Phase Conjugation with Loss or Gain

Phase conjugation, discovered over 20 years ago, now has a wide assortment of applications. However, phase conjugation requires that the medium in which the phase conjugation takes place in be lossless. Based on recent preliminary research for which it is anticipated a patent will be applied for, it now appears possible for a limited though important class of materials to extend the phase conjugation concept to loss or gain. Specifically, the loss or gain medium must be first order, that is have a symplectic matrix representation. Prototypical devices satisfying this condition are Gaussian apertures, Gaussian ducts, and Gaussian "lasers". It has been proved recently that any first order system with loss or gain can be modeled exactly using such devices, which indicates that a phase conjugator for loss or gain can indeed be built, at least in principle. It is easy to show mathematically that for first order systems this generalized phase conjugation reduces to just ordinary phase conjugation when the system is lossless.