Abstract
Standard formulations of rigorous Fourier-expansion analysis methods of lamellar gratings reduce, irrespective of the state of polarization, to the TE result of the lowest-order theory of form birefringence when only the zeroth-order terms are retained in the field and permittivity expansions. A reformulation is presented that reduces to the correct form-birefringence result also in the TM case. Expressions are given for the effective relative permittivities ∊eff of a subwavelength-period grating with an arbitrary relative-permittivity profile ∊r(x): the lowest-order approximation for ∊eff is given by the zeroth-order Fourier coefficient of ∊r(x) in TE polarization and of 1/∊r(x) in TM polarization.
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