar dielectric waveguide are investigated for the case of even TE modes. Either the index or the gain is assumed to have a sinusoidal variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the nature of the Bragg interactions are systematically deduced and the characteristics of this instability are examined. For the gain-modulated waveguide having an average loss, there are two threshold values for the modulation index of the gain, one for absolute instability and the other for traveling wave amplification, and these threshold values are deduced. Representative numerical results are presented to illustrate the characteristics of the Bragg interactions.     

高阶非线性薛定谔方程的精确周期解和孤波解

本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应.     

The Reflection of electromagnetic waves from almost periodic structures

We investigate the reflection of electromagnetic waves from structures charaterized by a spatially varying dielectric permittivity of an almost periodic nature. The reflection from almost periodic structures is compared and contrasted with the reflection from periodic structures. Paradoxically, it is found that almost periodic structures may prove superior to their periodic counterparts when these structures are used as filters. The major portion of this work was performed while the author was with the California Institute of Technology, Pasadena, California 91125, USA     

Nonlinear wave propagation along periodic-loaded transmission line

A high frequency transmission line periodically loaded with varactor diodes is presented to study nonlinear wave propagation. The nonlinearity and dispersion characteristics are experimentally and theoretically analysed. Experimental results on shock wave formation and harmonic frequency generation are found to be in good agreement with theoretical predictions. The influence of dispersion on second-harmonic frequency generation is particularly discussed yielding large values of the efficiency.     

Harmonic wave propagation in an infinite viscoelastic medium with a periodic array of cylindrical elastic fibers

The work involves the propagation of plane harmonic waves in an infinite isotropic medium in which a doubly periodic array of cylindrical fibers is embedded. The direction of propagation is perpendicular to the fibers and the matrix material is taken to be viscoelastic in shear, modeled through hereditary integrals. A finite element method based on Galerkin's technique is employed, which leads to a non-linear eigenvalue problem. An iterative scheme is used to obtain two modes of dispersion, for both real and imaginary wave numbers, for a specific composite.     

Nonlinear localized waves in a periodic medium

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.     

Liquids in a periodic medium: Commensurability effects

The inhomogeneous version of the Percus-Yevick theory is used to study the static properties (pair correlations, structure factor, density distribution) of a one-dimensional liquid embedded in a periodic medium. Thedc-conductivity based on a dynamical model of strongly damped Brownian particles is also investigated. The numerical calculations performed over a wide range of temperatures, interaction strengths, and average densities show the onset of commensurability effects in the static and dynamic quantities.The results are compared with those based on the homogeneous version of the Percus-Yevick theory. The range of validity of this considerably simpler treatment is estimated.     

Coupled flexural-longitudinal wave motion in a periodic beam

Periodic structure theory is used to study the interactions between flexural and longitudinal wave motion in a beam (representing a plate) to which offset spring-mounted masses (representing stiffeners) are attached at regular intervals. An equation for the propagation constants of the coupled waves is derived. The response of a semi-infinite periodic beam to a harmonic force or moment at the finite end is analyzed in terms of the characteristic free waves corresponding to these propagation constants. Computer results are presented which show how the propagation constants are affected by the coupling, and how the forced response varies with distance from the excitation point. The spring-mounted masses can provide very high attenuation of both longitudinal and flexural waves when no coupling is present, but when coupling is introduced the two waves combine to give very low (or zero) attenuation of the longitudinal wave. The influence of different damping levels on spatial attenuation is also studied.