Propagation out of the principal planes

Boulanger, B.; Zyss, J.

doi:10.1107/97809553602060000634

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

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International Tables for Crystallography (2006). Vol. D. ch. 1.7, p. 187

Section 1.7.3.1.4.2. Propagation out of the principal planes

B. Boulanger^a ^* and J. Zyss^b

^a Laboratoire de Spectrométrie Physique, Université Joseph Fourier, 140 avenue de la Physique, BP 87, 38 402 Saint-Martin-d'Hères, France, and ^bLaboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France
Correspondence e-mail: benoitb@satie-bourgogne.fr

1.7.3.1.4.2. Propagation out of the principal planes

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It is impossible to define ordinary and extraordinary waves out of the principal planes of a biaxial crystal: according to (1.7.3.6) and (1.7.3.9), e⁺ and e⁻ have a nonzero projection on the z axis. According to these relations, it appears that e⁺ and e⁻ are not perpendicular, so relation (1.7.3.10) is never verified. The walk-off angles ρ⁺ and ρ⁻ are nonzero, different, and can be calculated from the electric field vectors: $[\rho^\pm(\theta,\varphi,\omega)=\varepsilon\arccos[{\bf e}^\pm(\theta,\varphi,\omega)\cdot{\bf u}(\theta,\varphi,\omega)]-\varepsilon\pi/2.\eqno(1.7.3.18)]$ $[\varepsilon = +1]$ or [-1] for a positive or a negative optic sign, respectively.

References

International Tables for Crystallography (2006). Vol. D. ch. 1.7, p. 187