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.

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

The investigation of nonlinear wave phenomena has been one of the main direc tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described.

Optical Solitons

A set of two coupled nonlinear Schrodinger equations (CNLS) describes the two mode propagation in an optical fibre. The Painleve singularity structure analysis singles out two integrable parametric choices, including the Manakov model. Using the results of Painleve analysis, we succeed in Hirota bilinearizing the CNLS equations in both the anomalous as well as normal dispersion regions for the integrable cases. Solving the Hirota bilinear equations, bright and dark N-soliton solutions are explicitly obtained.

https://iopscience.iop.org/article/10.1088/0305-4470/28/9/025/pdf

Bright and dark soliton solutions to coupled nonlinear Schrodinger equations

We present the first mixed-type solutions to the coupled nonlinear Schr\"odinger equations which govern optical pulse propagation in a birefringent fiber. These represent polarization-modulated pulses which, apart from the absolute phase, propagate unchanged in form. It is shown they are bound states of two solitary waves which separately have constant and uniform orthogonal linear polarizations. Furthermore, there exists a minimum-energy threshold for the formation of these bound states.

Bound solitary waves in a birefringent optical fiber.

We show that the instability threshold for a laser in which both polarizations are active can be much lower than the Haken second threshold and does not require the bad-cavity limit.

Low instability threshold in a laser operating in both states of polarization

We consider the polarization dynamics of a pulse propagating through an arbitrary nonlinear medium, in the limit of small nonlinearities, anisotropies, and dispersion, using the full SO(3) covariance of the Stokes parameters. The invariants of the motion are discovered and physically interpreted, a complete analogy with the ``airplane-and-rotor'' problem of rigid-body dynamics is established, and a full classification of the solutions for parity-invariant and non-parity-invariant media, with all propagation-axis rotation symmetries, is presented. In all cases, the problem is reduced to quadrature; in most cases, we find analytic solutions in terms of well-known functions.

M. V. Tratnik

Papers

Bound solitary waves in a birefringent optical fiber.

Low instability threshold in a laser operating in both states of polarization

Nonlinear polarization dynamics. I. The single-pulse equations

Nonlinear polarization dynamics. II. Counterpropagating-beam equations: New simple solutions and the possibilities for chaos.

Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams.