Variational approach to nonlinear pulse propagation in optical fibers
TL;DR: In this paper, the problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schrodinger equation, is reformulated as a variational problem and approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp.
Abstract: The problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schr\"odinger equation, is reformulated as a variational problem. By means of Gaussian trial functions and a Ritz optimization procedure, approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp. Comparisons with results from inverse-scattering theory and/or numerically obtained solutions show very good agreement.
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TL;DR: The development of microresonator-generated frequency combs is reviewed to map out how understanding and control of their generation is providing a new basis for precision technology and establish a nascent research field at the interface of soliton physics, frequency metrology, and integrated photonics.
Abstract: The development of compact, chip-scale optical frequency comb sources (microcombs) based on parametric frequency conversion in microresonators has seen applications in terabit optical coherent communications, atomic clocks, ultrafast distance measurements, dual-comb spectroscopy, and the calibration of astophysical spectrometers and have enabled the creation of photonic-chip integrated frequency synthesizers. Underlying these recent advances has been the observation of temporal dissipative Kerr solitons in microresonators, which represent self-enforcing, stationary, and localized solutions of a damped, driven, and detuned nonlinear Schrodinger equation, which was first introduced to describe spatial self-organization phenomena. The generation of dissipative Kerr solitons provide a mechanism by which coherent optical combs with bandwidth exceeding one octave can be synthesized and have given rise to a host of phenomena, such as the Stokes soliton, soliton crystals, soliton switching, or dispersive waves. Soliton microcombs are compact, are compatible with wafer-scale processing, operate at low power, can operate with gigahertz to terahertz line spacing, and can enable the implementation of frequency combs in remote and mobile environments outside the laboratory environment, on Earth, airborne, or in outer space.
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...An approximate solution for the dissipative soliton may be found using Lagrangian perturbation approach [74, 75]....
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TL;DR: In this article, the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators is described and analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems.
Abstract: This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.
754 citations
TL;DR: In this paper, the collapse of self-focusing waves described by the nonlinear Schrodinger (NLS) equation and the Zakharov equations in nonlinear optics and plasma turbulence is reviewed.
641 citations
TL;DR: In this paper, a femtosecond laser pulse propagates in an optical medium, self-focusing occurs, and the most powerful part of the pulse self focuses first during its propagation.
Abstract: When a powerful femtosecond laser pulse propagates in an optical medium, self-focusing occurs. Normally, it is the most powerful part (slice) of the pulse that self-focuses first during its propaga...
559 citations
349 citations