Martínez Matos, ÓscarVaveliuk, PabloTorchia, Gustavo Adrián2023-06-192023-06-1920131. 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, 1987.1559-898510.2528/PIER13050606https://hdl.handle.net/20.500.14352/33516© 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.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.engjournal articlehttp://jpier.org/PIER/pier.php?paper=13050606http://jpier.orgopen access535Bessel BeamsOptical-FieldsMathieu BeamsDiffractionInvarianceShiftLightÓptica (Física)2209.19 Óptica Física