A QED framework for nonlinear and singular optics
The theory of quantum electrodynamics is employed in the description of linear and nonlinear optical effects. We study the effects of using a two energy level approximation in simplifying expressions obtained from perturbation theory, equivalent to truncating the completeness relation. However, applying a two-level model with a lack of regard for its domain of validity may deliver misleading results. A new theorem on the expectation values of analytical operator functions imposes additional constraints on any atom or molecule modelled as a two-level system. We introduce measures designed to indicate occasions when the two-level approximation may be valid. Analysis of the optical angular momentum operator delivers a division into spin and orbital parts satisfying electric-magnetic democracy, and determine a new compartmentalisation of the optical angular momentum. An analysis is performed on the recently rediscovered optical chirality, and its corresponding flux, delivering results proportional to the helicity and spin angular momentum in monochromatic beams. A new polarisation basis is introduced to determine the maximum values that an infinite family of optical helicity- and spin- type measures may take, and disproves recent claims of ‘superchiral light’. A theoretical description of recent experiments relate helicity- and spin- type measures to the circular differential response of molecules, and show that nodal enhancements to circular dichroism relate only to photon number-phase uncertainty relation and do not signify ‘superchiral’ regions. The six-wave mixing of optical vortex input, in nonlinear media, demonstrates the quantum entanglement of pairs of optical vortex modes. The probability for each possible output pair displays a combinatorial weighting, associated with Pascal’s triangle. A quantum electrodynamic analysis of the effect of a second body on absorption can be extended by integrating over all possible positions of the mediator molecules, modelling a continuous medium. This provides links with both the molecular and bulk properties of materials.
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