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Annual Meeting Optical Society of America

Raman solitons and self-phase modulation

R. Wolfson, Kai J. Drühl

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Homogeneous broadening leads to the decay of Raman solitons,1,2 if pump and Stokes are not exactly on Raman resonance. This is due to a dispersive frequency shift at the soliton center. Media with strong self-phase modulation (SPM) can balance this dispersive effect and even show an amplification of peak pump intensity. In this case, the net decrease in pump power is compensated by narrowing from SPM. We present analytical and numerical results, which demonstrate this effect for media with strong Stark shift.

DOI
10.1364/oam.1988.fv4

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
Homogeneous broadening leads to the decay of Raman solitons,1,2 if pump and Stokes are not exactly on Raman resonance. This is due to a dispersive frequency shift at the soliton center. Media with strong self-phase modulation (SPM) can balance this dispersive effect and even show an amplification of peak pump intensity. In this case, the net decrease in pump power is compensated by narrowing from SPM. We present analytical and numerical results, which demonstrate this effect for media with strong Stark shift.
The exact resonance of pump and Stokes with the Raman transition is essential for successful generation of Raman solitons.1 Even slight detuning (~1 % of the Raman linewidth) leads to rapid soliton decay. Viewed in frequency space, this is due to an asymmetric gain profile for the injected Stokes seed. Through the frequency dependence of gain and Raman dispersion, this leads to the rapid growth of an out-of-phase component of the Stokes beam, which does not participate in the transient reversal of pump depletion. The asymmetric gain profile can be compensated by suitably modifying the total phase shift of the injected seed, resulting in an enhancement of those frequency components that see lower gain. We show that almost complete soliton stability can be achieved this way.
In the case of the scattering Raman amplification of light beams in a field of powerful ultrashort pulses, the back influence of the amplified radiation on the fundamental wave may be significant. Moreover, properties of the media, such as a population of atomic states, may significantly change. That leads to amplitude-phase modulation of the fundamental pulse owing to change of direction of intensity exchange in the pulse.1 As a result, the bond between the fundamental and Stokes waves becomes weaker, that results in a decrease in the frequency conversion efficiency. For spatial inhomogeneous beams this effect is different in various beam sections.
The regular structure in frequency broadening spectrum of the self-trapped laser and Raman radiations is produced by the phase-modulation of light waves propagating in the filament with intensity-dependent index of refraction. A quantum-mechanical calculation of double quantum transition in a three-level system is shown to explain the process of self-modulation and the production of picosecond pulses in the Raman process. Coherent coupling of the laser and the Stokes waves produces mutual modulation of large amplitude, if the optical field is strong and the vibrational relaxation time is long. Numerical evaluation for CS2 gives a modulation frequency of about 1011 Hz, when an optical power of 10 kW is trapped in a filament of 2 µm radius. Besides, the effect of self-modulation on the spatial distribution of anti-Stokes emission along the filament is discussed and shown to agree with the experimental results observed by Stoicheff and his co-workers.
When vacuum fluctuations at the Stokes frequency are amplified through the interaction of a coherent pump with a Raman medium, large phase shifts in the Stokes field may survive well into its macroscopic regime. Because the response time of the medium’s polarizability is finite, the relative phase of the polarizability and the Stokes field exhibits a peak, called a phase wave. Correspondingly, the pump reacts to a sufficiently large phase shift by briefly repleting before continuing its depletion, thus forming a solitary wave or soliton. It is possible to use the statistical properties of phase waves to predict such observables as the frequency of soliton production, the distribution of soliton amplitudes, and the soliton delay-time statistics.