Laser Beam Propagation in Nonlinear Optical Media

1.7.3      Propagation along the principal plane Y Z

Another special case of light propagation in an anisotropic crystal is that of propagation along a principal plane, such as the XY, YZ or ZX planes. We start with the propagation vector k lying in the YZ plane, so that m_X = 0 and $m_Y^2+m_Z^2=1$. With m_X = 0, Eqns. 1.55 give

$\mathcal{A}=n_Y^2{m}_Y^2+n_Z^2{n}_Z^2,\mathcal{B}=n_Y^2{m}_Z^2+n_X^2\mathcal{A},\text{and}\mathcal{C}=n_X^2{n}_Y^2{n}_Z^2.$

(1.109)

The two cases of n_X < n_Y < n_Z and n_X > n_Y > n_Z are considered separately in the next two subsections.

1.7.4      k along YZ plane, Case 1: n_X < n_Y < n_Z

In this case, from 1.56 $\mathcal{D}=n_Y^2{n}_Z^2-n_X^2\mathcal{A}$, since $\mathcal{D}$ is defined to be positive and $\mathcal{A}$ takes the values from $n_Y^2$ to $n_Z^2$ as m_Y goes from 1 to 0. Thus, the possible values of n (from Eqn. 1.57) are

$n_{}$