Laser Beam Propagation in Nonlinear Optical Media

Positive uniaxial crystal with point group 6mm

For positive uniaxial crystals such as cadmium selenide (CdSe) belonging to the point group 6mm, Table 2.3 shows that the non-zero d coefficients are d₁₅, d₂₄, d₃₁, d₃₂ and d₃₃, of which d₂₄ = d₁₅ and d₃₂ = d₃₁. Further, under Kleinman symmetry condition, d₃₁ = d₁₅.

	SSf(ooe)	Sff(oee)	fSf(eoe)
$\begin{array}{c}{d}_{15}\\ d_{24}\\ d_{31}\\ d_{32}\\ d_{33}\end{array}$	$\begin{array}{c}–\sin \varphi \cos \varphi \sin \left({\theta }_1^{\prime }+{\theta }_2^{\prime }\right)\\ \sin \varphi \cos \varphi \sin \left({\theta }_1^{\prime }+{\theta }_2^{\prime }\right)\\ 0\\ 0\\ 0\end{array}$	$\begin{array}{c}–{\sin }^2\varphi \sin {\theta }_1^{\prime }\\ –{\cos }^2\varphi \sin {\theta }_1^{\prime }\\ 0\\ 0\\ 0\end{array}$	$\begin{array}{c}–{\sin }^2\varphi \sin {\theta }_2^{\prime }\\ –{\cos }^2\varphi \sin {\theta }_2^{\prime }\\ 0\\ 0\\ 0\end{array}$

${\theta }_1^{\prime }\equiv \theta –\rho ({\omega }_1),{\theta }_2^{\prime }\equiv \theta –\rho ({\omega }_2),$ with ρ given in Table 1.6.

TABLE 3.16. Geometric factors contributing to d_eff(ω₁) for each of the nonzero elements of the d matrix, for positive uniaxial crystals with point group 6mm, such as CdSe

The geometric factors ...