Vol. 140
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2013-06-26
Features of the Gouy Phase of Nondiffracting Beams
By
Progress In Electromagnetics Research, Vol. 140, 599-611, 2013
Abstract
It is shown how the linear Gouy phase of an ideal nondiffracting beam of ±(k-kz)z form, with kz being the projection of the wavevector of modulus k of the plane wave spectrum onto the propagation axis z, is built from a rigorous treatment based on the successive approximations to the Helmholtz equation. The so much different families of nondiffracting beams with a continuum spectrum, as Bessel beams, Mathieu beams and Parabolic ones, as well as nondiffracting beams with a discrete spectrum, as kaleidoscopic beams, have an identical Gouy phase, which fully governs the beam propagation dynamics. Hence, a real beam whose Gouy phase is close to that linear Gouy phase in a given range, will have nondiffracting-like properties on such a range. These results are applied to determine the effective regime in which a physically realizable beam can be treated as a nondiffracting one. As an fruitful example, the Gouy phase analysis is applied to fully establish the regime in which a Helmholtz-Gauss beam propagates with nondiffracting-like properties.
Citation
Pablo Vaveliuk, Oscar Martinez Matos, and Gustavo Adrian Torchia, "Features of the Gouy Phase of Nondiffracting Beams," Progress In Electromagnetics Research, Vol. 140, 599-611, 2013.
doi:10.2528/PIER13050606
References

1. Bajer, J. and R. Horak, "Nondiffractive fields," Phys. Rev. E, Vol. 54, No. 3, 3052-3054, 1996.
doi:10.1103/PhysRevE.54.3052

2. Yu, Y.-Z. and W.-B. Dou, "Vector analyses of nondiffracting Bessel beams," Progress In Electromagnetics Research Letters, Vol. 5, 57-71, 2008.
doi:10.2528/PIERL08110906

3. Bouchal, Z., "Nondiffracting optical beams: Physical properties, experiments, and applications," Czech. J. Phys., Vol. 53, No. 7, 537-624, 2003.
doi:10.1023/A:1024802801048

4. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, 1941.

5. Durnin, J., "Exact solutions for nondiffraction beams. I. The scalar theory," J. Opt. Soc. Am. A, Vol. 4, No. 4, 651-654, 1987.
doi:10.1364/JOSAA.4.000651

6. Gutiérrez-Vega, J. C., M. D. Iturbe-Castillo, and S. Chávez-Cerda, "Alternative formulation for invariant optical fields: Mathieu beam," Opt. Lett., Vol. 25, No. 20, 1493-1495, 2000.
doi:10.1364/OL.25.001493

7. Bandres, M. A., J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Parabolic nondiffracting optical wavefields," Opt. Lett., Vol. 29, No. 1, 44-46, 2004.
doi:10.1364/OL.29.000044

8. McGloin, D. and K. Dholakia, "Bessel beams: Diffraction in a new light," Contemp. Phys., Vol. 46, No. 1, 15-28, 2005.
doi:10.1080/0010751042000275259

9. Yu, Y.-Z. and W.-B. Dou, "Properties of approximate Bessel beams at millimeter wavelengths generated by fractal conical lens," Progress In Electromagnetics Research, Vol. 87, 105-115, 2008.
doi:10.2528/PIER08100606

10. Yu, Y.-Z. and W.-B. Dou, "Quasi-optical Bessel resonator," Progress In Electromagnetics Research, Vol. 93, 205-219, 2009.
doi:10.2528/PIER09042902

11. Durnin, J., J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett., Vol. 58, No. 15, 1499-1501, 1987.
doi:10.1103/PhysRevLett.58.1499

12. Arlt, J. and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun., Vol. 177, No. 1-6, 297-301, 2000.
doi:10.1016/S0030-4018(00)00572-1

13. Vaveliuk, P., "Nondiffracting wave properties in radially and azimuthally symmetric optical axis phase plates," Opt. Lett., Vol. 34, No. 23, 3641-3643, 2009.
doi:10.1364/OL.34.003641

14. Gutiérrez-Vega, J. C., M. D. Iturbe-Castillo, J. A. Ramírez, E. Tepichín, R. M. Rodríguez-Dagnino, S. Chávez-Cerda, and J. H. C. New, "Experimental demonstration of optical Mathieu beams," Opt. Commun., Vol. 195, No. 1, 35-40, 2001.
doi:10.1016/S0030-4018(01)01319-0

