Numerical investigation of the M2 factor of paraxial Ince-Gaussian beams

Document Type : Full length research Paper

Authors

Abstract

Ince-Gaussian beams are a complete member of Helmholtz-Gauss beams and are exact and orthogonal solution of paraxial wave equation in elliptical cylindrical coordinates. In this paper, numerical evaluation of the M2 factor of Ince-Gaussan beams based on second order moments of intensity is presented. The results show that the M2 factor is an increasing function of mode order whereas it is independent of mode number. These calculations can help optical system designers to compute the quality factor of these beams very easily without the need to use other complex calculations. 

Keywords

Main Subjects

References

[1] M.A. Bandres, J.C. Gutierrez-Vega, Ince-Gaussian beams, Optics Letters 29 (2004) 144-146.
 
[2] M. Woerdemann, C. Alpmann, C. Denz, Optical assembly of microparticles into highly ordered structures using Ince-Gaussian beams, Applied Physics Letters 98 (2011) 111101.
 
[3] U.T. Schwarz, M.A. Bandres, J.C. Gutiérrez-Vega, Observation of Ince–Gaussian modes in stable resonators, Optics Letters 29 (2004) 1870-1872.
 
[4] C. Shu-Chun, O. Kenju, Numerical study for selective excitation of Ince-Gaussian modes in end-pumped solid-state lasers, Optics Express, 15 (2007) 16506-16519.
 
[5] M. Sabaeian, H. Nadgaran, Bessel–Gauss beams: Investigations of thermal effects on their generation, Optics Communications 281 (2008) 672-678.
 
[6] D. Deng, Q. Guo, Ince–Gaussian beams in strongly nonlocal nonlinear media, Journal of Physics B: Atomic, Molecular and Optical Physics 41 (2008) 145401.
 
[7] H. Nadgaran, M. Servatkhah, The effects of induced heat loads on the propagation of Ince–Gaussian beams, Optics Communications 284 (2011) 5329-5337.
 
[8] H. Nadgaran, M. Servatkhah, M. Sabaeian, Mathieu-Gauss beams: A thermal consideration, Optics Communications 283 (2010) 417-426.
 
[9] G. Zhou, K. Zhu, F. Liu, Vectorial structure of Ince–Gaussian beam in the far field Journal of Modern Optics, 54 (2007) 2807-2817.
 
[10] A. Mathew, K. Choudhury, A. Garg, S. Kanojia, P. Sen, T.J. Andrews, Generation and Propagation of Higher order Gaussian Beams, International Conference on Optics and photonics, CSIO, Chandigarh, India, 30 Oct.-1 Nov.(2009).
 
[11] D. Aguirre-Olivas, G. Mellado-Villaseñor, D. Sánchez-de-la-Llave, V. Arrizón, Efficient generation of Hermite–Gauss and Ince–Gauss beams through kinoform phase elements, Applied Optics, 54 (2015) 8444-8452.
 
[12] Y. Ren, Z. Fang, L. G, Kun Huang, Y. Chen, R. Lu, Dynamic generation of Ince-Gaussian modes with a digital micromirror device, Journal of Applied Physics 117 (2015) 133106.
 
[13] H. Eyyuboğlu, Propagation analysis of Ince–Gaussian beams in turbulent atmosphere, Applied Optics 53 (2014) 2290-2296.
 
[14] L. Carbone, P. Fulda, C. Bond, F. Brueckner, D. Brown, M. Wang, D. Lodhia, R. Palmer, A. Freise, “The generation of higher-order Laguerre-Gauss optical beams for high-precision interferometry, Journal of Visualized Experiments. 78 (2013) 50564.
 
[15] R. Borghi, and M. Santarsiero, M2 factor of Bessel–Gauss beams, Optics Letters 22 (1997) 262-264.
 
[16] A. Siegman, New developments in laser resonators, Proceedings of SPIE, 1224 (1990) 2.
[17] P.A. Belanger, Beam propagation and the ABCD ray matrices, Optics Letters 16 (1991) 196-198.
 
[18] M. Mahdieh, Numerical approach to laser beam propagation through turbulent atmosphere and evaluation of beam quality factor, Optics Communications 281 (2008) 3395–3402.
 
[19] K. Xiaoping, L. Baida, The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams, Optical and Quantum Electronics, 38 (2006) 547-556.

[20] G. Wu, Q. Lou, J. Zhou, J. Dong, Y. Wei, Z. Su, Propagation of flat-topped beams, Optics & Laser Technology, 40 (2008) 494-98.

[21] X. Kang, B. Lu, The M2 factor of nonparaxial Hermite-Gaussian beams and related problems, Optik, 116 (2005) 232-236.

[22] Z. Guo-Quan and F. Yan, M2 factor of four-petal Gaussian beam, Chinese Physics B, 17 (2008) 3708.

[23] A. Chafiq, Z. Hricha, A. Belafhal, Parametric characterization of Mathieu–Gauss beams, Optics Communications 282 (2009) 2590-2594.

[24] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific, Cambridge University Press (1992).

Files

History

  • Receive Date: 28 November 2014
  • Revise Date: 02 March 2016
  • Accept Date: 19 June 2016

Share

How to cite

Statistics