Birefringence in a dielectric with periodic structure

A general analysis is presented of birefringence in a periodic structure medium. The dielectric anisotropy is approximated by the weighted sum of the squared Fourier coefficients for the permittivity distribution function. It is clarified that a periodic stepwise structure, whose permittivity is either ε
1
or ε
2
, has a larger anisotropy than that of any other graded structure whose maximum and minimum permittivities are ε
1
and ε
2
, respectively. It is also pointed out that the dielectric anisotropy in a sinusoidal structure is about 60 percent of that in a stepwise structure.