Approximate analytical expressions of apertured broadband beams in the far field

The approximate analytical expressions of the apertured broadband beams in the far field with Gaussian and Laguerre--Gaussian spatial modes are presented. For the radially polarized Laguerre--Gaussian beam, the result reveals that the electromagnetic field in the far field is transverse magnetic. The influences of bandwidth (\varGamma) and truncation parameter (C_0) on the transverse intensity distribution of the Gaussian beam and on the energy flux distribution of radially polarized Laguerre--Gaussian beam are analysed.