  On the basis of the Edward-Kornfeld formulation, we study the effective
susceptibility of secondharmonic generation (SHG) in colloidal crystals, which
are made of graded metallodielectric nanoparticles with an intrinsic SHG
susceptibility suspended in a host liquid. We find a large enhancement and
redshift of SHG responses, which arises from the periodic structure, local
field effects and gradation in the metallic cores. The optimization of the
Ewald-Kornfeld formulation is also investigated.
