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Electronics Letters

Depletion and saturation effect of stimulated Raman scattering

Yijiang Chen, Allan W. Snyder

Published Nov 10, 1988• 2 citations
Publisher

Abstract

The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.

DOI
10.1049/el:19880991

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The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
The Raman effect is the inelastic scattering of photons by matter. When a monochromatic light beam (pump beam) propagates in an optical fibre, spon- taneous Raman scattering transfers some of the photons to new frequencies. The probability of a photon scattering to a particular frequency shift, depends on that frequency shift, forming a characteristic spectrum. The scattered photons may lose energy (Stokes) or gain energy (anti-Stokes). If the pump beam is linearly polarized, then the polarization of scattered photons may be the same (parallel scattering) or orthogonal (perpendicular scattering). If photons are already present at other frequencies then the probability of scattering to those frequencies is enhanced (stimulated scattering). In this thesis, the equations governing the Raman effect, both in bulk glass and single mode fibre, are restated. The probability of spontaneous scattering (parallel and perpendicular) in an optical fibre has been measured for frequency shifts between 4THz and 58THz. Particular attention has been given to those frequency shifts where the scattering is intrinsically weak. This has identified those frequency shifts where it might be possible to eliminate Raman noise from experiments designed to generate quantum states of light in optical fibres using four wave mixing. From the measured scattering probabilities, the Raman equations can be used to predict the scattering cross-section in bulk glass. The prediction is found to be in reasonable agreement with measurements of the bulk glass cross-section published by other authors. By increasing the pump power, the transition to stimulated scattering has been observed. In the case of Stokes scattering there is reasonable agreement between the Raman equations and experimental observations. In the case of anti-Stokes scattering, and in the limit of very high pump power, behaviour is observed which is not predicted by the Raman equations, indicating that other processes must be included to successfully describe such experiments.
Two-beam stimulated Raman scattering with pump and Stokes beams is manifest in both the Raman loss of the pump beam and the Raman gain of the Stokes beam, and it has been used in various label-free bioimaging applications. Here, a three-beam stimulated Raman scattering that involves pump, Stokes, and depletion beams is considered, where two stimulated Raman gain-loss processes are deliberately made to compete with each other. It is shown that the three-beam Raman scattering process can be described by coupled differential equations for the increased numbers of Stokes and depletion beam photons. From approximate solutions of the coupled differential equations and numerical calculation results, it is shown that a highly efficient suppression of the Stokes Raman gain is possible by using an intense depletion beam whose frequency difference from that of the pump beam is identical to another acceptor Raman mode frequency. I anticipate that the present work will provide a theoretical framework for super-resolution stimulated Raman scattering microscopy.
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.
We theoretically and experimentally investigate an all optical switch based on stimulated Raman scattering in optical fibers. The experimental setup consists of a Raman circuit of two stages connected in series through a bandpass filter. In the first stage, we have a saturated amplifier, in this stage the pump pulses are saturated when pump and signal are launched to the input or the pump pulses remain without saturation when pump only is launched at the input. The second stage works as the Raman amplifier; for this stage amplification is directly dependent on the pump power entering from the first stage. For the case when pump pulse only is launched at the input pass to the second stage without saturation and amplifies the signal entering in the second stage, very intense signal pulses appear at the output of this stage. For the case when both pump and signal pulses are launched to the input, the pump pulse is saturated in the first stage and the filter rejected the amplified signal, so that only low power pump enters the second stage and consequently no signal pulses appear at the output. We show that the contrast can be improved when using fibers with normal and anomalous dispersion connected in series in the first stage. The best contrast (the ratio of energies) obtained was 15 dB at 6 W pump peak power.