Share This Article:

Theoretical Introduction and Generation Method of a Novel Nondiffracting Waves: Olver Beams

Abstract Full-Text HTML Download Download as PDF (Size:1010KB) PP. 234-246
DOI: 10.4236/opj.2015.57023    4,309 Downloads   4,863 Views   Citations

ABSTRACT

In this paper, we introduce a new class of scalar nondiffracting Helmholtz-equation solution. We demonstrate that this novel wave-equation solution has some specific orders; among these ordinary Airy beams which are regarded as the zeroth order. Moreover, a general expression of these novel beams, which are named Olver Beams and referred to OBs, is developed. The zeroth and the first high orders of the incident OBs are presented theoretically and numerically in this paper. Yet, based on a computer generated holograms method, the generation’s masks of the Finite OBs in first orders are given in this work. Also, the incident transverse intensity distribution in 1-D and 2-D of the first orders of OBs is performed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Belafhal, A. , Ez-Zariy, L. , Hennani, S. and Nebdi, H. (2015) Theoretical Introduction and Generation Method of a Novel Nondiffracting Waves: Olver Beams. Optics and Photonics Journal, 5, 234-246. doi: 10.4236/opj.2015.57023.

References

[1] Berry, M.V. and Balazs, N.L. (1979) Non-Spreading Wave Packets. American Journal of Physics, 47, 264-267. http://dx.doi.org/10.1119/1.11855
[2] Siviloglou, G.A. and Christodoulides, D.N. (2007) Accelerating Finite Energy Airy Beams. Optics Letters, 32, 979-981. http://dx.doi.org/10.1364/ol.32.000979
[3] Siviloglou, G.A., Broky, J., Dogariu, A. and Christodoulides, D.N. (2007) Observation of Accelerating Airy Beams. Physical Review Letters, 99, 213901. http://dx.doi.org/10.1103/PhysRevLett.99.213901
[4] Chen, R.P., Zhong, L.X., Wu, Q. and Chew, K.H. (2012) Propagation Properties and M2 Factors of a Vortex Airy Beams. Optics & Laser Technology, 44, 2015-2019.
http://dx.doi.org/10.1016/j.optlastec.2012.03.038
[5] Zhokovsky, K.V. and Dattoli, G. (2011) Evolution of Non-Spreading Airy Wave-Packets in Time Dependent Linear Potentials. Applied Mathematics and Computation, 217, 7966-7974.
http://dx.doi.org/10.1016/j.amc.2011.02.088
[6] Khonina, S.N. (2011) Specular and Vortical Airy Beams. Optics Communication, 284, 4263-4271.
http://dx.doi.org/10.1016/j.optcom.2011.05.068
[7] Eyyuboglu, H.T. (2013) Scintillation Behavior of Airy Beam. Optics & Laser Technology, 47, 232-236.
http://dx.doi.org/10.1016/j.optlastec.2012.08.029
[8] Cheng, H., Zang, W., Zhou, W. and Tian, J. (2010) Analysis of Optical Trapping and Propulsion of Rayleigh Particles Using Airy Beam. Optical Society of America, 18, 20384.
http://dx.doi.org/10.1364/oe.18.020384
[9] Deng, D. and Li, H. (2012) Propagation Properties of Airy-Gaussian Beams. Applied Physics B, 106, 677-681. http://dx.doi.org/10.1007/s00340-011-4799-2
[10] Carvalho, M.I. and Facao, M. (2010) Propagation of Airy-Related Beams. Optical Society of America, 18, 21938-21949. http://dx.doi.org/10.1364/oe.18.021938
[11] Deng, D. (2012) Propagation of Airy Beams through a Hard-Edged Aperture. Applied Physics B, 107, 195-200. http://dx.doi.org/10.1007/s00340-012-4899-7
[12] Zhou, G., Chen, R. and Chu, X. (2012) Fractional Fourier Transform of Airy Beams. Applied Physics B, 109, 549-556. http://dx.doi.org/10.1007/s00340-012-5117-3
[13] Jiang, Y., Huang, K. and Lu, X. (2012) The Optical Airy Transform and Its Application in Generating and Controlling the Airy Beam. Optics Communications, 285, 4840-4843.
http://dx.doi.org/10.1016/j.optcom.2012.08.003
[14] Deng, D. and Guo, Q. (2009) Airy Complex Variable Function Gaussian Beams. New Journal of Physics, 11, Article ID: 103029. http://dx.doi.org/10.1088/1367-2630/11/10/103029
[15] Han, D., Liu, C. and Lai, X. (2012) The Fractional Fourier Transform of Airy Beams Using Lohmann and Quadratic Optical Systems. Optics & Laser Technology, 44, 1463-1467.
