Directionality of general beams

doi:10.1364/OE.16.018850

Directionality of general beams

Xiaoling Ji, Xiaoqing Li, and Guangming Ji »View Author Affiliations

Optics Express, Vol. 16, Issue 23, pp. 18850-18856 (2008)
http://dx.doi.org/10.1364/OE.16.018850

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Abstract

The directionality of general beams propagating in free space and in atmospheric turbulence is studied. Based on the partial-coherence theory, the analytical expressions for the mean-squared width and the angular spread of general beams are derived by using the integral transform technique. It is shown that the mean-squared width and the angular spread depend not only on the weighting factors of all basis modes but also on the weighting factors of the corresponding mode coherence coefficients of the ith and the (i+2)th if the Hermite-Gaussian modes are adopted. It is found that under a certain condition there exist the equivalent general beams which may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The result holds true, irrespective of the model of turbulence used.

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(030.4070) Coherence and statistical optics : Modes

ToC Category:
Atmospheric and oceanic optics

History
Original Manuscript: June 30, 2008
Revised Manuscript: August 20, 2008
Manuscript Accepted: October 28, 2008
Published: October 31, 2008

Citation
Xiaoling Ji, Xiaoqing Li, and Guangming Ji, "Directionality of general beams," Opt. Express 16, 18850-18856 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18850

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References

A. E. Siegman, Laser (University Science Books Mill Valley, 1986).
L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 1998).
E. Collett and E. Wolf, "Is complete spatial coherence necessary for the generation of highly directional light beams?," Opt. Lett. 2, 27-29 (1978). [CrossRef] [PubMed]
E. Wolf and E. Collett, "Partially coherent sources which produce the same far-field intensity distribution as a laser," Opt. Commun. 25, 293-296 (1978). [CrossRef]
P. De Santis, F. Gori, G. Guattari, and C. Palma, "An example of a Collett-Wolf source," Opt. Commun. 29, 256-260 (1979). [CrossRef]
J. D. Farina, L. M. Narducci, and E. Collett, "Generation of highly directional beams from a globally incoherent source," Opt. Commun. 32, 203-208 (1980). [CrossRef]
G. Gbur and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A 19, 1592-1598 (2002). [CrossRef]
A. Dogariu and S. Amarande, "Propagation of partially coherent beams: turbulence-induced degradation," Opt. Lett. 28, 10-12 (2003). [CrossRef] [PubMed]
H. T. Eyyubo?lu and Y. Baykal, "Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere, " J. Opt. Soc. Am. A 22, 2709-2718 (2005). [CrossRef]
Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006). [CrossRef] [PubMed]
T. Shirai, A. Dogariu, and E. Wolf, "Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence," Opt. Lett. 28, 610-612 (2003). [CrossRef] [PubMed]
X. Ji, X. Chen, and B. Lü, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25, 21-28 (2008). [CrossRef]
A. Yang, E. Zhang, X. Ji, and B. Lü, "Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence," Opt. Express, 16, 8366-8380 (2008). [CrossRef] [PubMed]
K. M. Du, G. Herziger, P. Loosen, and F. Rühl, "Coherence and intensity moments of laser light," Opt. Quantum Electron. 24, 1081-1093 (1992). [CrossRef]
A. Starikov and E. Wolf, "Coherent-mode representation of Gaussian Schell-model sources and their radiation fields," J. Opt. Soc. Am. 72, 923-928 (1982). [CrossRef]
A. E. Siegman, "New developments in laser resonators," Proc. SPIE 1224, 2-14 (1990). [CrossRef]
A. A. Tovar and L. W. Casperson, "Production and propagation of Hermite-sinusoidal-Gaussian laser beams," J. Opt. Soc. Am. A 15, 2425-2432 (1998). [CrossRef]

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[1] A. E. Siegman, Laser (University Science Books Mill Valley, 1986).

[2] L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, 1998).

[3] E. Collett and E. Wolf, "Is complete spatial coherence necessary for the generation of highly directional light beams?," Opt. Lett. 2, 27-29 (1978). [CrossRef] [PubMed]

[4] E. Wolf and E. Collett, "Partially coherent sources which produce the same far-field intensity distribution as a laser," Opt. Commun. 25, 293-296 (1978). [CrossRef]

[5] P. De Santis, F. Gori, G. Guattari, and C. Palma, "An example of a Collett-Wolf source," Opt. Commun. 29, 256-260 (1979). [CrossRef]

[6] J. D. Farina, L. M. Narducci, and E. Collett, "Generation of highly directional beams from a globally incoherent source," Opt. Commun. 32, 203-208 (1980). [CrossRef]

[7] G. Gbur and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A 19, 1592-1598 (2002). [CrossRef]

[8] A. Dogariu and S. Amarande, "Propagation of partially coherent beams: turbulence-induced degradation," Opt. Lett. 28, 10-12 (2003). [CrossRef] [PubMed]

[9] H. T. Eyyubo?lu and Y. Baykal, "Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere, " J. Opt. Soc. Am. A 22, 2709-2718 (2005). [CrossRef]

[10] Y. Cai and S. He, "Propagation of various dark hollow beams in a turbulent atmosphere," Opt. Express 14, 1353-1367 (2006). [CrossRef] [PubMed]

[11] T. Shirai, A. Dogariu, and E. Wolf, "Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence," Opt. Lett. 28, 610-612 (2003). [CrossRef] [PubMed]

[12] X. Ji, X. Chen, and B. Lü, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A 25, 21-28 (2008). [CrossRef]

[13] A. Yang, E. Zhang, X. Ji, and B. Lü, "Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence," Opt. Express, 16, 8366-8380 (2008). [CrossRef] [PubMed]

[14] K. M. Du, G. Herziger, P. Loosen, and F. Rühl, "Coherence and intensity moments of laser light," Opt. Quantum Electron. 24, 1081-1093 (1992). [CrossRef]

[15] A. Starikov and E. Wolf, "Coherent-mode representation of Gaussian Schell-model sources and their radiation fields," J. Opt. Soc. Am. 72, 923-928 (1982). [CrossRef]

[16] A. E. Siegman, "New developments in laser resonators," Proc. SPIE 1224, 2-14 (1990). [CrossRef]

[17] A. A. Tovar and L. W. Casperson, "Production and propagation of Hermite-sinusoidal-Gaussian laser beams," J. Opt. Soc. Am. A 15, 2425-2432 (1998). [CrossRef]

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Directionality of general beams