Propagation of a four-beamlets laser array through an apertured optical system

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, an analytical formula for a four-beamlets laser array propagating through an apertured ABCD optical system is derived based on the generalized Collins formula. As a numerical example, the on-axis irradiance of a four-beamlets laser array focused by a squarely apertured bifocal thin lens is studied, and it is found that the focused irradiance is closely related to the parameters of the optical system and the laser array. Our formula provides a convenient way for studying the paraxial propagation of a four-beamlets laser array through an apertured ABCD optical system.