Abstract

We calculate the elements of the 4 × 4 matrix that completely describes the geometrical optic properties of a planar surface of an anisotropic crystal as an optical instrument. The linear and angular magnification submatrices clearly demonstrate the lack of rotational symmetry about the principal ray. The results also show that the astigmatism produced by the surface has in general, nonorthogonal axes. The calculations apply to crystals of arbitrary symmetry, surfaces of arbitrary orientation, and rays of arbitrary direction. The results are applicable to sound waves as well as light waves. Byproducts of this calculation are the ratio of solid angles of ray vectors inside and outside the crystals, as well as the demagnification of a source volume. These factors are combined to relate the ratio of scattered to incident power outside the crystal to the corresponding ratio inside the crystal for a general scattering experiment such as Raman or Brillouin scattering.

© 1976 Optical Society of America

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  1. G. Szivessy, Handbuch der Physik, Vol. XX (Springer-Verlag, Berlin, 1928), p. 635.
  2. M. Lax and D. F. Nelson, J. Opt. Soc. Am. 65, 668 (1975).
  3. R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, 1966), Chap. IV. See also S. Liebes, Jr., Am. J. Phys. 37, 932 (1967); A. Arakenzy, ibid. 25, 519 (1957); M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (Wiley-Interscience, New York, 1965).
  4. M. Lax and D. F. Nelson, in Polaritons, edited by E. Burstein and F. De Martini (Pergamon, New York, 1974), p. 27.
  5. M. Lax and D. F. Nelson, in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 415.
  6. J. J. Stoker, Differential Geometry (Wiley-Interscience, New York, 1969).
  7. M. J. Lighthill, Philos. Trans. R. Soc. Lond. Ser. A 252, 397 (1960).
  8. M. V. Klein, Optics (Wiley, New York, 1970), p. 100 ff.
  9. M. Lax and D. F. Nelson, Proceedings of the 1975 Moscow Symposium on Light Scattering (Plenum, New York, 1976).

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), p. 100 ff.

Lax, M.

M. Lax and D. F. Nelson, in Polaritons, edited by E. Burstein and F. De Martini (Pergamon, New York, 1974), p. 27.

M. Lax and D. F. Nelson, in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 415.

M. Lax and D. F. Nelson, J. Opt. Soc. Am. 65, 668 (1975).

M. Lax and D. F. Nelson, Proceedings of the 1975 Moscow Symposium on Light Scattering (Plenum, New York, 1976).

Lighthill, M. J.

M. J. Lighthill, Philos. Trans. R. Soc. Lond. Ser. A 252, 397 (1960).

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, 1966), Chap. IV. See also S. Liebes, Jr., Am. J. Phys. 37, 932 (1967); A. Arakenzy, ibid. 25, 519 (1957); M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (Wiley-Interscience, New York, 1965).

Nelson, D. F.

M. Lax and D. F. Nelson, in Polaritons, edited by E. Burstein and F. De Martini (Pergamon, New York, 1974), p. 27.

M. Lax and D. F. Nelson, Proceedings of the 1975 Moscow Symposium on Light Scattering (Plenum, New York, 1976).

M. Lax and D. F. Nelson, J. Opt. Soc. Am. 65, 668 (1975).

M. Lax and D. F. Nelson, in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 415.

Stoker, J. J.

J. J. Stoker, Differential Geometry (Wiley-Interscience, New York, 1969).

Szivessy, G.

G. Szivessy, Handbuch der Physik, Vol. XX (Springer-Verlag, Berlin, 1928), p. 635.

Other (9)

G. Szivessy, Handbuch der Physik, Vol. XX (Springer-Verlag, Berlin, 1928), p. 635.

M. Lax and D. F. Nelson, J. Opt. Soc. Am. 65, 668 (1975).

R. K. Luneberg, Mathematical Theory of Optics (University of California, Berkeley, 1966), Chap. IV. See also S. Liebes, Jr., Am. J. Phys. 37, 932 (1967); A. Arakenzy, ibid. 25, 519 (1957); M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (Wiley-Interscience, New York, 1965).

M. Lax and D. F. Nelson, in Polaritons, edited by E. Burstein and F. De Martini (Pergamon, New York, 1974), p. 27.

M. Lax and D. F. Nelson, in Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 415.

J. J. Stoker, Differential Geometry (Wiley-Interscience, New York, 1969).

M. J. Lighthill, Philos. Trans. R. Soc. Lond. Ser. A 252, 397 (1960).

M. V. Klein, Optics (Wiley, New York, 1970), p. 100 ff.

M. Lax and D. F. Nelson, Proceedings of the 1975 Moscow Symposium on Light Scattering (Plenum, New York, 1976).

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