Reciprocity in optics

The application of reciprocity principles in optics has a long history that goes back to Stokes, Lorentz, Helmholtz and others. Moreover, optical applications need to be seen in the context of applications of reciprocity in particle scattering, acoustics, seismology and the solution of inverse problems, generally. In some of these other fields vector wave propagation is, as it is in optics, of the essence. For this reason the simplified approach to light wave polarization developed by, and named for, Jones is explored initially to see how and to what extent it encompasses reciprocity. The characteristic matrix of a uniform dielectric layer, used in the analysis of interference filters and mirrors, is reciprocal except when the layer is magneto-optical. The way in which the reciprocal nature of a characteristic matrix can be recognized is discussed next. After this, work on the influence of more realistic attributes of a dielectric stack on reciprocity is reviewed. Some of the numerous technological applications of magneto-optic non-reciprocal media are identified and the potential of a new class of non-reciprocal components is briefly introduced. Finally, the extension of the classical reciprocity concept to systems containing components that have nonlinear optical response is briefly mentioned.