Double-slit Interference as a Lossy Beam-splitter

A post-selected unitary description of optical interferometers makes them a good machine for quantum information processing and computation. However, slit diffraction/interference lacks a unitary description. We present a classical post-selected unitary description of slit diffraction, bringing it at par with other interferometries.
The solution of Helmholtz equation in three dimensions with N sources are projected on two-dimensional surfaces called slices, all parallel to each other. A post-selected unitary description of slit-diffraction is achieved by representing diffraction as a map between slices as they pass through slits and projecting the slices on N detectors to obtain an N × N transfer matrix.
Using such a formalism, we show that a double-slit with post-selection taking into account the losses in the diffraction process, is a beam-splitter. With the use of FDTD simulations, the application of this formalism is demonstrated for near-field and far-field cases. We also show that such a framework can be used to get a post-selected unitary description of a diffraction grating.
The classical treatment sets the stage for future research on diffraction-based quantum interferometry which involves quantizing the fields and the construction of sophisticated interferometers.