Efficient Modeling of 3D-Printed Freeform Waveguides with a Transformation Optics-Based Beam Propagation Method

An efficient numerical method is introduced for simulating wave propagation in 3D-printed freeform waveguides, referred to as photonic wire bonds (PWBs). This approach integrates transformation optics (TO) with curvilinear meshing to map the original 3D freeform PWB structure onto a straight waveguide, which possesses anisotropic material characteristics. The resulting waveguide is then analyzed using an anisotropic full-vectorial beam propagation method (BPM). To validate the performance and effectiveness of the proposed TO-BPM algorithm, a comparison is made with the finite-difference time-domain (FDTD) technique. Our approach reduces the simulation time by more than two orders of magnitude, depending on the degree of trajectory bending, in combination with a mean absolute percentage error (MAPE) of 3.9% in power transmission simulation relative to the FDTD.