Rem Viktorovich Khokhlov (Obituary)

Akhmanov, S. A.; Basov, N G; Voronin, É S; Gaponov, A V; Kadomtsev, B. B.; Keldysh, L. V.; Logunov, A. A.; Migulin, V. V.; Prokhorov, Anton M.; Rytov, S. M.; Stel'makh, M F; Ternov, I M; Fursov, V S; Yakovlev, I. A.

doi:10.1070/pu1978v021n02abeh005523

Cited by 6 publications

(8 citation statements)

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“…Here we report on the discovery of a new type of oscillation within high-finesse nonlinear cavities driven by Gaussian beams. This optical whistle oscillation occurs as a competition between spatial soliton formation [8] [9] and the driving input, and can exhibit oscillatory or chaotic behavior.…”

Section: Introductionmentioning

confidence: 99%

Transverse oscillation arising from spatial soliton formation in nonlinear optical cavities

Boyce

Chiao

1999

Phys. Rev. A

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A new type of transverse instability in dispersively nonlinear optical cavities, called the optical whistle, is discussed. This instability occurs in the mean field, soliton forming limit when the cavity is driven with a finite width Gaussian beam, and gives rise to oscillation, period doubling, and chaos. It is also seen that bistability is strongly affected due to the oscillation within the upper transmission branch. The phenomenon is interpreted as a mode mismatch in the soliton formation process and is believed to have broad applicability.

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Section: Introductionmentioning

confidence: 99%

Transverse oscillation arising from spatial soliton formation in nonlinear optical cavities

Boyce

Chiao

1999

Phys. Rev. A

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“…Rigorous proofs of the point-wise convergence, as ε → 0, of solutions of the 1D-NLSE (1) to the solutions of the dispersionless system (16) with the same initial data, prior to the formation of gradient catastrophe, can be found for certain classes of initial data in [52] (defocussing) and in [53,54] (focussing). Some important particular exact solutions of system (16) for the focusing case have been found as early as in 1960-70s (see [55][56][57]). A detailed mathematical analysis of the pre-breaking dynamics in the defocusing case can be found in [47] (see also [58] for the special case of the wave breaking into vacuum).…”

Section: The Dispersionless Limit Of the 1d-nlse And The Time Evomentioning

confidence: 99%

Early stage of integrable turbulence in the one-dimensional nonlinear Schrödinger equation: A semiclassical approach to statistics

Roberti

Randoux

et al. 2019

Phys. Rev. E

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We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrödinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially coherent waves having Gaussian statistics at time t = 0. Using short time asymptotic expansions and taking advantage of the scale separation in the semiclassical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the "tailedness" of the probability density function. Our results show excellent agreement with numerical simulations of the full 1D-NLSE random field dynamics and provide insight into the emergence of the well-known phenomenon of heavy (resp. low) tails of the statistical distribution emerging in the focusing (resp. defocusing) regime of 1D-NLSE.

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“…The dark-dark, bright-bright and dark-bright soliton pair solutions of these Manakov equations can be obtained under appropriate bias and photovoltaic fields [117]. With the growing applications of self focusing and spatial solitons in modern technology, several mathematical methods have evolved to address soliton dynamics [124][125][126][127][128][129]. In particular, Christodoulides et.…”

Section: Coupled Solitary Wave Equations Due To Single Photon Phenomenonmentioning

confidence: 99%

“…For a pair of nondiverging solitons at ξ = 0, we should have f j = 1 and dfj dξ = 0. Substituting for Ψ j and Ω j in (88), using paraxial ray approximation [86,126,127] and equating coefficients of s 2 from both sides of (88), we obtain…”

Section: Missing Bright Screening Pv Solitonsmentioning

confidence: 99%

Incoherent spatial optical solitons in photorefractive crystals

Konar

Jovanoski

Towers

2011

Optics & Laser Technology

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a b s t r a c tIn this paper we have presented a theoretical investigation on the propagation properties of incoherent solitons in photorefractive media which is characterized by noninstantaneous saturating nonlinearity. Using mutual coherence function approach, we have obtained the equation of existence curve for such solitons. We have discussed the coherence characteristics of these solitons. We have found that solitons with a particular radius can possess two different critical powers. The dynamical evolution of these solitons has been discussed in detail by both analytical and numerical simulation.

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Rem Viktorovich Khokhlov (Obituary)

Cited by 6 publications

References 0 publications

Transverse oscillation arising from spatial soliton formation in nonlinear optical cavities

Transverse oscillation arising from spatial soliton formation in nonlinear optical cavities

Early stage of integrable turbulence in the one-dimensional nonlinear Schrödinger equation: A semiclassical approach to statistics

Incoherent spatial optical solitons in photorefractive crystals

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