15. López-Mariscal, C., M. A. Bandres, S. Chávez-Cerda, and J. C. Gutiérrez-Vega, "Observation of parabolic nondiffracting wave fields," Opt. Express, Vol. 13, No. 7, 2364-2369, 2005.
doi:10.1364/OPEX.13.002364

16. Soares, W. C., D. P. Caetano, and J. M. Hickmann, "Hermite-Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum," Opt. Express, Vol. 14, No. 11, 4577-4582, 2006.
doi:10.1364/OE.14.004577

17. Siegman, A. E., Lasers, University Science Books, 1986.

18. Simon, R. and N. Mukunda, "Bargmann invariant and the goemetry of the Gouy effect," Phys. Rev. Lett., Vol. 70, No. 7, 880-883, 1993.
doi:10.1103/PhysRevLett.70.880

19. Feng, S. and H. G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett., Vol. 26, No. 8, 485-487, 2001.
doi:10.1364/OL.26.000485

20. Borghi, R., M. Santarsiero, and R. Simon, "Shape invariance and a universal form for the Gouy phase," J. Opt. Soc. Am. A, Vol. 21, No. 4, 572-579, 2004.
doi:10.1364/JOSAA.21.000572

21. Pang, X. and T. Visser, "Manifestation of the Gouy phase in strongly focused, radially polarized beams," Opt. Express, Vol. 21, No. 7, 8331-8341, 2013.
doi:10.1364/OE.21.008331

22. Rolland, J. P., K. P. Thompson, K.-S. Lee, J. Tamkin, Jr., T. Schimd, and E. Wolf, "Observation of the Gouy phase anomaly in astigmatic beams," Appl. Opt., Vol. 51, No. 17, 1-7, 2012.

23. Martelli, P., M. Tacca, A. Gatto, G. Moneta, and M. Martinelli, "Gouy phase shift in nondiffracting Bessel beams," Opt. Express, Vol. 18, No. 7, 7108-7120, 2010.
doi:10.1364/OE.18.007108

24. Lohmann, A. H., J. Ojeda Castañeda, and N. Streibl, "Differential operator for three dimensional imaging," Proc. of SPIE, Vol. 402, 186-191, 1983.

25. Ruiz, B. and H. Rabal, "Differential operators, the Fourier transform and its applications to optics," Optik, Vol. 103, No. 4, 171-178, Stuttgart, 1996.

26. Vaveliuk, P., G. F. Zebende, M. A. Moret, and B. Ruiz, "Propagating free-space nonparaxial beams," J. Opt. Soc. Am. A, Vol. 24, No. 10, 3297-3302, 2007.
doi:10.1364/JOSAA.24.003297

27. Turunen, J., A. Vasara, and A. T. Friberg, "Propagation invariance and self-imaging in variable-coherence optics," J. Opt. Soc. Am. A, Vol. 8, No. 2, 282-289, 1991.
doi:10.1364/JOSAA.8.000282

28. Goodman, J. W., Introduction to Fourier Optics, McGraw-Hill Inc., New York, 1968.

29. Indebetouw, G., "Nondiffracting optical fields: Some remarks on their analysis and synthesis ," J. Opt. Soc. Am., Vol. 6, No. 1, 150-152, 1989.
doi:10.1364/JOSAA.6.000150

30. Vaveliuk, P., B. Ruiz, and A. Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett., Vol. 32, No. 8, 927-929, 2007.
doi:10.1364/OL.32.000927

31. Vaveliuk, P., "Comment on degree of paraxiality for monochromatic light beams," Opt. Lett., Vol. 33, No. 24, 3004-3005, 2008.
doi:10.1364/OL.33.003004

32. Vaveliuk, P. and O. Martinez Matos, "Physical interpretation of the paraxial estimator," Opt. Commun., Vol. 285, No. 24, 4816-4820, 2012.
doi:10.1016/j.optcom.2012.07.134

33. Gutiérrez-Vega, J. C. and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am., Vol. 22, No. 2, 289-298, 2005.
doi:10.1364/JOSAA.22.000289

34. López-Mariscal, C. and K. Helmerson, "Shaped nondiffracting beams," Opt. Lett., Vol. 35, No. 8, 1215-1217, 2010.
doi:10.1364/OL.35.001215

35. Gori, F., G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun., Vol. 64, No. 6, 491-495, 1987.
doi:10.1016/0030-4018(87)90276-8