Fast Hankel transform and its application for studying the propagation of cylindrical electromagnetic fields.

We present a fast Hankel transform (FHTn) method for direct numerical evaluation of electromagnetic (EM) field propagation through an axially symmetric system. Comparing with the vector-based plane-wave spectrum (VPWS) method, we present an alternative approach to implement the fast Hankel transform which does not require an additional coordinate transformation for Fourier transform. The proposed FHTn method is an efficient approach for numerical evaluation of an arbitrary integer order of the Hankel transform (HT). As an example to demonstrate the effectiveness of the proposed method, we apply the FHTn technique to the analysis of cylindrical EM field propagation through a diffractive microlens.