Propagation Properties of Finite Olver-Gaussian Beams Passing through a Paraxial ABCD Optical System

Salima Hennani, Lahcen Ez-Zariy^*, Abdelmajid Belafhal^*

Laboratory of Nuclear, Atomic and Molecular Physics, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, Jadida, Morocco.

DOI: 10.4236/opj.2015.59026                

Abstract

In this paper, an exact analytical propagation formula of Finite Olver-Gaussian Beams (FOGBs) passing through a paraxial ABCD optical system is developed and some numerical examples are performed. The propagation properties of the FOGBs through general optical systems characterized by given ABCD matrix are studied on the basis of the generalized Huygens-Fresnel diffraction integral, which permits to show the behavior of this laser beams family and its properties de-pending of the laser parameters. This research is of interest to prove some investigations done in the past by other researchers.

Keywords

Finite Olver-Gaussian Beams, Generalized Huygens-Fresnel Diffraction, ABCD Optical Systems

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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. http://dx.doi.org/10.4236/opj.2015.57023
[2]	Gutiérrez-Vega, J.C. and Bandres, M.A. (2005) Helmholtz-Gauss Waves. Journal of the Optical Society of America A, 22, 289-298. http://dx.doi.org/10.1364/JOSAA.22.000289
[3]	Guizar-Sicairos, M. and Gutiérrez-Vega, J.C. (2006) Generalized Helmholtz-Gauss Beam and Its Transformation by Paraxial Optical Systems. Optics Letters, 31, 2912-2914. http://dx.doi.org/10.1364/OL.31.002912
[4]	Ding, G.L. and Lü, B.D. (2003) Decentered Twisted Gaussian Schell-Model Beams and Their Propagation through a Misaligned First-Order Optical System. Optical and Quantum Electronics, 35, 91-100. http://dx.doi.org/10.1023/A:1022478608090
[5]	Gu, J.G., Zhao, D.M., Mei, Z.R. and Mao, H.D. (2004) The Relative Phase Shift of Off-Axial Gaussian Beams through an Apertured and Misaligned Optical System. Optik-International Journal for Light and Electron Optics, 115, 187-191. http://dx.doi.org/10.1016/S0030-4026(08)70009-3
[6]	Cai, Y.J. and Lin, Q. (2004) Light Beams with Elliptical Flat-Topped Profiles. Journal of Optics A: Pure and Applied Optics, 6, 390-395. http://dx.doi.org/10.1088/1464-4258/6/4/015
[7]	Belafhal, A. and Dalil-Essakkali, L. (2000) Collins Formula and Propagation of Bessel-Modulated Gaussian Light Beams through an ABCD Optical System. Optics Communications, 177, 181-188. http://dx.doi.org/10.1016/S0030-4018(00)00600-3
[8]	Wang, X.Q. and Lü, B.D. (2002) The Beam Propagation Factor and Far-Field Distribution of Bessel-Modulated Gaussian Beams. Optical and Quantum Electronics, 34, 1071-1077. http://dx.doi.org/10.1023/A:1021160303678
[9]	Mei, Z.R., Zhao, D.M., Wei, X.F., Jing, F. and Zhu, Q.H. (2005) Propagation of Bessel-Modulated Gaussian Beams through a Paraxial ABCD Optical System with an Annular Aperture. Optik—International Journal for Light and Electron Optics, 116, 521-526. http://dx.doi.org/10.1016/j.ijleo.2005.05.003
[10]	Zhao, C.L., Wang, L.G., Lu, X.H. and Chen, H. (2007) Propagation of High-Order Bessel-Gaussian Beam through a Misaligned First-Order Optical System. Optics & Laser Technology, 39, 1199-1203. http://dx.doi.org/10.1016/j.optlastec.2006.08.015
[11]	Zhou, G.Q. (2010) Propagation of a Lorentz-Gauss Beam through a Misaligned Optical System. Optics Communications, 283, 1236-1243. http://dx.doi.org/10.1016/j.optcom.2009.12.006
[12]	Dartora, C.A. and Hernández-Figueroa, H.E. (2004) Properties of a Localized Mathieu Pulse. Journal of the Optical Society of America A, 21, 662-667. http://dx.doi.org/10.1364/JOSAA.21.000662
[13]	Chafiq, A., Hricha, Z. and Belafhal, A. (2005) Paraxial Propagation of Mathieu Beams through an Apertured ABCD Optical System. Optics Communications, 253, 223-230. http://dx.doi.org/10.1016/j.optcom.2005.04.068
[14]	Chafiq, A., Hricha, Z. and Belafhal, A. (2007) Flat-Topped Mathieu-Gauss Beam and Its Transformation by Paraxial Optical Systems. Optics Communications, 278, 142-146. http://dx.doi.org/10.1016/j.optcom.2007.05.042
[15]	Ez-Zariy, L., Nebdi, H., Chafiq, A. and Belafhal, A. (2012) Mathieu-Gauss Beam and Its Propagation. Physical and Chemical News, 64, 42-52.
