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Annual Meeting Optical Society of America

Raman soliton generation and spectral biasing

Kai J. Drühl

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1988.fv1

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
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.
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.
We have studied the phase pulling and locking of an injected Stokes pulse in a transient Raman amplifier both experimentally and theoretically. In addition, we have investigated the pulse energy statistics and related spatial modes of a high gain amplified Stokes pulse. Experiments reported here show that in the unsaturated case, the phase of the amplified Stokes is pulled almost instantaneously to that of the pump, as soon as integrated gain levels of slightly greater than unity are reached. For higher input seed-Stokes levels, such that the amplified Stokes energy is saturated, the phase locking is completed early, and the phase of the amplified Stokes then follows the phase excursion of the pump. The phase pulling has been modelled theoretically for the specific parameters of our experiment. We have also used the pulse energy statistics to study the seed-Stokes control of a high gain Raman amplifier. For an input seed-Stokes beam to control a transient, high gain Raman amplifier, operated near threshold, it must dominate the self-generated Raman which builds from quantum noise. For a near-unity-Fresnel-number Raman amplifier we have measured the number of input seed-Stokes photons needed to produce an unchanged statistical signature on the amplified Stokes pulse and have found that a surprisingly large number (109) were needed. For a larger Fresnel number Raman amplifier, a near-field camera was used to study the level at which the seed-Stokes pulse controlled the spatial output of the amplifier. Control of the spatial modes seems to have a sharp threshold with input Stokes energy and was fully established with an input of 2x103 photons per mode.
This paper examines the effect of index guiding on Raman gain. The slowly varying Maxwell wave equation including both the real and imaginary parts of the Raman susceptibility for a seeded Raman amplifier is explored. Using a Gauss-Laguerre mode expansion for the Stokes field, the output Stokes energy is numerically studied as a function of gain and detuning from the Raman resonance. The calculations indicate that the real part of the Raman susceptibility causes the Raman medium to act as a lens when the Stokes seed is detuned from the Raman resonance. This focusing effect leads to higher peak Stokes energy when the Stokes seed is tuned to the blue side of the Raman resonance. Specifically for Raman scattering in H2{\mathrm{H}}_{2}H2​ with a pump laser at 532 nm and an input seed near 683 nm, the peak Stokes energy can shift by as much as 300 MHz from the Raman resonance. An experiment which confirms these predictions is also presented. \textcopyright{} 1996 The American Physical Society.
Several groups1,2 are studying the use of optical phase shifts to initiate soliton formation in transient stimulated Raman scattering. Our experiments use a generator-amplifier Raman laser pumped by a frequency-doubled Nd:YAG laser at 532 nm. The Raman medium is hydrogen at 1-100 atm. We use an electrooptic crystal to place a π phase shift in the Stokes beam between the generator and amplifier. This shift momentarily reverses the direction of gain. The phase shift is produced by modulating the amplitude of the Stokes envelope through zero using polarizers and a Pockels cell. Numerical calculations indicate that solitons can be initiated by switching the Pockels cell voltage over a time of several nanoseconds. Development of the temporal pulse is shown in Fig. 1. Once initiated the soliton pulse can narrow to a width of a few picoseconds if the collisional dephasing time (1/Γ) is 60 ps. The width W (HWHM) of the evolving pulse is shown in Fig. 2 (⨉). The solid curve is the pulse width predicted by steady- state theory, which is initially valid because the field envelopes change slowly compared with 1/Γ.
Recent studies of soliton formation in a Raman amplifier by a \ensuremath{\pi} phase shift have shown that the soliton will decay if the input Stokes beam is off resonance. Initial experiments indicated that this soliton decay is related to frequency shifts of the input Stokes beam that result from quantum fluctuations. In this paper we use the quantum statistics of the Raman spectral fluctuations to compare the predicted decay statistics of the soliton decay with the experimentally measured distribution. We find that, as conjectured, the soliton decay is directly related to the statistics of the initiating quantum fluctuations.
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.