3.1: The Optical Kerr Effect

In an isotropic and homogeneous medium, the refractive index can not depend on the direction of the electric field. Therefore, to lowest order, the refractive index of such a medium can only depend quadratically on the field, i.e. on the intensity [22]

\[\begin{align*} n &= n(\omega, |A|^2) \\[4pt] &\approx n_0 (\omega) + n_{2, L} |A|^2. \end{align*} \nonumber \]

Here, we assume, that the pulse envelope \(A\) is normalized such that \(|A|^2\) is the intensity of the pulse. This is the optical Kerr effect and \(n_{2,L}\) is called the intensity dependent refractive index coefficient. Note, the nonlinear index depends on the polarization of the field and without going further into details, we assume that we treat a linearly polarized electric field. For most transparent materials the intensity dependent refractive index is positive.

Material	Refractive index \(n\)	\(n_{2, L} [cm^2/W]\)
Sapphire (\(\ce{Al2O3}\))	1.76 @ 850 nm	\(3 \times 10^{-16}\)
Fused Quarz	1.45 @ 1064 nm	\(2.46 \times 10^{-16}\)
Glass (LG-760)	1.5 @ 1064 nm	\(2.9 \times 10^{-16}\)
YAG (\(\ce{Y3AL5O12}\))	1.82 @ 1064 nm	\(6.2 \times 10^{-16}\)
YLF (\(\ce{LiYF4}\)), \(n_e\)	1.47 @ 1047 nm	\(1.72 \times 10^{-16}\)
Si	3.3 @ 1550 nm	\(4 \times 10^{-14}\)