Crystals biaxial

Biaxial crystals offer the possibiUty of coincidence of the phase matching direction with one of the optic axes. This highly desirable situation, called non-critical phase matching, is quite tolerant of divergence of the incident beam from the most efficient phase matching direction. 

Refractive index, where given for a uniaxial crystal, is for the ordinary (co) ray where given for a biaxial crystal, the index given is for the median ((3) value. Unless otherwise specified, the index is given for the sodium D-line (X = 589.3 m i). 

Figure 7. Diagram (ui fi) showing phase-matching scheme for guided wave SHG in a biaxial crystal cored fiber with both the fundamental and the SH as HEU modes.

For biaxial crystals, similar results are obtained as with uniaxial crystals. The exception to this rule is that in monoclinic and triclinic systems, the polarization directions need not be parallel to faces or to the bisectors of face angles. If the prominent faces or edges of an extinguished crystal are not parallel to the axes of the initial polarizer, the extinction is said to be oblique (Fig. 3d). 

Note 2 The physical properties of a smectic C mesophase are those of a biaxial crystal. 

Fig. 52. Convergent light figures, a. Uniaxial crystal with optic axis parallel (left) and slightly inclined (right) to line of vision. 6. Biaxial crystal with acute bisectrix parallel (left) and inclined (right) to fine of vision.

Biaxial crystals under similar optical conditions produce convergent light figures like that shown in Fig. 52 6, when the acute bisectrix of the optic axes lies along the line of vision and the vibration directions... 

The investigation of elementary excitations in solids by Raman spectroscopy has developed very quickly in the last few years and will certainly lead to many more new results in the future. For example, the huge class of biaxial crystals has so far been avoided by many workers because of the difficulty of the experimental techniques required, but many interesting effects are to be expected from their study. 

If we try to understand the transmission of light waves in biaxial crystals, we start from the concept of the indicatrix, and to attempt to visualize what shape this must have to show the variation of refractive index with vibration direction for such crystals. From our previous knowledge of the indicatrix for uniaxial crystals, an ellipsoid of revolution with two principal refractive indices, n0 and ne, it is a simple step to see that the indicatrix for biaxial crystals will be a triaxial ellipsoid with three principal refractive indices, n7, np and na. 

Minerals having preferred directions of cleavage will not necessarily randomly lay in all possible orientations. If the orientation is random, the following four orientations may occur with biaxial crystals ... 

Consider the relationship between A and the dielectric tensor e. In ellipsometry, there is reflection and transmission by the surface (z = 0) of a semi-infinite anisotropic substrate (biaxial crystal) into an isotropic ambient (air, for z<0). Suppose that this semi-infinite anisotropic medium (the crystal) is homogeneous and that its optical matrix M is independent of z (if A does depend on z—that is, on how far into the crystal one goes—then the problem becomes much more difficult). If the optical matrix M of the substrate is independent of z, then so is the differential propagation matrix A if A is independent of z and has a value (, to be found below, the solution of Eq. (2.15.25) is given by... 

The practical method to compute "backward"—that is, to calculate the dielectric constant tensor values, or the complex index of refraction—from a set of the observed polarizer and analyzer angles is not presented here. Instead, for a biaxial crystal, the technique indicated below is as follows ... 

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