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AIP conference proceedings

Role of fluctuations in nonlinear optical absorption processes

Stephen J. Smith

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Fully quantitative experimental investigations of nonlinear optical absorption processes can only be carried out with optical fields for which higher order correlation functions are known. A technical capability for synthesizing such laser power spectra by introducing Gaussian frequency fluctuations to the external field of a well‐stabilized single‐mode laser has been developed and applied to double‐optical‐resonance measurements in atomic sodium. Experimental results agree well with predictions of a full theoretical treatment.

DOI
10.1063/1.36725

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Fully quantitative experimental investigations of nonlinear optical absorption processes can only be carried out with optical fields for which higher order correlation functions are known. A technical capability for synthesizing such laser power spectra by introducing Gaussian frequency fluctuations to the external field of a well‐stabilized single‐mode laser has been developed and applied to double‐optical‐resonance measurements in atomic sodium. Experimental results agree well with predictions of a full theoretical treatment.
The power spectrum of a well-stabilized single-mode laser is deliberately broadened by introducing Gaussian frequency fluctuations in order to synthesize laser power spectra statistically well characterized to all orders. The objective is to carryout fully quantitative investigations of certain nonlinear atomic absorption processes. The results of a calculation of the power spectrum of a carrier frequency modulated by Gaussian noise will be outlined, and the approach to Lorentzian and Gaussian power spectra demonstrated as limiting cases. Experimental methodology for controlling the power spectrum to ~1 GHz from line center is discussed briefly.
Techniques are described for synthesizing a statistically well-characterized radio-frequency noise spectrum and imposing this noise spectrum on a well-stabilized laser beam by means of extracavity phase and frequency modulation. The basis of the noise spectrum is the Gaussian noise-voltage spectrum derived from shot noise. The Gaussian property is carefully preserved at every step, ensuring that correlation functions to all orders can be represented in terms of the lowest-order correlation function, which, in turn, is the Fourier transform of the power spectrum, according to the Wiener–Khintchine theorem. The power spectrum can be measured and controlled, in a range that has Lorentzian and Gaussian forms as limiting cases, by controlling the bandwidth and amplitude of the noise voltage at the source. The objective of this methodology is the definitive experimental study of nonlinear-optical absorption processes, all such processes requiring knowledge of higher-order correlation functions for complete definition.
A number of experimental investigations have been carried out over the past fifteen years which have been used to study the effect of the bandwidth of the laser on various nonlinear optical interactions. These are useful and interesting for a number of reasons. On the technical side laser bandwidth effects can limit the accuracy of measurements of the frequency of atomic transitions as well as the determination of the strength of the interaction. Of a more fundamental interest is the question of the behavior of the nonlinear atomic system when interacting with the non-monochromatic field. In the first experiments carried out to investigate these effects lasers were used which could be operated on a single longitudinal mode or on multiple modes corresponding to the presence or absence of an intra-cavity etalon. Following this a number of techniques were developed to modulate the amplitude phase and/or frequency of the output of a stabilized cw laser with a random (but well-characterized) signal. In this way laser fields could be generated in the laboratory which closely approximate models of laser fields on which theorists have based calculations of laser bandwidth effects. These works allow direct quantitative comparison of results with theory. A number of these field models which can now be generated in the laboratory will be discussed as well as measurements of the role they play in nonlinear interactions.
We have developed a method of generating a field whose amplitude is a randomly fluctuating variable, known as a real Gaussian field, as a means of testing the effect of laser bandwidth on nonlinear optical interactions. The frequency of this field is constant, and its amplitude, restricted to real values, varies about a mean value of zero. We have measured the intensity autocorrelation function of the light, and it shows good agreement with expected results. We are now measuring the effect of this field on nonlinear systems. The first is the 3S-5S two-photon resonance in atomic sodium. Enhancement of the two- photon absorption rate by a factor of three over the absorption rate from a monochromatic field of the same average intensity is expected. The real Gaussian field is also being applied to studies of transmission through a Fabry-Perot interferometer. The intensity spectrum is expected to consist of peaks centered at zero frequency and at the difference between the laser frequency and that of the peak of the interferometer transmission.
Experimental evidence of field-correlation effects on weak-field two-photon absorption in atomic sodium is presented. In the case of a nearly Lorentzian laser power spectrum the absorption profile has four times the spectral width of the exciting field, in agreement with predictions by Mollow. The measurement is carried out with counterpropagating laser beams to cancel Doppler broadening. The width of the two-photon absorption spectrum is decreased by partially decorrelating the counterpropagating laser beams. Increasing the correlation time of the frequency fluctuations, resulting in a nearly Gaussian laser power spectrum, has also been observed to decrease the width of the absorption spectrum. An extension of the time-dependent second-order perturbation theory to these additional cases yields good agreement.
We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with non‐Gaussian statistics: the expansion of stochastic processes in terms of first and higher power of Gaussian components, which are used like a basis set. This approach is applied to treat the non‐Gaussian correlation effects observed in coherent anti‐Stokes Raman scattering experiments using frequency‐doubled pump‐laser fields. Our results give much better agreement with experimental data than previous theories.