Electromagnetic field expression of a laser sheet and the order of approximation

The laser sheet (Gaussian beam with an elliptical cross-section) is a powerful tool in optical particle characterization such as in PIV or dual cylindrical wave devices. In order to be able to predict the properties of such devices, an approximate description of laser sheets is introduced. The involved approximation order is then discussed in Cartesian and spherical coordinate systems. It is found that the expressions obtained obey the vector potential equation, the Maxwell equations, and the Bromwich formalism at order O(s 2 ), in which s is a characteristic dimensionless parameter. The approach proposed in this paper may be applied to other shaped beams.