Abstract

Stable and spiral coherent beams, which do not change the form of their intensity distribution apart from possible scaling and rotation during propagation and therefore possess self-healing properties, are widely applied in science and technology. On the other hand, it has been found that partially coherent light often provides better output than coherent light. Here we consider two methods for the design and experimental generation of partially coherent stable and spiral beams.

© 2013 Optical Society of America

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2012 (2)

P. Senthilkumaran, J. Masajadar, and S. Sato, “Interferometry with vortices,” Int. J. Opt. 2012, 517591 (2012).

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

2011 (2)

2010 (2)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system,” Opt. Express 18, 3568–3573 (2010).
[CrossRef]

2009 (4)

2008 (3)

2007 (2)

2006 (2)

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

C. Schwartz and A. Dogariu, “Mode coupling approach to beam propagation in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 329–338 (2006).
[CrossRef]

2005 (5)

2004 (5)

2003 (2)

2002 (1)

2001 (2)

A. O’Neil and M. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun. 193, 45–50 (2001).
[CrossRef]

S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (3)

1996 (2)

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[CrossRef]

1995 (1)

1994 (1)

T. Alieva, V. Lopez, F. A. Lopez, and L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

1993 (3)

1991 (1)

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
[CrossRef]

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

1986 (1)

Abramochkin, E.

T. Alieva, E. Abramochkin, A. Asenjo-Garcia, and E. Razueva, “Rotating beams in isotropic optical system,” Opt. Express 18, 3568–3573 (2010).
[CrossRef]

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
[CrossRef]

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157 (2004).

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Uspekhi 47, 1177–1203 (2004).

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Alieva, T.

Almeida, L. B.

T. Alieva, V. Lopez, F. A. Lopez, and L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Arce, G. R.

Asenjo-Garcia, A.

Baleine, E.

Bandres, M. A.

Barbé, A. M.

T. Alieva and A. M. Barbé, “Self-fractional Fourier images,” J. Mod. Opt. 46, 83–99 (1999).

Barnett, S.

Bastiaans, M.

Bastiaans, M. J.

Baykal, Y.

Bogatyryova, G. V.

Borghi, R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2006).

Cai, Y.

Calvo, M. L.

Cámara, A.

Cheben, P.

Chen, Z.

Y. Qiu, H. Guo, and Z. Chen, “Paraxial propagation of partially coherent Hermite–Gauss beams,” Opt. Commun. 245, 21–26 (2005).
[CrossRef]

Courtial, J.

Davidson, F. M.

de la Torre, L.

De Santis, P.

Dogariu, A.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Dubois, F.

Eyyuboglu, H. T.

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Fel’de, C. V.

Franke-Arnold, S.

Fürhapter, S. B. S.

Gbur, G.

Gibson, G.

Gori, F.

Greengard, A.

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

Guattari, G.

Guo, H.

Y. Qiu, H. Guo, and Z. Chen, “Paraxial propagation of partially coherent Hermite–Gauss beams,” Opt. Commun. 245, 21–26 (2005).
[CrossRef]

Gutiérrez-Vega, J.

Gutiérrez-Vega, J. C.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Jesacher, A.

Joannes, L.

Korobtsov, A.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

Korotkova, O.

Kotova, S.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Legros, J.-C.

Lopez, F. A.

T. Alieva, V. Lopez, F. A. Lopez, and L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Lopez, V.

T. Alieva, V. Lopez, F. A. Lopez, and L. B. Almeida, “The fractional Fourier transform in optical propagation problems,” J. Mod. Opt. 41, 1037–1044 (1994).
[CrossRef]

Losevsky, N.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

Ma, X.

Mandel, L.

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

Martínez-Matos, O.

Masajadar, J.

P. Senthilkumaran, J. Masajadar, and S. Sato, “Interferometry with vortices,” Int. J. Opt. 2012, 517591 (2012).

Mayorova, A.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

Mendlovic, D.

Mukunda, N.

O’Neil, A.

A. O’Neil and M. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun. 193, 45–50 (2001).
[CrossRef]

Ozaktas, H. M.

Padgett, M.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef]

A. O’Neil and M. Padgett, “Axial and lateral trapping efficiency of Laguerre–Gaussian modes in inverted optical tweezers,” Opt. Commun. 193, 45–50 (2001).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Palma, C.

Pas’ko, V.

Pavani, S. R. P.

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

Piestun, R.

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

R. Piestun and J. Shamir, “Generalized propagation-invariant wave fields,” J. Opt. Soc. Am. A 15, 3039–3044 (1998).
[CrossRef]

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[CrossRef]

Polyanskii, P. V.

Ponomarenko, S. A.

Qiu, Y.

Y. Qiu, H. Guo, and Z. Chen, “Paraxial propagation of partially coherent Hermite–Gauss beams,” Opt. Commun. 245, 21–26 (2005).
[CrossRef]

Qu, J.

Rakhmatulin, M.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

Razueva, E.

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Ricklin, J. C.

Ritsch-Marte, M.

Rodrigo, J. A.

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Santarsiero, M.

Sato, S.

