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Physical Review A

Beam-pointing fluctuations in a gain-guided Raman amplifier

S. J. Kuo, D. T. Smithey, M. G. Raymer

Published Feb 1, 1992• 14 citations
Publisher

Abstract

We present a measurement of the beam-pointing fluctuations of a transient Raman-amplifier output using an interferometric method and a theoretical treatment of the three-dimensional, spatial propagation of transient stimulated Raman scattering (SRS) including the fluctuations of the Stokes field giving rise to the beam-pointing fluctuations. The theory is based on an effective steady-state model for the transient SRS process. By using nonorthogonal transverse modes to expand the field, we incorporate the effects of excess spontaneous-emission noise associated with gain-guided amplifiers. The agreement of the measurements with the theoretical treatment demonstrates that the beam-pointing jitter is caused by quantum noise. The beam-pointing fluctuations increase as the Fresnel number of the interaction volume increases because more spatial modes are excited.

DOI
10.1103/physreva.45.2031

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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.

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•Jan 1, 1993•1 citation
We present a measurement of the beam-pointing fluctuations of a transient Raman-amplifier output using an interferometric method and a theoretical treatment of the three-dimensional, spatial propagation of transient stimulated Raman scattering (SRS) including the fluctuations of the Stokes field giving rise to the beam-pointing fluctuations. The theory is based on an effective steady-state model for the transient SRS process. By using nonorthogonal transverse modes to expand the field, we incorporate the effects of excess spontaneous-emission noise associated with gain-guided amplifiers. The agreement of the measurements with the theoretical treatment demonstrates that the beam-pointing jitter is caused by quantum noise. The beam-pointing fluctuations increase as the Fresnel number of the interaction volume increases because more spatial modes are excited.
We have observed fluctuations in the direction of propagation of light pulses generated by stimulated Raman scattering (SRS). This fluctuation is analogous to the pointing fluctuation of laser beams,1 and is due to quantum mechanical uncertainties in the occupation numbers of different spatial modes. When SRS is generated in an interaction region with Fresnel number less than unity, the lowest order spatial mode dominates the generation process, but higher order spatial modes are also weakly and randomly excited. This results in small fluctuations in the wavefront of the light field. The direction of propagation is characterized by the transverse component of an average wave-vector determined by the gradient of the wave-front. We report experimental results by measuring the "center of mass" of the far-field intensity pattern of a single Stokes beam, and the fringe separation of an interference pattern formed by superposing two independently generated Stokes pulses. The experimental results are compared to theory.2
Gain-guiding in an optical amplifier can have a significant effect on the quantum noise properties of the amplified signal. It has been demonstrated, both theoretically and experimentally, that gain-guiding in a steady state Raman amplifier can lead to excess noise in the output signal. Experiments using a Raman amplifier operating in the extreme transient regime also indicate that gain-guiding can have a significant effect on the output Stokes field. In this paper, a theoretical description of transient stimulated Raman scattering in a focused gain geometry is developed. The theory accounts for diffraction, gain-guiding, and quantum initiation.
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.
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.
Measurements of the output of a Raman amplifier when there is no input Stokes seed are presented.It is shown that a fully quantum mechanical scaled planewave theory describes the growth from spontaneous emission well in the high gain limit.However, in the low gain regime there is a significant increase in the amount of Stokes output which is not predicted by the plane wave theory.To account for the deviation from planewave growth observed at low gain, a fully quantum mechanical theory of amplification in a focused gain geometry is presented.The theory is based on a non-orthogonal mode expansion of the amplified field and incorporates the effects of both gain-guiding and diffraction.In addition to accounting for the observed Stokes output at low gain the non-orthogonal mode theory predicts that the Stokes field cart experience enhanced gain as well as have excess noise.Results from an experiment are presented which verify the existence of enhanced gain in a multipass Raman amplifier.Though the experiment does not give a direct measure of the excess noise factor the results