Implementation of Tightly Focused Gaussian Beams in FDTD Method

Abstract

A novel approach for the introduction of tightly focused Gaussian beams in finite-difference time-domain (FDTD) utilizing a seventh-order correction formula is proposed. The correction is implemented to address the limitations of the paraxial approximation in terms of accuracy under tight focus conditions. Furthermore, it is a more straightforward method than the plane wave expansion method. The beam is introduced in FDTD by utilizing the field distribution of a specific cross section along the propagation direction as the source plane, based on the equivalence principle. Consequently, the proposed method is readily capable of facilitating the generation of a convergent light beam through amplitude and phase modulation, in contrast to the conventional approach of introduction using field values at the waist as the source. Finally, the accuracy and applicability of the proposed method are validated through numerical examples.