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Analytic solution of flat-top Gaussian and Laguerre-Gaussian laser field components.

We generalized the nonparaxial field components of Laguerre-Gaussian and flattened Gaussian beams obtained using the angular spectrum method to include symmetric radial and angular expansions and simplified them using an approximate evaluation of the integral equations for the field components. These field components possess series expressions in orders of a natural expansion parameter, which clarifies the physical interpretation of the series expansion. A connection between Laguerre-Gaussian and flat-top Gaussian profiles is obtained.