Few-cycle optical solitary waves in nonlinear dispersive media

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons

Sasa-Satsuma hierarchy of integrable evolution equations

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixth-order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.The authors gratefully acknowledge the support of the Australian Research Council (Discovery Projects DP140100265 and DP150102057) and support from the Volkswagen Stiftung. N.A. is a recipient of the Alexander von Humboldt Award. U.B. acknowledges support by the German Research Foundation in the framework of the Collaborative Research Center 787 “Semiconductor Nanophotonics” under project B5. Sh.A. acknowledges support of the German Research Foundation under Project No. 389251150

Radiometric force in dusty plasmas

A radiofrequency glow discharge plasma, which is polluted with a certain number of dusty grains, is studied. In addition to various dusty plasma phenomena, several specific colloidal effects should be considered. We focus on radiometric forces, which are caused by inhomogeneous temperature distribution. Aside from thermophoresis, the role of temperature distribution in dusty plasmas is an open question. It is shown that inhomogeneous heating of the grain by ion flows results in a new photophoresis like force, which is specific for dusty discharges. This radiometric force can be observable under conditions of recent microgravity experiments.Comment: 4 pages, amsmat

A for-loop is all you need. For solving the inverse problem in the case of personalized tumor growth modeling

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity of finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression (Schmidhuber and Fridman, 2018), we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow. The code is available at https://github.com/IvanEz/for-loop-tumor

Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion

We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity

Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion

We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity

Dispersion of nonlinear group velocity determines shortest envelope solitons

We demonstrate that a generalized nonlinear Schrödinger equation (NSE), which includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge t

Few-cycle Solitons that do not want to be too short in duration

We review recent achievements in theory of ultrashort optical pulses propagating in nonlinear fibers. In particular we are interested in the shortest duration (the highest peak power) of an optical soliton. Optical solitons are found to cannot go beyond the critical single-cycle duration even for the most favorable medium dispersion. A formation of singular cusps prohibits the existence of too short solitons, which seems to be unavoidable universal feature of bright solitons.Sh.A. and U.B. gratefully acknowledge support by The Einstein Center for Mathematics Berlin, MATHEON, under Project D-OT2

Recent progress in theory of nonlinear pulse propagation in optical fibers

We review recent achievements in theory of ultra-short optical pulses propagating in nonlinear fibers. The following problem is especially emphasized: what is the shortest duration (the highest peak power) of an optical soliton and which physical phenomenon is responsible for breakdown of too short pulses. We argue that there is an universal mechanism that destroys sub-cycle solitons even for the most favorable dispersion profile