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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 10 — Oct. 1, 1976
  • pp: 1042–1047

Time-dependent geometrical optics

J. S. Desjardins  »View Author Affiliations

JOSA, Vol. 66, Issue 10, pp. 1042-1047 (1976)

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The basic relations of geometrical optics for the case of an isotropic, time-dependent medium are derived from Fermat’s principle. The time-dependent theory is applied by discussing the Debye-Sears effect and the frequency fluctuations in a plane light wave induced by atmospheric turbulence and a steady cross wind. In the former case it is shown that the Brillouin scattering relation Δω = VΔ k holds in the geometrical optics limit where V is the sound velocity, while in the latter case we find, using a method due to Tatarski, that the fluctuations in frequency are of the order of a few kilohertz under the most extreme conditions of turbulence, wind speed, and range. The intensity law of geometrical optics, I σ = constant, is generalized to read Iσ/v2 = constant, where v is the frequency of the light wave.

© 1976 Optical Society of America

J. S. Desjardins, "Time-dependent geometrical optics," J. Opt. Soc. Am. 66, 1042-1047 (1976)

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  1. M. Born and E. Wolf, Principles of Optics, 4thed. (Pergamon, New York, 1970), Chap. 3.
  2. S. Weinberg, Phys. Rev. 126, 1899 (1962).
  3. L. A. Pars, A Treatise on Analytical Dynamics (Wiley, New York, 1968), Chap. XVI.
  4. A. Cohen, An Elementary Treatise on Differential Equations, 2nd. ed. (Heath, Boston, 1933), p. 261.
  5. M. V. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966), Chap. 1.
  6. V. I. Tatarski, Propagation of WavesinTurbulentAtmosphere (Nauka, Moscow, 1967).
  7. J. W. Strohbehn, Optical Propagation Through the Turbulent Atmosphere in Progress in Optics, edited by E. Wolf North-Holland, Amsterdam, 1971), Vol. IX, p. 81.

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