Abstract

In a previous paper [Opt. Express 22, 31691 (2014)] two different wave optics methodologies (phase screen and complex screen) were introduced to generate electromagnetic Gaussian Schell-model sources. A numerical optimization approach based on theoretical realizability conditions was used to determine the screen parameters. In this work we describe a practical modeling approach for the two methodologies that employs a common numerical recipe for generating correlated Gaussian random sequences and establish exact relationships between the screen simulation parameters and the source parameters. Both methodologies are demonstrated in a wave-optics simulation framework for an example source. The two methodologies are found to have some differing features, for example, the phase screen method is more flexible than the complex screen in terms of the range of combinations of beam parameter values that can be modeled. This work supports numerical wave optics simulations or laboratory experiments involving electromagnetic Gaussian Schell-model sources.

© 2017 Optical Society of America

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References

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  1. D. F. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11(5), 1641–1649 (1994).
    [Crossref]
  2. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
    [Crossref]
  3. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
    [Crossref]
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 2005).
  5. 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]
  6. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249(4-6), 379–385 (2005).
    [Crossref]
  7. A. S. Ostrovsky, G. Martínez-Niconoff, V. Arrizón, P. Martínez-Vara, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Modulation of coherence and polarization using liquid crystal spatial light modulators,” Opt. Express 17(7), 5257–5264 (2009).
    [Crossref] [PubMed]
  8. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
    [Crossref]
  9. F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36(14), 2722–2724 (2011).
    [Crossref] [PubMed]
  10. 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]
  11. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  12. D. Voelz, X. Xiao, and O. Korotkova, “Numerical modeling of Schell-model beams with arbitrary far-field patterns,” Opt. Lett. 40(3), 352–355 (2015).
    [Crossref] [PubMed]
  13. J. W. Goodman, Statistical Optics (John Wiley & Sons, Inc., 2015).
  14. M. W. 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]
  15. D. Voelz, Computational Fourier Optics, A MatLab Tutorial (SPIE Press, 2010).
  16. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, Inc., 1999).

2015 (2)

D. Voelz, X. Xiao, and O. Korotkova, “Numerical modeling of Schell-model beams with arbitrary far-field patterns,” Opt. Lett. 40(3), 352–355 (2015).
[Crossref] [PubMed]

M. W. 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]

2014 (1)

2011 (1)

2009 (1)

2008 (1)

2005 (2)

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

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

2004 (1)

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
[Crossref]

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

1994 (1)

Arrizón, V.

Basu, S.

M. W. 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]

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]

Borghi, R.

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]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Cai, Y.

Gori, F.

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]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Hyde, M. W.

M. W. 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]

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]

James, D. F.

Korotkova, O.

D. Voelz, X. Xiao, and O. Korotkova, “Numerical modeling of Schell-model beams with arbitrary far-field patterns,” Opt. Lett. 40(3), 352–355 (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]

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

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
[Crossref]

Liu, X.

Martínez-Niconoff, G.

Martínez-Vara, P.

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Ramírez-Sánchez, V.

Rickenstorff-Parrao, C.

Roychowdhury, H.

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

Salem, M.

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
[Crossref]

Santarsiero, M.

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]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

Voelz, D.

Voelz, D. G.

M. W. 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]

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.

Wolf, E.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
[Crossref]

Wu, G.

Xiao, X.

Zhu, S.

J. Appl. Phys. (1)

M. W. 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. Opt. A, Pure Appl. Opt. (2)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001).
[Crossref]

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

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

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233(4–6), 225–230 (2004).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Other (5)

J. W. Goodman, Statistical Optics (John Wiley & Sons, Inc., 2015).

D. Voelz, Computational Fourier Optics, A MatLab Tutorial (SPIE Press, 2010).

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons, Inc., 1999).

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 2005).

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Figures (5)

Fig. 1
Fig. 1 Conceptual diagram for EGSM beam formation.
Fig. 2
Fig. 2 Correlation coefficient |Bxy| as a function of Γ when Rx = 0.75 and Ry = (a) 0.90, (b) 1.00, and (c) 1.10 with both σϕx2 and σϕy2 ≥ 6 (—), ≥ 9 (—), ≥ 12(···).
Fig. 3
Fig. 3 Correlation coefficient |Bxy| as a function of Γ with Rx = 0.9650 and Ry = 1.0338 (δxx = 0.1500 mm, δyy = 0.1607 mm, and δxy = 0.1554 mm) with (a) PS approach when both σ ϕ y 2 and σ ϕ y 2 ≥ π2, and (b) CS approach. The green line denotes the range of |Bxy| = 0.15.
Fig. 4
Fig. 4 Correlation coefficient |Bxy| as a function of Γ for Rx = 0.8751 and Ry = 0.9376 (δxx = 0.1500 mm, δyy = 0.1607 mm, and δxy = 0.1714 mm) when both σ ϕ x 2 and σ ϕ y 2 ≥ π2. Green line denotes the available range for |Bxy| = 0.15.
Fig. 5
Fig. 5 PS and CS simulation results vs. theory. The rows are S0, S1, S2, and S3, and the columns are the PS, CS, and the analytical results, respectively.

