Accuracy of effective medium parameter extraction procedures for optical metamaterials

An effective medium parameter extraction procedure that incorporates first-order spatial dispersion effects is devised to study the homogenization of a one-dimensional stack. It is shown that for such a stack, the proposed extraction procedure yields effective medium parameters that characterize the medium with improved accuracy and are independent of the number of unit cells composing the stack. It is also shown that in the optical regime, where it is difficult to realize a unit cell of a width that is much smaller than the wavelength, the inaccuracy due to use of an extraction procedure that assumes no spatial dispersion can be prohibitively high. This work establishes the importance of extending the common extraction procedure so as to account for spatial dispersion contributions.