Focal shift and concept of effective Fresnel number for a Gaussian laser beam.

The actual focal plane for a laser beam under frequently encountered conditions is shifted from the plane given by geometrical optics. The concept of effective Fresnel number for an unapertured Gaussian laser beam is defined and used to examine focal shifts. It is found that the effective Fresnel number has a simple physical interpretation that makes clear its relationship to the focal shift phenomena. Expressions are obtained that relate the important Gaussian beam parameters to the effective Fresnel number, and a method of correcting for the focal shift in optical systems design is described.