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Spatial correlation functions of inhomogeneous random electromagnetic fields.

Luk R Arnaut1

  • 1National Physical Laboratory, Division of Enabling Metrology, Hampton Road, Teddington TW11 0LW, United Kingdom. luk.arnaut@npl.co.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2006
PubMed
Summary

A conducting surface alters spatial correlations in classical electromagnetic fields, creating inhomogeneous correlations dependent on field point locations. This effect shows damped oscillations and offers a geometric interpretation of correlation cells.

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Area of Science:

  • Electromagnetism
  • Classical Field Theory
  • Wave Phenomena

Background:

  • Spatial correlation functions characterize random electromagnetic fields.
  • The behavior of fields near conducting surfaces is crucial in various applications.
  • Understanding field correlations is key to analyzing wave propagation and scattering.

Purpose of the Study:

  • To investigate the impact of an infinite planar perfectly conducting surface on spatial correlation functions.
  • To analyze the transition from homogeneous to inhomogeneous correlations in the presence of a surface.
  • To provide a theoretical framework and computational examples for these effects.

Main Methods:

  • Decomposition of the electromagnetic field into Transverse Electric (TE) and Transverse Magnetic (TM) modes.

Related Experiment Videos

  • Analysis of the angular spectrum of random plane waves.
  • Calculation of spatial correlation functions for field points near the conducting surface.

    • Main Results:

    • The conducting surface induces inhomogeneous correlations, dependent on both absolute and relative positions of field points.
    • The correlation distance displays a damped oscillatory behavior related to the local center point.
    • Special cases recover known results for statistically homogeneous random free fields.

    Conclusions:

    • The presence of a perfectly conducting surface significantly modifies the spatial correlation properties of classical electromagnetic fields.
    • The study provides a detailed analytical and computational understanding of these surface-induced correlations.
    • A geometric interpretation of correlation cell fluctuations near the surface is established.