Decomposition of a field with smooth wavefront into a set of Gaussian beams with non-zero curvatures

Decomposition of a general arbitrary field into a set of Gaussian beams has been one of the challenges in the Gaussian beam decomposition method for field propagation through optical systems. The most commonly used method in this regard is the Gabor expansion, which decomposes initial fields into shifted and rotated Gaussian beams in a plane. Since the Gaussian beams used have zero initial curvatures, the Gabor expansion method does not utilize the ability of the Gaussian beams to represent the quadratic behavior of the local wavefront. In this paper, we describe an alternative method of decomposing an arbitrary field with smooth wavefront into a set of Gaussian beams with non-zero initial curvatures. The individual Gaussian beams are used to represent up to the quadratic term in the Taylor expansion of the local wavefront. This significantly reduces the number of Gaussian beams required for the decomposition of the field with smooth wavefront and gives more accurate decomposition results. The proposed method directly gives the five ray sets representing the parabasal Gaussian beams, which can then be directly used for propagation of the Gaussian beams through optical systems. To demonstrate the application of the method, we have presented results for the decomposition of fields with strongly curved spherical wavefronts, a cone shaped wavefront, and a wavefront with large spherical aberration. The numerical comparison of the input field with the field reconstructed after the decomposition shows very good agreement in both amplitude and phase profiles. We also show results for the far field intensity distributions of the decomposed wavefronts by propagating in free space using the Gaussian beam propagation method.