Variant of the angular spectrum decomposition method for evaluating the beam shape coefficients: a comparison with the finite series technique

This paper develops a variant of the angular spectrum decomposition (VASD) method for evaluating the beam shape coefficients (BSCs) of light beams containing both forward and backward propagating/attenuating components. Unlike the traditional ASD method, which is limited to unidirectional beams and is based on one boundary condition, the VASD method requires two boundary conditions. Using the VASD method, the BSCs of the on-axis located scalar Gaussian beam are formulated in one dimensional integrals and are further transformed to finite series expressions. It is found that the VASD-BSCs are exactly consistent with the BSCs derived in the finite series (FS) method. Based on the consistency of the VASD and the FS methods, the unexpected far-field divergence and the near-field oscillations observed in the remodeled Gaussian beam can be explained. Besides, the VASD method offers an alternative way to deduce the finite series expressions of the BSCs, thus enabling efficient computation.