Abstract

We introduce two novel classes of partially coherent sources whose degrees of coherence are described by the rectangular Lorentz-correlated Schell-model (LSM) and rectangular fractional multi-Gaussian-correlated Schell-model (FMGSM) functions. Based on the generalized Collins formula, analytical expressions are derived for the spectral density distributions of these beams propagating through a stigmatic ABCD optical system. It is shown that beams belonging to both classes form the spectral density apex that is much higher and sharper than that generated by the Gaussian Schell-model (GSM) beam with a comparable coherence state. We experimentally generate these beams by using a nematic, transmissive spatial light modulator (SLM) that serves as a random phase screen controlled by a computer. The experimental data is consistent with theoretical predictions. Moreover, it is illustrated that the FMGSM beam generated in our experiments has a better focusing capacity than the GSM beam with the same coherence state. The applications that can potentially benefit from the use of novel beams range from material surface processing, to communications and sensing through random media.

© 2016 Optical Society of America

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  58. M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
    [Crossref]
  59. M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
    [Crossref]

2016 (1)

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

2015 (12)

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

2014 (10)

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

G. Wu and T. D. Visser, “Hanbury Brown-Twiss effect with partially coherent electromagnetic beams,” Opt. Lett. 39(9), 2561–2564 (2014).
[Crossref] [PubMed]

G. Gbur, “Partially coherent beam propagation in atmospheric turbulence [invited],” J. Opt. Soc. Am. A 31(9), 2038–2045 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

X. Xiao, O. Korotkova, and D. G. Voelz, “Laboratory implementation of partially coherent beams with Super-Gaussian distribution,” Proc. SPIE 9224, 92240N (2014).
[Crossref]

2013 (6)

2012 (6)

2011 (4)

2010 (1)

2009 (1)

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

2005 (1)

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

2004 (2)

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

Y. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29(23), 2716–2718 (2004).
[Crossref] [PubMed]

2003 (1)

Y. Li, “Flat-topped beam with non-circular cross-sections,” J. Mod. Opt. 50(13), 1957–1966 (2003).
[Crossref]

2002 (2)

2001 (2)

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64(4), 311–316 (1987).
[Crossref]

1983 (1)

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18(4), 551–556 (1983).
[Crossref]

1978 (1)

E. Wolf and E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25(3), 293–296 (1978).
[Crossref]

1970 (1)

Agrawal, G. P.

Basu, S.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Baykal, Y.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18(4), 551–556 (1983).
[Crossref]

Borghi, R.

Cai, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Y. Cai, Y. Chen, and F. Wang, “Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited],” J. Opt. Soc. Am. A 31(9), 2083–2096 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

Y. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29(23), 2716–2718 (2004).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

Carney, P. S.

Chen, Y.

Cheng, X.

Collett, E.

E. Wolf and E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25(3), 293–296 (1978).
[Crossref]

Collins, S. A.

de Sande, J. C. G.

Dong, Y.

Drexler, K.

K. Drexler and M. Roggemann, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng. 50(2), 025002 (2011).
[Crossref]

García-Guerrero, E. E.

Gbur, G.

Gori, F.

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Gu, Z. H.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64(4), 311–316 (1987).
[Crossref]

Hyde, M. V.

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

Hyde, M. W.

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Korotkova, O.

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

X. Xiao, O. Korotkova, and D. G. Voelz, “Laboratory implementation of partially coherent beams with Super-Gaussian distribution,” Proc. SPIE 9224, 92240N (2014).
[Crossref]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

Z. Mei, E. Schchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[Crossref] [PubMed]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

Lahiri, M.

M. Lahiri and E. Wolf, “Negative refraction of a partially coherent electromagnetic beam,” Opt. Lett. 38(9), 1407–1409 (2013).
[Crossref] [PubMed]

M. Lahiri and E. Wolf, “Theory of refraction and reflection with partially coherent electromagnetic beams,” Phys. Rev. A 86(4), 043815 (2012).
[Crossref]

Lajunen, H.

Leskova, T. A.

Li, Y.

Y. Li, “Flat-topped beam with non-circular cross-sections,” J. Mod. Opt. 50(13), 1957–1966 (2003).
[Crossref]

Li, Z.

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

Liang, C.

Lin, Q.

Liu, S.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Liu, X.

Liu, Z.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Mao, Y.

Maradudin, A. A.

Mei, Z.

Méndez, E. R.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64(4), 311–316 (1987).
[Crossref]

Piquero, G.

Plonus, M. A.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18(4), 551–556 (1983).
[Crossref]

Ponomarenko, S. A.

