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Physical Review A

Laser-noise-induced intensity fluctuations in an optical interferometer

Bruce A. Ferguson, Daniel S. Elliott

Published Jun 1, 1990• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.6183

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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.
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 have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
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.
Significant fluctuations, above the shot-noise limit, have been observed in the intensity of fluorescent light scattered from atoms excited by an intense noisy laser, where a central role is played by the nonlinearity of the atom-field interaction. By considering the variance of the atomic populations, we show that ``noise spectroscopy'' is sensitive to the field statistics of the laser. We specifically consider the cases of resonance fluorescence (analogous in the weak-field limit to analysis by a Fabry-P\'erot interferometer), two-photon excitation, and double optical resonance for variable laser intensity and bandwidth. We show that large differences in the ``noise'' spectra can occur between lasers characterized by a phase-diffusion or a phase-jump model, although these models would give the same values for the mean atomic populations. We believe that observation of population fluctuations can become a useful method for characterizing laser noise.
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)].