Four-beamlets laser array and its propagation

A new type of laser array named four-beamlets laser array is proposed. Based on the diffraction integrals, analytical propagation formulae for the four-beamlets laser array passing through paraxial aligned and misaligned optical systems are derived, respectively. The four-beamlets laser array can also be expressed as a superposition of a series of Hermite Gaussian modes by using polynomial expansion. As a numerical example, the propagation properties of a four-beamlets laser array in free space are illustrated graphically. The fractional Fourier transform of the four-beamlets laser array is also studied. Our model provides a convenient way to describe laser array with four-beamlets.