Theoretical Calculation of Reference Focal and Diffractional Electromagnetic Fields Based on Wave Catastrophe Special Functions

摘要

A method is developed for calculating wave catastrophe special functions (WCSFs) and their derivatives which describe reference fields corresponding to principal, edge, and angular catastrophes. The method is employed to obtain uniform asymptotical representations of electromagnetic fields in regions of structurally stable wave catastrophe focusing due to electromagnetic wave focusing and diffraction. In order to provide efficient calculation of WCSFs, systems of ordinary differential equations (ODEs), which can be solved using fast, high-accuracy, and stable standard algorithms, are derived from systems of canonical partial differential equations. The ODEs for WCSFs corresponding to principal (A_2, A_3, and D_4), edge (B_(2-4), C_(2-4), F_4, K_(4,2), and F_(1,0)), and angular (A_1~4 and A_1A_2A_1~2) catastrophes are presented.