This Review explains the concept of dissipative solitons and their application to high-energy mode-locked fibre laser cavities. Dynamics and effects such as dissipative soliton ‘explosions’ and ‘rain’ are summarized, and an outlook of the field is also provided.

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Dissipative solitons for mode-locked lasers

Dark optical solitons: physics and applications

Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

https://science.sciencemag.org/content/sci/286/5444/1518.full.pdf

Optical Spatial Solitons and Their Interactions: Universality and Diversity.

Dissipative solitons

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrodinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

http://www.physics.sfsu.edu/~laser/pdf/rop347172p20.pdf

Optical spatial solitons: historical overview and recent advances

Soliton solutions of the one-dimensional (1D) complex Ginzburg-Landau equations (CGLE) are analyzed. We have developed a simple approach that applies equally to both the cubic and the quintic CGLE. This approach allows us to find an extensive list of soliton solutions of the CGLE, and to express all these solutions explicitly. In this way, we were able to classify them clearly. We have found and analyzed the class of solutions with fixed amplitude, revealed its singularities, and obtained a class of solitons with arbitrary amplitude, as well as some other special solutions. The stability of the solutions obtained is investigated numerically.

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Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation

Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation (CGLE) are analyzed for the case of normal group-velocity dispersion Exact soliton solutions are found for both the cubic and the quintic CGLE The stability of these solutions is investigated numerically The regions in the parameter space in which stable pulselike solutions of the quintic CGLE exist are numerically determined These regions contain subspaces where analytical solutions may be found An investigation of the role of group-velocity dispersion changes in magnitude and sign on the spectral and temporal characteristics of the stable pulse solutions is also carried out

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Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion

We performed a detailed investigation of the stability of analytic pulselike solutions of the quintic complex Ginzburg–Landau equation that describes the dynamics of the field in a passively mode-locked laser. We found that in general they are unstable except in a few special cases. We also obtained regions in the parameter space in which stable pulse solutions exist. These stable solutions do not have analytical expressions and must be calculated numerically. We compared and connected the regions in which stable solitonlike solutions exist with the lines for which we had analytical solutions.

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Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation

Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation.

We report numerical observation of two new forms of stable localized solutions of the quintic complex Ginzburg-Landau equation. The first form is a stationary zero-velocity solution, which consists of two motionless fronts and a source between them. We call this structure the ``composite'' pulse. We show that in some range of parameters, a composite pulse can coexist with a plain pulse solution. At the boundary of their region of existence in the parameter space, composite pulses exhibit a complicated behavior, which includes periodical dynamics and transition into another new form of localized solutions, namely, uniformly translating, or moving pulses. A careful study shows that the moving pulses have an even wider range of existence than the composite pulses. The interactions between different combinations of moving and stationary pulses are also studied. A qualitative explanation of the observed structures is proposed. \textcopyright{} 1996 The American Physical Society.

/pdf/three-forms-of-localized-solutions-of-the-quintic-complex-4cqzlzonf1.pdf

V. V. Afanasjev

Papers

Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation

Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion

Stability of the pulselike solutions of the quintic complex Ginzburg-Landau equation

Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation.

Three forms of localized solutions of the quintic complex Ginzburg-Landau equation