Fundamental properties of beamsplitters in classical and quantum optics

A lossless beamsplitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws classical and quantum optics to obtain general relations among the magnitudes phases these amplitudes. Proceeding examine a pair (nearly) single-mode wavepackets in number-states [Formula: see text] that simultaneously arrive at splitter's input ports, we find distribution photon-number states output ports using argument inspired by Feynman's scattering analysis indistinguishable Bose particles. The result thus obtained coincides with standard quantum-optical treatment beamsplitters via annihilation creation operators text]. simple application Feynman method provides form justification enhancement implicit well-known formulas