A master equation approach to nonlinear optics and chemical reactions

Part 1 of this thesis consists of a theoretical quantum statistical analysis of several nonlinear optical processes. As an introduction a master equation describing the time behaviour of the field in a general irreversible nonlinear interaction between an optical photon field and a number of two level atoms is given. This master equation is then used to calculate the exact time dependent statistical properties of the light fields in certain special processes: two photon emission by atoms, two photon absorption by atoms and Raman scattering of photons by atoms. The steady states of the emission-absorption processes are examined, and found to have interesting statistical properties not found in the field states normally met with. Part 1 is concluded with a brief examination of approximate methods of solutions for the nonlinear processes studied. Part 2 is a brief study of the nature of concentration fluctuations and correlations in chemically reacting systems, using the stochastic master equation approach. The time dependent fluctuations and spatial correlations are discussed for a space dependent model of a linear chemically reacting system. These results are compared with those obtained when correlations are ignored. The steady state behaviour of a particular nonlinear chemical system is then examined. Deterministic and non space-dependent stochastic analysis show that when certain system parameters are varied, the system’s behaviour is very similar to that of a thermodynamic system which undergoes a second order phase transition. A space-dependent analysis is then given, and this makes the analogy very close indeed.

Grantor dc:publisher.institution

The University of Waikato

Year dc:date.issued

1976

Author dc:creator

• McNeil, Kenneth James

Advisors dc:contributor.advisor

• Walls, D.F.
• Gardiner, Crispin

Statement dc:rights

• All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.

Licence

• https://researchcommons.waikato.ac.nz/bitstreams/fd46dd8a-9545-484f-8cd5-3679f2b5b725/download