Abstract

The truncated second-order moments and generalized M2 factor (MG2 factor) of two-dimensional beams in the Cartesian coordinate system are extended to the case of three-dimensional rotationally symmetric hard-edged diffracted beams in the cylindrical coordinate system. It is shown that the propagation equations of truncated second-order moments and the MG2 factor take forms similar to those for the nontruncated case. The closed-form expression for the MG2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams is derived that depends on the truncation parameter β and beam order N. For N, the MG2 factor equals 4/3 corresponding to the value of truncated plane waves, which guarantees consistency of the formalism.

© 2004 Optical Society of America

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