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American Journal of Physics

Fluctuations in light beams: A simple student experiment

R. P. Wolf, Peter P. Crooker

Published May 1, 1982• 1 citation
Publisher

Abstract

Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.

DOI
10.1119/1.12825

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Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.
A quasithermal, quasmonochromatic lamp is described which serves as a highly degenerate light source with adjustable coherence time between 10−5 sec and 1 sec. This lamp is used for several demonstration experiments concerning the relations between coherence and fluctuations: The intensity interferometer of Hanbury Brown and Twiss is applied to measure the correlations between intensity fluctuations. The double slit experiment of Young serves to stress the role of fluctuations for classical interferometry. Interference patterns from two independent quasithermal lamps are presented.
Abstract It is shown by a quantum-mechanical treatment that the emission times of photoelectrons at different points illuminated by a plane wave of light are partially correlated, and identical results are obtained by a classical theory in which the photocathode is regarded as a square-law detector of suitable conversion efficiency. It is argued that the phenomenon exemplifies the wave rather than the particle aspect of light and that it may most easily be interpreted as a correlation between the intensity fluctuations at different points on a wavefront which arise because of interference between different frequency components of the light. From the point of view of the corpuscular picture the interpretation is much less straight­forward but it is shown that the correlation is directly related to the so-called bunching of photons which arises because light quanta are mutually indistinguishable and obey Bose-Einstein statistics. However, it is stressed that the use of the photon concept before the light energy is actually detected is highly misleading since, in an interference experiment, the electromagnetic field behaves in a manner which cannot be explained in terms of classical particles. The quantitative predictions of the theory have been confirmed by laboratory experi­ments and the phenomenon has been used, in an interferometer, to measure the apparent angular diameter of Sirius: these results, together with further applications to astronomy, will be discussed in detail in later papers. It is shown that the classical and quantum treatments give identical results when applied to find the fluctuations in the photoemission current produced by a single light beam, and the connexion between these fluctuations and the correlation between photons in coherent beams is pointed out. The results given here are in full agreement with those obtained by Kahn from an analysis based on quantum statistics: however, they differ from those derived on thermodynamical grounds by Fellgett and by Clark Jones and the reasons for this discrepancy are discussed.
We present a photon counting experiment designed for an undergraduate physics laboratory. The statistics of the number of photons of a pseudo thermal light source is studied in two limiting cases: well above and well below the coherence time, giving Poisson and Bose-Einstein distributions, respectively. We show that using a digital oscilloscope the experiment can be done in a reasonable time, without need of counting boards. The use of the oscilloscope has the additional advantage of allowing the storage of the data for further processing. Hence, using the same set of data, the analysis of the statistics of the occurrence of n photons as a function of the time windows adds important evidence to determine accurately the nature of the light source. The stochastic nature of the detection phenomena adds an additional value to this type of experiments, since the student is forced to a thorough visit through data processing and statistics.
The probability distribution p ( n , T ) of the number of counts n from a photoelectric detector illuminated by coherent light for a time T is studied, by associating photons stochastically with Gaussian random waves. The cumulants of the distribution are derived and it is shown to be of the expected form for a boson assembly in a limited volume of phase space. The distribution depends strongly on the degeneracy of the light beam. It approaches the Poisson form for classical particles at low degeneracies and the distribution characteristic of classical waves at high degeneracies. The analysis leads, incidentally, to an expression for the extent of the unit cell of phase space in the direction of the beam. It is argued that this should be adopted as the measure of coherence length.