Optical theory of partially coherent thin-film energy-absorbing structures for power detectors and imaging arrays

Free-space power detectors often have energy absorbing structures comprising multilayer systems of patterned thin films. We show that for any system of interacting resistive films, the expectation value of the absorbed power is given by the contraction of two tensor fields: one describes the spatial state of coherence of the incoming radiation, the other the state of coherence to which the detector is sensitive. Equivalently, the natural modes of the optical field scatter power into the natural modes of the detector. We describe a procedure for determining the amplitude, phase, and polarization patterns of a detector's optical modes and their relative responsivities. The procedure gives the state of coherence of the currents flowing in the system and leads to important conceptual insights into the way the pixels of an imaging array interact and extract information from an optical field.