[16]	Ez-Zariy, L., Zouhal, B., Nebdi, H. and Belafhal, A. (2012) Generalization of the Transformation of Flat-Topped Mathieu-Gauss Beams by Paraxial Optical Systems. Physical and Chemical News, 65, 9-17.
[17]	Eyyuboglu, H.T. (2008) Propagation Aspects of Mathieu-Gaussian Beams in Turbulence. Applied Physics B, 91, 611-619. http://dx.doi.org/10.1007/s00340-008-3020-8
[18]	Bandres, M.A., Gutiérrez-Vega, J.C. and Chávez-Cerda, S. (2004) Parabolic Nondiffracting Optical Wave Fields. Optics letters, 29, 44-46. http://dx.doi.org/10.1364/OL.29.000044
[19]	López-Mariscal, C., Bandrés-Motola, M., Gutiérrez-Vega, J.C. and Chávez-Cerda, S. (2004) Experimental Realization of Nondiffracting Parabolic Beams. Diffractive Optics and Micro-Optics, Optical Society of America, Paper DMA7. http://dx.doi.org/10.1364/domo.2004.dma7
[20]	Khilo, N.A. (2013) Conical Diffraction and Transformation of Bessel Beams in Biaxial Crystals. Optics Communications, 286, 1-5. http://dx.doi.org/10.1016/j.optcom.2012.07.030
[21]	Tang, B. (2009) Hermite-Cosine-Gaussian Beams Propagating in Uniaxial Crystals Orthogonal to the Optical Axis. Journal of the Optical Society of America A, 26, 2480-2487. http://dx.doi.org/10.1364/JOSAA.26.002480
[22]	Magni, V., Cerullo, G. and De Silvestri, S. (1993) ABCD Matrix Analysis of Propagation of Gaussian Beams through Kerr Media. Optics Communications, 96, 348-355. http://dx.doi.org/10.1016/0030-4018(93)90284-C
[23]	Chen, C.D., Chen, B., Peng, X. and Deng, D.M. (2015) Propagation of Airy-Gaussian Beam in Kerr Medium. Journal of Optics, 17, Article ID: 035504. http://dx.doi.org/10.1088/2040-8978/17/3/035504
[24]	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
[25]	Siviloglou, G.A., Broky, J., Dogariu, A. and Christodoulides, D.N. (2007) Observation of Accelerating Airy Beams. Physical Review Letters, 99, Article ID: 213901. http://dx.doi.org/10.1103/PhysRevLett.99.213901
[26]	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
[27]	Kaganovsky, Y. and Heyman, E. (2010) Wave Analysis of Airy Beams. Optics Express, 18, 8440-8452. http://dx.doi.org/10.1364/OE.18.008440
[28]	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
[29]	Polynkin, P., Kolesik, M., Moloney, J.V., Siviloglou, G.A. and Christodoulides, D.N. (2009) Curved Plasma Channel Generation Using Ultraintense Airy Beams. Science, 324, 229-232. http://dx.doi.org/10.1126/science.1169544
[30]	Morris, J.E., Mazilu, M., Baumgartl, J., Cizmár, T. and Dholakia, K. (2009) Propagation Characteristics of Airy Beams: Dependence upon Spatial Coherence and Wavelength. Optics Express, 17, 13236-13245. http://dx.doi.org/10.1364/OE.17.013236
[31]	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
[32]	Han, D.H., Liu, C.T. and Lai, X.Y. (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
[33]	Wen, W., Lu, X.Y., Zhao, C.L. and Cai, Y.J. (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
[34]	Nelson, W., Palastro, J.P., Davis, C.C. and Sprangle, P. (2014) Propagation of Bessel and Airy Beams through Atmospheric Turbulence. Journal of the Optical Society of America A, 31, 603-609. http://dx.doi.org/10.1364/JOSAA.31.000603
[35]	Zhou, G.Q., Chen, R.P. and Chu, X.X. (2012) Propagation of Airy Beams in Uniaxial Crystals Orthogonal to the Optical Axis. Optics Express, 20, 2196-2205. http://dx.doi.org/10.1364/OE.20.002196
[36]	Zhang, Y.Q., Belic, M.R., Zheng, H.B., Chen, H.X., Li, C.B., Li, Y.Y. and Zhang, Y.P. (2014) Interactions of Airy Beams, Nonlinear Accelerating Beams, and Induced Solitons in Kerr and Saturable Nonlinear Media. Optics Express, 22, 7160-7171. http://dx.doi.org/10.1364/OE.22.007160
[37]	Liu, H.L., Lü, Y.F., Xia, J., Pu, X.Y. and Zhang, L. (2015) Propagation of an Airy-Gaussian Beam Passing through the ABCD Optical System with a Rectangular Aperture. Optics Communications, 355, 438-444. http://dx.doi.org/10.1016/j.optcom.2015.07.017
[38]	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.
[39]	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
[40]	Collins, S.A. (1970) Lens-System Diffraction Integral Written in Terms of Matrix Optics. Journal of the Optical Society of America A, 60, 1168-1177. http://dx.doi.org/10.1364/JOSA.60.001168
[41]	Gradshteyn, I.S. and Ryzhik, I.M. (1994) Tables of Integrals Series and Products. 5th Edition, Academic Press, New York.