The paper contains a quantum theoretical analysis of laser beam fluctuations and of the light beat experiments with two lasers. With the help of experimental results on photon counting fluctuations in a single-mode laser field, some correlation properties of the field are derived. It is shown that the correlation equations are satisfied by states of the field which are much more general than "coherent" states. The equations lead directly to the spectral density of the intensity operator in the light beat experiments, which can be obtained from photoelectric measurements. The resulting expression is practically identical to that found by Forrester for light having thermal statistical properties. The reasons for this are discussed by a comparison of the corresponding probability distributions of photon counts and of the classical wave amplitude.
The paper contains a quantum theoretical analysis of laser beam fluctuations and of the light beat experiments with two lasers. With the help of experimental results on photon counting fluctuations in a single-mode laser field, some correlation properties of the field are derived. It is shown that the correlation equations are satisfied by states of the field which are much more general than "coherent" states. The equations lead directly to the spectral density of the intensity operator in the light beat experiments, which can be obtained from photoelectric measurements. The resulting expression is practically identical to that found by Forrester for light having thermal statistical properties. The reasons for this are discussed by a comparison of the corresponding probability distributions of photon counts and of the classical wave amplitude.
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.
Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.
The relation between the two-quantum photocounting distribution p(n, T) and the intensity fluctuations of the radiation incident on the detector is obtained and compared with the one-quantum results. The actual statistics are evaluated for several cases of interest, including a chaotic source, an amplitude-stabilized wave, and the output of a single-mode laser (Van der Pol oscillator). The two-quantum count rate 〈n〉/T is found to depend on the mean-square intensity of the radiation, in contrast to the one-quantum count rate which is proportional to the mean intensity. The effects of photon correlations in the radiation beam become apparent since the two-quantum distributions manifest a distinctly more positive second derivative than the corresponding one-quantum distributions. Both the low-and the high-count probabilities are therefore increased at the expense of counts near the mean. The quantum-theoretical treatment is found to be equivalent to the semiclassical treatment for density operators possessing a positive-definite weight function in the P-representation. Some possible experiments to verify the theory are discussed and shown to be feasible.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
The basic formulae governing the fluctuations of counts registered by photoelectric detectors in an optical field are derived. The treatment, which has its origin in Purcell's explanation of the Hanbury Brown-Twiss effect, is shown to apply to any quasi-monochromatic light, whether stationary or not, and whether of thermal origin or not. The representation of the classical wave amplitude, of the light by Gabor's complex analytic signal appears naturally in this treatment. It is shown that the correlation of counts registered by N separate photodetectors at N points in space is determined by a 2 N th order correlation function of the complex classical field. The variance of the individual counts is shown to be expressible as the sum of terms representing the effects of classical particles and classical waves, in analogy to a well-known result of Einstein relating to black-body radiation. Since the theory applies to correlation effects obtained with any type of light it applies, in particular, to the output of an optical maser, although, for a maser operating on one mode, correlation effects are likely to be very small.