We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.

Conservative and dissipative fiber Bragg solitons (a review)

The frequency dependence of the gain required to compensate for absorption is determined for a layered structure consisting of alternating absorbing and amplifying layers. It is shown that the fulfillment of the same conditions is required for the existence of a band structure consisting of alternating bands allowed and forbidden for optical radiation propagation in the frequency-wave vector parametric region. Conditions are found under which the gain required for compensation is smaller than thresholds for absolute (parasitic lasing) and convective (waveguide amplification of radiation) instabilities.

/pdf/band-structure-and-broadband-compensation-of-absorption-by-1vqk6j2xew.pdf

Band structure and broadband compensation of absorption by amplification in layered optical metamaterials

Spontaneous soliton motion has been demonstrated in different systems supporting cavity solitons. Here we consider the case of a semiconductor laser with an intracavity saturable absorber, and study the interactions between self-propelled solitons when two of them collide or when they hit a localised defect in the material gain. According to the soliton velocity and impact parameter, destructive or repulsive collisions may take place between travelling solitons. On the other hand, a very rich variety of dynamical behaviors can be observed when a travelling soliton hits a material defect of comparable size. We observe soliton destruction, repulsive or attractive interaction and two trapped cases. The behavior is mainly determined by the gain contrast between the defect and the background.

Self–propelled soliton collisions in a semiconductor cavity soliton laser

The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the switching waves connecting the states of different symmetries are studied numerically. It is shown that the switching waves can form stable resting and moving bound states (dissipative solitons). The protocols of the creation of the discussed nonlinear localized waves are suggested and verified by numerical simulations.

Dissipative switching waves and solitons in the systems with spontaneously broken symmetry.

This thesis focuses on a wide range of contemporary
topics in modern electromagnetics and technology including
topologically protected one-way modes, integrated photonic LIDAR,
and optical neural networks. First, we numerically investigate
large Chern numbers in photonic crystals and explore their origin
from simultaneously gapping multiple band degeneracies. Following
this, we perform microwave transmission measurements in the bulk
and at the edge of ferrimagnetic photonic crystals. Bandgaps with
large Chern numbers of 2, 3, and 4 are present in the experimental
results 'which show excellent agreement with theory. We measure the
mode profiles and Fourier transform them to produce dispersion
relations of the edge modes, whose number and direction match our
Chern number calculations. We use these waveguides to realize
reflectionless power splitters and outline their application to
general one-way circuits. Next we create a new chip-scale LIDAR
architecture in analogy to planar RF lenses. Instead of relying
upon many continuously tuned thermal phase shifters to implement
nonmechanical beam steering, we use aplanatic lenses excited in
their focal plane feeding ID gratings to generate discrete beams.
We design devices which support up to 128 resolvable points
in-plane and 80 resolvable points out-of-plane, which are currently
being fabricated and tested. These devices have many advantages
over conventional optical phased arrays including greatly increased
optical output power and decreased electrical power for in-plane
beamforming. Finally we explore a new approach for implementing
convolutional neural networks through an integrated photonics
circuit consisting of Mach-Zehnder Interferometers, optical delay
lines, and optical nonlinearity units. This new platform, should be
able to perform the order of a thousand inferences per second, at
[mu]J power levels per inference, with the nearest state of the art
ASIC and GPU competitors operating 30 times slower and requiring
three orders of magnitude more power.

Photonics for technology : circuits, chip-scale LIDAR, and optical neural networks

Motionless dissipative vector solitons are found numerically in a birefringent polarization-conserving optical fiber with a longitudinal Bragg grating and nonlinear amplification and absorption in the polarization capture regime. It is shown that dissipative vector Bragg solitons exist and are stable even if the birefringence is comparatively strong.

Dissipative vector Bragg solitons in a birefringent optical fiber

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Conservative and dissipative fiber Bragg solitons (a review)

Dissipative vector Bragg solitons in a birefringent optical fiber