Signal Flow Analysis

Signal flow graphs are a viable alternative to block diagrammatic representation of a system. What makes signal flow graphs attractive is that certain features from graph theory can be applied to the simplification and the synthesis of complex systems

Guest Editorial: Special Section on Photorefractive Nonlinear Optics

Hand in hand with experimental work in photorefractives, there is a lot of activity in modeling photorefractive materials and experimental observations in the open literature. This special section contains a paper by Banerjee and Jarem, who use a rigorous coupled wave theory to analyze two- and multiple-wave mixing photorefractive barium titanate, modeled through the Kukhtarev equations

Study of Soliton Stabilization in D+1 Dimensions using Novel Analytical and Numerical Techniques

In this Chapter, we provide a brief review of the underlying nonlinear Schrödinger and associated equations that model spatio-temporal propagation in one and higher dimensions in a nonlinear dispersive environment. Particular attention is given to fast adaptive numerical techniques to solve such equations, and in the presence of dispersion and nonlinearity management, saturating nonlinearity and nonparaxiality. A unique variational approach is also outlined which helps in determining the ranges of nonlinearity and dispersion parameters to ensure stable solutions of the nonlinear equations. The propagation of 3+1 dimensional spatio-temporal pulses, or optical bullets is also modeled using a fast adaptive split-step Hankel transform technique

Subharmonic Generation by Resonant Three‐Wave Interaction of Deep‐Water Capillary Waves

Subharmonic generation has been observed during the propagation of deep‐water capillary waves. The observations are shown to be in agreement with the theory of degenerate resonant noncollinear three‐wave interaction in a nonlinear, dispersive medium

Analysis of Multifrequency Dispersive Optical Bistability and Switching in Nonlinear Ring Cavities with Large Medium-Response Times

Using a simple model of a ring cavity comprising a cubically nonlinear medium, we analyze dispersive optical bistability in the presence of more than one spectral component. We show the phenomenon of so-called competition for resonance. In addition to presenting cavity characteristics for the cases of two and three different frequencies, we also discuss the general method for finding steady-state solutions and checking their stability. A simple and efficient algorithm, based on a relaxation method, is devised to find steady-state solutions satisfying appropriate boundary conditions. The relaxation dynamics is physically related to a finite response time of the medium

Scalar EM Beam Propagation in Inhomogeneous Media

In the previous chapter, we reviewed some of the mathematical preliminaries that will be useful later on in the text. In this chapter, we discuss some of the basic concepts of scalar wave propagation, and discuss an important numerical method, called the beam propagation method (BPM), to study propagation in linear media and in media with induced nonlinearities. Furthermore, we also discuss propagation through induced gratings, both transmission and reflection type, in order to assess energy coupling between participating waves. Finally, we introduce readers to an important characterization method, called the z-scan method, which is often used to determine the focal length of an induced lens

Guest Editorial: Special Section on Acousto-optic Devices and Optical Information Processing: Research and Developments

This guest editorial provides an overview of the topical area and an introduction to the articles featured in the special section

Modeling and Characterization of Adaptive Lanthanum-Modified Lead Zirconate Titanate (PLZT) Microlenses

We report the modeling and characterization of adaptive voltage controlled electro-optic microlenses. First, we utilize finite element analysis (FEA) to simulate the induced electro-optic effect in lanthanum-modified lead zirconate titanate (PLZT). FEA simulation provides microlens parameters such as phase and focal length. A simple z-scan method is developed to fully characterize the adaptive voltage controlled linear lens. Experimental z-scan results are shown to match the theoretical predictions from FEA

Examination of Energy and Group Velocities in Positive and Negative Index Chiral Materials with and without Dispersion

Concepts of energy and group velocities, Poynting and propagation vectors are examined for both positive and negative index materials. Known definitions for these entities are explored in terms of the interplay of chirality and dispersion

Consideration of Dispersion and Group Velocity Dispersion in the Determination of Velocities of Electromagnetic Propagation

Electromagnetic (EM) propagation velocities play an important role in the determination of power and energy flow in materials and interfaces. It is well known that group and phase velocities need to be in opposition in order to achieve negative refractive index. Recently, we have shown that considerable differences may exist in phase, group and signal/energy velocities for normal and anomalous dispersion, especially near dielectric resonances. This paper examines the phase and group velocities in the presence of normal and anomalous dispersion, and group velocity dispersion (GVD), which requires introduction of the second order coefficient in the permittivity and permeability models