Analysis of guided-resonance-based polarization beam splitting in photonic crystal slabs

We present an analysis of the phase and amplitude responses of guided resonances in a photonic crystal slab. Through this analysis, we obtain the general rules and conditions under which a photonic crystal slab can be employed as a general elliptical polarization beam splitter, separating an incoming beam equally into its two orthogonal constituents, so that half the power is reflected in one polarization state, and half the power is transmitted in the other state. We show that at normal incidence a photonic crystal slab acts as a dual quarter-wave retarder in which the fast and slow axes are switched for reflection and transmission. We also analyze the case where such a structure operates at oblique incidences. As a result we show that the effective dielectric constant of the photonic crystal slab imposes the Brewster angle as a boundary, separating two ranges of angles with different mechanisms of polarization beam splitting. We show that the diattenuation can be tuned from zero to one to make the structure a circular or linear polarization beam splitter. We verify our analytical analysis through finite-difference time-domain simulations and experimental measurements at infrared wavelengths.