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 , the radial index , and the azimuthal index , which make it difficult to determine the optimal value of and the truncation order on . 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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