Abstract

A novel method is presented for the beam shaping of far field intensity distributions of coherently combined fiber arrays. The fibers are arranged uniformly on the perimeter of a circle, and the linearly polarized beams of equal shape are superimposed such that the far field pattern represents an effective radially polarized vector beam, or discrete cylindrical vector (DCV) beam. The DCV beam is produced by three or more beams that each individually have a varying polarization vector. The beams are appropriately distributed in the near field such that the far field intensity distribution has a central null. This result is in contrast to the situation of parallel linearly polarized beams, where the intensity peaks on axis.

© 2009 Optical Society of America

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References

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  1. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  6. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  14. K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
    [Crossref] [PubMed]
  15. T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1–3), 12–21 (2005).
    [Crossref]
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    [Crossref]
  17. Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
    [Crossref] [PubMed]
  18. Y. I. Salamin, “Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 31(17), 2619–2621 (2006).
    [Crossref] [PubMed]
  19. I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush, “2 kW, M2 ¡ 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers,” Opt. Lett. 32(1), 47–49 (2007).
    [Crossref]
  20. I. Moshe, S. Jackel, and A. Meir, “Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects,” Opt. Lett. 28(10), 807–809 (2003).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  27. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref] [PubMed]
  28. T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1–2), 1–5 (2002).
    [Crossref]
  29. G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
    [Crossref]
  30. J. L. Li, K. Ueda, M. Musha, A. Shirakawa, and L. X. Zhong, “Generation of radially polarized mode in Yb fiber laser by using a dual conical prism,” Opt. Lett. 31(20), 2969–2971 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2007 (5)

2006 (6)

2005 (5)

2004 (1)

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[Crossref]

2003 (4)

2002 (3)

2000 (3)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

A. V. Nesterov and V. G. Niziev, J. Phys. D Appl. Phys. 33(15), 1817–1822 (2000).
[Crossref]

K. Youngworth and T. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nestorov, and J. Phys, “D,” Appl. Phys. (Berl.) 32, 1455 (1999).

1990 (1)

1978 (1)

1974 (1)

J. J. Wynne, “Generation of the rotationally symmetric TE01 and TM01 from a wavelength-tunable laser,” IEEE J. Quantum Electron. 10(2), 125–127 (1974).
[Crossref]

Armstrong, D. J.

At-Ameur, K.

Baets, R.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

Balmer, J.

Belanger, P.-A.

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[Crossref]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

Brown, T.

Bruesselbach, H.

Courjon, D.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1–3), 12–21 (2005).
[Crossref]

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1–2), 1–5 (2002).
[Crossref]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

de Saint Denis, R.

Delbeke, D.

Doft, F.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Ford, D. H.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

Gavrielides, A.

Glur, H.

Grosjean, T.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1–3), 12–21 (2005).
[Crossref]

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1–2), 1–5 (2002).
[Crossref]

Hasman, E.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[Crossref]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

Hierle, R.

Hirayama, T.

Iftiquar, S. M.

S. M. Iftiquar and J. Opt, “A tunable doughnut laser beam for cold-atom experiments,” B: Quantum Semiclass. Opt. 5(1), 40–43 (2003).
[Crossref]

Jackel, S.

Jones, D. C.

Kimura, W. D.

Kleiner, V.

Kozawa, Y.

Leibush, E.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, J. L.

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

Lumer, Y.

Machavariani, G.

Mangir, M. S.

Meir, A.

Minden, M. I.

Moser, T.

Moshe, I.

Musha, M.

Muys, P.

Nakamura, T.

Nesterov, A. V.

A. V. Nesterov and V. G. Niziev, J. Phys. D Appl. Phys. 33(15), 1817–1822 (2000).
[Crossref]

Nestorov, A. V.

V. G. Niziev and A. V. Nestorov, and J. Phys, “D,” Appl. Phys. (Berl.) 32, 1455 (1999).

Niziev, V. G.

A. V. Nesterov and V. G. Niziev, J. Phys. D Appl. Phys. 33(15), 1817–1822 (2000).
[Crossref]

V. G. Niziev and A. V. Nestorov, and J. Phys, “D,” Appl. Phys. (Berl.) 32, 1455 (1999).

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

Passilly, N.

Peterson, P. R.

Petrov, D.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[Crossref]

Phillips, M. C.

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Rioux, M.

Roch, J.-F.

Rogers, J. L.

Roth, M.

Sabac, A.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1–3), 12–21 (2005).
[Crossref]

Saitou, T.

Salamin, Y. I.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

Sato, S.

Sekiguchi, T.

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006).
[Crossref] [PubMed]

Shirakawa, A.

Simpson, T. B.

Smith, A. V.

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1–2), 1–5 (2002).
[Crossref]

Tidwell, S. C.

Tremblay, R.

Treussart, F.

Ueda, K.

Verstuyft, S.

Volpe, G.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[Crossref]

Weber, H. P.

Wynne, J. J.

J. J. Wynne, “Generation of the rotationally symmetric TE01 and TM01 from a wavelength-tunable laser,” IEEE J. Quantum Electron. 10(2), 125–127 (1974).
[Crossref]

Wyss, E.

