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Annual Meeting Optical Society of America

Transient stimulated Raman amplification with picosecond pulse trains

Jui‐Teng Lin, John F. Reintjes

Published Jan 1, 1985• 0 citations
Publisher

Abstract

We consider transient stimulated Raman amplification of trains of picosecond pulses. In this regime the gain of a single pulse is reduced from its steady-state value because of the inability of the nonlinear polarization to follow the time variations of the pump pulse. In addition oscillatory behavior of the pump and Stokes pulse amplitudes have been predicted in the transient regime in conditions of high pump depletion. When the pump radiation is in the form of a train of pulses whose separation is comparable to or shorter than the dephasing time of the nonlinear medium, increased gain can be experienced by later pulses in the train because they can grow from the material polarization created by earlier pulses. We have analyzed this type of amplification as a function of pulse spacing, pump energy, and pump intensity in the regime of high pump depletion. In addition we have considered the effects of Stark shifts of the two-photon resonant Raman level on the Stokes conversion efficiency. We find that at constant pulse intensity the conversion efficiency increases with time through the pulse train, gradually approaching steady state at low conversion efficiencies at times long compared to T2. The maximum conversion efficiency increases as the pulse spacing is decreased. If the pump depletion is too high the peak conversion of the Stokes oscillates through the train in a manner similar to the oscillations of the intensity of a single pulse. A Stark shift of the resonant level can cause reduced gain as well as introduce phase shifts on the Stokes and pump beams. The effects of these processes on the conversion efficiency are discussed.

