Abstract

Using the criterion for a genuine cross-spectral density function, we demonstrate the realization of an Im-Bessel correlated source, which has only recently been achieved using the source’s coherent-mode representation. In addition, with just a simple change, we create a whole new class of partially coherent sources that have not been realized. We simulate the generation of these sources and compare the results to theoretical predictions to validate our analysis. The partially coherent sources described herein can easily be synthesized using spatial light modulators, and the approach presented in this Letter can be used to design sources for optical trapping, optical tweezers, and other related applications.

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References

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  1. Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
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    [Crossref]
  6. X. Chen, J. Li, S. M. H. Rafsanjani, and O. Korotkova, Opt. Lett. 43, 3590 (2018).
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  7. M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
    [Crossref]
  8. S. A. Ponomarenko, J. Opt. Soc. Am. A 18, 150 (2001).
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    [Crossref]
  11. Y. Gu and G. Gbur, Opt. Lett. 38, 1395 (2013).
    [Crossref]
  12. M. W. Hyde, S. R. Bose-Pillai, and R. A. Wood, Appl. Phys. Lett. 111, 101106 (2017).
    [Crossref]
  13. M. W. Hyde and S. R. Bose-Pillai, Opt. Lett. 42, 3084 (2017).
    [Crossref]
  14. M. Santarsiero, R. Martínez-Herrero, D. Maluenda, J. C. G. de Sande, G. Piquero, and F. Gori, Opt. Lett. 42, 4115 (2017).
    [Crossref]
  15. F. Gori, Opt. Commun. 46, 149 (1983).
    [Crossref]
  16. X. Yu, A. Todi, and H. Tang, Appl. Opt. 57, 4677 (2018).
    [Crossref]
  17. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).
  18. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).
  19. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, 2nd ed. (SPIE, 2007).

2018 (2)

2017 (6)

M. W. Hyde and S. R. Bose-Pillai, Opt. Lett. 42, 3084 (2017).
[Crossref]

M. Santarsiero, R. Martínez-Herrero, D. Maluenda, J. C. G. de Sande, G. Piquero, and F. Gori, Opt. Lett. 42, 4115 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

M. W. Hyde, S. R. Bose-Pillai, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

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

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

2016 (1)

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

2013 (2)

2007 (1)

2006 (1)

2001 (1)

1983 (1)

F. Gori, Opt. Commun. 46, 149 (1983).
[Crossref]

Bose-Pillai, S.

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

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, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

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

M. W. Hyde and S. R. Bose-Pillai, Opt. Lett. 42, 3084 (2017).
[Crossref]

Cai, Y.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

Chen, X.

Chen, Y.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

de Sande, J. C. G.

Gbur, G.

Gbur, G. J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Gori, F.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

Gu, Y.

Hyde, M. W.

M. W. Hyde and S. R. Bose-Pillai, Opt. Lett. 42, 3084 (2017).
[Crossref]

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

M. W. Hyde, S. R. Bose-Pillai, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

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

Korotkova, O.

Li, J.

Liu, L.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

Liu, X.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

Mack, C. A.

Maluenda, D.

Mandel, L.

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

Martínez-Herrero, R.

Piquero, G.

Ponomarenko, S. A.

Rafsanjani, S. M. H.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

Santarsiero, M.

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, 2nd ed. (SPIE, 2007).

Tang, H.

Todi, A.

Voelz, D. G.

M. W. Hyde, S. R. Bose-Pillai, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

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

Wolf, E.

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

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. R. Bose-Pillai, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

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

Yu, J.

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

Yu, X.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

J. Opt. (1)

M. W. Hyde, S. Bose-Pillai, X. Xiao, and D. G. Voelz, J. Opt. 19, 025601 (2017).
[Crossref]

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

Microw. Opt. Technol. Lett. (1)

M. W. Hyde, S. R. Bose-Pillai, X. Xiao, and D. G. Voelz, Microw. Opt. Technol. Lett. 59, 2731 (2017).
[Crossref]

Opt. Commun. (1)

F. Gori, Opt. Commun. 46, 149 (1983).
[Crossref]

Opt. Express (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]

Prog. Opt. (1)

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, Prog. Opt. 62, 157 (2017).
[Crossref]

Other (4)

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

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms, 2nd ed. (SPIE, 2007).