http://dx.doi.org/10.1016/j.optlastec.2011.12.017
[16] Liu, X., Li, J., Chen, H. and Fan, Y. (2013) The Deflected Angle and Reflected Displacement of Airy Beams. Optik, 124, 6519-6522. http://dx.doi.org/10.1016/j.ijleo.2013.05.044
[17] Broky, J., Siviloglou, G.A., Dogariu, A., and Christodoulides, D.N. (2008) Self-Healing Properties of Optical Airy Beams. Optics Express, 16, 12880-12891. http://dx.doi.org/10.1364/OE.16.012880
[18] Wen, W., Lu, X., Zhao, C. and Cai, Y. (2014) Propagation of Airy Beam Passing through the Misaligned Optical System with Hard Aperture. Optics Communications, 313, 350-355.
http://dx.doi.org/10.1016/j.optcom.2013.10.056
[19] Liu, Z. and Zhao, D. (2014) Propagation of Airy-Related Beams Generated from Flat-Topped Gaussian Beams through a Chiral Slab. Optics and Lasers in Engineering, 52, 13-18.
http://dx.doi.org/10.1016/j.optlaseng.2013.07.011
[20] Chen, C., Yang, H., Kavehrad, M. and Zhou, Z. (2014) Propagation of Radial Airy Array Beams through Atmospheric Turbulence. Optics Communications, 52, 106-114.
http://dx.doi.org/10.1016/j.optlaseng.2013.07.003
[21] Cheng, K., Zhong, X. and Xiang, A. (2014) Propagation Dynamics, Poynting Vector and Accelerating Vortices of a Focused Airy Vortex Beam. Optics & Laser Technology, 57, 77-83.
http://dx.doi.org/10.1016/j.optlastec.2013.09.039
[22] Deng D., Du S. and Guo, Q. (2013) Energy Flow and Angular Momentum Density of Non Paraxial Airy Beams. Optics Communications, 289, 6-9. http://dx.doi.org/10.1016/j.optcom.2012.09.007
[23] Ez-zariy, L., Nebdi, H., Boustimi, M. and Belafhal, A. (2014) Transformation of a Two-Dimensional Finite Energy Airy Beam an ABCD Optical System with a Rectangular Annular Aperture. Physical and Chemical News, 73, 39-51.
[24] Ez-zariy, L., Hennani, S., Nebdi, H. and Belafhal, A. (2014) Propagation Characteristics of Airy-Gaussian Beams Passing through a Misaligned Optical System with Finite Aperture. Optics and Photonics Journal, 4, 325-336. http://dx.doi.org/10.4236/opj.2014.411033
[25] Ebrahim, A.A.A., Ez-zariy, L., Boustimi, M., Chafiq, A., Nebdi, H. and Belafhal, A. (2014) Diffraction of Finite Airy-Hermite-Gaussian Beams by an Apertured Misaligned Optical System. Physical and Chemical News, 73, 21-29.
[26] Alaidi, I., Boustimi, M., Nebdi, H. and Belafhal, A. (2014) Propagation through a Paraxial ABCD Optical System of a Novel Beams Family: Finite Airy-Gaussian Hermite-Gaussian Beams. Physical and Chemical News, 73, 10-13.
[27] Olver, F.W.J. (1975) Connection Formulas for Second-Order Differential Equations with Multiple Turning Points. SIAM Journal on Mathematical Analysis, 8, 127-154. http://dx.doi.org/10.1137/0508009
[28] Bandres, M.A. and Gutierrez-Vega, J.C. (2007) Airy-Gauss Beams and Their Transformation by Paraxial Optical Systems. Optics Express, 15, 16719-16728. http://dx.doi.org/10.1364/OE.15.016719
[29] He H., Heckenberg, N.R. and Dunlop, H.R. (2007) Optical Particle Trapping with Higher-order Doughnut Beams Produced Using High Efficiency Computer Generated Holograms. Journal of Modern Optics, 42, 217-223. http://dx.doi.org/10.1080/09500349514550171
[30] Carpentier, A.V., Michinel, H., Salgueiro, J.R. and Olivieri, D. (2008) Making Optical Vortices with Computer-Generated Holograms. American Journal of Physics, 76, 916-921.
http://dx.doi.org/10.1119/1.2955792
[31] Vallée, O. and Soares, M. (2004) Airy Functions and Applications to Physics. Imperial College Press, London. http://dx.doi.org/10.1142/p345
[32] Gradshteyn, I.S. and Ryzhik, I.M. (1994) Tables of Integrals Series and Products. 5th Edition, Academic Press, New York.
[33] Abramowitz, M. and Stegun, I.A., Eds. (1964) Handbook of Mathematical Functions. Nath Bureau of Standards, Washington.
[34] Andrews, L. and Philips, R. (1998) Laser Beams Propagation through Random Media. SPIE Press, Washington.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.