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 (Γ) and truncation parameter (C0) on the transverse intensity distribution of the Gaussian beam and on the energy flux distribution of radially polarized Laguerre—Gaussian beam are analysed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)