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Low coherence-induced resonance in double-layer structures having parity-time symmetry

We derive simple formulae for the transmittance $T$ and reflectance $R$ of Gaussian-Schell beams incident upon any stratified dielectric structure by using second-order classical coherence theory in the space-frequency picture. The formalism is applied to a particular structure consisting of a double-layer, with balanced gain and loss, satisfying the parity-time symmetry conditions. It is shown that sources with a low degree of spatial coherence, on the order of the wavelength, can induce large resonant peaks in the transmitted and reflected amplitudes. The resonance peaks vanish as the spatial coherence increases.