Quasi-discrete Hankel transform of integer order for wave propagation

A numerical method for computing integer order Hankel transforms using a Fourier-Bessel expansion is presented. The method satisfies the discrete form of the Parseval theorem assuring energy conservation, this makes the formulation particularly useful for field propagation. Some relevant properties of the transformation matrix are discussed. Additionally, a numerical comparison with other typical methods is performed, the advantages and disadvantages of the method are discussed. To verify its accuracy to propagate an optical field, the method is used to obtain higher azimuthal order modes in an optical resonator using the iterative Fox & Li approach, resulting in a reduction of memory requirements and processing time, the results are compared to the traditional two-dimensional Fourier transform approach.