Mathieu functions


The Mathieu functions are solutions of the Ordinary and the Modified Mathieu differential equations

Ordinary           Modified

Notes on the theory and numerical analysis of the Mathieu functions
Theory and numerical analysis of the Mathieu functions. v.2.11   [pdf (921 kB)]

 

Mathieu functions, a visual approach
Julio C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, M. A. Meneses-Nava, and S. Chávez-Cerda
Am. J. Phys. 71 (3),  233-242, Mar. 2003.

 

Biography of Emile Mathieu
http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Mathieu_Emile.html

 

Related links on Mathieu functions
http://functions.wolfram.com/MathieuFunctions/
http://mathworld.wolfram.com/MathieuFunction.html
http://math.nist.gov/mcsd/Reports/2001/nesf/node27.html

 

Mathieu beam

Mathieu beams

Mathieu beams are orthogonal eigensolutions of the three-dimensional wave equation in elliptic coordinates.
Their applications are in optics, acoustics, and related wave phenomena.

Related papers on Mathieu beams and Mathieu functions

The articles are Copyright © by the respective publishers, and may be downloaded for personal use only. Any other use requires prior permission of the author and the respective publisher.
 
 
If you know about other paper related to Mathieu beams that is not included  in this list, let me know.

 

  43 Generation of a vectorial elliptic hollow beam by an elliptic hollow fiber
Huirong Li and Jianping Yin
Opt. Lett., 36, (4) 457-459 (2011)
 
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  42 Numerical study for selective excitation of Mathieu-Gauss modes in end-pumped solid-state laser systems
Shu-Chun Chu and Ko-Fan Tsai
Opt. Express, 19, (4) 3236-3250 (2011)
 
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  41 Experimental generation of Mathieu–Gauss beams with a phase-only spatial light modulator
R. J. Hernández-Hernández, R. A. Terborg, I. Ricardez-Vargas and K. Volke-Sepúlveda
Appl. Opt., 49, (36) 6903-6909 (2010)
 
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  40 Propagation of generalized Mathieu–Gauss beams through paraxial misaligned optical systems
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun., 282, (19) 3934-393 (2009)
 
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  39 Parametric characterization of Mathieu-Gauss beams
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun., 282, (13) 2590-2594 (2009)
 
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  38 Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry
B. M. Rodríguez-Lara and R. Jáuregui
Phys. Rev. A, 78, 033813 (2008)
 
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  37 Elliptical beams
M. A. Bandres and Julio C. Gutiérrez-Vega
Opt. Express, 16 (25), 21087–21092, 2008
 
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  36 Stable solitons in elliptical photonic lattices
Adrian Ruelas, Servando López-Aguayo, and Julio C. Gutiérrez-Vega
Opt. Lett. 33 (23), 2785-2787 (2008)
 
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  35 Generation of Mathieu-Gauss modes with an axicon-based laser resonator
Martha B. Alvarez-Elizondo, Rodolfo Rodríguez-Masegosa, and Julio C. Gutiérrez-Vega
Opt. Express, 16 23, 18770-18775, 2008
 
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  34 Propagation aspects of Mathieu-Gaussian beams in turbulence
H. T. Eyyuboğlu
Appl. Phys. B, 91 (3), 629-637, 2008
 
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  33 A study of source plane Mathieu beams
H. T. Eyyuboğlu
Appl. Phys. B, 91 (3), 611-619, 2008
 
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  32 Focal shift in vector Mathieu-Gauss beams
Raul I. Hernandez-Aranda and Julio C. Gutiérrez-Vega
Opt. Express, 16 (8), 5838-5848, 2008
 
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  31 Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere
Rodrigo J. Noriega-Manez and Julio C. Gutiérrez-Vega
Opt. Express, 15 (25), 16328-16341, 2007
 
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  30 Propagation properties of vector Mathieu–Gauss beams
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun. 275, 165-169 (2007).
 
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  29 Helical Mathieu and Parabolic localized pulses
Josué Davila-Rodriguez and Julio C. Gutiérrez-Vega
J. Opt. Soc. Am. A, 24 (11), 3449-3455, 2007
 
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  28 Self-trapped modes in highly nonlocal nonlinear media
Servando López-Aguayo and J. C. Gutiérrez-Vega
Phys. Rev. A, 76, 023814, 2007
 
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  27 Normalization of the Mathieu-Gauss optical beams
J. C. Gutiérrez-Vega and Miguel A. Bandrés,
J. Opt. Soc. Am. A, 24(1), 215-220, 2007
 
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  26 The generation of nondiffracting beams using unexpensive computer-generated holograms
Carlos López-Mariscal and Julio C. Gutiérrez-Vega ,
Am. J. Phys, 75(1), 36-42, 2007
 
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  25 Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems
Raul I. Hernandez-Aranda, J. C. Gutiérrez-Vega, Manuel Guizar-Sicairos, and Miguel A. Bandres
Opt. Express, 14 (20), 8974-8988, 2 Oct. 2006
 
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  24 Generalized Helmholtz-Gauss beams and its transformation by paraxial optical systems
Manuel Guizar-Sicairos and J. C. Gutiérrez-Vega,
Opt. Lett. 31 (19), 2912-2915, 1 Oct. 2006
 
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  23 General construction and connections of vector propagation invariant optical fields: TE and TM modes and polarization states
K. Volke-Sepulveda and E. Ley-Koo
J. Opt. A: Pure Appl. Opt. 8, 867-877 (2006)
 
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  22 A detailed study of Mathieu–Gauss beams propagation through an apertured ABCD optical system
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun. 265, 594-602 (2006).
 
