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On the statistical moments of the wave field in the presence of caustics

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Abstract

The diffraction of a scalar wave field by a screen causing random and regular phase modulation is considered. The regular phase advance causes focusing of the field (i.e., the development of foci or caustic surfaces). It is shown that for strong phase fluctuations geometric optics is suitable for calculating the statistical moments of the field even in focusing regions if the singularity of the moment on the caustic is integrable. This is valid specifically for the average intensity. In calculating the higher moments it is necessary to take diffraction effects into account. Estimates are obtained of the intensity fluctuations in the region of the caustic shadow.

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 4, pp. 550–556, April, 1972.

In conclusion the author is pleased to thank P. V. Bliokh for his constant interest in the work and his help, and likewise F. G. Bass and I. M. Fuks for their helpful advice.

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Sinitsyn, V.G. On the statistical moments of the wave field in the presence of caustics. Radiophys Quantum Electron 15, 414–419 (1972). https://doi.org/10.1007/BF02210732

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Keywords

  • Phase Modulation
  • Average Intensity
  • Quantum Electronics
  • Nonlinear Optic
  • Wave Field