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Stability Of Pulses In Nonlinear Optical Fibers Using Phase Sensitive Amplifiers
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Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages : pages Book Rating :4.:/5 (123 download)
Book Synopsis Stability of Pulses in Nonlinear Optical Fibers Using Phase-sensitive Amplifiers by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Stability of Pulses in Nonlinear Optical Fibers Using Phase-sensitive Amplifiers written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pulse Propagation in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers by :
Download or read book Pulse Propagation in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers written by and published by . This book was released on 1994 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical model for pulse propagation in a nonlinear fiber-optic communications line is presented where linear loss in the fiber is balanced by a chain of periodically-spaced, phase-sensitive amplifiers (PSAs). A multiple scale analysis is employed to average over the strong, rapidly-varying and periodic perturbations to the governing nonlinear Schrodinger equation (NLS). The analysis indicates that the averaged evolution is governed by a fourth-order nonlinear diffusion equation which evolves on a length scale much greater than that of the typical soliton period. In a particular limit, stable steady-state hyperbolic secant solutions of the averaged equation are analytically found to exist provided a minimum amount of over-amplification is supplied. Further, arbitrary initial conditions within a wide stability region exponentially decay onto the steady-state. Outside of this analytic regime, extensive numerical simulations indicate that soliton-like steady-states exist and act as exponential attractors for a wide region of parameter space. These simulations also show that the averaged evolution is quite accurate in modeling the full NLS with loss and phase-sensitive gain. The bifurcation structure of the fourth-order equation is explored. A subcritical bifurcation from the trivial solution is found to occur for a specific over-amplification value. Further, a limit point, or fold, is also found which connects the stable branch of solutions with the unstable branch from the subcritical bifurcation. The bifurcation structure can be further explored in parameter space with the use of AUTO which is capable of tracking steady-state solutions for a wide range of parameters.
Book Synopsis Stability of Pulses on Optical Fibers with Phase Sensitive Amplifiers by :
Download or read book Stability of Pulses on Optical Fibers with Phase Sensitive Amplifiers written by and published by . This book was released on 1995 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Stability and Dynamics of Optical Waveguides, Lasers, and Amplifiers by :
Download or read book The Stability and Dynamics of Optical Waveguides, Lasers, and Amplifiers written by and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specifically, we have investigated mathematically the dynamics of pulses in nonlinear optical fibers, helped design a highly-stable 60 GHz soliton source, investigated methods for controlling solitons using phase-sensitive amplifiers (PSAs), modeled the application of PSAs to optical storage loops and other optical devices, studied timing jitter in mode-locked erbium fiber lasers, and explored a new method for controlling streams of high-speed optical pulses using periodic optical phase conjugation.
Book Synopsis Existence and Stability of Multi-pulses with Applications to Nonlinear Optics by : Vahagn Emil Manukian
Download or read book Existence and Stability of Multi-pulses with Applications to Nonlinear Optics written by Vahagn Emil Manukian and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In the present work we study the existence and stability of multi-pulses in dynamical systems that arise as traveling-wave equations for a partial differential equation (PDE) with symmetries. The motivation comes from two different models that describe the propagation of pulses in optical fibers. In the first part of the thesis we consider reversible, Z2 symmetric dynamical systems with heteroclinic orbits related via symmetries. The heteroclinic orbits are assumed to undergo an orbit flip bifurcation upon changing appropriate parameters. We construct multi-bump solutions close to the heteroclinic orbits and investigate their PDE stability by using Lin's method and Lyapunov-Schmidt reduction. We apply this abstract theory to a model equation that describes the propagation of pulses in optical fibers with phase sensitive amplifiers. Our results show that stable multi-pulses exist. In the second part we consider parameter-dependent dynamical systems with reflection and SO(2) symmetry, which possess a homoclinic solution to a saddle focus. The reflection symmetry is broken by the second parameter which plays the role of the wave speed. We derive the bifurcation equations for the existence of N-pulse solutions and solve them for N = 3. As a result we obtain standing and traveling 3-pulse solutions which we describe through the phase differences and the distances between consecutive bumps. We also investigate stability of these 3-pulses. We derive the stability matrix for multi-bump solutions and compute to the leading order the location of the eigenvalues for the 3-pulses.
Book Synopsis Computational Wave Propagation by : Bjorn Engquist
Download or read book Computational Wave Propagation written by Bjorn Engquist and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications COMPUTATIONAL WAVE PROPAGATION is based on the workshop with the same title and was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Bjorn Engquist and Gregory A. Kriegsmann for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the Office of Naval Research, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE Although the field of wave propagation and scattering has its classical roots in the last century, it has enjoyed a rich and vibrant life over the past 50 odd years. Scientists, engineers, and mathematicians have devel oped sophisticated asymptotic and numerical tools to solve problems of ever increasing complexity. Their work has been spurred on by emerging and maturing technologies, primarily concerned with the propagation and reception of information, and the efficient transmission of energy. The vitality of this scientific field is not waning. Increased demands to precisely quantify, measure, and control the propagation and scattering of waves in increasingly complex settings pose challenging scientific and mathematical problems. These push the envelope of analysis and comput ing, just as their forerunners did 50 years ago. These modern technological problems range from using underwater sound to monitor and predict global warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure long range digital communication.
Book Synopsis Spectral and Dynamical Stability of Nonlinear Waves by : Todd Kapitula
Download or read book Spectral and Dynamical Stability of Nonlinear Waves written by Todd Kapitula and published by Springer Science & Business Media. This book was released on 2013-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Dynamical Systems by : B. Fiedler
Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
Book Synopsis Pulse Propagation in Nonlinear Optical Fibers Using Phrase-sensitive Amplifiers by : Jose Nathan Kutz
Download or read book Pulse Propagation in Nonlinear Optical Fibers Using Phrase-sensitive Amplifiers written by Jose Nathan Kutz and published by . This book was released on 19?? with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation by : Alfredo Berm?dez
Download or read book Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation written by Alfredo Berm?dez and published by SIAM. This book was released on 2000-01-01 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.
Book Synopsis Nonlinear Dynamics and Chaos by : J Hogan
Download or read book Nonlinear Dynamics and Chaos written by J Hogan and published by CRC Press. This book was released on 2002-08-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys
Download or read book Optics Letters written by and published by . This book was released on 1996 with total page 1326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Shaping Light in Nonlinear Optical Fibers by : Sonia Boscolo
Download or read book Shaping Light in Nonlinear Optical Fibers written by Sonia Boscolo and published by John Wiley & Sons. This book was released on 2017-03-15 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area. The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.
Book Synopsis Discrete and Continuous Dynamical Systems by :
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2004 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Localization And Solitary Waves In Solid Mechanics by : Alan R Champneys
Download or read book Localization And Solitary Waves In Solid Mechanics written by Alan R Champneys and published by World Scientific. This book was released on 1999-11-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.
Book Synopsis Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference by :
Download or read book Summaries of Papers Presented at the Quantum Electronics and Laser Science Conference written by and published by . This book was released on 2005 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt:
