Efficient numerical calculation method for eigenmodes of diluted waveguide

Diluted waveguides are an important type of structure in regards of on-chip mode conversion devices. This paper addresses the need for rapidly solving the effective refractive index and mode field distribution of diluted waveguides, This paper combines solving the effective refractive index method with the partitioned field matching method in order to systematically analyze the effective refractive index characteristics of quasi-TE modes and quasi-TM modes in diluted waveguides. The numerical calculation results show that when the dilution waveguide size is 3.5μm × 3.75μm, with 5 core layers and 5 cladding layers, modes such as TE11, TE21, and TE13 can exist. Furthermore, compared with the conventional FDTD method, the hybrid numerical calculation method proposed in this paper significantly improves the computational efficiency while maintaining the same level of accuracy. The calculation time is reduced from minutes to seconds. Further analysis was conducted on the mode distribution in the diluted waveguide under the coupling condition of the lensed fiber and the diluted waveguide. The results show that when the diluted waveguide has the above dimensions, the core diameter of the lensed fiber was 9 μm, the grinding radius was 5 μm, and the grinding angle was 45°, the excited modes in the diluted waveguide and their proportions were 82.5% for the TE11 mode, 7.21% for the TE13 mode, and 0.50% for the TE12 mode. The theoretical model and calculation method formed in this study provide a solid foundation for the design and optimization of diluted waveguide and relevant structures, especially for end-face mode spot converters.