Publication: Features of the gouy phase of nondiffracting beams
Loading...
Official URL
Full text at PDC
Publication Date
2013
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
EMW Publishing
Citations
Exportar
Abstract
It is shown how the linear Gouy phase of an ideal nondiffracting beam of +/-(k - k_z)z form, with k_z 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. All of 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 that 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 a fruitful example, the Gouy phase analysis is applied to fully establish the regime in which a Helmholtz-Gauss beam propagates with nondiffracting-like properties.
Description
© Copyright 2014 EMW Publishing.
Financial support from the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil, under project 477260/2010-1, and Spanish Ministry of Science and Innovation, under project TEC 2011-23629, is acknowledged. P. V. acknowledges a PQ fellowship of CNPq.
UCM subjects
Unesco subjects
Keywords
Citation
1. Bajer, J. and R. Horak, "Nondiffractive fields," Phys. Rev. E, Vol. 54, No. 3, 3052-3054, 1996.
2. Yu, Y.-Z. and W.-B. Dou, "Vector analyses of nondiffracting Bessel beams," Progress In Electromagnetics Research Letters, Vol. 5, 57-71, 2008.
3. Bouchal, Z., "Nondiffracting optical beams: Physical properties, experiments, and applications," Czech. J. Phys., Vol. 53, No. 7, 537-624, 2003.
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.
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.
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.
8. McGloin, D. and K. Dholakia, "Bessel beams: Diffraction in a new light," Contemp. Phys., Vol. 46, No. 1, 15-28, 2005.
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.
10. Yu, Y.-Z. and W.-B. Dou, "Quasi-optical Bessel resonator," Progress In Electromagnetics Research, Vol. 93, 205-219, 2009.
11. Durnin, J., J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett., Vol. 58, No. 15, 1499-1501, 1987.
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.
13. Vaveliuk, P., "Nondiffracting wave properties in radially and azimuthally symmetric optical axis phase plates," Opt. Lett., Vol. 34, No. 23, 3641-3643, 2009.
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.
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.
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.
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.
19. Feng, S. and H. G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett., Vol. 26, No. 8, 485-487, 2001.
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.
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.
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.
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.
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.
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.
31. Vaveliuk, P., "Comment on degree of paraxiality for monochromatic light beams," Opt. Lett., Vol. 33, No. 24, 3004-3005, 2008.
32. Vaveliuk, P. and O. Martinez Matos, "Physical interpretation of the paraxial estimator," Opt. Commun., Vol. 285, No. 24, 4816-4820, 2012.
33. Gutiérrez-Vega, J. C. and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am., Vol. 22, No. 2, 289-298, 2005.
34. López-Mariscal, C. and K. Helmerson, "Shaped nondiffracting beams," Opt. Lett., Vol. 35, No. 8, 1215-1217, 2010.
35. Gori, F., G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun., Vol. 64, No. 6, 491-495, 1987.