Ramírez-Sánchez, V.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25(5), 1016–1021 (2008).
[Crossref] [PubMed]

Roggemann, M.

K. Drexler and M. Roggemann, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng. 50(2), 025002 (2011).
[Crossref]

Roychowdhury, H.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Schchepakina, E.

Shchepakina, E.

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

Shirai, T.

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

Singh, M.

Song, Z.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Sun, Q.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Tervo, J.

Tong, Z.

Turunen, J.

Visser, T. D.

G. Wu and T. D. Visser, “Hanbury Brown-Twiss effect with partially coherent electromagnetic beams,” Opt. Lett. 39(9), 2561–2564 (2014).
[Crossref] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

Voelz, D. G.

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

X. Xiao, O. Korotkova, and D. G. Voelz, “Laboratory implementation of partially coherent beams with Super-Gaussian distribution,” Proc. SPIE 9224, 92240N (2014).
[Crossref]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Wang, F.

Wang, H.

Wang, J.

Wang, S. J.

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18(4), 551–556 (1983).
[Crossref]

Wang, X.

Wolf, E.

Wu, G.

Xiao, X.

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

X. Xiao, O. Korotkova, and D. G. Voelz, “Laboratory implementation of partially coherent beams with Super-Gaussian distribution,” Proc. SPIE 9224, 92240N (2014).
[Crossref]

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Yao, M.

Yuan, Y.

Zhang, R.

Zhao, C.

Zhao, D.

Zhou, K.

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Zhu, S.

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

Zhu, S. Y.

Appl. Phys. B (2)

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

S. Zhu and Z. Li, “Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam,” Appl. Phys. B 118(3), 481–487 (2015).
[Crossref]

J. Appl. Phys. (1)

M. V. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Experimentally generating any desired partially coherent Schell-model source using phase-only control,” J. Appl. Phys. 118(9), 093102 (2015).
[Crossref]

J. Mod. Opt. (1)

Y. Li, “Flat-topped beam with non-circular cross-sections,” J. Mod. Opt. 50(13), 1957–1966 (2003).
[Crossref]

J. Opt. (4)

M. V. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

Z. Song, Z. Liu, K. Zhou, Q. Sun, and S. Liu, “Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam,” J. Opt. 18(1), 015606 (2016).
[Crossref]

Z. Mei, O. Korotkova, and E. Shchepakina, “Electromagnetic multi-Gaussian Schell-model beams,” J. Opt. 15(2), 025705 (2013).
[Crossref]

M. W. Hyde, S. Basu, X. Xiao, and D. G. Voelz, “Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source,” J. Opt. 17(5), 055607 (2015).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

F. Gori, V. Ramírez-Sánchez, M. Santarsiero, and T. Shirai, “On genuine cross-spectral density matrices,” J. Opt. A, Pure Appl. Opt. 11(8), 085706 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

Opt. Commun. (3)

E. Wolf and E. Collett, “Partially coherent sources which produce the same far-field intensity distribution as a laser,” Opt. Commun. 25(3), 293–296 (1978).
[Crossref]

F. Gori, G. Guattari, and C. Padovani, “Modal expansion for J0-correlated Schell-model sources,” Opt. Commun. 64(4), 311–316 (1987).
[Crossref]

H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
[Crossref]

Opt. Eng. (2)

K. Drexler and M. Roggemann, “Use of a partially coherent transmitter beam to improve the statistics of received power in a free-space optical communication system: theory and experimental results,” Opt. Eng. 50(2), 025002 (2011).
[Crossref]

M. W. Hyde, S. Basu, D. G. Voelz, and X. Xiao, “Generating partially coherent Schell-model sources using a modified phase screen approach,” Opt. Eng. 54(12), 120501 (2015).
[Crossref]

Opt. Express (11)

S. Basu, M. W. Hyde, X. Xiao, D. G. Voelz, and O. Korotkova, “Computational approaches for generating electromagnetic Gaussian Schell-model sources,” Opt. Express 22(26), 31691–31707 (2014).
[Crossref] [PubMed]

Z. Mei, Z. Tong, and O. Korotkova, “Electromagnetic non-uniformly correlated beams in turbulent atmosphere,” Opt. Express 20(24), 26458–26463 (2012).
[Crossref] [PubMed]

Z. Mei, E. Schchepakina, and O. Korotkova, “Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence,” Opt. Express 21(15), 17512–17519 (2013).
[Crossref] [PubMed]

S. Zhu, Y. Chen, J. Wang, H. Wang, Z. Li, and Y. Cai, “Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization,” Opt. Express 23(26), 33099–33115 (2015).
[Crossref] [PubMed]

