Characteristics of coherent and incoherent off-axis elegant Hermite-Gaussian beam combinations

Applying the definitions of the generalized second and fourth order moments, the beam propagation M-2-factor and the kurtosis parameter of coherent and incoherent combinations of two-dimensional off-axis elegant Hermite-Gaussian beams are derived analytically and numerically, and the power in bucket is also presented numerically. Our results illustrate the propagation properties of the beam through a first-order optical ABCD system. A comparison of the irradiance for coherent and incoherent combinations shows that high peak irradiance can be obtained for coherent combination at the focal plane.