Abstract
The truncated second-order moments and generalized factor 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 factor take forms similar to those for the nontruncated case. The closed-form expression for the factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams is derived that depends on the truncation parameter β and beam order N. For the factor equals 4/ corresponding to the value of truncated plane waves, which guarantees consistency of the formalism.
© 2004 Optical Society of America
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