F. Wang, C. Liang, Y. Yuan, and Y. Cai, “Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment,” Opt. Express 22(19), 23456–23464 (2014).
[Crossref] [PubMed]

Y. Chen, F. Wang, C. Zhao, and Y. Cai, “Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam,” Opt. Express 22(5), 5826–5838 (2014).
[Crossref] [PubMed]

E. E. García-Guerrero, E. R. Méndez, Z. H. Gu, T. A. Leskova, and A. A. Maradudin, “Interference of a pair of symmetric partially coherent beams,” Opt. Express 18(5), 4816–4828 (2010).
[Crossref] [PubMed]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

R. Zhang, X. Wang, and X. Cheng, “Far-zone polarization distribution properties of partially coherent beams with non-uniform source polarization distributions in turbulent atmosphere,” Opt. Express 20(2), 1421–1435 (2012).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Non-uniformly correlated partially coherent pulses,” Opt. Express 21(1), 190–195 (2013).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Powers of the degree of coherence,” Opt. Express 23(7), 8519–8531 (2015).
[Crossref] [PubMed]

Opt. Lett. (17)

Z. Mei and O. Korotkova, “Alternating series of cross-spectral densities,” Opt. Lett. 40(11), 2473–2476 (2015).
[Crossref] [PubMed]

Z. Mei, D. Zhao, O. Korotkova, and Y. Mao, “Gaussian Schell-model arrays,” Opt. Lett. 40(23), 5662–5665 (2015).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Nonuniformly correlated light beams in uniformly correlated media,” Opt. Lett. 37(15), 3240–3242 (2012).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Devising genuine spatial correlation functions,” Opt. Lett. 32(24), 3531–3533 (2007).
[Crossref] [PubMed]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, “Difference of cross-spectral densities,” Opt. Lett. 39(7), 1713–1716 (2014).
[Crossref] [PubMed]

Z. Mei, O. Korotkova, and Y. Mao, “Products of Schell-model cross-spectral densities,” Opt. Lett. 39(24), 6879–6882 (2014).
[Crossref] [PubMed]

O. Korotkova and Z. Mei, “Convolution of degrees of coherence,” Opt. Lett. 40(13), 3073–3076 (2015).
[Crossref] [PubMed]

H. Lajunen and T. Saastamoinen, “Propagation characteristics of partially coherent beams with spatially varying correlations,” Opt. Lett. 36(20), 4104–4106 (2011).
[Crossref] [PubMed]

M. Lahiri and E. Wolf, “Negative refraction of a partially coherent electromagnetic beam,” Opt. Lett. 38(9), 1407–1409 (2013).
[Crossref] [PubMed]

Y. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29(23), 2716–2718 (2004).
[Crossref] [PubMed]

G. Wu and T. D. Visser, “Hanbury Brown-Twiss effect with partially coherent electromagnetic beams,” Opt. Lett. 39(9), 2561–2564 (2014).
[Crossref] [PubMed]

P. S. Carney and E. Wolf, “Power-excitation diffraction tomography with partially coherent light,” Opt. Lett. 26(22), 1770–1772 (2001).
[Crossref] [PubMed]

C. Liang, F. Wang, X. Liu, Y. Cai, and O. Korotkova, “Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry,” Opt. Lett. 39(4), 769–772 (2014).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Cosine-Gaussian Schell-model sources,” Opt. Lett. 38(14), 2578–2580 (2013).
[Crossref] [PubMed]

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

Phys. Rev. A (2)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

M. Lahiri and E. Wolf, “Theory of refraction and reflection with partially coherent electromagnetic beams,” Phys. Rev. A 86(4), 043815 (2012).
[Crossref]

Proc. SPIE (1)

X. Xiao, O. Korotkova, and D. G. Voelz, “Laboratory implementation of partially coherent beams with Super-Gaussian distribution,” Proc. SPIE 9224, 92240N (2014).
[Crossref]

Radio Sci. (1)

Y. Baykal, M. A. Plonus, and S. J. Wang, “The scintillations for weak atmospheric turbulence using a partially coherent source,” Radio Sci. 18(4), 551–556 (1983).
[Crossref]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

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Figures (9)

