A detailed study of Mathieu–Gauss beams propagation through an apertured ABCD optical system

Scattering of Mathieu beams by a rigid sphere

“…Especially, Mathieu beams have attracted much attention in optics since they have been introduced in 2000 by Gutiérrez-Vega et al [5,6]. So, many works in studying propagation properties of these beams through various optical systems have been investigated [7][8][9]. Many applications of these beams have been also proposed in various domains such as photonic lattices, transfer of angular moments and localized X waves among others.…”

Normalization of the Mathieu-Gauss optical beams

“…Several theoretical and experimental patterns have been reported elsewhere. [10][11][12] Like BG beams, the MG beams of the form (3) constitute a complete family of paraxial fields in the sense that any Helmholtz-Gauss beam with the same waist size and spatial frequency can be expressed as a superposition of MG beams with the appropriate weight factors. 10 BG beams represent a special case of the MG beams when the focal distance of the elliptical coordinates reduces to zero.…”

“…11 MG beams constitute one of the simplest approximations to the exact nondiffracting Mathieu beams, and their propagation properties have been studied in free space 10,11 and through apertured ABCD optical systems. 12,13 Although the propagation characteristics of the MG beams are well understood, the normalization factors of these beams have not been calculated until now. The object of the present investigation is to remedy this deficiency.…”

Helical Mathieu and parabolic localized pulses

“…Recently, these beams have been applied for example to photonic lattices [18] and the transfer of orbital angular momentum using optical tweezers [19,20]. Gaussian apodized Mathieu beams, which carry a finite power and can be generated experimentally to a very good approximation, have been already reported in free space [21,22] and through ABCD optical systems [23,24].…”