Influence of the higher-orders of diffraction on the pattern evolution for tightly focused beams

doi:10.1364/OE.19.011170

Influence of the higher-orders of diffraction on the pattern evolution for tightly focused beams

Daquan Lu, Zhenjun Yang, and Wei Hu »View Author Affiliations

Optics Express, Vol. 19, Issue 12, pp. 11170-11181 (2011)
http://dx.doi.org/10.1364/OE.19.011170

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Abstract
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Abstract

The mechanism of the nonparaxial propagation for tightly focused beams is investigated in the view of the influence of the higher-orders of diffraction (HOD). The HOD induce novel propagation characteristics which are crucially different from those predicted by the traditional paraxial theory. Based on the management of HOD, we propose an approach on controlling the intensity pattern of the focus to satisfy the application requirements.

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

History
Original Manuscript: March 22, 2011
Revised Manuscript: May 14, 2011
Manuscript Accepted: May 17, 2011
Published: May 24, 2011

Citation
Daquan Lu, Zhenjun Yang, and Wei Hu, "Influence of the higher-orders of diffraction on the pattern evolution for tightly focused beams," Opt. Express 19, 11170-11181 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11170

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References

M. A. Bandres and J. C. Gutiérrez-Vega, “Cartesian beams,” Opt. Lett. 32, 3459–3461 (2007). [CrossRef] [PubMed]
M. A. Bandres and J. C. Gutiérrez-Vega, “Circular beams,” Opt. Lett. 33, 177–179 (2008). [CrossRef] [PubMed]
M. A. Bandres and J. C. Gutiérrez-Vega, “Generalized Ince Gaussian beams,” Proc. SPIE 6290, 62900S (2006). [CrossRef]
N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4pi focusing of radially polarized light,” Opt. Lett. 29, 1968–1970 (2004). [CrossRef] [PubMed]
L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001). [CrossRef] [PubMed]
J. Pang, Y. K. Ho, X. Q. Yuan, N. Cao, Q. Kong, P. X. Wang, and L. Shao, “Subluminous phase velocity of a focused laser beam and vacuum laser acceleration,” Phys. Rev. E 66, 066501 (2002). [CrossRef]
P. Sprangle, E. Esarey, A. Ting, and G. Joyce, “Laser wakefield acceleration and relativistic optical guiding,” Appl. Phys. Lett. 53, 2146–2148 (1988). [CrossRef]
M. Lax, W. H. Loisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
R. Borghi and M. Santarsiero, “Summing Lax series for nonparaxial beam propagation,” Opt. Lett. 28, 774–776 (2003). [CrossRef] [PubMed]
Y. I. Salamin, “Fields of a Gaussian beam beyond the paraxial approximation,” Appl. Phys. B 86, 319–326 (2007). [CrossRef]
D. Deng, Q. Guo, S. Lan, and X. Yang, “Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space,” J. Opt. Soc. Am. A 24, 3317–3325 (2007). [CrossRef]
A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000). [CrossRef]
S. Sepke and D. Umstadter, “Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes,” Opt. Lett. 31, 1447–1449 (2006). [CrossRef] [PubMed]
Y. I. Salamin, “Fields of a focused linearly polarized Gaussian beam: truncated series versus the complex-source-point spherical-wave representation,” Opt. Lett. 34, 683–685 (2009). [CrossRef] [PubMed]
S. Orlov and U. Peschel, “Complex source beam: a tool to describe highly focused vector beams analytically,” Phys. Rev. A 82, 063820 (2010). [CrossRef]
G. P. Agrawal, Nonlinear Fiber Optics , 3rd ed. (Academic, 2001).
K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002). [CrossRef]
S. Orlov, A. Piskarskas, and A. Stabinis, “Localized optical subcycle pulses in dispersive media,” Opt. Lett. 27, 2167–2169 (2002) [CrossRef]
S. Orlov and U. Peschel, “Angular dispersion of diffraction-free optical pulses in dispersive medium,” Opt. Commun. 240, 1–8 (2004). [CrossRef]
M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersion broadening of light pulses with Bessel–Gauss beams,” Opt. Commun. 206, 235–241 (2003). [CrossRef]
M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett. 26, 1364–1366 (2001) [CrossRef]
M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004). [CrossRef]
R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Localization of optical wave packets by linear parametric amplification,” Opt. Commun. 227, 237–243 (2003). [CrossRef]
J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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[1] M. A. Bandres and J. C. Gutiérrez-Vega, “Cartesian beams,” Opt. Lett. 32, 3459–3461 (2007). [CrossRef] [PubMed]