Fig. 1
Fig. 1 Density plots of the DOC of the rectangular LSM beam for different coherence lengths. (a) δ = 0.1mm, (b) δ = 1mm, (c) δ = 2mm, (d) comparison of cross-section profiles of (a), (b) and (c) at yd = 0.
Fig. 2
Fig. 2 Density plots of the intensity distributions of the LSM beam in the focus plane with different coherence lengths. (a) δ = 0.1mm, (b) δ = 0.5mm, (c) δ = 1mm, (d) δ = 2mm.
Fig. 3
Fig. 3 Focused intensity distributions of the LSM and GSM beams at the cross-section y = 0.
Fig. 4
Fig. 4 DOC of the rectangular FMGSM beam in the initial plane. (a)-(c) are the contour plots of the DOC (M = 2) with different coherence lengths: δ = 2.25mm, 0.225mm and 0.113mm, respectively. (d)-(f) are the cross-section profiles of the DOC for M = 2, 5 and 10, respectively, while the coherence length remains the same, i.e. δ = 0.225mm.
Fig. 5
Fig. 5 Spectral density of the FMGSM beam at the focal plane. The density plot (a) shows the focused intensity profile produced by the GSM beam, (b)-(c) show the focused intensity of the FMGSM beam for M = 5 and M = 10, respectively. For comparison, the cross-section profiles (d)-(f) show the intensity distributions for M = 2, 5, 10 and the GSM beam, respectively. As the numerical parameter, the coherence length remains as a fixed value of δ = 1.13mm.
Fig. 6
Fig. 6 Experimental setup for generating the LSM and the FMGSM beams, and measuring their focused intensity distributions. NDF: neutral density filter; LP1 and LP2: linear polarizers; CA: circular aperture; SLM: spatial light modulator; L1, L2 and L3: thin lenses; PC1 and PC2: personal computers.
Fig. 7
Fig. 7 Experimental intensity distributions of the LSM beam. The contour plots (a)-(c) show the intensity profiles for δ = 0.4mm, 0.73mm and 1.1mm, respectively. The cross-section profiles (d)-(e) exhibit the comparisons between the experimental data and the theoretical fit results at the plane y = 0.
Fig. 8
Fig. 8 Experimental intensity distributions of the FMGSM beam. The contour plots (a)-(c) show the intensity distributions of the beam for M = 5, 10 and 20, respectively. The cross-section profiles (d)-(f) present the comparisons between the experimental data with the theoretical fit results at the plane y = 0.
Fig. 9
Fig. 9 Experimental intensity distributions of the focused FMGSM beam at the cross-section y = 0. Comparisons are made between the focused intensities of the FMGSM beam with M = 5, 10 and those produced by the GSM beam.

Equations (27)

