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Physical Review A

Generation and intensity-correlation measurements of the real Gaussian field

Cheng Jun Xie, Gerhard Klimeck, Daniel S. Elliott

Published Jun 1, 1990• 18 citations
Publisher

Abstract

The generation of a broadband laser field with well-defined and controllable statistical properties, known as the real Gaussian laser field, has been achieved through the random modulation of the amplitude of a stabilized laser beam. The verification of the field-generation technique is provided by measurements of the laser power spectrum (Lorentzian) and by measurements of the intensity autocorrelation function. The latter is shown to decrease exponentially from an initial value of nearly 3 to a final value of 1 with a decay time related to the inverse bandwidth of the field. The techniques for generating this field and for its characterization are discussed in this paper.

DOI
10.1103/physreva.41.6376

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The generation of a broadband laser field with well-defined and controllable statistical properties, known as the real Gaussian laser field, has been achieved through the random modulation of the amplitude of a stabilized laser beam. The verification of the field-generation technique is provided by measurements of the laser power spectrum (Lorentzian) and by measurements of the intensity autocorrelation function. The latter is shown to decrease exponentially from an initial value of nearly 3 to a final value of 1 with a decay time related to the inverse bandwidth of the field. The techniques for generating this field and for its characterization are discussed in this paper.
We have measured absorption spectra for Doppler-free two-photon absorption from a laser field characterized by strong amplitude fluctuations. This field, known as the real Gaussian field, is generated by randomly modulating the amplitude of the output of a cw stabilized dye laser. The absorption rate from this field is enhanced over that from a field whose intensity is nonvarying and of the same average value. When the laser bandwidth is very large, the absorption spectrum is limited, not by the laser width, but by the width of the atomic resonance. Our measurements are in excellent agreement with calculated spectra.
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.
We report measurements of the absorption spectrum for two-photon absorption from a variety of randomly amplitude-modulated laser fields. The fields are generated by modulating the output of a stabilized tunable ring dye laser external to the laser cavity. As such, the field statistical properties are controllable and well characterized. The fields which we have used in this investigation include the real Gaussian field, the complex Gaussian field, and the real Gaussian field with a coherent component. For the last field, an interesting correlation effect is seen when the coherent component is in phase or 90\ifmmode^\circ\else\textdegree\fi{} out of phase with the stochastic component. We have also investigated the effect of partial correlation of the two counterpropagating fields used in the measurements. In all cases we find excellent agreement between the measured absorption spectra and those calculated from the known fourth-order field-correlation functions.
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.
We have measured the power spectrum of the intensity fluctuations of light transmitted by a Fabry-P\'erot interferometer when the input field is the real Gaussian field. The real Gaussian field is a field characterized by real, random (Gaussian) amplitude fluctuations. The bandwidth of the real Gaussian field was varied, taking on values less than that of the interferometer, as well as greater. Comparisons of the measured spectra with calculated spectra are quite satisfactory. Of special interest is a feature in the spectra centered at the laser-interferometer detuning frequency.
We calculate the intensity fluctuations of the light transmitted by a Fabry-P\'erot interferometer when a broadband laser is incident upon it. The laser field is assumed to have a Lorentzian spectrum and to be broadened by random amplitude fluctuations (real or complex) or random frequency fluctuations. In each case we obtain closed-form expressions for the intensity autocorrelation function, from which we can obtain the magnitude of the intensity fluctuations, as well as the power spectrum. These results indicate a strong dependence of the transmitted intensity fluctuations on the higher-order statistical properties of the incident field. Agreement with similar results concerning atomic fluorescence fluctuations is very good.