On the rotation repetitions of Mathieu beams angular spectrum in frequency space.

In the recent works on Mathieu beams, the angular spectrums commonly used are even and odd angular Mathieu functions with an angular variation vary between 0 to 2 π. In this work, we propose to introduce a new index m characterizing the rotation repetitions (m- times) of the structure of the original angular spectrum of Mathieu beams on the total circle in the frequency space. With this index, the angular spectrum of Mathieu beams rotation can be controlled to change the beam symmetry. We study the effect of these repetitions of the angular spectrum on the even and odd Mathieu modes features when they propagate through a paraxial optical system. We show that rotated repetitions of the angular spectrum does not affect the nondiffracting property of the beams. To illustrate the rotation repetitions of the angular spectrum, the Fourier transform of the beam is calculated in the focal plane of a thin lens. From the obtained results, we can conclude that the rotation repetitions of the angular spectrum can be used to produce others Mathieu beams shapes and can enrich the applications of these kinds of beams. [ABSTRACT FROM AUTHOR]