The application of time evolution operators and Feynman diagrams to nonlinear optics

This paper develops a consistent formalism for describing nonlinear optical mixing and multiphoton processes of any arbitrary order. The theory uses the time-evolution operators of quantum mechanics, and the related Feynman diagrams

Universal relations for coupling of optical power between microresonators and dielectric waveguides

The most basic and generic configuration, which consists of a unidirectional coupling between a ring resonator and a waveguide, is considered. The fundamental working equations required to describe the associated power transfer are derived and the application of this geometry to a variety of optical phenomena is discussed. These phenomena include 'add/dropping' of optical beams, add/drop filtering and optical power switching

Fundamental media considerations for the propagation of phase-conjugate waves

Rigorous and approximate conditions that need to be satisfied by a propagation medium to enable phase conjugation to occur are derived. It is shown that, in spite of the fact that in general, losses spoil phase conjugation, in the important case of paraxial beam propagation (along z), a z-dependent loss can be tolerated. In addition, nonlinear losses (gain) and nonlinear dielectrics are also permitted under some fairly general circumstances

Operator algebra for propagation problems involving phase conjugation and nonreciprocal elements

A self-consistent formalism is developed for treating propagation of beams in situations which include phase conjugation and nonreciprocal elements. Two equivalent field representations, the rectangular polarization and the circular polarization representation, are considered, and the rules for transforming between them are derived. An example involving a proposed new current fiber sensor is analyzed using the formalism

Quantum theory for parametric interactions of light and hypersound

The problem of energy exchange between two electro-magnetic modes of different frequencies and an acoustic mode is formulated and solved. The results of the quantum mechanical analysis are also analyzed in classical terms and are found to be consistent with the theory for parametric interactions. Specific cases treated include: parametric amplification of light, stimulated Brillouin scattering, and frequency conversion

Three-dimensional pictorial transmission in optical fibers

Modal phase dispersion limits image transmission in optical fibers to distances too short to be of general interest. A technique based on nonlinear optical mixing is described for modal phase equalization and recovery of a transmitted image