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Optics Letters

Raman solitons in media with a Stark shift: soliton regeneration through self-phase modulation

R. Wolfson, Kai J. Drühl

Published Jan 15, 1989• 3 citations
Publisher

Abstract

An internal phase-shift mechanism can lead to the amplification of Raman solitons even in the presence of coherence decay and detuning. We study here the case of a Raman medium with strong ac Stark shift by using both analytical and numerical methods. Our results also suggest the possibility of propagating stable transient Raman solitons in optical fibers.

DOI
10.1364/ol.14.000125

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An internal phase-shift mechanism can lead to the amplification of Raman solitons even in the presence of coherence decay and detuning. We study here the case of a Raman medium with strong ac Stark shift by using both analytical and numerical methods. Our results also suggest the possibility of propagating stable transient Raman solitons in optical fibers.
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.
A theory is presented to describe the propagation of a laser pulse with several frequency components ${\ensuremath{\omega}}_{j}$=${\ensuremath{\omega}}_{O}$+j${\ensuremath{\omega}}_{R}$ through a Raman medium, where ${\ensuremath{\omega}}_{0}$ is the initial laser frequency and ${\ensuremath{\omega}}_{R}$ is the frequency of the Raman transition. We consider primarily the transient regime, where the pulse width is comparable to or less than the relaxation times of the medium. We formulate the Maxwell-Bloch equations in terms of a two-photon Rabi frequency \ensuremath{\Omega} and an overall phase theta. The resulting equations are similar in form to those describing self-induced transparency, and exhibit solutions corresponding to slowly traveling, but ultimately decaying, pulses. Numerical solutions to the equations are presented that include pump depletion, the ac Stark shift, and finite relaxation times. Significant frequency conversion to high-order (j\ensuremath{\sim}8) anti-Stokes modes is observed in the numerical results.
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.
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.
The amplification of intense light pulses in resonance active media with an optical Stark effect and coherence effects is examined theoretically. In the course of the amplification, the pulse may go through a stage of an incoherent Stark quasisoliton. The envelope of this quasisoliton has an approximately constant, highly asymmetric shape. The energy of the quasisoliton is approximately constant. Upon further amplification, the Stark quasisoliton "breaks up" into a train of shorter pulses. Over a sufficiently long amplification distance, a true soliton may form in the active medium. In general, this true soliton is not the same as a standard π pulse in a medium without a Stark effect.