The dynamics of a broad-area vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback
supporting bistable spatial solitons is analyzed experimentally and theoretically. The transient dynamics of a
switch-on of a soliton induced by an external optical pulse shows strong self-pulsing at the external-cavity round-trip
time with at least ten modes excited. The numerical analysis indicates an even broader bandwidth and a
transient sweep of the center frequency. It is argued that mode-locking of spatial solitons is an interesting and
viable way to achieve three-dimensional, spatio-temporal self-localization and that the transients observed are
preliminary indications of a transient cavity light bullet in the dynamics, though on a non negligible background.
The dynamics of free and optically induced decay of quasi-one-dimensional atomic Bose-Einstein condensates (BECs) is considered. The main characteristics of BEC modulation instability were found and compared for the cases of local and non-local interatomic interaction potential. The dynamics of BEC decay was studied numerically for the cases of positive and negative scattering length, absence or presence of optical standing wave, and for different shapes of initial BEC density distribution.
Spontaneous spatial patterns occur in nonlinear systems with spatial coupling, e.g. through diffraction or diffusion. Strong enough nonlinearity can induce spatial symmetry breaking, such that a pattern becomes more stable than the unpatterned state. Instances discussed are in nonlinear optics, but the phenomena have a universal character, and are the basis of spatial differentiation in nature, from crystals to clouds, from giraffe-coats to galaxies. The basic theory and phenomena of pattern formation are reviewed, with examples from experiments and simulations (mainly from optics). Patterns usually consist of repeated units, and such units may exist in isolation as a localized structure. Such structures are akin to spatial solitons, and are potentially useful in image and/or information processing. The nature and properties of such structures are discussed and illustrated.
Spatial solitons in cavities are being investigated with a view to applications in parallel information processing. This paper discusses the nature, experimental demonstration, and control of spatial solitons in cavities. Properties of interest for information processing are identified.
Optical cavities, including semiconductor microresonators, are predicted to support stable 2D cavity solitons. The cavity must contain a nonlinear material, but that material need not itself support solitons. The nature and properties of such cavity solitons, including optical control and manipulation, are discussed and novel array processing schemes taking advantage of their unique features are proposed.
Hexagonal structures have been observed and predicted in a number of nonlinear optical systems. After a brief general review of the field, the case of a slice of Kerr medium with single feedback mirror is analyzed in some detail. Its analogy to liquid-crystal light valve systems with feedback loop is noted. Recent experimental results are mentioned, and analytical results based on symmetry analysis are presented, along with simulations, for the practically important case of Gaussian beam excitation.
Thresholds of transverse instabilities arising from the mutual interaction of counterpropagating waves in a slab of Kerr medium without any cavity or mirror feedback are calculated from first principles, allowing for the effects of diffusion on the longitudinal index grating and for the field polarization. It is shown that the amplitude and polarization instabilities decouple in the linear limit under rather general conditions. Static polarization instabilities may have lowest threshold for finite transverse wave vector or on axis, depending on the Kerr constants. Analytic expressions are presented for the latter case. Numerical simulations show hexagon formation, consistent with related experiments.