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Physical Review A

Unified theory of Raman and parametric amplification in nonlinear microspheres

Mikhail V. Jouravlev, Gershon Kurizki

Published Nov 4, 2004• 12 citations
Publisher

Abstract

We investigate the scattering threshold and cavity-enhanced gain in nonlinear spheres with second- or third-order permeability. Pairs of pump-driven idler and signal modes are considered, satisfying morphology-dependent resonance conditions. The thresholds and gain coefficients of amplified and stimulated Raman scattering, parametric downconversion, and analogous parametric processes in microspheres are derived and evaluated under typical conditions. Applications may include the measurement of chemical impurity concentrations or the creation of low-threshold optical parametric amplifiers using microspheres.

DOI
10.1103/physreva.70.053804

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We investigate the scattering threshold and cavity-enhanced gain in nonlinear spheres with second- or third-order permeability. Pairs of pump-driven idler and signal modes are considered, satisfying morphology-dependent resonance conditions. The thresholds and gain coefficients of amplified and stimulated Raman scattering, parametric downconversion, and analogous parametric processes in microspheres are derived and evaluated under typical conditions. Applications may include the measurement of chemical impurity concentrations or the creation of low-threshold optical parametric amplifiers using microspheres.
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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.
In this paper we study photon pairs generated in a nonlinear cavity composed of a nonlinear crystal surrounded by mirrors, by the process of spotaneous parametric downconversion. We analyze two different regimes: singly-resonant cavities where the signal and idler modes are resonant and doubly-resonant cavities where the pump mode is also resonant. We present analytic expressions for the joint spectral amplitude in these two cases and study the reduction in emission bandwidth as the cavity coefficient finesse is increased. We also study the enhancement of the source brightness from the presence of the cavity.
Nonlinear optical processes in spherical microdroplets whose studies have been pioneered by Chang and co-workers are intriguing from the point of view of applications because of the extremely low thresholds they exhibit for the generation of stimulated output, but also from the theoretical point of view, because they require a synthesis between the methods of nonlinear optics and Mie scattering theory. The basis for such a synthesis has been given in the semiclassical theory of Kurizki and Nitzan, which implies that the nonlinearly amplified component of the scattered field is spatially orthogonal ('out of phase') with the linearly scattered field component (the ordinary Mie solution). This approach allows the calculation of amplification coefficients in various nonlinear processes, as a function of the Mie resonant denominators and spatial overlap of the input and output spherical waves. Recently, this approach has been extended to quantized solutions for parametric amplification and oscillation via four-wave mixing in microdroplets. The very low thresholds for oscillation at Mie resonances are predicted to correspond to strong squeezing, i.e., suppression of the photocurrent noise associated with the detection of the output waves below the noise level associated with an ideal laser. Even well below threshold, the spatially orthogonal output waves allow for strong squeezing at periodically recurring distances from the droplet.
The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.