Decentered Gaussian beams

A generalization of the Gaussian beam is obtained by introducing a complex-valued shift in the transverse dimension. The resulting beam has a Gaussian intensity distribution with width varying as an ordinary Gaussian beam, but whose peak traces an inclined linear trajectory. The wave fronts are displaced laterally in a sheared fashion. This generalized beam preserves its form after passing through arbitrary paraxial optical components, even if they are decentered. The peak-intensity line is modified by such systems as if it were a ray.