Bending induced phase shifts in arbitrarily bent rectangular-core dual-mode waveguides

We examine the variation of the effective indexes of the two modes of an arbitrarily bent dual-mode rectangular-core waveguide. We find that under the large bending radius approximation, which is indeed the practical case for most of the devices, the waveguide bent with bending radius ρ in a plane at an angle θ with the major axis is almost equivalent to bending it simultaneously in the plane of major and minor axes with bending radii ρsecθ and ρcosecθ, respectively. The bending-induced phase difference between the two modes is found (a) to be maximum when the waveguide is bent along the major axis, and (b) to decrease first and then increase in the opposite direction as the V-number is decreased. The results of our study can be used to improve the sensitivity of the dual-mode optical waveguide sensors and devices based on the bending of fiber