Issues of a fundamental quantum origin exert a significant effect on the output mode structures in optically parametric processes. An assumption that each frequency conversion event occurs in an infinitesimal volume produces uncertainty in the output wave-vector, but a rigorous, photon-based theory can provide for a finite conversion volume. It identifies the electrodynamic mechanisms operating within the corresponding region of space and time, on an optical wavelength and cycle timescale. Based on quantum electrodynamics, this theory identifies specific material parameters that determine the extent and measure of delocalized frequency conversion, and its equations deliver information on the output mode structures. The results also indicate that a system of optimally sized nanoparticles can display a substantially enhanced efficiency of frequency conversion.
Kayn A. Forbes, Jack S. Ford, and David L. Andrews, "Quantum localization issues in nonlinear frequency conversion and harmonic generation," Proc. SPIE 10359, Quantum Nanophotonics, 1035908 (Presented at SPIE Nanoscience + Engineering: August 07, 2017; Published: 29 August 2017); https://doi.org/10.1117/12.2269517.
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