Sixth-order generalised propagation techniques

The underlying structure of the fourth-order generalised propagation methods recently introduced by Hermansson and Yevick is examined and the methods are generalised further to the sixth-order. The new methods are then applied to the simulation of light focusing by an integrated optic microlens and for the first time an accuracy improvement is observed in representative calculations of up to 13 orders of magnitude in comparison with standard beam propagation techniques.