As the two main ways to enhance nonlinearity in nano-structured materials, field localization and slow light effects could cooperate to exert influence on nonlinear effect enhancement together. By considering the co-influence of them, we can make use of a field averaging method to calculate the effective nonlinear refractive index coefficient (n2) of Kerr photonic crystals (PhCs). In this paper, we treat the propagation of TE waves in Kerr PhCs in detail as a complementary to TM waves and calculate the effective n2in the first band. Although TM waves and TE waves may cause different nonlinear ...