Surfaces of Wave Normals in Crystals

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The surfaces of wave normals in crystals (Fresnel's equation of wave normals) are the solutions for the wavenumber of a monochromatic plane wave propagating inside an optical anisotropic material (crystal). This material is characterized by a dielectric permittivity tensor. Application of Maxwell's equations tells us that it is possible that two waves could propagate in the crystal, thus producing two wavenumbers obtained from the intersection of the wave propagation direction with the wave normal surfaces. When only one solution is obtained (one intersection), only one wave propagates and the direction is defined as the optical axis.

Contributed by: José A. Díaz (December 2011)
Open content licensed under CC BY-NC-SA




[1] M. Born and E. Wolf, Principles of Optics, 6th ed., New York: Pergamon Press, 1991.

[2] D. Goldstein, Polarized Light, 2nd ed., New York: Marcel Dekker Inc., 2003.

[3] E. Hecth, Optics, 4th ed., San Francisco: Addison–Wesley: 2002.

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