Parametric conversion in semi-classical optics

Poster-paper at the Aharonov Bohm and Berry Phase Anniversary (ABB 50/25) Conference at Bristol, 14-15 December 2009: Trevor W Marshall & Max K Wallis (Cardiff University)

The rainbow of down-converted radiation emerging from a laser-pumped nonlinear crystal has a natural explanation in classical optics via the zeropoint electromagnetic field with wide spectrum of modes.  Parametric down-conversion (PDC) from this viewpoint is the combination of the laser with each zeropoint field mode to generate a phase matched (frequencies and wave vectors) pair of output modes, given by perturbation solutions of Maxwell’s equations.
Phase matching occurs for the sum of frequencies as well as their difference, leading to the prediction of parametric up-conversion (PUC). This phenomenon of classical optics for a pair of lasers is predicted to occur also (‘spontaneously’) via zeropoint field modes*.  It does not have a counterpart in quantum optics.  The two phenomena would be better termed PDCV and PUCV, to express conversion from the ‘vacuum’.  For detection of the up-converted rainbow, emergent angles and intensities have been calculated for specific nonlinear crystals. The importance of such a description based on the unquantized light field lies in it being consistently local, unlike the nonlocal description of quantum optics.

The wider context and references are here.

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