[2] M. A. Bandres and J. C. Gutiérrez-Vega, “Circular beams,” Opt. Lett. 33, 177–179 (2008). [CrossRef] [PubMed]

[3] M. A. Bandres and J. C. Gutiérrez-Vega, “Generalized Ince Gaussian beams,” Proc. SPIE 6290, 62900S (2006). [CrossRef]

[4] N. Bokor and N. Davidson, “Toward a spherical spot distribution with 4pi focusing of radially polarized light,” Opt. Lett. 29, 1968–1970 (2004). [CrossRef] [PubMed]

[5] L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001). [CrossRef] [PubMed]

[6] J. Pang, Y. K. Ho, X. Q. Yuan, N. Cao, Q. Kong, P. X. Wang, and L. Shao, “Subluminous phase velocity of a focused laser beam and vacuum laser acceleration,” Phys. Rev. E 66, 066501 (2002). [CrossRef]

[7] P. Sprangle, E. Esarey, A. Ting, and G. Joyce, “Laser wakefield acceleration and relativistic optical guiding,” Appl. Phys. Lett. 53, 2146–2148 (1988). [CrossRef]

[8] M. Lax, W. H. Loisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]

[9] R. Borghi and M. Santarsiero, “Summing Lax series for nonparaxial beam propagation,” Opt. Lett. 28, 774–776 (2003). [CrossRef] [PubMed]

[10] Y. I. Salamin, “Fields of a Gaussian beam beyond the paraxial approximation,” Appl. Phys. B 86, 319–326 (2007). [CrossRef]

[11] D. Deng, Q. Guo, S. Lan, and X. Yang, “Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space,” J. Opt. Soc. Am. A 24, 3317–3325 (2007). [CrossRef]

[12] A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000). [CrossRef]

[13] S. Sepke and D. Umstadter, “Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes,” Opt. Lett. 31, 1447–1449 (2006). [CrossRef] [PubMed]

[14] Y. I. Salamin, “Fields of a focused linearly polarized Gaussian beam: truncated series versus the complex-source-point spherical-wave representation,” Opt. Lett. 34, 683–685 (2009). [CrossRef] [PubMed]

[15] S. Orlov and U. Peschel, “Complex source beam: a tool to describe highly focused vector beams analytically,” Phys. Rev. A 82, 063820 (2010). [CrossRef]

[16] G. P. Agrawal, Nonlinear Fiber Optics , 3rd ed. (Academic, 2001).

[17] K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002). [CrossRef]

[18] S. Orlov, A. Piskarskas, and A. Stabinis, “Localized optical subcycle pulses in dispersive media,” Opt. Lett. 27, 2167–2169 (2002) [CrossRef]

[19] S. Orlov and U. Peschel, “Angular dispersion of diffraction-free optical pulses in dispersive medium,” Opt. Commun. 240, 1–8 (2004). [CrossRef]

[20] M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersion broadening of light pulses with Bessel–Gauss beams,” Opt. Commun. 206, 235–241 (2003). [CrossRef]

[21] M. A. Porras, “Diffraction-free and dispersion-free pulsed beam propagation in dispersive media,” Opt. Lett. 26, 1364–1366 (2001) [CrossRef]

[22] M. A. Porras and P. Di Trapani, “Localized and stationary light wave modes in dispersive media,” Phys. Rev. E 69, 066606 (2004). [CrossRef]

[23] R. Butkus, S. Orlov, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Localization of optical wave packets by linear parametric amplification,” Opt. Commun. 227, 237–243 (2003). [CrossRef]

[24] J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Influence of the higher-orders of diffraction on the pattern evolution for tightly focused beams