Grothendieck duality made simple

It has long been accepted that the foundations of Grothendieck duality are complicated. This has changed recently. By "Grothendieck duality" we mean what, in the old literature, used to go by the name "coherent duality". This isn't to be confused with what is nowadays called "Verdier duality", and used to pass as "$\ell$-adic duality".Comment: Revised to incorporate improvements suggested by a few people, most notably an anonymous refere

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

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