P. Senthilkumaran, J. Masajadar, and S. Sato, “Interferometry with vortices,” Int. J. Opt. 2012, 517591 (2012).

Schechner, Y. Y.

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[CrossRef]

Schwartz, C.

Senthilkumaran, P.

P. Senthilkumaran, J. Masajadar, and S. Sato, “Interferometry with vortices,” Int. J. Opt. 2012, 517591 (2012).

Shamir, J.

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[CrossRef]

Simon, R.

Soskin, M. S.

Spektor, A. N. B.

Sundar, K.

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Tyson, R. K.

Vasnetsov, M.

Volostnikov, V.

E. Abramochkin, S. Kotova, A. Korobtsov, N. Losevsky, A. Mayorova, M. Rakhmatulin, and V. Volostnikov, “Microobject manipulations using laser beams with nonzero orbital angular momentum,” Laser Phys. 16, 842–848 (2006).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991).
[CrossRef]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157 (2004).

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Uspekhi 47, 1177–1203 (2004).

Wang, F.

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Wolf, E.

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28, 878–880 (2003).
[CrossRef]

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

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2006).

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[CrossRef]

Yuan, Y.

Yue, Y.

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Supplementary Material (3)

» Media 1: MOV (1195 KB)     
» Media 2: MOV (1365 KB)     
» Media 3: MOV (1429 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Evolution of the intensity distribution of the cSPB given by Eq. (9) and (b) the associated pSPB during propagation through the sFrFT system. See Media 1 online.

Fig. 2.
Fig. 2.

(a) Evolution of the intensity distribution of the cSTB, LG5,4(r,w), and (b), (c) the associated pSPB of different degrees of coherence during propagation through the sFrFT system. The radius of the coherence degree of the beam shown in (b) is larger than in (c). See Media 2 online.

Fig. 3.
Fig. 3.

(a) Intensity distribution of the pSTB constructed as an incoherent sum of the orthogonal modes ψ1(r)=LG0,0(r,w), ψ2(r)=LG0,1(r,w), and ψ3(r)=LG1,2(r,w) with weights a1=1.25, a2=4.4, and a3=1. (b) Simulated profiles of Γ(r,r) (dashed line) and |γ(r0,r)| (continuous line) for r0=(0,0)t and r=(x,0)t of this beam. (c) Intensity distribution of the pSTB constructed as an incoherent sum of the orthogonal modes ψ1(r)=LG2,0(r,w)+LG1,1(r,w), ψ2(r)=LG1,2(r,w), and ψ3(r)=LG1,0(r,w) with weights a1=1, a2=3.5, and a3=2. (d) Simulated profiles of Γ(r,r) (dashed line) and |γ(r0,r)| (continuous line) for r0=(0,0)t and r=(x,0)t of this beam.

Fig. 4.
Fig. 4.

(a) Evolution of the intensity distribution of the pSPB constructed as an incoherent sum with equal weights of two orthogonal beams, the cSPB Ψ2(r,w,1), see Eq. (9), and the cSTB LG5,4(r,w) during propagation through the sFrFT system. Media 3 online. (b) Simulated intensity distribution of this beam. (c) Simulated profiles of Γ(r,r) (dashed line) and the |γ(r0,r)| (continuous line) for r0=(x0,0) where x0=0.1mm and r=(x,0) of this beam.

Fig. 5.
Fig. 5.

(a) Evolution of the intensity distribution of the cSPB and (b) the associated pSPB during the propagation through the sFrFT system. (c) Evolution of the intensity distribution of the cSPB and (d) the associated pSPB disturbed by an obstacle at α=0 during the propagation through the sFrFT system.

Equations (15)

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f(r,α)=1is2sinα×exp[iπ(r2+ri2)cosα2rirts2sinα]f(ri,0)dri.
LGm,n(r,w)=[2(min{m,n})!(max{m,n})!]1/2exp(πr2w2)×(2πrw)|mn|exp[i(mn)θ]Lmin{m,n}(|mn|)(2πr2w2).
Ψ(r,w,υ)=m,ncm,nLGm,n(r,w),
m(1υ)+n(1+υ)=const,
Ψn(r,w,1)=m=0cm,nLGm,n(r,w),
υ=(m+n)(m0+n0)(mn)(m0n0).
ΓR(r1,r2)=I0exp[π|r1r2|2/w02].
Γ(r1,r2)=fC(r1)fC*(r2)ΓR(r1,r2)=ΓR(r1,r2)ΓC(r1,r2),
Ψ2(r,w,1)=n=18(3n+2)!(3n)!33nLG3n+2,2(r,w),
Γ(r1,r2)=nanψn(r1)ψn*(r2),
γ(r1,θ1;r2,θ2)=cos[(mn)(θ1θ2)].
(θ1θ2)/(mn)=π/2+πk,
Γ(r1,r2)=m,nm,ncm,ncm,n*LGm,n(r1,w)LGm,n*(r2,w),
Γ(r1,r2,α)=m,nm,ncm,ncm,n*×exp[i(m+nmn)α]LGm,n(r1,w)LGm,n*(r2,w).
Γ(r1,r2)=nanSPn(r1,w,υ)SPn*(r2,w,υ)+mbmSTm(r1,w)STm*(r2,w),

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