On the basis of superposition of beams, a group of virtual sources that generate a cosh-Gaussian wave is identified. A closed-form expression is derived for this cosh-Gaussian wave, which, in the appropriate limit, yields the paraxial approximation for the cosh-Gaussian beam. From this expression, the paraxial approximation and the nonparaxial corrections of all orders for the corresponding paraxial cosh-Gaussian beam are determined.
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Zhang et al. (2007) studied this question.
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