High Order Coherence and Interference

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What we mean by high order interference in this context is the measurement of high order correlations of a wave. It is not the second order diffraction from a grating, for example! The connection between interference and correlations is made clearest in optical coherence theory, and the commonest application is to the Fourier Transform Spectrometer. Correlation functions are a necessary part of the description of partial coherence, but usually these are auto- or cross-correlation functions which are second order. There is actually a hierarchy of more complicated higher order correlation functions as well; and sometimes they matter!

The best known high order correlation is the intensity autocorrelation function which was made famous by the Hanbury-Brown and Twiss experiment. This is a second order correlation of intensity, but a fourth order correlation of the wave field. Early applications of this effect were found in astronomy for measuring the angular diameter of stars. More recently it is used in particle physics and the study of Bose-Einstein condensates.

Although not widely appreciated, nonlinear optical experiments are able to measure more complicated high order correlations of the wave. In nonlinear optics there is a rather odd interference effect that is seen only with partially coherent waves [Kirkwood and Albrecht 2000]. That the maximum contrast of the interference fringes occurs for partial coherence was actually first demonstrated with an acoustic experiment [Hamilton 2002].

There are potential applications of this effect in such areas as differential GPS, because the interference is independent of the phase of the wave; it is, rather, a statistical effect. In a (somewhat glib) way it is the statistical nature that explains why the fringes require partial coherence; only then are the statistics of the wave non-trivial!!

Figure: An example of analysed data from an underwater acoustic second order interference experiment. A vertical section is a logarithmic plot of the Fourier transform of a four-time fourth-order correlation. The horizontal axis is a variable delay that is built into the experiment, making this a form of spectrogram. The second order fringes show up here as the hyperbolic features in the upper part of the contour plot. However, many other features seen here are puzzling (such as that indicated by "?")

References

1. M.W. Hamilton, Interference Fringes with Maximal Contrast at Finite Coherence Time, Physical Review Letters 89 173901 (2002)
2. J Kirkwood and Albrecht A.C., Down-conversion of electronic frequencies and their dephasing dynamics: Interferometric four-wave-mixing spectroscopy with broadband light, Phys. Rev. A61, 033802 (2000)

 

Publications

• A little incoherence to improve the clarity
  M.W.Hamilton
  Proceedings of the first SPIE International Symposium on Fluctuations and Noise: Fluctuations and Noise in Photonics and Quantum Optics Santa Fe, Proc. SPIE 5111, 48 (2003)
• Intensity coherence of a multimode Nd:YAG laser
  T. Hill, M.W. Hamilton, D. Pieroux and P. Mandel
  Physical Review A 66, 063803 (2002)
• Interference fringes with maximal contrast at finite coherence time
  M.W. Hamilton
  Physical Review Letters 89, 173901 (2002)

Personnel

A/Prof Murray Hamilton