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AIP conference proceedings

Steady state light pulses in stimulated backward scattering

Dilip N. Ghosh Roy, Devulapalli V. G. L. N. Rao

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Steady state backward SRS and SBS light pulses are analyzed in the limit where rate equation approximation fails and the dynamics of the medium fluctuations must be considered. If the pump and the medium have different attenuations, then it is shown that under certain assumptions, the parametrically coupled equations can be reduced to a one‐dimensional Dirac system.

DOI
10.1063/1.36757

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Physical Review A•Sep 1, 1971•91 citations
Steady state backward SRS and SBS light pulses are analyzed in the limit where rate equation approximation fails and the dynamics of the medium fluctuations must be considered. If the pump and the medium have different attenuations, then it is shown that under certain assumptions, the parametrically coupled equations can be reduced to a one‐dimensional Dirac system.
Characteristics of backward, stimulated light pulses are analyzed in the limit where rate equation approximation breaks down, and fluctuation dynamics (oscillator displacements for Raman and phonon amplitudes for Brillouin) must beconsidered. In this limit, the scattered photon flux N s is N s = a(dN l /dt), (d/dt + γ f )A f = bN l /Af,(d/dt + γ l ) = dN l /Af, where f,/referto fluctuations and pump, respectively; A f the fluctuation intensity, and constants a, b, and d depend on the medium characteristics. An analytical solution to this set of equations has been given by Maier et al.1 in the limit γ f →0 and γ l = 0. With these restrictions removed, analytical solution is difficult. Here, we are considering an analytical solution by reducing the set of equations to that of the cubic Schrodinger equation with real amplitude and by using Backlund transform. Preliminary calculations show that the solitary wave solutions are possible (a purely soliton solution is not admissible2 in the form of hyperbolic secant square).
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.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.
Abstract The semiclassical equations of SRS are derived by the following method: The many‐level molecule is described by the Schrödinger equation and subsequently all amplitudes but those of the essential two levels are eliminated by approximate integration. Especially the case of equal group velocities for pump and Stokes wave is considered. Terms describing a frequency shift due to dynamical Stark effect and a change of refraction index by vibrational excitation can be removed by a suitable transformation. Under various, physically different, assumptions the system of molecular and field equations is reduced to the equations describing a quasimonochromatic pulse propagating in a resonant two‐level system, and in this way we can find a rich manifold of solutions. E.g., the 2π‐pulse of self‐induced transparency can be transferred to SRS. By other assumptions we are led to equations defining the Bäcklund transformation for the sine‐Gordon equation. For this case also soliton type solutions can be constructed.
The equations describing the transfer of intensity from a pump beam simultaneously to forward and backward stimulated scattered beams in an infinite medium are shown to lead to pulsations similar to relaxation oscillations in the scattered intensities. The period of the pulsations is simply related to the gain length for the forward-scattered beam, and may be much longer than the ordinary transient time (related to the damping of material excitations) usually associated with stimulated scattering. Similar oscillations occur for backward scattering alone (stimulated Brillouin scattering) if the scattering medium is finite. In this case the period equals the photon round-trip time in the medium if the latter exceeds the backward gain length. Both phenomena should be observable in scattering from gases such as N2{\mathrm{N}}_{2}N2​ and H2{\mathrm{H}}_{2}H2​ at high pressure, and may also play a role in determining the temporal structure of light scattered from the region of a self-focus in liquids.