Closed-Form Solution for Evanescent Wave of a Two-Dimensional Point Source

Based on the angular spectrum representation (ASR), the total field can be separated into propagating and evanescent waves. This paper proposes a closed-form solution of the evanescent wave for a two-dimensional (2D) point source by using ASR, which considers the aperture facing an arbitrary orientation. To validate the proposed solution in terms of accuracy and computational time, a robust numerical method, i.e., a double exponential (DE) formula, is applied. Computer simulation is conducted in the near-field region (0.2λ-λ). The results show that the proposed method presents a good accuracy with a low error of less than 0.1 dB, compared with the DE formula. Moreover, the calculation time is improved by 7.9-16.4 times by comparing the proposal with the DE formula. From the simulated results, it can be found that the evanescent wave calculated by ASR has an angle dependence for a 2D point source when the aperture used in ASR faces an arbitrary orientation. Our proposal can mathematically explain the reason for an angle dependence. Furthermore, this work finds that fixing the aperture normal to the line of sight obtains the angle-independent evanescent wave for a 2D point source.