Effective Medium Theories EMTs for Subwavelength Gratings

Effective Medium Theories (EMTs) for Subwavelength Gratings 

Let us first consider the polarization for which the electrical field is perpendicular to the grating vector E ). Due to the continuity of the tangential component of the electrical field, the electrical field is the same in regions 1 and 2. If we define the filling factor/ by  

Equations (4) and (6) can also be written by using an ordinary (O) and an extraordinary (E) effective refractive index  

The effective refractive indices in (7) and (8) are labeled with a zero because in the literature, effective refractive indices based on static field considerations are called zero-order effective refractive indices as they have no correction term taking the ratio A/ 0 into account and this will be described below. 

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