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Optics Express

Coherent anti-Stokes Raman scattering in a high-finesse microcavity

Benjamin Petrak, Nicholas Djeu, Andreas Müller

Published Sep 3, 2014• 12 citations
Publisher

Abstract

We report the measurement of degenerate coherent anti-Stokes Raman scattering (CARS) in a high-finesse optical microcavity, with an atmospheric gas as the nonlinear medium. Unlike the well-known bulk process in which index-dispersion compensation is required for phase-matching, efficient microcavity CARS involves a resonant coupling at the Stokes, pump, and anti-Stokes frequencies which can be described using coupled-mode analysis. We show how the interaction is thereby dramatically enhanced in a microscopic sample volume and illustrate the technique for the measurement of CO₂ in air.

DOI
10.1364/oe.22.021999

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Phase cross correlation in Stokes, anti-Stokes generation

zhenqian Li, Czesław Radzewicz, Michael G. Raymer

The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
We report the measurement of degenerate coherent anti-Stokes Raman scattering (CARS) in a high-finesse optical microcavity, with an atmospheric gas as the nonlinear medium. Unlike the well-known bulk process in which index-dispersion compensation is required for phase-matching, efficient microcavity CARS involves a resonant coupling at the Stokes, pump, and anti-Stokes frequencies which can be described using coupled-mode analysis. We show how the interaction is thereby dramatically enhanced in a microscopic sample volume and illustrate the technique for the measurement of CO₂ in air.
Coherent anti-Stokes Raman scattering (CARS) is a well-known Raman scattering process that occurs when Stokes, anti-Stokes and pump waves are properly phase-matched. Using a quantum-field approach with Langevin noise sources, we calculate the noise figure for wavelength conversion between the Stokes and anti-Stokes waves in CARS and show its dependence on phase mismatch. Under phase matched conditions, the minimum noise figure is approximately 3 dB, with a correction that depends on the pump frequency, Stokes shift, refractive indices, and nonlinear susceptibilities. We calculate the photon statistics of CARS and show that the photon number distribution is non-Gaussian. Our findings may be significant for currently pursued applications of CARS including wavelength conversion in data transmission and spectroscopic detection of dilute biochemical species.
Coherent anti-Stokes Raman scattering (CARS) interferometry is used to deplete the anti-Stokes radiation emerging from a tightly focused spot. Near-to-complete depletion of the anti-Stokes radiation is obtained when a phase-controlled local oscillator field at the anti-Stokes frequency is out of phase with the induced CARS field in the focal volume. Unlike in traditional interferometry, this depleted energy is not spatially redistributed. A theoretical analysis shows that the energy loss in the anti-Stokes channel is accompanied by an energy gain in the pump and Stokes channels. Interferometric switching of anti-Stokes radiation may offer a route toward developing high-resolution CARS microscopy.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.
We propose an elegant scheme towards phase locking of two independent degenerate coherent anti-Stokes Raman scattering (CARS) processes. The optical implementation involves a modified Mach-Zehnder interferometer that is utilized to transfer phase coherence from three totally uncorrelated laser beams into two degenerate CARS beams which are independently produced in two distinct Raman active samples. Such a phase-transport interferometer allows for explicit measurement and control of phase differences between the two phase-locked degenerate CARS processes, hence may lead to applications in other pertinent research fields.
The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1