Stimulated Raman scattering in the transient limit

Hilfer, Godehard; Menyuk, Curtis R.

doi:10.1364/josab.7.000739

Cited by 41 publications

(18 citation statements)

References 15 publications

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“…As in two-wave SRS, 12,21,22 solitonic zero crossings (temporal locations where A n changes sign) are found to appear from large t and stack up to form a rapid train of short pulses. Figure 3 shows the soliton pulse trains generated with Gaussian input pulses when T 2 ͞t p 10.…”

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confidence: 78%

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains

McDonald

1995

Opt. Lett.

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confidence: 78%

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains

McDonald

1995

Opt. Lett.

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“…If B2 (&1 initially and we let Io(x) designate the modified Bessel function, we find mate to linearize the self-similar equation, Eq. (18) [10,23]. In this upper half of Fig.…”

Section: IVmentioning

confidence: 95%

“…While soliton solutions exist, they are always transient [20,21]. Numerical results [22,23] indicate that the evolution passes through three regimes: (1) an I regime in which the Stokes amplitude is small compared to the pump amplitude and grows exponentially, (2) a transition regime in which the Stokes and pump amplitudes are comparable, and (3) a J regime in which the pump amplitude is small compared to the Stokes amplitude and undergoes a slow algebraic decay -g ' . In the latter regime, toward which the system always tends, self-similar oscillations whose number is proportional to g' occur.…”

Section: Introductionmentioning

confidence: 92%

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Long-distance evolution in transient stimulated Raman scattering

1993

Phys. Rev. A

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Systems that exhibit stimulated Raman scattering in the transient limit have long been the subject of theoretical and experimental study, and recent experimental developments have made possible the observation of the long-distance evolution of these systems. These systems are integrable using the inverse scattering method; however, in contrast to the usual behavior in integrable systems, solitons do not dominate the long-distance behavior. Instead, solitons are transient, and self-similarity appears in the longdistance limit. In this paper, the similarity solutions of the equations which describe stimulated Raman scattering are first reviewed from a physical standpoint. Inverse scattering theory is then used to show that given physically reasonable initial data in which the pump and Stokes waves have no linear frequency mismatch, the solution will converge toward a self-similar solution. These results are confirmed by a numerical comparison of the solution of the transient, stimulated Raman-scattering equations to the appropriate self-similar solutions. The length scale over which convergence occurs and the transient generation of solitons are observed. From a physical standpoint, the appearance of self-similarity rather than solitons in the long-distance limit can be attributed to the presence of memory in the Raman-active medium. Other systems with memory also exhibit self-similarity, and the results which are described here may have applications to a wide array of optical systems with memory. An experiment which could observe self-similarity is described.PACS number(s): 42.65. Dr, 03.40.Kf, 42.50.Md prevents this approach from being applied to transient pulses, and an experimental configuration has already been proposed [12]. In this paper, we show how to calculate the evolution of transient SRS systems in the longdistance limit. At the end, we describe an experiment which could observe the predicted behavior.

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“…On the other hand, we note that it is physically reasonable to require that (1.2) Z(T) surprisingly, soliton-like pulses are not observed in experiments with laser beams whose durations are short compared to the molecular de-excitation time [4], [5] even though setting -y 0 is presumably "more legitimate" for the latter case. Indeed, numerical experiments indicate that both u and z tend toward zero almost everywhere as --+ oo for a fairly broad set of initial data [13], [7]; compare 5. Following the somewhat less formal argument of [12], we show here that z --, 0 as oo.…”

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confidence: 99%