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 ( n<sub>2</sub> ) 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 n<sub>2</sub> in the first band. Although TM waves and TE waves may cause different nonlinear effects in two-dimensional Kerr PhCs, it proves that our theoretical calculating method also works well for TE waves.
In this paper, we have systematically investigated light propagating in the hyperbolic metamaterials (HMMs) covered by a subwavelength grating. Based on the equal-frequency contour analyses, light in the HMM is predicted to propagate along a defined direction because of its hyperbolic dispersion, which is similar to the self-collimating effects in photonic crystals. By using the finite-difference time-domain, numerical simulations demonstrate a subwavelength bright spot at the intersection of the adjacent directional beams. Different from the images in homogeneous media, the magnetic fields and electric fields at the spot are layered, especially for the electric fields Ez that is polarized to the propagating direction, i.e., the layer normal direction. Moreover, the Ez is hollow in the layer plane and is stronger than the other electric field component Ex. Therefore, the whole electric field is structured and its pattern can be tuned by the HMM’s effective anisotropic electromagnetic parameters. Our results may be useful for generating subwavelength structured light.