Simulation of directional couplers using the coupled mode theory

Several modifications of coupled mode theory, along with its classical formulation, are examined and compared to commercial beam envelope method (BEM) and finite-difference time-domain (FDTD) software solutions. This research focuses on evaluating their applicability in determining the geometric parameters of a directional coupler composed of two slab dielectric waveguides, ensuring its functionality as a switch for an optical quantum-like CNOT gate. We assess the accuracy of these simulations for geometric parameters that minimize the device size, where the coupling becomes too strong to be accurately described by classical coupled mode theory. To account for lower-order interactions, we employ rigorous coupled mode theory. Both approaches are compared through simulations of the straight section of the directional coupler, using the BEM and the FDTD method as benchmarks. Furthermore, we analyze the waveguide bends surrounding the straight section and apply a modified effective index method to simulate both signal losses due to bending and mode profile distortions. This method, along with its simplified variant, is also compared to the BEM. It is shown that while both methods describe signal propagation with adequate accuracy at sufficiently large bending radii, the directional coupler introduces a computational error of approximately 2% due to the excitation of subsidiary modes predicted by both approaches.