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Journal of Optics B Quantum and Semiclassical Optics

On cavity modification of stimulated Raman scattering

Andrey B. Matsko, Anatoliy A. Savchenkov, Rodolphe Le Targat, Vladimir S. Ilchenko, Lute Maleki

Published May 9, 2003• 37 citations
Publisher

Abstract

We study theoretically stimulated Raman scattering (SRS) in a nonlinear dielectric microcavity and compare SRS thresholds for the cavity and the bulk material it is made of. We show that cavity SRS enhancement results solely from the intensity build up in the cavity and from the differences of the SRS dynamics in free and confined space. There is no significant modification of the Raman gain due to cavity QED effects. We show that the SRS threshold depends significantly on the nature of the dominating cavity decay as well as on the coupling technique with the cavity used for SRS measurements.

DOI
10.1088/1464-4266/5/3/312

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We study theoretically stimulated Raman scattering (SRS) in a nonlinear dielectric microcavity and compare SRS thresholds for the cavity and the bulk material it is made of. We show that cavity SRS enhancement results solely from the intensity build up in the cavity and from the differences of the SRS dynamics in free and confined space. There is no significant modification of the Raman gain due to cavity QED effects. We show that the SRS threshold depends significantly on the nature of the dominating cavity decay as well as on the coupling technique with the cavity used for SRS measurements.
A variety of stimulated nonlinear optical processes are observed under relatively low intensity cw excitation in droplet spherical microcavities. These include stimulated Raman and Rayleigh-wing scattering as well as four-wave parametric oscillation. The low thresholds for these stimulated processes are accounted for by all waves being in resonance with high-QQQ droplet modes and by the existence of a significant cavity QED enhancement (> 100 times) in the nonlinear gain coefficients.
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.
Continuous-wave stimulated Raman scattering was observed in 11-13-microm-diameter benzene and toluene microdroplets at pump intensities as low as 8 and 24 kW/cm(2), respectively. Low thresholds were achieved by exploiting simultaneous pump and Stokes wave resonance in the droplets and Raman gains that were cavity QED enhanced ~50 times with respect to bulk liquid values. Based on a photon-state conservation argument, the cavity gain enhancement factor may be approximated by the ratio of the spectral spacing between resonant modes of the same order to that of the homogeneous Raman linewidth. This relation appears to be consistent with the relative experimental behavior of benzene, ethanol, and toluene.
We present a three-dimensional theory of stimulated Raman scattering (SRS) or super-radiance. In particular we address how the spatial and temporal properties of the generated SRS beam or Stokes beam of radiation depends on the spatial properties of the gain medium. Maxwell equations for the Stokes field operators and of the atomic operators are solved analytically and a correlation function for the Stokes field is derived. In the analysis we identify a super-radiating part of the Stokes radiation that exhibit beam characteristics. We show how the intensity in this beam builds up in time and at some point largely dominates the total Stokes radiation of the gain medium. We show how the SRS depends on the Fresnel number and the optical depth and that in fact these two factors are the only factors describing the coherent radiation.
Remarkable demonstrations of a cavity-induced giant reduction of the Raman lasing threshold in silica microspheres have been reported in Spillane et al. [Nature (London) 415, 621 (2002)], yet a complete quantum electrodynamics (QED) treatment of this process including the rigorous expressions for the electromagnetic modes of the sphere is lacking. In this paper, we employ a cavity QED approach to describe Raman lasing in microscopic spherical dielectric resonators with third-order nonlinearity to derive explicit expressions for the Raman gain and lasing threshold in terms of mode-overlapping coefficients determined from full analytic expressions of the electromagnetic eigenmodes of a dielectric sphere. We present dependencies of the Raman lasing threshold on the the order nnn of overlapping whispering gallery modes for microspheres with diameter in the range 20--35 $\ensuremath{\mu}$m, demonstrating ultralow thresholds of between 70 and 90 $\ensuremath{\mu}$W, consistent with recent experimental results. We explain the reduction of the lasing threshold as due to an increase in the overlapping coefficients as the mode order is increased toward the regime where the modal energy is mostly confined to the surface region of the resonator. The presented theory can be easily generalized to any microcavity of regular morphology and for any combination of interacting whispering gallery modes.
Recent advances in generating light in specific quantum states facilitate new sensing applications and enhance or revitalize established measurement and sensing techniques. Stimulated Raman spectroscopy (SRS), a measurement modality based on Raman scattering, could benefit from tuning the quantum properties of the pump and the Stokes lights or the properties of quantum states of the stimulating and excitation fields. Additionally, this modality could also benefit from field enhancement accompanied by plasmon excitation in the surface regions of metal nanoparticles. We present a theoretical investigation of stimulated Raman scattering involving squeezed states of light. The concept of surface- and quantum-enhanced stimulated Raman scattering is introduced. Furthermore, expressions for the respective SRS transition rates are derived, and their dependence on the quantum states of the optical field is discussed, with particular emphasis on the squeezing parameters characterizing these states. For cases involving surface enhancements, we also employ classical computational electrodynamics to guide our exploration of atomically large systems that support plasmon excitation.