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

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

Frustration of Bragg reflection by cooperative dual-mode interference: a new mode of optical propagation

A new optical mode of propagation is described, which is the natural eigenmode (supermode) of a fiber (or any optical waveguide) with two cospatial periodic gratings. The mode frustrates the backward Bragg scattering from the grating by destructive interference of its two constituent submodes (which are eigenmodes of a uniform waveguide). It can be used in a new type of spatial mode conversion in optical guides

Interpage and interpixel cross talk in orthogonal (wavelength multiplexed) holograms

The problem of cross talk in image-bearing wavelength-multiplexed holograms was raised recently [A. Yariv, in Digest of Conference on Nonlinear Optics (Optical Society of America, Washington, D.C., 1992), postdeadline paper E-2]. In the limit of a large aperture (lens, crystal) it is shown that the cross talk is independent of the information content. The reduction of the hologram volume is shown to introduce interpixel as well as interpage cross talk

On the coupling coefficients in the "coupled-mode" theory

The "coupled-mode" theory has proved itself to be an important tool in the analysis of energy exchange phenomena between traveling waves. In its original form [1] it is capable of yielding important qualitative results. To extend its range of usefulness into the quantitative domain, one needs to evaluate the coupling coefficients which govern the energy exchange. This is done in this paper where we treat the 'small coupling' case. We assume that in obtaining the coupling coefficients for the small coupling case we may use for the different physical observables their values in the absence of coupling. This procedure is analogous to that used in evaluating the Q of a cavity or the attenuation constant of a waveguide, for the small loss case, where the loss-free field solutions are used instead of the actual solutions in the presence of losses, and is a type of perturbation theory formulated on physical grounds

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