1.1 Crystal Optics
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Fig. 1.1 Geometrical representation of a general refractive index ellipsoid of an anisotropic
medium. The unit vector u signifies an arbitrary direction of wave propagation through the medium,
with the eigenmodes of propagation (D a and D b ) and corresponding eigenvalues (n a and n b ) in the
plane perpendicular to u represented on the index ellipse
ellipsoid defined in the principal axes of a material system is schematically shown
in Fig. 1.1, where the half-lengths of the major and minor axes are the principal
refractive indices.
If all three principal refractive indices have the same value, e.g. n 1 = n 2 = n 3 ,
then the index ellipsoid reduces to a sphere and the medium is isotropic. For crystals
with certain symmetries two of the principal refractive indices may be the same,
e.g. n 1 = n 2 = n o , but the third is different, e.g. n 3 = n e . Here the subscripts o
and e denote the ordinary and extraordinary indices respectively, and the direction
corresponding to n e is known as the optical axis. For a wave propagating along the
optical axis the electric field will experience the same refractive index irrespective
of the orientation of E. Crystals with this type of symmetry are termed uniaxial. If
all three of the principal refractive indices are different, e.g. n 1 = n 2 = n 3 , then the
5
Fig. 1.1 Geometrical representation of a general refractive index ellipsoid of an anisotropic
medium. The unit vector u signifies an arbitrary direction of wave propagation through the medium,
with the eigenmodes of propagation (D a and D b ) and corresponding eigenvalues (n a and n b ) in the
plane perpendicular to u represented on the index ellipse
ellipsoid defined in the principal axes of a material system is schematically shown
in Fig. 1.1, where the half-lengths of the major and minor axes are the principal
refractive indices.
If all three principal refractive indices have the same value, e.g. n 1 = n 2 = n 3 ,
then the index ellipsoid reduces to a sphere and the medium is isotropic. For crystals
with certain symmetries two of the principal refractive indices may be the same,
e.g. n 1 = n 2 = n o , but the third is different, e.g. n 3 = n e . Here the subscripts o
and e denote the ordinary and extraordinary indices respectively, and the direction
corresponding to n e is known as the optical axis. For a wave propagating along the
optical axis the electric field will experience the same refractive index irrespective
of the orientation of E. Crystals with this type of symmetry are termed uniaxial. If
all three of the principal refractive indices are different, e.g. n 1 = n 2 = n 3 , then the