Yonezawa, K.

Youngworth, K.

Zhong, L. X.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

J. J. Wynne, “Generation of the rotationally symmetric TE01 and TM01 from a wavelength-tunable laser,” IEEE J. Quantum Electron. 10(2), 125–127 (1974).
[Crossref]

IEEE J. Sel. Top. Quant. El. (1)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-Synchronous and Self-Referenced Coherent Beam Combination for Large Optical Arrays,” IEEE J. Sel. Top. Quant. El. 13(3), 480–486 (2007).
[Crossref]

J. Opt (1)

S. M. Iftiquar and J. Opt, “A tunable doughnut laser beam for cold-atom experiments,” B: Quantum Semiclass. Opt. 5(1), 40–43 (2003).
[Crossref]

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

J. Phys, “D,” Appl. Phys. (Berl.) (1)

V. G. Niziev and A. V. Nestorov, and J. Phys, “D,” Appl. Phys. (Berl.) 32, 1455 (1999).

J. Phys. D Appl. Phys. (1)

A. V. Nesterov and V. G. Niziev, J. Phys. D Appl. Phys. 33(15), 1817–1822 (2000).
[Crossref]

Opt. Commun. (3)

T. Grosjean, D. Courjon, and M. Spajer, “An all-fiber device for generating radially and other polarized light beams,” Opt. Commun. 203(1–2), 1–5 (2002).
[Crossref]

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[Crossref]

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1–3), 12–21 (2005).
[Crossref]

Opt. Express (5)

Opt. Lett. (11)

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. I. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339 (2005).
[Crossref] [PubMed]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32(11), 1468–1470 (2007).
[Crossref] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[Crossref]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[Crossref] [PubMed]

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
[Crossref] [PubMed]

Y. I. Salamin, “Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation,” Opt. Lett. 31(17), 2619–2621 (2006).
[Crossref] [PubMed]

I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush, “2 kW, M2 ¡ 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers,” Opt. Lett. 32(1), 47–49 (2007).
[Crossref]

I. Moshe, S. Jackel, and A. Meir, “Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects,” Opt. Lett. 28(10), 807–809 (2003).
[Crossref] [PubMed]

M. Roth, E. Wyss, H. Glur, and H. P. Weber, “Generation of radially polarized beams in a Nd:YAG laser with self-adaptive overcompensation of the thermal lens,” Opt. Lett. 30(13), 1665 (2005).
[Crossref] [PubMed]

J. L. Li, K. Ueda, M. Musha, A. Shirakawa, and L. X. Zhong, “Generation of radially polarized mode in Yb fiber laser by using a dual conical prism,” Opt. Lett. 31(20), 2969–2971 (2006).
[Crossref] [PubMed]

Y. I. Salamin, “Mono-energetic GeV electrons from ionization in a radially polarized laser beam,” Opt. Lett. 32(1), 90–92 (2007).
[Crossref]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

Example of the multiple fiber setup. A specific case of N = 3 is shown, where each beam is represented by a circle of radius a and arranged uniformly on a circle of radius R. Points within the ith hole are located by d = s i , + r, with the vector r originating at the center of each hole.

Fig. 2.
Fig. 2.

Diagram of the experimental setup for DCV beam generation. The oscillator output is split and phase modulated (S/PM). The output of each fiber is collimated by means of a lens, L1, and then the polarization is rotated by a half-wave plate (HWP). The beam ensemble is then focused to a point which is imaged by a microscope objective (MO) onto a charge-coupled-device (CCD) array.

Fig. 3.
Fig. 3.

Far field intensity profiles of effectively radially polarized beams. The left panels correspond to the experimental images and the right panels represent the theoretical results. We consider a 3 (top row), 4 (middle row), and 6 (bottom row) beam arrangement. For N = 3, we take w 0 = 32 μm and R = 5w 0. For N = 4, w 0 = 42 μm, and R = 2.7w 0. For N = 6, we have w 0 = 43 μm and R = 3.8w 0. Note that in general, a radially polarized beam undergoes a discontinuity at the origin, and thus the intensity must vanish there.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E(kx,ky)=exp(ik0ρ22z)exp(ik0z)iλz j=1N0ardr02π eik·(r+sj) E0 (r+sj,0) ,
E(kx,ky)=(ρ,z)j=1Neik·sjr̂j,
3(ϕ)=3cos(3kyR)2cos(32kyR)cos(32kxR),
𝓚4(ϕ)=4[sin2(kxR)+sin2(kyR)],
K6(ϕ)=4[(cos(32kyR)sin(12kxR)+sin(kxR))2+3cos2(12kxR)sin2(32kyR)],
𝓤4k0ρw0248z2(e−2R2/w02−1){k0ρ[24+12w02R2J2(2Rk0ρ/z)+w02k0ρz2[k03ρ3w02z26k0ρ
+3J3(2Rk0ρ/z)(k02ρ2w02Rz2zw02R34zR)] ] 24zR J1 (2Rk0ρ/z) } .

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