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Last actualization:   27 dic 2008
 

Mathieu functions

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

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 [pdf]
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 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.

  35

Elliptical beams
M. A. Bandres and Julio C. Gutiérrez-Vega
Opt. Express, 16 (25), 21087–21092, 2008
 

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  34 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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  33 Generation of Mathieu-Gauss modes with an axicon-based laser resonator
Martha B. Alvarez-Elizondo, Rodolfo Rodríguez-Masegosa, and Julio C. Gutiérrez-Vega
Opt. Exp
ress, 16 (23), 18770-18775, 2008
 
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  32 Propagation aspects of Mathieu-Gaussian beams in turbulence
H. T. Eyyuboğlu
Appl. Phys. B, 91 (3), 629-637, 2008
 
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  31 A study of source plane Mathieu beams
H. T. Eyyuboğlu
Appl. Phys. B, 91 (3), 611-619, 2008
 
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  30 Focal shift in vector Mathieu-Gauss beams
Ra
ul I. Hernandez-Aranda and Julio C. Gutiérrez-Vega
Opt. Exp
ress, 16 (8), 5838-5848, 2008
 
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  29 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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  28 Propagation properties of vector Mathieu–Gauss beams
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun. 275, 165-169 (2007).
 
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  27 On the 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 Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems
Ra
ul 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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  25 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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  24 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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  23 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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  22 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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  21 Observation of the experimental propagation properties of Helmholtz-Gauss beams
Carlos López-Mariscal, Miguel A. Bandrés, and Julio C. Gutiérrez-Vega
Opt. Eng. 45 (6), 068001, June 2006
 
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  20 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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  19 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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  18 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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  17 Paraxial propagation of Mathieu beams through an apertured ABCD optical system
A. Chafiq, Z. Hricha, A. Belafhal
Opt. Commun. 253, 223-230 (2005).
 
[Journal]
  16 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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  15 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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  14 Classical Solutions for a free Particle in a Confocal Elliptic Billiard
Miguel A. Bandres and Julio C. Gutiérrez-Vega
Am. J. Phys, 76(6), 810-817, June 2004
 
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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).
 
[Journal]
  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)
 
[Journal]
  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.
 
[pdf]
[Journal]
  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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[Journal]
  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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