|
[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.
|
|