Three-Dimensional Compacted Optical Waveguide Mode Converter/Splitter Designed by Invariant Engineering

In this paper we demonstrate an analytical method, basing on the invariant engineering, to solve the relevant coupled mode equations for designing various grating-assisted 3D optical waveguide mode converter/splitter. Our method is based on the quantum-optical analogy, i.e., the Maxwell equation for the electromagnetic wave propagating along a waveguide structure in the spatial domain is formally equivalent to the Schrödinger equation for the evolution of a quantum system in the time domain. It is found that, the spatial domain invariants can be effectively constructed to solve the 3D coupled-mode equations, analogously to solve the dynamical evolution for the quantum systems in the time domain. The present approach overcomes the complication of solving the coupled-mode equation by the usual numerical method. As a consequence, by appropriately setting the coupling parameters between the grating-assisted interconnected waveguides, the desired mode conversion/splitting based on 3D coupler can be designed conveniently. As the invariant method is a natural shortcut to the adiabaticity, the compacted devices designed by the invariant-based engineering are useful for the fabrications of various 3D integrated optical devices.