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  • Print publication year: 2009
  • Online publication date: January 2011

9 - Second-order coherence and the Hanbury Brown–Twiss experiment



The degree of first-order temporal coherence, a function denoted by g(1)(τ), provides information about the coherence length and the power spectral density of a light source. However, without additional information, g(1)(τ) has no bearing on intensity fluctuations and higher-order statistics of the emitted light. A quasi-monochromatic laser beam and the beam of light from an incandescent light bulb, provided that the latter is properly filtered to match the spectral line-shape of the former, will have identical degrees of first-order coherence. Any interferometric experiment involving the splitting and superposition of amplitudes would yield identical results for the laser beam and the (properly filtered) thermal light. Therefore, on the basis of such experiments alone, there is no way to distinguish the two light sources. It turns out, however, that the intensity fluctuations of laser light are fundamentally different from those of thermal light. The two sources can, therefore, be distinguished based on their second-order coherence properties.

An ideal photodetector produces an electrical signal proportional to the “cycle-averaged intensity” of the E-field (or B-field) of the light beam at the location of the detector. Assuming that the electrical bandwidth of the detector (including all associated circuitry) is greater than the bandwidth of the incident light wave by at least a factor of 2, the output of the detector should accurately represent the intensity fluctuations of the light beam as a function of time.

References for Chapter 9
Goodman, J. W., Statistical Optics, Wiley, New York, 1985.
Mandel, L. and Wolf, E., Optical Coherence and Quantum Optics, Cambridge University Press, London, 1995.
Loudon, R., The Quantum Theory of Light, third edition, Clarendon Press, Oxford, 2000.
Brown, R. Hanbury and Twiss, R. Q., Correlation between photons in two coherent beams of light, Nature 177, 27–29 (1956).
Brown, R. Hanbury and Twiss, R. Q., The question of correlation between photons in coherent light rays, Nature 178, 1447–1448 (1956).
Brown, R. Hanbury and Twiss, R. Q., interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation, Proc. Roy. Soc. London A, 242, 300–324 (1957).
Brown, R. Hanbury and Twiss, R. Q., Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light, Proc. Roy. Soc. London A, 243, 291–319 (1958).
Brown, R. Hanbury, The Intensity Interferometer, Taylor and Francis, London, 1974.