Abstract

Laguerre–Gaussian (LG) mode decomposition has found applications in various optics fields. However, numerical LG mode expansion for arbitrary field is still a problem, since the physical dimension of LG modes would vary with three parameters—the beam waist width w, the radial index p, and the azimuthal index m, which make it difficult to determine the optimal value of w and the truncation order on p. Here a general method of LG mode expansion for an arbitrary field is developed. It is found that the local frequency distribution of the LG function consists of two parts, the quasi-periodic part and the chirped part. The effective space-bandwidth product of the LG function is defined as the product of the spatial width and frequency-domain width of the quasi-periodic part. Then, based on this space-bandwidth product definition, the criteria for determining the beam waist parameter and the truncation order of LG series expansion are given. The scheme is tested for the representation of off-axis Hermite–Gaussian mode, which shows that our method is of high accuracy.

© 2019 Optical Society of America

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