Abstract

In this paper we consider a generalization of standard nondiffracting parabolic beams. The proposed generalized beams have two orders: a continuous parameter $a$, as in standard beams, and the new parameter is an integer index $m$. Physically, the last parameter is equal to the number of rotated repetitions of the structure of the original angular spectrum on the total circle in the frequency space. Theoretical investigation shows that for $a=0$ the beams are real functions and have a symmetry of order $2m$. If $a\ne 0$ the beams will be real functions only for odd values of $m$. Moreover, in this case the beams have a symmetry of order $m$, while for even values of $m$ the order of symmetry is $2m$. The results of numerical simulation confirm these conclusions. Examples of generalized traveling parabolic waves, which are formed on the basis of generalized static parabolic beams, are also given.

© 2018 Optical Society of America

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