Download or read book Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves written by Gadi Fibich and published by . This book was released on 2002 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-20 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering. Fibich, G. and Ilan, B. and Tsynkov, S. Langley Research Center NASA/CR-2002-211764, NAS 1.26:211764, ICASE-2002-30

Download or read book The Nonlinear Schr dinger Equation written by Gadi Fibich and published by Springer. This book was released on 2015-03-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Self focusing Past and Present written by Robert W. Boyd and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-focusing has been an area of active scientific investigation for nearly 50 years. This book presents a comprehensive treatment of this topic and reviews both theoretical and experimental investigations of self-focusing. This book should be of interest to scientists and engineers working with lasers and their applications. From a practical point of view, self-focusing effects impose a limit on the power that can be transmitted through a material medium. Self-focusing also can reduce the threshold for the occurrence of other nonlinear optical processes. Self-focusing often leads to damage in optical materials and is a limiting factor in the design of high-power laser systems. But it can be harnessed for the design of useful devices such as optical power limiters and switches. At a formal level, the equations for self-focusing are equivalent to those describing Bose-Einstein condensates and certain aspects of plasma physics and hydrodynamics. There is thus a unifying theme between nonlinear optics and these other disciplines. One of the goals of this book is to connect the extensive early literature on self-focusing, filament-ation, self-trapping, and collapse with more recent studies aimed at issues such as self-focusing of fs pulses, white light generation, and the generation of filaments in air with lengths of more than 10 km. It also describes some modern advances in self-focusing theory including the influence of beam nonparaxiality on self-focusing collapse. This book consists of 24 chapters. Among them are three reprinted key landmark articles published earlier. It also contains the first publication of the 1964 paper that describes the first laboratory observation of self-focusing phenomena with photographic evidence.

Download or read book Optical Tweezers written by Philip H. Jones and published by Cambridge University Press. This book was released on 2015-12-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the theory, practice and applications of optical tweezers, combining state-of-the-art research with a strong pedagogic approach.

Download or read book High order Two way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering written by Gadi Fibich and published by . This book was released on 2000 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Download or read book Optical Fiber Sensor Technology written by L.S. Grattan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Environmental and chemical sensors in optical fiber sensor technology The nature of the environment in which we live and work, and the precarious state of many aspects of the natural environment, has been a major lesson for scientists over the last few decades. Public awareness of the issues involved is high, and often coupled with a scepticism of the ability of the scientist and engineer to provide an adequate, or even rapid solution to the preservation of the environment before further damage is done, and to achieve this with a mini mum of expenditure. Monitoring of the various aspects of the environment, whether it be external or internal to ourselves and involving chemical, physical or biomedical parameters is an essential process for the well-being of mankind and of the individual. Legis lative requirements set new standards for measurement and control all around us, which must be met by the most appropriate of the technologies available, commensurate with the costs involved. Optical fiber sensor technology has a major part to play in this process, both to complement existing technologies and to promote new solutions to difficult measurement issues. The developments in new sources and detectors covering wider ranges of the electromagnetic spectrum, with higher sensitivity, allow the use of techniques that some time ago would have been considered inappropriate or lacking in sufficient sensitivity.

Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Download or read book Physics Briefs written by and published by . This book was released on 1991 with total page 1132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sound Propagation written by Yang-Hann Kim and published by John Wiley & Sons. This book was released on 2010-08-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Sound Propagation: An Impedance Based Approach, Professor Yang-Hann Kim introduces acoustics and sound fields by using the concept of impedance. Kim starts with vibrations and waves, demonstrating how vibration can be envisaged as a kind of wave, mathematically and physically. One-dimensional waves are used to convey the fundamental concepts. Readers can then understand wave propagation in terms of characteristic and driving point impedance. The essential measures for acoustic waves, such as dB scale, octave scale, acoustic pressure, energy, and intensity, are explained. These measures are all realized by one-dimensional examples, which provide mathematically simplest but clear enough physical insights. Kim then moves on to explaining waves on a flat surface of discontinuity, demonstrating how propagation characteristics of waves change in space when there is a distributed impedance mismatch. Next is a chapter on radiation, scattering, and diffraction, where Kim shows how these topics can be explained in a unified way, by seeing the changes of waves due to spatially distributed impedance. Lastly, Kim covers sound in closed space, which is considered to be a space that is surrounded by spatially distributed impedance, and introduces two spaces: acoustically large and small space. The bulk of the book is concerned with introducing core fundamental concepts, but the appendices are included as the essentials as well to cover other important topics to extend learning. Offers a less mathematically-intensive means to understand the subject matter Provides an excellent launching point for more advanced study or for review of the basics Based on classroom tested materials developed over the course of two decades Companion site for readers, containing animations and MATLAB code downloads Videos and impedance data available from the author's website Presentation slides available for instructor use Sound Propagation is geared towards graduate students and advanced undergraduates in acoustics, audio engineering, and noise control engineering. Practicing engineers and researchers in audio engineering and noise control, or students in engineering and physics disciplines, who want to gain an understanding of sound and vibration concepts, will also find the book to be a helpful resource.

Download or read book Atom Chips written by Jakob Reichel and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This stimulating discussion of a rapidly developing field is divided into two parts. The first features tutorials in textbook style providing self-contained introductions to the various areas relevant to atom chip research. Part II contains research reviews that provide an integrated account of the current state in an active area of research where atom chips are employed, and explore possible routes of future progress. Depending on the subject, the length of the review and the relative weight of the 'review' and 'outlook' parts vary, since the authors include their own personal view and style in their accounts.

Download or read book The Electric Furnace written by Henri Moissan and published by . This book was released on 1904 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optical Antennas written by Mario Agio and published by Cambridge University Press. This book was released on 2013-01-03 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This consistent and systematic review of recent advances in optical antenna theory and practice brings together leading experts in the fields of electrical engineering, nano-optics and nano-photonics, physical chemistry and nanofabrication. Fundamental concepts and functionalities relevant to optical antennas are explained, together with key principles for optical antenna modelling, design and characterisation. Recognising the tremendous potential of this technology, practical applications are also outlined. Presenting a clear translation of the concepts of radio antenna design, near-field optics and field-enhanced spectroscopy into optical antennas, this interdisciplinary book is an indispensable resource for researchers and graduate students in engineering, optics and photonics, physics and chemistry.

Download or read book Gratings Theory and Numeric Applications written by and published by Popov, Institut Fresnel. This book was released on with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Label Free Super Resolution Microscopy written by Vasily Astratov and published by Springer Nature. This book was released on 2019-08-31 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the advances in super-resolution microscopy in physics and biomedical optics for nanoscale imaging. In the last decade, super-resolved fluorescence imaging has opened new horizons in improving the resolution of optical microscopes far beyond the classical diffraction limit, leading to the Nobel Prize in Chemistry in 2014. This book represents the first comprehensive review of a different type of super-resolved microscopy, which does not rely on using fluorescent markers. Such label-free super-resolution microscopy enables potentially even broader applications in life sciences and nanoscale imaging, but is much more challenging and it is based on different physical concepts and approaches. A unique feature of this book is that it combines insights into mechanisms of label-free super-resolution with a vast range of applications from fast imaging of living cells to inorganic nanostructures. This book can be used by researchers in biological and medical physics. Due to its logically organizational structure, it can be also used as a teaching tool in graduate and upper-division undergraduate-level courses devoted to super-resolved microscopy, nanoscale imaging, microscopy instrumentation, and biomedical imaging.

Download or read book Light Scattering Reviews 8 written by Alexander A. Kokhanovsky and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Light scattering review (vol 8) is aimed at the presentation of recent advances in radiative transfer and light scattering optics. The topics to be covered include: scattering of light by irregularly shaped particles suspended in atmosphere (dust, ice crystals), light scattering by particles much larger as compared the wavelength of incident radiation, atmospheric radiative forcing, astrophysical radiative transfer, radiative transfer and optical imaging in biological media, radiative transfer of polarized light, numerical aspects of radiative transfer.