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arXiv:0705.1274

Generation and amplification of Raman Stokes and anti-Stokes waves

Edouard Brainis, Stéphane Clemmen, Serge Massar

Published May 9, 2007• 0 citations
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Abstract

We present general analytical expressions of Stokes and anti-Stokes spectral photon-flux densities that are spontaneously generated by a single monochromatic pump wave propagating in a single-mode optical fiber. We validate our results by comparing them with experimental data. Limiting cases of the general expressions corresponding to interesting physical situations are discussed.

DOI
10.48550/arxiv.0705.1274

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Physical Review A•Apr 1, 1988•40 citations
We present general analytical expressions of Stokes and anti-Stokes spectral photon-flux densities that are spontaneously generated by a single monochromatic pump wave propagating in a single-mode optical fiber. We validate our results by comparing them with experimental data. Limiting cases of the general expressions corresponding to interesting physical situations are discussed.
A theoretical analysis is made of generation and amplification of Stokes and anti-Stokes waves in gaseous media allowing for Raman and parametric processes and saturation effects. Allowance is also made for any difference between the Raman polarizabilities of the Stokes and anti-Stokes waves which may be caused in particular by the occurrence of one-photon quasiresonances of the interacting waves. Assuming that pump and Stokes (or anti-Stokes) waves are applied at the entrance to a medium (inverted or uninverted), a general solution is found for the amplitudes of the interacting waves under exact resonance and phase-matching conditions. This is used as the basis to investigate their spatial evolution (in particular, for inverse Raman light scattering) and expressions are found for the maximum efficiencies for conversion of the pump to Stokes and/or anti-Stokes waves. It is shown that depending on the relationship between the Raman polarizabilities and also on the input parameters of the waves, conditions of parametric bleaching of the medium with nonzero amplitudes of all the waves or conditions of complete conversion of the pump to the Stokes and anti-Stokes waves or to one of these are established asymptotically. An investigation is made of the stability of these solutions.
A theoretical analysis is made of the simultaneous generation of Stokes and anti-Stokes waves initiated by two-photon additional illumination. This is done allowing for Raman and parametric processes, saturation effects, and also for a possible difference between the Raman polarizabilities for the Stokes and anti-Stokes waves. The conditions for the establishment of various asymptotic regimes are determined and general expressions are derived for the ultimate conversion efficiencies, assuming that pump and additional illumination are fed into a medium (inverted or uninverted) under exact resonance and phase-matching conditions. The spatial evolution of the amplitudes of the interacting waves is investigated by an accurate analytic solution of the problem in an important particular case and using solutions in the approximation of a constant pump wave or constant additional illumination.
Statistical properties of light produced in spontaneous Raman scattering on an ensemble of molecules indicate the quantum nature of this phenomenon. The scattered light is non-classical and has high non-classical intensity correlations between Stokes and anti-Stokes components. The temporal coherence of this light is well investigated, while many questions related to spatial coherence remain open. Recent experiments reveal two peculiar features of the spatial coherence of the Stokes and anti-Stokes light. First, the intensity correlations between Stokes and anti-Stokes light remain non-classical even for macroscopic samples containing many molecules. Second, these correlations decrease when signal propagates through a multi-mode optical fiber: the more propagating fiber modes at Stokes and anti-Stokes frequencies the less the correlations. Moreover, the second-order autocorrelation function of Stokes and anti-Stokes light also decreases with the number of propagating modes in multi-mode fiber. In this paper, we build a model of spontaneous Raman scattering correlations of light produced by an ensemble of molecules and propagating through weakly guiding optical fiber that quantitatively explains all these observations. We show that spacial orthogonality of the fiber modes makes the light propagating through these modes uncorrelated in the standard detection scheme. This leads to suppression of non-classical intensity correlations of the total field in the multi-mode fiber. We find the degree of non-classical correlations on fiber parameters. The obtained results pave the way for engineering of non-classical Stokes -- anti-Stokes correlations.
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.
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.