Applied Physics B

, 91:629 | Cite as

A study of source plane Mathieu beams



We derive the source field expressions of different Mathieu beams. In particular, Mathieu beams consisting of the infinite summations of J-type Bessel functions and their Gaussian counterparts are studied. Mathieu beams based on the summation of I-type Bessel functions are introduced as well. By plotting the source intensities of such beams, the variations of the related profiles are examined against the changes in the source parameters. It is found that, via the adjustment of these parameters, it is possible to obtain completely new beam configurations and also those similar to the existing beams of the present literature.


Bessel Function Gaussian Beam Helmholtz Equation Side Lobe Bessel Beam 
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  1. 1.
    J.C. Gutierrez-Vega, Theory and numerical analysis of the Mathieu functions, available at Scholar
  2. 2.
    R. Chakraborty, A. Ghosh, J. Opt. Soc. Am. A 23, 2278 (2006)CrossRefADSGoogle Scholar
  3. 3.
    A. Chafiq, Z. Hricha, A. Belafhal, Opt. Commun. 253, 223 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    J.C. Gutierrez-Vega, R.M. Rodriguez-Dagnino, Am. J. Phys. 71, 233 (2003)CrossRefADSGoogle Scholar
  5. 5.
    A. Chafiq, Z. Hricha, A. Belafhal, Opt. Commun. 275, 165 (2007)CrossRefADSGoogle Scholar
  6. 6.
    C.A. Dartora, M. Zamboni-Rached, K.Z. Nobrega, E. Recami, H.E. Hernandez-Figueroa, Opt. Commun. 222, 75 (2003)CrossRefADSGoogle Scholar
  7. 7.
    J.C. Gutierrez-Vega, M.D. Iturbe-Castillo, S. Chavez-Cerda, Opt. Lett. 25, 1493 (2000)CrossRefADSGoogle Scholar
  8. 8.
    C.A. Dartora, H.E. Hernandez-Figueroa, J. Opt. Soc. Am. A 21, 662 (2004)CrossRefADSGoogle Scholar
  9. 9.
    A. Chafiq, Z. Hricha, A. Belafhal, Opt. Commun. 265, 594 (2006)CrossRefADSGoogle Scholar
  10. 10.
    J.C. Gutierrez-Vega, M.A. Bandres, J. Opt. Soc. Am. A 22, 289 (2005)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    A. Chafiq, Z. Hricha, A. Belafhal, Opt. Commun. 278, 142 (2007)CrossRefADSGoogle Scholar
  12. 12.
    M. Guizar-Sicairos, J.C. Gutierrez-Vega, Opt. Lett. 31, 2912 (2006)CrossRefADSGoogle Scholar
  13. 13.
    J.C. Gutierrez-Vega, M.A. Bandres, J. Opt. Soc. Am. A 24, 215 (2007)CrossRefADSGoogle Scholar
  14. 14.
    I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series and Products (Academic Press, San Diego, 2000)Google Scholar
  15. 15.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970)Google Scholar
  16. 16.
    S. Ruschin, J. Opt. Soc. Am. A 11, 3224 (1994)ADSGoogle Scholar
  17. 17.
    H.T. Eyyuboğlu, Appl. Phys. B 88, 259 (2007)CrossRefADSGoogle Scholar
  18. 18.
    F.A. Alhargan, ACM Trans. Math. Software 26, 390 (2000)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Electronic and Communication Engineering DepartmentÇankaya UniversityAnkaraTurkey

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