Effective third-order susceptibility of silicon-nanocrystal-doped silica

We derive approximate analytic expressions for the effective susceptibility tensor of a nonlinear composite, consisting of silicon nanocrystals embedded in fused silica. Two types of composites are considered: by assuming that (i) the crystallographic axes of different crystallites are the same, or (ii) crystallites are oriented randomly. In the first case, the tensor properties of the effective third-order susceptibility are shown to coincide with those of the bulk silicon. In the second case, however, the tensor properties of the susceptibility of the composite material are found to be quite different due to drastic modification of light interaction with optical phonons inside the composite. The newly derived expressions should be useful for modeling nonlinear optical phenomena in silica fibers and waveguides doped with silicon nanocrystals.