Holographic generation and orbital angular momentum of high-order Mathieu beams

We report the first experimental generation of high-order Mathieu beams and confirm their propagation invariance over a limited range. In our experiment we use a computer-generated phase hologram. The peculiar behaviour of the vortices in Mathieu beams gives rise to questions about their orbital-angular-momentum content, which we calculate by performing a decomposition in terms of Bessel beams.

[1]  J. Durnin Exact solutions for nondiffracting beams. I. The scalar theory , 1987 .

[2]  J. Gutiérrez-Vega,et al.  Elliptic vortices of electromagnetic wave fields. , 2001, Optics letters.

[3]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[4]  Attenuation characteristics in confocal annular elliptic waveguides and resonators , 2002 .

[5]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[6]  Michael V. Berry,et al.  Paraxial beams of spinning light , 1998, Other Conferences.

[7]  N. Mclachlan Theory and Application of Mathieu Functions , 1965 .

[8]  J Turunen,et al.  Realization of general nondiffracting beams with computer-generated holograms. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[9]  E. A. Sziklas,et al.  Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method. , 1975, Applied optics.

[10]  Joseph R. Cavallaro,et al.  Generation of diffraction-free beams for applications in optical microlithography , 1997 .

[11]  A. Friberg,et al.  Holographic generation of diffraction-free beams. , 1988, Applied optics.

[12]  J. Greenleaf,et al.  A study of two-dimensional array transducers for limited diffraction beams , 1994, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[13]  Edmund Taylor Whittaker,et al.  On the partial differential equations of mathematical physics , 1903 .

[14]  Miceli,et al.  Diffraction-free beams. , 1987, Physical review letters.

[15]  Shiping He,et al.  Optical X wave communications , 1999 .

[16]  M. S. Soskin,et al.  Chapter 4 - Singular optics , 2001 .

[17]  J. Gutiérrez-Vega,et al.  Alternative formulation for invariant optical fields: Mathieu beams. , 2000, Optics letters.

[18]  Ramón M. Rodríguez-Dagnino,et al.  Experimental demonstration of optical Mathieu beams , 2001 .