Tables (2)

Tables Icon

Table 1 EGSM Beam Parameters

Tables Icon

Table 2 EGSM Beam Screen Simulation Parameters for both PS and CS Approaches

Equations (40)

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E(ρ;0)= x ^ E x (ρ)+ y ^ E y (ρ),
E x (ρ)= E 0x (ρ) T x (ρ); and E y (ρ)= E 0y (ρ) T y (ρ).
E 0α ( ρ )= A α e j θ α exp( ρ 2 4 σ α 2 ),
W( ρ 1 , ρ 2 )=[ W xx ( ρ 1 , ρ 2 ) W xy ( ρ 1 , ρ 2 ) W yx ( ρ 1 , ρ 2 ) W yy ( ρ 1 , ρ 2 ) ],
W αβ ( ρ 1 , ρ 2 )= E α ( ρ 1 ) E β ( ρ 2 ) ,
W αβ ( ρ 1 , ρ 2 )= A α A β e j( θ α θ β ) exp[ ( ρ 1 2 4 σ α 2 + ρ 2 2 4 σ β 2 ) ] μ αβ ( | ρ 1 ρ 2 | ).
μ αβ ( ρ 1 , ρ 2 )= T α ( ρ 1 ) T β * ( ρ 2 ) .
μ αβ ( Δρ )=| B αβ |exp( Δ ρ 2 2 δ αβ 2 ),
T x ( ρ )= 2π δ xx [ r x ( ρ ) g x ( ρ ) ],
T y ( ρ )= 2π δ yy { Γ[ r x ( ρ ) g x ( ρ ) ]+ 1 Γ 2 [ r y ( ρ ) g y ( ρ ) ] },
T ˜ x ( f x , f y )= π l φ x φ x σ φ x r ˜ x ( f x , f y ) G x ( f x , f y ),
T ˜ y ( f x , f y )= π l φ y φ y σ φ y [ r ˜ x Γ+ r ˜ y 1 Γ 2 ] G y ( f x , f y ).
G α ( f x , f y )=exp[ π 2 l φ α φ α 2 ( f x 2 + f y 2 )/2 ],
e j ϕ α1 PS e j ϕ α2 PS =exp{ σ ϕ α 2 [ 1exp( Δ ρ 2 l ϕ α ϕ α 2 ) ] },
e j ϕ α1 PS e j ϕ β2 PS =exp[ 1 2 ( σ ϕ α 2 + σ ϕ β 2 4Γ σ ϕ α σ ϕ β l ϕ α ϕ α l ϕ β ϕ β l ϕ α ϕ α 2 + l ϕ β ϕ β 2 e 2Δ ρ 2 l ϕ α ϕ α 2 + l ϕ β ϕ β 2 ) ].
σ ϕ x 2 >>1 and σ ϕ y 2 >>1,
| B xx | = | B yy | =1,
δ xx 2 = l ϕ x ϕ x 2 2 σ ϕ x 2 ,
δ yy 2 = l ϕ y ϕ y 2 2 σ ϕ y 2 ,
δ xy 2 = ( l ϕ x ϕ x 2 + l ϕ y ϕ y 2 ) 2 8Γ σ ϕ x σ ϕ y l ϕ x ϕ x l ϕ y ϕ y ,
| B xy |=exp[ 1 2 ( σ ϕ x 2 + σ ϕ y 2 4Γ σ ϕ x σ ϕ y l ϕ x ϕ x l ϕ y ϕ y l ϕ x ϕ x 2 + l ϕ y ϕ y 2 ) ].
4Γ= ( σ ϕ x 2 δ xx 2 + σ ϕ y 2 δ yy 2 ) 2 σ ϕ x 2 σ ϕ y 2 δ xx δ yy δ xy 2 ,
| B xy |=exp[ 1 2 ( σ ϕ x 2 + σ ϕ y 2 σ ϕ x 2 δ xx 2 + σ ϕ y 2 δ yy 2 δ xy 2 ) ].
4Γ= ( R x σ ϕ x σ ϕ y R x R y + R y σ ϕ y σ ϕ x R y R x ) 2 ,
| B xy |=exp{ 1 2 [ ( 1 R x 2 ) σ ϕ x 2 +( 1 R y 2 ) σ ϕ y 2 ] }.
0 ( R x σ ϕ x σ ϕ y R x R y R y σ ϕ y σ ϕ x R y R x ) 2 .
R x R y Γ 1
ϕ α1 CS ϕ α2 CS* = σ ϕ α 2 exp( Δ ρ 2 l ϕ α ϕ α 2 ),
ϕ x1 CS ϕ y2 CS* = 2Γ l ϕ x ϕ x l ϕ y ϕ y l ϕ x ϕ x 2 + l ϕ y ϕ y 2 exp( 2Δ ρ 2 l ϕ x ϕ x 2 + l ϕ y ϕ y 2 ).
σ ϕ x 2 = σ ϕ y 2 =1,
δ xx 2 = l ϕ x ϕ x 2 2 ,
δ yy 2 = l ϕ y ϕ y 2 2 ,
δ xy 2 = l ϕ x ϕ x 2 + l ϕ y ϕ y 2 4 ,
B xy = 2Γ l ϕ x ϕ x l ϕ y ϕ y l ϕ x ϕ x 2 + l ϕ y ϕ y 2 .
R x 2 + R y 2 = 2,
| B xy | = Γ R x R y .
S 0 (ρ)= | E x (ρ) | 2 + | E y (ρ) | 2 ,
S 1 (ρ)= | E x (ρ) | 2 | E y (ρ) | 2 ,
S 2 (ρ)=2Re[ E x * (ρ) E y (ρ) ],
S 3 (ρ)=2Im[ E x * (ρ) E y (ρ) ].

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