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Annual Meeting Optical Society of America

Limitations on Stokes beam coherence for broadband pumping

Kai J. Drühl

Published Jan 1, 1985• 0 citations

Abstract

We address the problem of pumping Stokes radiation by broadband incoherent laser beams in contrast to aberrated beams. While for aberrated beams the transversal phase variations in any given plane of reference are constant in time, they will fluctuate in time for incoherent beams. As is well known for Raman scattering by broadband lasers, the frequency mode structure of the amplified Stokes beam will be modified by the pump laser, leading to an increase in temporal correlation between pump and Stokes. For collinear pumping by an incoherent pump this implies that the amplified Stokes beam will also be incoherent, even if seeded initially with a coherent beam. For transversal pumping geometries Stokes beam coherence will be affected by the reduced temporal correlation between the pump fields at different transversal locations. In the case of resonant scattering (linewidth much smaller than mode spacing), we show that the transversal Stokes coherence length is limited by the longitudinal coherence length of the pump. In addition, a reduction in gain occurs. We present analytical and numerical results which indicate corresponding limitations for intermediate scattering (linewidth comparable to mode spacing), which is the case of practical interest in gases.

DOI: 10.1364/oam.1985.tua8

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We address the problem of pumping Stokes radiation by broadband incoherent laser beams in contrast to aberrated beams. While for aberrated beams the transversal phase variations in any given plane of reference are constant in time, they will fluctuate in time for incoherent beams. As is well known for Raman scattering by broadband lasers, the frequency mode structure of the amplified Stokes beam will be modified by the pump laser, leading to an increase in temporal correlation between pump and Stokes. For collinear pumping by an incoherent pump this implies that the amplified Stokes beam will also be incoherent, even if seeded initially with a coherent beam. For transversal pumping geometries Stokes beam coherence will be affected by the reduced temporal correlation between the pump fields at different transversal locations. In the case of resonant scattering (linewidth much smaller than mode spacing), we show that the transversal Stokes coherence length is limited by the longitudinal coherence length of the pump. In addition, a reduction in gain occurs. We present analytical and numerical results which indicate corresponding limitations for intermediate scattering (linewidth comparable to mode spacing), which is the case of practical interest in gases.

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The cross-correlation function between the pump and Stokes intensities in stimulated Raman scattering has been measured. It has previously been conjectured 1 and theoretically shown2 that the Stokes light generated in the presence of a multimode or broadband pump is generated with mode amplitudes and phases in perfect correlation with those of the pump. We present here experimental evidence of such cross correlations for scattering in hydrogen gas. The measurement technique used is the same as that previously used for measuring the intensity autocorrelation function of a multimode dye laser.3 This technique is based on detecting the frequency doubled light from a nonlinear crystal as a function of time delay between the pump and Stokes beams. We have performed cross-correlation measurements using as a pump the light from a multimode dye laser which is operated in two different cavity configurations: one in which the mode spacing Δυ is large compared with the spontaneous linewidth of the Raman transition Γ, Δυ > Γ; and one in which the mode spacing is small, Δυ < Γ.

A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.

The authors have extended the theory of stimulated Raman scattering to include the effects of laser bandwidths, in both the transient and steady-state regimes. The case of two interacting laser beams, a pump laser and a probe (Stokes) laser, is treated. Using the phase-diffusion model for laser bandwidth, the authors demonstrate that in the absence of dispersion, the forward Raman gain is essentially independent of the laser bandwidths in the high-gain limit, while in the low-gain limit the gain coefficient is inversely proportional to the sum of the bandwidths. It is further shown that when the pump-laser bandwidth is much larger than the linewidth of the Raman medium, the stimulated Stokes output assumes the same spectrum as the pump laser in the high-gain limit. A possible interpretation of these results is discussed assuming a "phase-locking" of the Stokes phase to the fluctuations in the pump-laser phase, due to the nonlinear interaction of the two beams through the Raman medium.

In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.