Lossy Lamellar Gratings in the Quasistatic Limit

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Abstract
We use a rigorous formalism for lossy lamellar gratings to establish the validity of the quasistatic approximation for this structure in the limit as its period d becomes much finer than the wavelength u of incident light. In the quasistatic limit, the grating behaves like a uniaxial film in its interaction light, its principal refractive indices being given by simple formulae. We show numerically that the quasistatic model of the grating is accurate to better than an absolute tolerance of 0·005 if u/d>40. In the case of perfectly conducting lamellar gratings, we show that the model of a uniaxial film cannot be used in the quasistatic limit. This invalidates the optical model of Yeh for wire-grid polarizers.