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Figures (4)

Fig. 1.
Fig. 1. Complex s plane corresponding to Eq. (15).
Fig. 2.
Fig. 2. Spectral density S ( ρ ) = W ( ρ , ρ ) results: (a)  I m -Bessel theory, (b)  I m -Bessel simulation, (c) Eq. (17) theory, (d) Eq. (17) simulation, and (e) RMSEs for the simulated I m -Bessel (blue trace) and Eq. (17) sources (red trace) versus trial number.
Fig. 3.
Fig. 3. W ( ρ 1 , ϕ ; ρ 2 , ϕ ) results versus ρ 1 and ρ 2 : (a)  I m -Bessel theory, (b)  I m -Bessel simulation, (c) Eq. (17) theory, and (d) Eq. (17) simulation.
Fig. 4.
Fig. 4. Magnitude (top) and phase (bottom) of W ( x 1 , y 1 ; , 0 ) versus x 1 and y 1 : (a)  I m -Bessel theory, (b)  I m -Bessel simulation, (c) Eq. (17) theory, and (d) Eq. (17) simulation. For the I m -Bessel source, = 1.15 mm , and for the Eq. (17) source, = 1.55 mm . The color bars above (a) and (b), and (c) and (d) correspond to the I m -Bessel and Eq. (17) magnitude results, respectively. All the phase results are plotted on the same ( π , π ] color scale.

Equations (19)

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W ( ρ 1 , ρ 2 ) = p ( v ) H ( ρ 1 , v ) H * ( ρ 2 , v ) d 2 v ,
H ( ρ , v ) = τ ( ρ ) J m ( ρ v ) ,
W J m ( ρ 1 , ρ 2 ) = τ ( ρ 1 ) τ * ( ρ 2 ) p ( v ) J m ( ρ 1 v ) J m ( ρ 2 v ) d 2 v .
W J m ( ρ 1 , ρ 2 ) = τ ( ρ 1 ) τ * ( ρ 2 ) 2 π 0 v p ( v ) J m ( ρ 1 v ) J m ( ρ 2 v ) d v .
p G ( v ) = δ 2 π exp ( δ 2 v 2 ) ,
W J m G ( ρ 1 , ρ 2 ) = τ ( ρ 1 ) τ * ( ρ 2 ) exp ( ρ 1 2 + ρ 2 2 4 δ 2 ) I m ( ρ 1 ρ 2 2 δ 2 ) ,
W I m ( ρ 1 , ρ 2 ) = ξ m / 2 1 ξ exp ( 1 + ξ 1 ξ ρ 1 2 + ρ 2 2 σ 2 ) × exp [ j m ( ϕ 1 ϕ 2 ) ] I m ( 4 ξ 1 ξ ρ 1 ρ 2 σ 2 ) ,
δ = σ 2 8 1 ξ ξ , τ ( ρ ) = ξ m / 2 1 ξ exp ( j m ϕ ) exp [ ( 1 ξ ) 2 1 ξ ρ 2 σ 2 ] .
U I m ( ρ ) = ξ m / 2 1 ξ exp ( j m ϕ ) exp [ ( 1 ξ ) 2 1 ξ ρ 2 σ 2 ] J m ( ρ v ) ,
p G ( v x , v y ) = σ 2 8 π 1 ξ ξ exp [ σ 2 8 1 ξ ξ ( v x 2 + v y 2 ) ] .
p U ( v ) = δ 2 π circ ( δ v ) ,
W J m U ( ρ 1 , ρ 2 ) = τ ( ρ 1 ) τ * ( ρ 2 ) 2 δ 2 0 1 / δ v J m ( ρ 1 v ) J m ( ρ 2 v ) d v .
W J m U ( ρ 1 , ρ 2 ) = τ ( ρ 1 ) τ * ( ρ 2 ) × 2 ρ 2 δ J m ( ρ 1 δ ) J m 1 ( ρ 2 δ ) ρ 1 δ J m 1 ( ρ 1 δ ) J m ( ρ 2 δ ) ( ρ 1 δ ) 2 ( ρ 2 δ ) 2 .
W J m U ( ρ , ϕ 1 ; ρ , ϕ 2 ) = τ ( ρ , ϕ 1 ) τ * ( ρ , ϕ 2 ) 2 0 d v v v 2 θ ( 1 v ) J m 2 ( ρ δ v ) ,
W J m U ( ρ , ϕ 1 ; ρ , ϕ 2 ) = τ ( ρ , ϕ 1 ) τ * ( ρ , ϕ 2 ) × 1 π 1 j 2 π C ( δ ρ ) 2 s Γ ( m s ) Γ ( s + 1 / 2 ) Γ ( s + 2 ) Γ ( s + m + 1 ) d s ,
W J m U ( ρ , ϕ 1 ; ρ , ϕ 2 ) = τ ( ρ , ϕ 1 ) τ * ( ρ , ϕ 2 ) [ ρ 2 / ( 4 δ 2 ) ] m Γ ( m + 1 ) Γ ( m + 2 ) × F 1 2 ( m + 1 / 2 ; m + 2 , 2 m + 1 ; ρ 2 / δ 2 ) ,
W J m U ( ρ 1 , ρ 2 ) = { Eq. ( 13 ) ρ 1 ρ 2 Eq. ( 16 ) ρ 1 = ρ 2 = ρ .
U J m U ( ρ ) = τ ( ρ ) J m ( ρ v ) ,
RMSE = 1 N 2 k = 1 N 2 ( S sim [ k ] S thy [ k ] ) 2 ,

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