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W ( 0 ) ( ρ 1 ', ρ 2 ';ω )= S( ρ 1 ';ω ) S( ρ 2 ';ω ) μ( ρ 1 ', ρ 2 ';ω ),
W ( 0 ) ( ρ 1 ', ρ 2 ' )= p( v ) H 0 * ( ρ 1 ',v ) H 0 ( ρ 2 ',v ) d 2 v,
H 0 ( ρ j ',v )=f( ρ j ' )exp( 2πi ρ j 'v ). ( j=1, 2 ).
W ( 0 ) ( ρ 1 ', ρ 2 ' )= f * ( ρ 1 ' )f( ρ 2 ' ) p ˜ ( ρ 2 ' ρ 1 ' ),
p ˜ ( ρ 2 ' ρ 1 ' )= p( v )exp[ 2πi( ρ 2 ' ρ 1 ' )v ] ,
p( v )=π δ 2 exp[ 2πδ( | v x |+| v y | ) ],
μ( x d ,y d )= δ 4 ( x d 2 + δ 2 )( y d 2 + δ 2 ) ,
W ( 0 ) ( ρ 1 ', ρ 2 ' )=exp( ρ ' 1 2 +ρ ' 2 2 4 σ 0 2 ) δ 4 [ ( x 2 x 1 ) 2 + δ 2 ][ ( y 2 y 1 ) 2 + δ 2 ] ,
W( ρ 1 , ρ 2 ,z )= k 2 4 π 2 B 2 + + + + W ( 0 ) ( ρ 1 ', ρ 2 ' )exp [ ik 2B ( A ρ 1 ' 2 2 ρ 1 ' ρ 1 +D ρ 1 2 ) + ik 2B ( A ρ 2 ' 2 2 ρ 2 ' ρ 2 +D ρ 2 2 ) ]d x 1 'd x 2 'd y 1 'd y 2 ',
u - = x 1 ' x 2 ', u + = x 1 '+ x 2 ', v - = y 1 ' y 2 ', v + = y 1 '+ y 2 ',
I( ρ,z )=W( ρ,ρ,z )= k 2 δ 4 16 π 2 B 2 + + + - + exp( u + 2 + u 2 + v + 2 + v 2 8 σ 0 2 ) 1 ( u 2 + δ 2 )( v 2 + δ 2 ) ×exp[ ik 2B A u + u ik 2B A v + v + ik B u x+ ik B v y ]d u + d u d v + d v .
F 1 ( τ ) F 2 ( τ )= + f 1 ( κ ) f 2 ( κ )exp( iτκ )dκ,
I( ρ,z )= k 2 δ 4 2π B 2 σ 0 2 j=x,y [ F 1 ( k B j ) F 2 ( k B j ) ],
F 1 ( τ )= π δ exp[ δ| τ | ], F 2 ( τ )= 2π k 2 A 2 B 2 σ 0 2 + 1 4 σ 0 2 exp[ τ 2 2 k 2 A 2 B 2 σ 0 2 + 1 2 σ 0 2 ].
F 1 ( τ ) F 2 ( τ )= + F 1 ( ξ ) F 2 ( τξ )dξ.
I( ρ,z )= π 3 k 2 δ 2 σ 0 2 2 B 2 exp( Q δ 2 ){ exp( kδ B x )erfc{ 1 2 Q [ δ kx BQ ] } +exp( kδ B x )erfc{ 1 2 Q [ δ+ kx BQ ] }{ exp( kδ B y )erfc{ 1 2 Q [ δ ky BQ ] } +exp( kδ B y )erfc{ 1 2 Q [ δ+ ky BQ ] } },
Q= k 2 A 2 B 2 σ 0 2 + 1 4 σ 0 2 ,
erfc(u)=1 2 π 0 u exp( t 2 )dt,
( A B C D )=( 1 z 0 1 )( 1 0 1/f 1 )( 1 f 0 1 )=( 1z/f f 1/f 0 ).
p( v )={ 1 [ 1exp( 2 π 2 δ 2 v x 2 ) ] 1/M }{ 1 [ 1exp( 2 π 2 δ 2 v y 2 ) ] 1/M },
p( v )={ n=1 ( 1 ) n m=1 n [ 1( m1 )M ] n! M n exp( 2n π 2 δ 2 v x 2 ) }{ n'=1 ( 1 ) n' m'=1 n' [ 1( m'1 )M ] n'! M n' exp( 2n π 2 δ 2 v y 2 ) }.
μ( x d , y d )= 1 C 0 2 { n=1 ( 1 ) n+1 m=1 n [ 1( m1 )M ] n n! M n exp( x d 2 2n δ 2 ) } ×{ n'=1 ( 1 ) n'+1 m'=1 n' [ 1( m'1 )M ] n' n'! M n' exp( y d 2 2n' δ 2 ) },
C 0 = n=1 ( 1 ) n m=1 n [ 1( m1 )M ] n n! M n ,
W ( 0 ) ( ρ 1 ', ρ 2 ' )= 1 C 0 2 exp( ρ ' 1 2 +ρ ' 2 2 4 σ 0 2 ){ n=1 ( 1 ) n+1 m=1 n [ 1( m1 )M ] n n! M n exp( x d 2 2n δ 2 ) } ×{ n'=1 ( 1 ) n'+1 m'=1 n' [ 1( m'1 )M ] n' n'! M n' exp( y d 2 2n' δ 2 ) }.
W( x 1 , y 1 , x 2 , y 2 ,z )= 1 C 0 2 { n=1 ( 1 ) n+1 m=1 n [ 1( m1 )M ] nQ' n! M n exp[ ( x 1 + x 2 ) 2 8 σ 0 2 Q' ] exp[ k 2 σ 0 2 2 B 2 ( 1 A 2 Q' ) ( x 2 x 1 ) 2 ] ×exp[ ik 2B ( D A Q' )( x 2 2 x 1 2 ) ] }{ n'=1 ( 1 ) n'+1 m'=1 n' [ 1( m'1 )M ] n'Q' n'! M n' exp[ ( y 1 + y 2 ) 2 8 σ 0 2 Q' ] ×exp[ k 2 σ 0 2 2 B 2 ( 1 A 2 Q' ) ( y 2 y 1 ) 2 ]exp[ ik 2B ( D A Q' )( y 2 2 y 1 2 ) ] },
Q'= A 2 + B 2 4 k 2 σ 0 4 + B 2 n k 2 σ 0 2 δ 2 .
I( x,y,z )= 1 C 0 2 { n=1 ( 1 ) n+1 m=1 n [ 1( m1 )M ] nQ' n! M n exp( x 2 2 σ 0 2 Q' ) }{ n'=1 ( 1 ) n'+1 m'=1 n' [ 1( m'1 )M ] n'Q' n'! M n' exp( y 2 2 σ 0 2 Q' ) }.

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