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  21 Propagation of Helmholtz-Gauss beams in absorbing and gain media
Manuel Guizar-Sicairos and J. C. Gutiérrez-Vega
J. Opt. Soc. Am. A, 23 (8), 1994-2001, Aug. 2006
 
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  20 Observation of the experimental propagation properties of Helmholtz-Gauss beams
Carlos López-Mariscal, Miguel A. Bandrés, and J. C. Gutiérrez-Vega
Opt. Eng. 45 (6), 068001, June 2006
 
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  19 Shaping soliton properties in Mathieu lattices
Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner
Opt. Lett. 31, 238–240 (2006)
 
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  18 Orbital angular momentum transfer in helical Mathieu beams
Carlos López-Mariscal, Julio C. Gutiérrez-Vega, Graham Milne and Kishan Dholakia
Opt. Express, 14 (9), 4182-4187, May 2006
 
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  17 Rows of optical vortices from elliptically perturbing a high-order beam
Marc. R. Dennis
Opt. Lett., 31(9), 1325-1327 (2006)
 
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  16 Paraxial propagation of Mathieu beams through an apertured ABCD optical system
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun. 253, 223-230 (2005).
 
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  15 Vector Helmholtz-Gauss and vector Laplace-Gauss beams
Miguel A. Bandres and J. C. Gutiérrez-Vega
Opt. Lett., 30 (16), 2155-2157, 15 Aug. 2005
 
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  14 Helmholtz-Gauss waves
Julio C. Gutiérrez-Vega and Miguel A. Bandres
J. Opt. Soc. Am. A, 22(2), 289-298, Feb. 2005
 
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  13 Properties of a localized Mathieu pulse
C. A. Dartora and H. E. Hernández-Figueroa
J. Opt. Soc. Am. A 21, 662-667 (2004).
 
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  12 Nondiffracting optical beams: physical properties, experiments, and applications
Z. Bouchal
Czech. J Phys., 53, 537-578 (2003).
 
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  11 Focusing evolution of Generalized Propagation Invariant Optical Fields
Julio C. Gutiérrez-Vega, Rodolfo Rodríguez-Masegosa, and S. Chávez-Cerda
J. Opt. A: Pure Appl. Opt. 5, 276-282, May 2003.
 
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  10 General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams
C.A. Dartora, M. Zamboni-Racheda, K.Z. Nobrega, E. Recami, H.E. Hernandez- Figueroa
Opt. Commun. 222, 75–80 (2003)
 
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  09 Mathieu functions, a visual approach
Julio C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, M. A. Meneses-Nava, and S. Chávez-Cerda
Am. J. Phys. 71 (3),  233-242, Mar. 2003.
 
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  08 Holographic generation and orbital angular momentum of high-order Mathieu beams
S. Chávez-Cerda, M.J. Padgett, I. Allison, G.H.C. New, Julio C. Gutiérrez-Vega, A.T. O’Neil, I. MacVicar, and J. Courtial
J. Opt. B: Quantum Semiclass. Opt. 4, S52–S57, Apr. 2002.
 
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  07 Attenuation Characteristics in Confocal Annular Elliptic Waveguides and Resonators
Julio C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, and S. Chávez-Cerda
IEEE Trans. Microwave Theory Tech., 50 (4),  1095-1100,  April 2002.
Additional material and extended version of the paper
 
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  06 Elliptic vortices of electromagnetic wavefields
S. Chávez-Cerda, Julio C. Gutiérrez-Vega, and G.H.C. New
Opt. Lett., 26 (22),  1803-1805,15-Nov. 2001.
 
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  05 Probability distributions in classical and quantum elliptic billiards
Julio C. Gutiérrez-Vega, S. Chávez-Cerda y R. M. Rodríguez-Dagnino
Rev. Mex. Fis., 47 (5),  480-488, Oct. 2001.
 
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  04 Experimental demonstration of optical Mathieu beams
Julio C. Gutiérrez-Vega, M. D. Iturbe-Castillo, G. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and G.H.C. New
Opt. Comm., 195 (1-4),  35-40, 1 Aug. 2001.
 
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  03 New Member in the Family of Propagation Invariant Optical Fields: Mathieu beams
Julio C. Gutiérrez-Vega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramírez, R. M. Rodríguez-Dagnino, and S. Chávez-Cerda
Opt. and Phot. News, 11 (12),  35-36, Dec. 2000
 
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  02 Alternative formulation for invariant optical fields: Mathieu beams
Julio C. Gutiérrez-Vega, M. D.Iturbe-Castillo, and S.Chávez-Cerda
Opt. Lett., 25 (20), 1493-1495, Oct. 15, 2000.
 
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  01 Free oscillations in an elliptic membrane
Julio C. Gutiérrez-Vega, S. Chávez-Cerda and R. M. Rodríguez-Dagnino
Rev. Mex. Fis., 45 (6),  613-622, Dec. 1999.
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