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Quantum Electronics

Dynamics and quantum fluctuations of light in nonstationary operation modes of a Raman fibre amplifier

Leonid A. Melnikov, Yulia A. Mazhirina

Published Nov 29, 2019• 0 citations
Publisher

Abstract

Abstract We report the results of numerical simulation of the radiation dynamics in a Raman fibre amplifier taking into account quantum fluctuations of the pump fields and Stokes waves. The simulation relies on an approach based on solutions of the transport equations for complex amplitudes and on the ‘backward’ propagation method for operators describing quantum fluctuations. It is shown that there exists an optimal Raman amplifier length corresponding to the minimum level of fluctuations of the amplified Stokes pulse.

DOI
10.1070/qel17172

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Abstract We report the results of numerical simulation of the radiation dynamics in a Raman fibre amplifier taking into account quantum fluctuations of the pump fields and Stokes waves. The simulation relies on an approach based on solutions of the transport equations for complex amplitudes and on the ‘backward’ propagation method for operators describing quantum fluctuations. It is shown that there exists an optimal Raman amplifier length corresponding to the minimum level of fluctuations of the amplified Stokes pulse.
Stimulated Raman scattering of femtosecond pulses in a photonic crystal consisting of alternating quarter-wave dielectric layers and layers of a nonlinear-scattering medium is calculated taking into account the quantum fluctuations of the medium polarisation. Analysis of the calculations showed that the Stokes pulse duration and intensity depend substantially on the statistic properties of polarisation. The efficient SRS conversion in a photonic crystal occurs under certain dispersion conditions providing the minimum difference between dispersions of the pump and Stokes frequencies, which are determined by the length and the number of periods of the photonic crystal.
A simple model of a traveling-wave parametric amplifier is discussed in quantum-mechanical terms. The amplifier consists of a slab of Raman-active material, illuminated on one face by an intense laser beam that serves as the pump mode; an optical-phonon oscillation serves as the idler mode, and the scattered Stokes light occupies the signal mode. With only a few simplifying assumptions, it is possible to solve the equation of motion for the signal field operator exactly. For large times, both an amplified steady signal and the quantum noise contributed by the material assume simple steady states in an amplifier of finite length. The transient and asymptotic behaviors of the signal and noise intensities are found, together with the corresponding first-order correlation functions. The quasiprobability distribution which specifies the complete density operator for the electric field strength of the amplified signal is also derived.
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.
A semiclassical model of nonstationary stimulated Raman scattering with account of forward and backward waves of different frequencies is proposed. Equations for the elements of a collective density matrix and electric-field amplitudes are obtained applying the averaging method. It is shown that forward waves are generated by a united polarization component, whereas each of the backward waves is formed by its own component. The description is based on the approximation of small scattering angles and assumes that the quantities considered do not depend on transverse coordinates. The emission dynamics of forward-backward Stokes pulses is investigated both for the linear case and under the strong depletion of pumping and level populations. The domain of applicability of the model of nonstationary forward stimulated Raman scattering is determined.