Effective medium theory is of great importance for using the artificial microstructure materials to extend the optical parameters. In this article, we develop a new kind of effective medium theory for artificial microstructures with nonlocal effects, like photonic crystals, which we name the pseudo-local effective medium theory. The optical properties of the pseudo-local effective medium are described by effective local permittivity
${\overleftrightarrow \varepsilon ^{\rm{p}}}\left( \omega \right)$
and permeability
${\overleftrightarrow \mu ^{\rm{p}}}\left( \omega \right)$
, together with an additional wave vector
${{{k}}_a}$
. We find that the pseudo-local medium exhibits a unique blend of local and nonlocal characteristics. On the surface normal to
${{{k}}_a}$
, the pseudo-local medium is optically equivalent to its local medium counterpart. While on the surface parallel to
${{{k}}_a}$
, the abnormal wave phenomena induced by inherent nonlocality, such as negative refraction and total reflection, may occur. Furthermore, it is found that a
$\text{π}$
phase shift is added to transmission wave through the pseudo-local medium composed of odd number of unit cells under all incident angles. Based on this unique feature, an all-angle phase grating is proposed. Our work opens a route towards the advanced optical devices based on the pseudo-local effective media.
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