Abstract

We develop a method to generate electromagnetic nonuniformly correlated (ENUC) sources from vector Gaussian Schell-model (GSM) beams. Having spatially varying correlation properties, ENUC sources are more difficult to synthesize than their Schell-model counterparts (which can be generated by filtering circular complex Gaussian random numbers) and, in past work, have only been realized using Cholesky decomposition—a computationally intensive procedure. Here we transform electromagnetic GSM field instances directly into ENUC instances, thereby avoiding computing Cholesky factors resulting in significant savings in time and computing resources. We validate our method by generating (via simulation) an ENUC beam with desired parameters. We find the simulated results to be in excellent agreement with the theoretical predictions. This new method for generating ENUC sources can be directly implemented on existing spatial-light-modulator-based vector beam generators and will be useful in applications where nonuniformly correlated beams have shown promise, e.g., free-space/underwater optical communications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. Lajunen and T. Saastamoinen, Opt. Lett. 36, 4104 (2011).
    [Crossref]
  2. Z. Tong and O. Korotkova, J. Opt. Soc. Am. A 29, 2154 (2012).
    [Crossref]
  3. Y. Gu and G. Gbur, Opt. Lett. 38, 1395 (2013).
    [Crossref]
  4. M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
    [Crossref]
  5. M. Santarsiero, R. Martínez-Herrero, D. Maluenda, J. C. G. de Sande, G. Piquero, and F. Gori, Opt. Lett. 42, 4115 (2017).
    [Crossref]
  6. S. Cui, Z. Chen, L. Zhang, and J. Pu, Opt. Lett. 38, 4821(2013).
    [Crossref]
  7. M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
    [Crossref]
  8. X. Xiao and D. Voelz, Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP), OSA Technical Digest (online) (OSA, 2017), paper PTu1D.3.
    [Crossref]
  9. D. Voelz, X. Xiao, and O. Korotkova, Opt. Lett. 40, 352 (2015).
    [Crossref]
  10. M. W. Hyde, Results Phys. 15, 102663 (2019).
    [Crossref]
  11. O. Korotkova, Random Light Beams: Theory and Applications (CRC Press, 2014).
  12. M. Hyde, “MATLAB R2018b ENUC simulation code,” figshare, 2019, https://doi.org/10.6084/m9.figshare.9901724 .

2019 (1)

M. W. Hyde, Results Phys. 15, 102663 (2019).
[Crossref]

2017 (2)

2016 (1)

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

2015 (1)

2013 (2)

2012 (1)

2011 (1)

Bose-Pillai, S.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Bose-Pillai, S. R.

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
[Crossref]

Chen, Z.

Cui, S.

de Sande, J. C. G.

Gbur, G.

Gori, F.

Gu, Y.

Hyde, M. W.

M. W. Hyde, Results Phys. 15, 102663 (2019).
[Crossref]

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Korotkova, O.

Lajunen, H.

Maluenda, D.

Martínez-Herrero, R.

Piquero, G.

Pu, J.

Saastamoinen, T.

Santarsiero, M.

Tong, Z.

Voelz, D.

D. Voelz, X. Xiao, and O. Korotkova, Opt. Lett. 40, 352 (2015).
[Crossref]

X. Xiao and D. Voelz, Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP), OSA Technical Digest (online) (OSA, 2017), paper PTu1D.3.
[Crossref]

Voelz, D. G.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Wood, R. A.

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
[Crossref]

Xiao, X.

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

D. Voelz, X. Xiao, and O. Korotkova, Opt. Lett. 40, 352 (2015).
[Crossref]

X. Xiao and D. Voelz, Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP), OSA Technical Digest (online) (OSA, 2017), paper PTu1D.3.
[Crossref]

Zhang, L.

Appl. Phys. Lett. (1)

M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Lett. (5)

Phys. Rev. Appl. (1)

M. W. Hyde, S. Bose-Pillai, D. G. Voelz, and X. Xiao, Phys. Rev. Appl. 6, 064030 (2016).
[Crossref]

Results Phys. (1)

M. W. Hyde, Results Phys. 15, 102663 (2019).
[Crossref]

Other (3)

O. Korotkova, Random Light Beams: Theory and Applications (CRC Press, 2014).

M. Hyde, “MATLAB R2018b ENUC simulation code,” figshare, 2019, https://doi.org/10.6084/m9.figshare.9901724 .

X. Xiao and D. Voelz, Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP), OSA Technical Digest (online) (OSA, 2017), paper PTu1D.3.
[Crossref]

Supplementary Material (1)

NameDescription
» Code 1       MATLAB R2018 simulation code.

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Figures (3)

Fig. 1.
Fig. 1. ENUC T α generation process. (a) Real part of an EGSM T α on the r = x ^ ξ + y ^ η grid, (b) radial slice along ξ axis of the EGSM T α in (a), (c) real part of ENUC T α formed from mapping the T α values in (b) to ρ using Eq. (5), and (d)  y = γ α y slice through (c).
Fig. 2.
Fig. 2. ENUC physical realizability [Eq. (9)] versus synthesizability [Eq. (10)] for δ x x = δ y y = δ .
Fig. 3.
Fig. 3. ENUC simulation results: subfigures (a) and (b) show the theoretical and simulated spectral densities overlaid with the polarization ellipses. Subfigures (c)–(r) show the elements of W _ ( x 1 , 0 , x 2 , 0 ) . Each element (labeled for the reader’s convenience) is a 2 × 2 group of images, where the theoretical and simulated W α β are in columns 1 and 2 and the real and imaginary parts of W α β are in rows 1 and 2, respectively.

Tables (1)

Tables Icon

Table 1. ENUC Parameters

Equations (10)

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W α β ( ρ 1 , ρ 2 ) = A α exp ( ρ 1 2 4 σ α 2 ) A β exp ( ρ 2 2 4 σ β 2 ) × B α β exp [ ( | ρ 1 γ α | 2 | ρ 2 γ β | 2 ) 2 / δ α β 4 ] ,
E ( ρ ) = x ^ E x ( ρ ) + y ^ E y ( ρ ) E α ( ρ ) = C α exp ( ρ 2 4 σ α 2 ) T α ( ρ ) ,
T α ( ρ 1 ) T β * ( ρ 2 ) = | B α β | exp [ ( | ρ 1 γ α | 2 | ρ 2 γ β | 2 ) 2 / δ α β 4 ] .
W α β ( ρ 1 , ρ 2 ) = A α exp ( ρ 1 2 4 σ α 2 ) A β exp ( ρ 2 2 4 σ β 2 ) × B α β exp ( | r 1 r 2 | 2 / δ α β 4 ) .
r = α ^ | ρ γ | 2 .
T α [ i , j ] = m , n r α [ m , n ] Φ α α [ m , n ] 2 ( N Δ ) 2 exp [ j 2 π N ( m i + n j ) ] ,
Φ α α ( f ) = π δ α α 4 exp ( π 2 δ α α 4 f 2 ) .
R ( f ) = δ x y 4 δ x x 2 δ y y 2 / | B x y | exp [ π 2 ( δ x y 4 δ x x 4 + δ y y 4 2 ) f 2 ] ,
B α α = 1 , B x y = B y x * , | B x y | 1 , δ x y = δ y x , δ x x 4 + δ y y 4 2 4 δ x y δ x x δ y y | B x y | .
δ x x 4 + δ y y 4 2 4 δ x y δ x x δ y y | B x y |

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