Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures

Akhmanov, S. A.; Vorontsov, Mikhail A.; Ivanov, Vladimir; Larichev, A. V.; Zheleznykh, N. I.

doi:10.1364/josab.9.000078

Cited by 190 publications

(55 citation statements)

References 11 publications

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“…A typical nonlinear optical system with rich spatio-temporal dynamics comprises a thin layer of nonlinear Kerr medium and a ring cavity (feedback loop). Phase modulation in the nonlinear Kerr slice within an aperture Q & R 2 -real-valued function uðr; tÞ -is described by the following parabolic equation [2]: u t ðr; tÞ þ uðr; tÞ À DÁuðr; tÞ ¼ jA FB j 2 ; r 2 Q; t > 0; ð1:1Þ…”

Section: Introductionmentioning

confidence: 99%

Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction

Budzinskiy

2016

IIS

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We study a delayed parabolic functional differential equation on a circle that is coupled with an initial value problem for the Schrodinger equation. Such equations arise as models of nonlinear optical systems with a timedelayed feedback loop, when diffusion of molecular excitation and diffraction are taken into account. The goal of this paper is to prove the existence of spatially inhomogeneous rotating-wave solutions bifurcating from homogeneous equilibria. We pass to a rotating coordinate system and seek an inhomogeneous solution to an ordinary functional differential equation. We find the solution in the form of a small parameter expansion and explicitly compute the first-order coefficients. We also provide examples of parameters that satisfy the constraints imposed throughout the analysis.

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Section: Introductionmentioning

confidence: 99%

Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction

Budzinskiy

2016

IIS

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“…The direct time-resolved observation of the propagation of intensity femtosecond laser pulses experiencing SF, beam filamentation is investigated extensively [24][25][26]. Previously, we have observed the evolution of spatial modulation in the process of SSSF of a beam, the impact of relaxation effect in the media on spatial-temporal instability [27,28]. However, these studies mostly concentrate on the spatial evolution and temporal evolution independent.…”

Section: Introductionmentioning

confidence: 99%

Effect of Spatial Modulation on Pulse Width for Ultrashort Laser Pulse during Small-Scale Self-Focusing

Wang¹,

Fu²

2015

Proceedings of the 2015 International Power, Electronics and Materials Engineering Conference

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Abstract. Small-scale self-focusing (SSSF) causes the distribution of spatial intensity to become asymmetrical. Spatial distribution would generate new growth point during SSSF. We measure the spatial-temporal evolution for ultrashort laser pulse with different truncation parameter of knife-edge during SSSF. Our results show that the new growth point is increasingly far away from center of beam and its intensity increases with decrease of truncation parameter. Meanwhile, the pulse width at the growth point becomes narrower. We find that our experimental results are in good agreement with an approximate theoretical analysis.

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“…In one of these works (Ref. [24]) the emergence of turbulent-like behavior was associated with the excitation of many strongly interacting spatio-temporal structures, but the phenomenon was not analyzed quantitatively. In addition, direct mathematical links between dynamics in systems described by NLS and related models and dynamics observed in models of turbulent flow have been obtained in Refs.…”

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confidence: 99%

Energy exchange in fast optical soliton collisions as a random cascade model

Peleg

2009

Physics Letters A

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We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the τ q exponents from multifractal theory and by the Cramér function S(x). We find that the nth moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of τ q or S(x).

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Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures

Cited by 190 publications

References 11 publications

Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction

Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction

Effect of Spatial Modulation on Pulse Width for Ultrashort Laser Pulse during Small-Scale Self-Focusing

Energy exchange in fast optical soliton collisions as a random cascade model

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