Beam propagation of a higher-order cosh-Gaussian beam

On the basis of the second-order moment, the beam propagation of a higher-order cosh-Gaussian beam has been investigated. Two analytical expressions of the M2 factor have been derived, which corresponds to the parity of the beam order n. The M2 factor is determined by the beam order n and the parameter δ. The influences of the beam order n and the parameter δ on the M2 factor are illustrated with numerical examples. The analytical kurtosis parameter has also been presented. The analytical formula is further simplified in the source plane and the far field, respectively. With given appropriate values of n and δ, the kurtosis parameter in the far field is smaller than 3. This research is helpful to the practical applications of a higher-order cosh-Gaussian beam.