DOI
10.1364/oam.1985.wr3

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We consider transient stimulated Raman amplification of trains of picosecond pulses. In this regime the gain of a single pulse is reduced from its steady-state value because of the inability of the nonlinear polarization to follow the time variations of the pump pulse. In addition oscillatory behavior of the pump and Stokes pulse amplitudes have been predicted in the transient regime in conditions of high pump depletion. When the pump radiation is in the form of a train of pulses whose separation is comparable to or shorter than the dephasing time of the nonlinear medium, increased gain can be experienced by later pulses in the train because they can grow from the material polarization created by earlier pulses. We have analyzed this type of amplification as a function of pulse spacing, pump energy, and pump intensity in the regime of high pump depletion. In addition we have considered the effects of Stark shifts of the two-photon resonant Raman level on the Stokes conversion efficiency. We find that at constant pulse intensity the conversion efficiency increases with time through the pulse train, gradually approaching steady state at low conversion efficiencies at times long compared to T2. The maximum conversion efficiency increases as the pulse spacing is decreased. If the pump depletion is too high the peak conversion of the Stokes oscillates through the train in a manner similar to the oscillations of the intensity of a single pulse. A Stark shift of the resonant level can cause reduced gain as well as introduce phase shifts on the Stokes and pump beams. The effects of these processes on the conversion efficiency are discussed.
In transient stimulated Raman scattering (SRS), efficient conversion of short pump pulses to Stokes radiation is difficult to obtain. A short seed pulse at the Stokes frequency increases the efficiency and may induce full depletion of the pump pulse, even when the pump power is too low to scatter efficiency without seed. However, for low pump powers the Ra­man polarizability induced by the pump and seed pulse decays, which results in a terminating Stokes pulse, even when the pump pulse itself is long. Nevertheless, the Stokes pulse can be wider than the dephasing time of the Raman polarizability or the width of the seed pulse by an order of magnitude. Applying a second seed may once again induce a sufficiently large Raman polarizability but only if the phase of the Stokes seed matches the phase difference between the pump and remaining Raman polarizability. If not, the polarizability induced by the first pulse and consequently the conversion efficiency for the Stokes radiation decreases. Therefore, it is possible to switch off the Stokes pulse by applying a second seed with appropriate phase and intensity.
The high pulse repetition rates (~100 MHz) of radio-frequency free-electron lasers make possible the investigation of molecular response to a rapid pulse train.1 When the molecular decay time T2 is much larger than the time between pulses T, molecular memory is carried from pulse to pulse. For stimulated Raman scattering (SRS) the memory effect can lead to an increase in the size of the Raman dipole resulting in enhanced scattering. We analyze the 1-D SRS equations in the condition that the scattering under an individual pulse occurs in the transient regime (~10 ps). We obtain a general expression for the behavior of SRS which reduces to the following long-time limits: (1) When T2 ≪ T, the SRS from each pulse in the train develops independently from the others; (2) When T2 ≫ T, the transient SRS response is equivalent to the steady-state response to a constant pump at the time-averaged pump intensity. We also perform this analysis for a medium such as the atmosphere where the density of scatterers and Raman bandwidth decrease exponentially with distance.
Parametric instability induced by the medium saturation in stimulated Raman scattering is investigated theoretically via a generalized detuning (1) where ω p,s,o are the frequency of the pump, Stokes, and phonon, ϕ ˙ p s is the phase modulation, and the last term is the nonlinear correction of the highly excited anharmonic molecule with an amplitude Q.The steady-state gain and hence the Stokes efficiency, in the presence of the anharmonic term, are governed by a cubic equation of |Q|2which is to be solved from the Bloch and Maxwell equations including the pump depletion. Numerical results are shown for the transition diagram of Stokes efficiency vs input pump intensity at various system conditions at the steady-state. For the transient regime, with pulse duration shorter than the dephasing time, we analyze the temporal profiles of the Stokes and the depleted pump based on a transformed equation which combines Bloch and Maxwell equation as follows: (2) where Tis a nonlinear time, G s is the steady-state gain, l0is the input pump intensity, and Uis the real part of the phonon amplitude Q.For an input pulse intensity given by sech2(t/t p ), Eq. (2) is solved numerically to study the transient pulse profiles in the presence of pump depletion and medium saturation.
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.
A general theory of transient stimulated Raman scattering and the phase-matching diagrams are developed based on an interaction Hamiltonian which includes all the possible competing interaction channels. In a Raman system pumped by multiple crossing beams with multiple Stokes and anti-Stokes components, these channels are defined by the interactions among fields at different frequencies and/or k vectors of the pump pairs and Stokes and anti-Stokes fields. An ensemble-averaged equation of motion for the active phonon mode is derived within the Markovian approximation in which the phonon-phonon coupling (pressure effect) is reduced to an energy relaxation and a phase fluctuation. A complete set of transient coupled equations including phase modulation, Stark shift, medium (anharmonic) saturation, and all the possible four-wave-mixing channels is presented. In the transient regime, it is found that the effects of the Stark shift on the Raman efficiency are mainly governed by the input pump energy in contrast to the steady-state theory where the pump intensity plays the main role. Both analytic and numerical methods are developed in describing the nonlinear effects due to the energy feedback mechanism in the strong pump-depletion regime. Twelve possible four-wave-mixing channels are analyzed for nonlinear phase diagrams characterized by the angles among pump pairs, and Stokes and anti-Stokes fields. Finally, numerical examples are shown for the effects of the coherence lengths of high-order Stokes fields and pump pairs on the generation of low-order Stokes fields.
Transient stimulated rotational Raman scattering induced by a polarization-modulated femtosecond pulse whose polarization varies with time is reported. The peak intensity of the polarization-modulated pulse produced in this study is low compared to that of a pulse without polarization variation, and this leads to the low efficiency of self-phase-modulation and thus the high efficiency of stimulated Raman scattering compared to the case of a pump pulse without polarization modulation. The scattering process is unique in terms of the high peak ratio of the anti-Stokes to Stokes emissions compared to the ratio in the case of the scattering induced by linearly, circularly, and elliptically polarized pump pulses. Under optimum conditions, the ratio approaches 1, which is not realized in the general case of stimulated rotational Raman scattering.