Lorenzo M. Narducci

Scattering of Light from a Rotating Ground Glass

We report some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with average-size inhomogeneities of approximately 1 μm. Photocount statistics measured at different scattering angles and for different angular velocities of the ground glass have confirmed the known result that the scattered-light amplitude is a stochastic gaussian variable. The Bose–Einstein nature of the photocount statistics has been verified with an accuracy of a few parts per thousand. Self-beating measurements on the scattered light of a He–Ne laser in a TEM00 configuration have shown that the power spectrum is a gaussian function of the frequency. The dependence of its half-width on the angular velocity of the ground glass and on the focal length of the lens that focuses the beam on the scattering surface has been measured. The experimental results agree very closely with our theoretical predictions.

Photon-Count Distributions and Irradiance Fluctuations of a Log-Normally Distributed Light Field*

We discuss some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with large surface inhomogeneities (average size 20 μm), when the illuminated area of the scattering surface contains only a few scattering centers. Photon-count distribution measurements indicate that, to a high degree of accuracy, the field amplitude of the scattered light fluctuates as a log-normal variate. The irradiance correlation function is a gaussian function of time with a half-width at half-height that varies inversely with the angular speed of the ground glass but is largely independent of the angle of scattering. Identical functional dependence was previously found, using a ground glass with much smaller surface inhomogeneities (average size 1 μm). Finally, we report some experimental tests of a recent calculation by Mitchell concerning what has been defined as the permanence of the log-normal distribution. We find that, even when the detecting surface of the photomultiplier is illuminated by several coherence areas of the scattered field during a single counting interval, the field-amplitude distribution remains log-normal to an excellent approximation.

Measurement of the Light-Field Amplitude-Correlation Function through Joint Photon-Count Distributions*

When an amplitude-stabilized He–Ne laser beam is scattered by a rotating ground glass with small surface inhomogeneities, the probability density of the instantaneous scattered-wave amplitude is gaussian. This has been verified experimentally in the past few years by several independent groups. In this paper, we suggest the use of the joint photon-count probability distribution p (n = 0, m = 0, τ) to measure the absolute value of the electric-field amplitude-correlation function for random gaussian light fields, and report the results of an experiment in which the gaussian field is produced by scattering a light beam through a rotating ground glass. This procedure offers an alternative to other conventional methods, such as self-beating spectroscopy and irradiance-correlation techniques. The correlation time of the scattered-field amplitude in the present experiment has been measured with an accuracy of approximately 0.8%.

C-Number Representation for Multilevel Systems and the Quantum-Classical Correspondence

We use the r-mode direct product coherent states as generating functions for r-level coherent states which are ideal for the description of collective behavior of an ensemble of N identical r-level atoms or molecules, where the r-levels are not necessarily evenly spaced. It is noted that the Lie algebra for an r-level system can be given a realization in terms of bilinear combinations of boson creation and annihilation operators. This provides a homomorphism from the algebra describing a multimode system to the algebra describing a multilevel system. This in turn provides a homomorphism from the multimode coherent states and their diagonal projectors onto the multilevel coherent states and their diagonal projectors. The action of a creation or annihilation operator on a multimode projector can be replaced by the action of a first order differential operator.

Light intensity correlation measurements in the presence of multiple scattering

Abstract We discuss the results of a model calculation of the intensity correlation function for multiply scattered light and compare our analytic predictions with experiments.