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Journal of the Optical Society of America B

Experimental synthesis of phase-diffusing optical fields

Daniel S. Elliott, Stephen J. Smith

Published Sep 1, 1988• 47 citations
Publisher

Abstract

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.

DOI
10.1364/josab.5.001927

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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.
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.
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.
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.
We have investigated theoretically the possibility of employing noisy laser fields for spectroscopic purposes. The basis for this spectroscopy is a modification of the statistic of the fluctuations caused by the nonlinear interaction. All atomic resonances within the range of several bandwidths can be observed in the power spectrum, even in case of large inhomogeneous broadening. We have derived analytical, nonperturbative results for a real Gaussian, a complex Gaussian, and a phase-diffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for two-level systems. Without modification, we can apply our results also to other transition schemes. As an example, the power spectrum of the D2{\mathit{D}}_{2}D2​ transition of 133Cs^{133}\mathrm{Cs}133Cs driven by a phase-diffusing field is calculated. For this four-level system we find qualitative agreement with experimental results by Yabuzaki et al. [Phys. Rev. Lett. 67, 2453 (1991)].
Three methods are given for imposing random telegraph phase or frequency noise on a stabilized cw laser thus giving explicit control of the coherence of the laser field. In the case of phase noise, the resulting laser spectrum consists of a carrier part with nearly Lorentzian shaped noise sidebands which have full-width at half maximum up to 14 MHz. Complete suppression of the carrier is possible if the phase is made to jump by π radians. Frequency telegraph noise results in a laser power spectrum that can be single or double peaked, depending on the relative sizes of the average dwell time and the frequency jump. The laser field has been produced for studies of noise in nonlinear spectroscopic interactions. Measurements of the resulting laser spectra are presented. As an example of the application of such a noisy laser, some results from studies of the dependence of two photon absorption on higher-order optical coherences are given.
We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.