Shape-invariance properties of a quartic-aberrated TEM00 Gaussian beam

The concepts of shape-invariance error (SIE) and shape-invariance range (SIR) have recently been introduced to specify in a quantitative way the shape changes suffered by a beam on propagation. Here such parameters are evaluated for the case of a fundamental Gaussian beam in the presence of a quartic aberration of its wave front. Numerical results are presented for the case of a collimated aberrated beam. Generalization to the case of noncollimated beams is also given