J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005).

[CrossRef]

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).

[CrossRef]

K. Duan, B. Wang, and B. Lü, "Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A 22, 1976-1980 (2005).

[CrossRef]

S. R. Seshadri, "Nonparaxial corrections for the fundamental Gaussian beam," J. Opt. Soc. Am. A 19, 2134-2141 (2002).

[CrossRef]

C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations," J. Opt. Soc. Am. A 19, 404-412 (2002).

[CrossRef]

H. C. Kim and Y. H. Lee, "Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Commun. 169, 9-16 (1999).

[CrossRef]

B. Ruiz and H. Rabal, "Differential operators, the Fourier transform and its applications to optics," Optik (Stuttgart) 103, 171-178 (1996).

G. P. Agrawal and M. Lax, "Free-space propagation beyond the paraxial approxiamtion," Phys. Rev. A 27, 1693-1695 (1983).

[CrossRef]

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

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).

[CrossRef]

L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).

[CrossRef]

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980), pp. 716, 718, 1037, 1058.

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).

[CrossRef]

H. C. Kim and Y. H. Lee, "Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Commun. 169, 9-16 (1999).

[CrossRef]

H. Laabs, "Propagation of Hermite-Gaussian beams beyond the paraxial approximation," Opt. Commun. 147, 1-4 (1998).

[CrossRef]

G. P. Agrawal and M. Lax, "Free-space propagation beyond the paraxial approxiamtion," Phys. Rev. A 27, 1693-1695 (1983).

[CrossRef]

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).

[CrossRef]

H. C. Kim and Y. H. Lee, "Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Commun. 169, 9-16 (1999).

[CrossRef]

P. Vaveliuk, B. Ruiz, and A. Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007).

[CrossRef]
[PubMed]

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).

[CrossRef]

A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published) doi:10.1016/j.ijleo.2006.11.006.

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

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).

[CrossRef]

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).

[CrossRef]

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

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).

[CrossRef]

B. Ruiz and H. Rabal, "Differential operators, the Fourier transform and its applications to optics," Optik (Stuttgart) 103, 171-178 (1996).

P. Vaveliuk, B. Ruiz, and A. Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007).

[CrossRef]
[PubMed]

B. Ruiz and H. Rabal, "Differential operators, the Fourier transform and its applications to optics," Optik (Stuttgart) 103, 171-178 (1996).

A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published) doi:10.1016/j.ijleo.2006.11.006.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980), pp. 716, 718, 1037, 1058.

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

P. Vaveliuk, B. Ruiz, and A. Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007).

[CrossRef]
[PubMed]

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).

[CrossRef]

A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published) doi:10.1016/j.ijleo.2006.11.006.

R. Borghi, M. Santarsiero, and M. A. Porras, "Nonparaxial Bessel-Gauss beams," J. Opt. Soc. Am. A 18, 1618-1626 (2001).

[CrossRef]

S. R. Seshadri, "Nonparaxial corrections for the fundamental Gaussian beam," J. Opt. Soc. Am. A 19, 2134-2141 (2002).

[CrossRef]

T. Takenaka, M. Yokota, and O. Fukumitsu, "Propagation of light beams beyond the paraxial approximation," J. Opt. Soc. Am. A 2, 826-829 (1985).

[CrossRef]

A. Wünsche, "Transition from the paraxial to the exact solutions of the wave equation and application to Gaussian beams," J. Opt. Soc. Am. A 9, 765-774 (1992).

[CrossRef]

Q. Cao and X. Deng, "Corrections to the paraxial approximation of an arbitrary free-propagation beam," J. Opt. Soc. Am. A 15, 1144-1148 (1998).

[CrossRef]

C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations," J. Opt. Soc. Am. A 19, 404-412 (2002).

[CrossRef]

K. Duan, B. Wang, and B. Lü, "Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A 22, 1976-1980 (2005).

[CrossRef]

J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005).

[CrossRef]

M. A. Bandres and J. C. Gutiérrez-Vega, "Ince-Gaussian modes of the paraxial wave equation and stable resonators," J. Opt. Soc. Am. A 21, 873-880 (2004).

[CrossRef]

J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).

[CrossRef]

H. C. Kim and Y. H. Lee, "Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," Opt. Commun. 169, 9-16 (1999).

[CrossRef]

H. Laabs, "Propagation of Hermite-Gaussian beams beyond the paraxial approximation," Opt. Commun. 147, 1-4 (1998).

[CrossRef]

B. Ruiz and H. Rabal, "Differential operators, the Fourier transform and its applications to optics," Optik (Stuttgart) 103, 171-178 (1996).

A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published) doi:10.1016/j.ijleo.2006.11.006.

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).

[CrossRef]

L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979).

[CrossRef]

G. P. Agrawal and M. Lax, "Free-space propagation beyond the paraxial approxiamtion," Phys. Rev. A 27, 1693-1695 (1983).

[CrossRef]

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).

[CrossRef]

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1980), pp. 716, 718, 1037, 1058.

The coordinate z was normalized in terms of L instead of D=kw0/β (see ) because L is not dependant on β.