The finite-difference frequency-domain (FDFD) method is an effective method for numerical simulation of electromagnetic fields. It has great advantages in dealing with electromagnetic scattering problems of complex structures and complex media. This method can transform the frequency-domain Maxwell equations into a linear system for solution by difference operation on the spatial grid. However, high-precision differential calculations can result in more memory consumption and a decrease in computational speed. In previous reports, subgridding technique is often used to solve such problems, where mesh refinement is only performed in local areas, while coarse mesh partitioning is still used in other areas. However, the refinement area can only be manually set, lacking flexibility and accuracy. Therefore, we propose a novel FDFD method based on adaptive grids, which uses the cartesian tree-based hierarchical grids to discrete the spatial domain. It can automatically refine the local grids according to the geometrical characteristic of the model to improve the accuracy of specific areas, without significantly increasing the number of unknowns, and has strong flexibility while improving the calculation efficiency. In this study, we use two levels of grids for adaptive grids construction, with a mesh size ratio of 3:1. Using second-order interpolation to handle the transmission problem of electromagnetic field components at different grid boundaries. The simulation results show that the computation speed of the adaptive grids FDFD system is faster than that of structured grids.
Fiber-tip lens not only makes the optical system more flexible and compact, but also eliminates complex alignment process, which makes it widely used in the fields of spatial light-fiber coupling, laser direct writing and fiber optic imaging. Compared to traditional glass lens, metalens is easier to be processed and integrated on fiber tip because of its special planar structure and small footprint. Fiber-tip metalens with high efficiency achromatic focusing ability has great application potential in multimode endoscope and other optical fiber imaging systems, so we designed a metalens with Si nanopost array that can achieve broadband focusing in the wavelength range of 1.2μm - 1.6μm. For realizing broadband achromatic focusing, it is the crucial to meet the focusing phase and phase dispersion requirements simultaneously. Then we built a library of unit pillars with three kinds of cross-sectional geometries to provide diverse focusing phase (φ) and phase dispersion (δφ) combinations and defined a phase-dispersion space composed of parameters. In order to find the optimal unit pillar at each cell, we regarded the minimum Euclid distance between the points from the library and the target point in the phase-dispersion space as the criterion. Photonic crystal fiber (PCF) is a suitable integration platform for metalens because of the large core diameter and good dispersion property, so the PCF guided mode and plane wave are selected to lunch into the metalens for comparison and verification in the present work. The simulation results demonstrated that the metalens had a good achromatic focusing performance in the target wavelength band and changed little at different polarization of the source, which showed a good polarization-insensitive property.
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