The extinction ratio in optical two-guide coupler Delta beta switches

Two-guide Δβ optical couplers that operate as on-off switches are reexamined using the exact eigenmodes of a slab waveguide model of the coupler. Two-section alternately detuned couplers, with the first section detuned by D and the second section by -D, are treated. The input/output configurations analyzed are case (1) where a single output guide is connected to the same guide of the coupler as the input guide, and case (2) where a single output guide is connected to the coupled guide. For both cases, ideal switching, i.e. complete extinction of the off state, can be obtained in the two-section Δβ coupler over a wide range of coupler lengths. The results differ from those of conventional coupled-mode theory, however, in that complete extinction can be obtained when the two sections of the coupler have equal lengths only in a few special cases. Over most of the total coupler length range in which ideal switching is possible in both input/output configurations, the lengths of the two sections cannot be equal if complete extinction is to be obtained.