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We analyze the effect of transverse inhomogeneity on nonlinear beam propagation in a dielectric medium. Specifically, we consider the propagation of both CW beams and pulses in optical waveguides possessing a real nonlinear refractive index of the form n=n1 ( ̄r,?) + n2|E|2. The CW problem is treated within the paraxial approximation, for the case of a Gaussian beam incident on-axis. For powers lower than the homogeneous medium critical power, waveguiding dominates, and the beam focal parameter, although altered quantitatively, continues to vary sinusoidally as a function of distance as in the linear waveguide case, with a spectral period independent of the nonlinearity. Above the critical power, however, waveguiding is superceded and nonlinearity dominates. The beam becomes unstable, and displays oscillatory focussing in a fashion which is very similar to self-focussing in homogeneous media. Our pulse propagation studies employ a rather different starting point, based on the slowly varying envelope approximation and involving an averaging over the transverse coordinates. Our principal objective is to determine the conditions for undistorted pulse propagation, i.e., the existence of optical solitons. We obtain the equations governing the existence of solitons and find that they differ significantly from those for the homogeneous medium case. In particular, while "bright" soliton propagation is restricted to the anomolous dispersion regime in homogeneous media, in waveguides it is possible to propagate "bright" solitons in regimes of normal dispersion as well.
Fundamentals of Optical Waveguides is an essential resource for any researcher, professional or student involved in optics and communications engineering. Any reader interested in designing or actively working with optical devices must have a firm grasp of the principles of lightwave propagation. Katsunari Okamoto has presented this difficult technology clearly and concisely with several illustrations and equations. Optical theory encompassed in this reference includes coupled mode theory, nonlinear optical effects, finite element method, beam propagation method, staircase concatenation method, along with several central theorems and formulas. Since the publication of the well-received first edition of this book, planar lightwave circuits and photonic crystal fibers have fully matured. With this second edition the advances of these fibers along with other improvements on existing optical technologies are completely detailed. This comprehensive volume enables readers to fully analyze, design and simulate optical atmospheres. Exceptional new chapter on Arrayed-Waveguide Grating (AWG) In-depth discussion of Photonic Crystal Fibers (PCFs) Thorough explanation of Multimode Interference Devices (MMI) Full coverage of polarization Mode Dispersion (PMD)
Although the theory and principles of optical waveguides have been established for more than a century, the technologies have only been realized in recent decades. Optical Waveguides: From Theory to Applied Technologies combines the most relevant aspects of waveguide theory with the study of current detailed waveguiding technologies, in particular, photonic devices, telecommunication applications, and biomedical optics. With self-contained chapters written by well-known specialists, the book features both fundamentals and applications. The first three chapters examine the theoretical foundations and bases of planar optical waveguides as well as critical optical properties such as birefringence and nonlinear optical phenomena. The next several chapters focus on contemporary waveguiding technologies that include photonic devices and telecommunications. The book concludes with discussions on additional technological applications, including biomedical optical waveguides and the potential of neutron waveguides. As optical waveguides play an increasing part in modern technology, photonics will become to the 21st century what electronics were to the 20th century. Offering both novel insights for experienced professionals and introductory material for novices, this book facilitates a better understanding of the new information era—the photonics century.
Theory of Dialectric Optical Waveguides, Second Edition focuses on the practical usage of optical waveguides. This book explores the rapid growth of integrated optics, which is devoted to the development of microscopic optical circuits based on thin film technology. Organized into nine chapters, this edition starts with an overview of the properties of dielectric slab waveguides. This book then examines the theory of directional couplers with and without diffraction gratings. Other chapters describe the numerical methods for solving guided mode as well as wave propagation problems. This text discusses as well the beam propagation method and the popular effective refractive index method. The final chapter deals with the significance of nonlinear phenomena. This book is a valuable resource for undergraduate and graduate students of physics and electrical engineering. Practicing engineers and scientists in the fields of integrated optics, optical communications, and fiber sensors will find this book extremely useful.
Theory of Dielectric Optical Waveguides
The basic of the BPM technique in the frequency domain relies on treating the slowly varying envelope of the monochromatic electromagnetic field under paraxial propagation, thus allowing efficient numerical computation in terms of speed and allocated memory. In addition, the BPM based on finite differences is an easy way to implement robust and efficient computer codes. This book presents several approaches for treating the light: wide-angle, scalar approach, semivectorial treatment, and full vectorial treatment of the electromagnetic fields. Also, special topics in BPM cover the simulation of light propagation in anisotropic media, non-linear materials, electro-optic materials, and media with gain/losses, and describe how BPM can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectional-BPM. BPM in the time domain is also described, and the book includes the powerful technique of finite difference time domain method, which fills the gap when the standard BPM is no longer applicable. Once the description of these numerical techniques have been detailed, the last chapter includes examples of passive, active and functional integrated photonic devices, such as waveguide reflectors, demultiplexers, polarization converters, electro-optic modulators, lasers or frequency converters. The book will help readers to understand several BPM approaches, to build their own codes, or to properly use the existing commercial software based on these numerical techniques.
This book is subdivided into three main Parts. The common spirit in these parts is to provide, at the beginning of each, a comprehensive introduction into the subject treated, followed by specific aspects pertaining to the modelling and/or measuring particularities arlsmg from the investigation of photonic devices for telecommunications. Some of the devices treated here can be considered as widely known and well established. Others are rather new and their potential for applications is not yet fully exploited. The methods to model and measure photonic in this book and the comparison of results obtained devices and structures outlined by applying such methods are likely to interest both the engineer investigating the of a device in a system and the engineer looking for new ways to explore behaviour the possibilities offered by emerging devices. Many authors have contributed to this book. There are two main reasons for this. in photonic device research, modelling First, the book addresses two broad fields and measurements, for which a vast knowledge exists in many research groups that was not integrated in a book before. Second, a significant number of laboratories decided to closely co-operate in order to gain additional information on merits and drawbacks of their own methods for simulation and experimentation of devices as compared to the methods used by their colleagues in other laboratories. The outcome are new aspects and approaches that would not have been investigated in the absence of a framework for a co-operative programme.