Linear guidance properties of solitonic Y-junction waveguides

Abstract

A linear Y-junction waveguide device is designed using a generalization of the theory of solitonic potentials for the linear Schrödinger equation. This Y-junction device, unlike other adiabatic Y-junctions, has the advantage that it may be directly written into a planar medium with homogeneous saturable nonlinearity by a strong light beam. The generalized theory provides the error terms that are introduced when the parameters of a solitonic potential are allowed to vary in the propagation direction, and shows that under certain adiabaticity conditions the error is small although the deformation of the potential is significant. At the operating wavelength for which the device is designed to function optimally, the Y-junction has two approximate bound modes that we find explicitly. Each mode has the property that when it is excited at the neck of the junction, it exits in only one of the two output ports. In this way, the device functions like a standard modal splitter in a multimode slab waveguide. When the wavelength is detuned, modal beating is introduced that degrades the optimal switching characteristics. We describe this effect in terms of four universal coupling functions using perturbation theory.