A QED framework for nonlinear and singular optics

Coles, Matthew (2014) A QED framework for nonlinear and singular optics. Doctoral thesis, University of East Anglia.

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Abstract

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.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Chemistry
Depositing User: Mia Reeves
Date Deposited: 12 Mar 2014 09:48
Last Modified: 12 Mar 2014 09:48
URI: https://ueaeprints.uea.ac.uk/id/eprint/48104
DOI:

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