The article focuses on investigation of nonlocal effects in 3D periodic dielectric composites operating in the effective medium regime. Ab-initio simulations using the modified Plane-Wave method provide reliable quantitative description of spatial-dispersion effects, including unusual birefringence, dispersion of optical axes and noticeable isofrequency surface deformations. Additionally, such simulation allows one to derive numerical coefficients for the effective medium approximation and to estimate its accuracy. In our work we consider plane interfaces between isotropic media and dielectric composites, and demonstrate a theoretical possibility to excite surface Dyakonov waves with strong temporal dispersion, which appears to be induced by the mentioned spatial dispersion, and does not exist in case of natural anisotropic dielectrics.

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