Three-space representation of phase-mismatch switching in coupled two-state optical systems

A three-space graphical representation for the operation of optical switch/modulators based on two-state systems is reviewed. This visual framework provides insight into the behavior of devices such as the waveguide directional coupler and Mach-Zehnder interferometric switches and combiners and the concept of delta-beta reversal. I is based on the covering map of the group onto and is analogous to the Poincaré formulation for polarization. Because of its pictorial nature, this representation can serve as an aid in the conception of innovative device structures. A class of switches identified using this approach is described and demonstrated by experiment.