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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 60, Iss. 6 — Jun. 1, 1970
  • pp: 830–834

Refraction in Stratified, Anisotropic Media

S. TEITLER and B. W. HENVIS  »View Author Affiliations

JOSA, Vol. 60, Issue 6, pp. 830-834 (1970)

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The Abelès treatment of refraction in stratified isotropic media is extended to stratified anisotropic media. The present treatment is restricted to linear refraction problems with incident light assumed to be plane waves of infinite extent. A mathematical restriction excludes application to singular cases. Subject to these restrictions, the treatment is quite generally applicable. It is applied to the case of an isotropic semiconductor in an external magnetic field; results agreeing with published experimental data and with an alternative method of calculation for normal incidence are obtained.

S. TEITLER and B. W. HENVIS, "Refraction in Stratified, Anisotropic Media," J. Opt. Soc. Am. 60, 830-834 (1970)

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  1. F. Abelès, Ann. Phys. (Paris) 5, 596, 706 (1950).
  2. See also M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press, Inc., New York, 1965), pp. 51 ff.
  3. See also R. Jacobsson, in Progress in Optics, V, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1965), pp. 247 ff.
  4. This may be seen directly by applying the D operator to the determinant of the matrix L(z) in Eq. (4) and then evaluating DL(z) using Eqs. (2).
  5. Note that we follow the coordinate notation used in O. S. Heavens, Optical Properties of Thin Films (Dover Publications, Inc., New York, 1955), Fig. 4.1. This means that the reflected light is described in a left-hand coordinate system if the direction of propagation is taken as the third axis.
  6. This quartic equation corresponds to the Booker equation, familiar in discussions of radio waves in the ionosphere. See, e.g., K. G. Budden, Radio Waves in the Ionosphere (Cambridge University Press, New York, 1961).
  7. See, e.g., E. D. Palik and G. B. Wright, in Free-Carrier Magneto-optical Effects in Semiconductors and Semimetals, III, R. K. Willardson and A. C. Beer, Eds. (Academic Press Inc., New York, 1967), Ch. 10.
  8. E. D. Palik, J. R. Stevenson, and J. Webster, J. Appl. Phys. 37, 1982 (1966).
  9. Although the true energy-band structure for the conduction band of PbS is a set of [111] ellipsoids, the simple Drude model with isotropic mass may be used if all frequencies are much larger than the cyclotron frequency. See Ref. 8, Sec. IV.
  10. For the magnetic field in the z direction, the dielectric function for a simple Drude model with isotropic free-carrier mass m*, takes the form ε=ε∞-4πiσ/ω, where ε∞ is the high frequency dielectric constant and [Equation] Here B3is the applied magnetic field, ω is the angular frequency of the light, ν is the scattering frequency, and ωc=eB3/m*c. For electrons, e = -|e|, where |e| is the magnitude of electronic charge.
  11. We define the ellipsometric variables in the following way. The angle ψ is obtained from tanψ = |Ep| / |Es|,. The angle Δ is the difference of phase between the "parallel" and "senkrecht" fields. See, e.g., Ellipsometry in the Measurement of Surfaces and Thin Films, E. Passaglia, R. R. Stromberg, and J. Kruger, Eds., Natl. Bur. Std. Misc. Publ. 256 (U. S. Govt. Printing Office, Washington, D. C., 1964).

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