Numerical analysis of optical vortex generation with helical filter using empirical mode decomposition

Abstract

In the Finite-Difference Time-Domain (FDTD) method, the analysis domain is divided into orthogonal meshes, the space is discretized by the finite difference method, and the time step is advanced by the Leap-Frog method. Therefore, it is difficult to accurately model analysis regions with complex shapes or smooth curved surfaces, such as modeling a helical filter with spiral curves to generate an optical vortex. When the filter is modeled with orthogonal meshes, it results in a staircase-like representation. For this reason, reflections at the gaps on the staircase surface will occur in the computational results as non-physical phenomena, which require sufficient numerical verification. In this study, the HE₁₁ mode is injected into a corrugated waveguide, and a helical filter is set to generate an optical vortex using the FDTD method. Moreover, the Empirical Mode Decomposition (EMD) is adopted to remove gap reflections and extract the clear physical phenomenon of the optical vortex. The results revealed that our method could extract the generated optical vortex correctly by removing the non-physical phenomena that occurred in the electric field as a post-processing technique. In addition, these results have also been quantitatively verified in the time-frequency domain using spectrum analysis.