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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 26 — Dec. 25, 2006
  • pp: 12839–12845
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Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability

Toru Hirayama, Yuichi Kozawa, Takahiro Nakamura, and Shunichi Sato  »View Author Affiliations


Optics Express, Vol. 14, Issue 26, pp. 12839-12845 (2006)
http://dx.doi.org/10.1364/OE.14.012839


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Abstract

We demonstrated a generation of cylindrically symmetric, polarized laser beams with narrow linewidth and fine tunability. Since an LP11 mode beam in an optical fiber is a superposition of an HE21 (hybrid) mode beam and a TE01 or TM01 mode beam, firstly, a higher order transverse (TEM01 or TEM10) mode laser beam with narrow linewidth and fine tunability was generated from an external cavity diode laser (ECDL) in conjunction with a phase adjustment plate. Then the beam generated was passed in a two mode optical fiber. A doughnut shaped laser beam with the cylindrically symmetric polarization (a radially or azimuthally polarized beam) was obtained by properly adding stress-induced birefringence in the optical fiber.

© 2006 Optical Society of America

1. Introduction

Recently, doughnut shaped laser beams with cylindrically symmetric polarization, especially, radially and azimuthally polarized beams are attracting many attentions because of their unique focusing properties [1

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

, 2

2. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beam,” Opt. Express 10, 324–331 (2002). [PubMed]

]. A large number of applications [3–6

3. A. V. Nestrov and V. G. Niziev, “Laser beam with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000). [CrossRef]

] and generation methods [7–13

7. E. G. Churin, J. Hosfeld, and T. Tschudi, “Polarization configuration with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993). [CrossRef]

] of the cylindrically symmetric, polarized beams have been proposed and demonstrated.

On the other hand, doughnut shaped beams are thought to be suitable for optical guiding [14

14. D. P. Rhodes, G. P. T. Lancster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002). [CrossRef]

], a conical funnel reflector [15

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

] and an atom lens [16

16. J. J. McClelland and M. R. Scheinfein, “Laser focusing of atoms: a particle-optics approach” J. Opt. Soc. Am. B 8, 1974–1986 (1991). [CrossRef]

] in the field of atom optics. Especially, the atom lens created by a doughnut shaped beam is expected to be able to focus an atomic beam to the spot diameter of 2 nm [17

17. G. M. Gallatin and P. L. Gould, “Laser focusing of atomic beams,” J. Opt. Soc. Am. B 8, 502–508 (1991). [CrossRef]

]. Typical doughnut shaped beam is a Laguerre-Gaussian (LG) beam with linear polarization. However, disappear of the zero-intensity point at the focal point and an elongation in the polarization direction are predicted [18

18. D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003). [CrossRef] [PubMed]

] indicating that the LG beam is no longer an ideal laser beam as an atom lens. By contrast, an azimuthally polarized beam can maintain the zero-intensity on the beam axis and complete cylindrical symmetry in the intensity distribution near the focal point even under tight focusing condition [1

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

]. Thus, an azimuthally polarized beam is a promising laser beam for achieving a high quality atom lens. Although narrow linewidth and fine tunability are inherently necessary for the atom lens, the cylindrically symmetric, polarized beam with fine tunability has not been reported.

In this paper, we demonstrated the generation of cylindrically symmetric, polarized laser beams with narrow linewidth and fine tunability. Our method is based on the fact that an LP11 mode beam in an optical fiber is a superposition of an HE21 (hybrid) mode beam and a TE01 or TM01 mode beam [19

19. 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, 12–21 (2005). [CrossRef]

]. Firstly, a higher order transverse mode beam with narrow linewidth and fine tunability was generated from an external cavity diode laser (ECDL) in conjunction with a phase adjustment plate. Secondly, cylindrically symmetric, polarized beams were generated by passing the higher order transverse mode beam in a two mode optical fiber.

2. Experimental methods

2.1 Generation of a TEM01 mode beam from an ECDL

As a preliminary stage for generating a cylindrically symmetric, polarized mode beam, a TEM01 or TEM10 mode beam was generated. An ECDL in a Littrow configuration (Sacher: TEC100) was used in our experiment. The wavelength of the ECDL was about 852 nm. The ECDL has both the wavelength stability and the tunability owing to the wavelength control by a grating used as a cavity mirror. The spectrum of the ECDL beam was measured by a Fabry-Perot interferometer (free spectral range: 2 GHz, resolution: 10 MHz). Two kinds of phase adjustment plates (a glass plate of 170 µm thickness and a quartz plate of 100 µm thickness) were applied and inserted inside the laser cavity of the ECDL as shown in Fig. 1. In the case of the quartz plate, the direction of the crystal axis was set to be the same with that of the polarization of the laser beam in order to avoid polarization change due to the birefringence of the plate. It is noted that both the plates worked well for generating a higher order transverse mode beam. The position of the plate was aligned to transmit a half of the laser beam and then tilted to make π phase difference between one half of the beam passing through the plate and the other half of that passing in the air. Since a TEM01 or TEM10 mode beam has two lobes in intensity distribution and a π phase sift between the lobes, achievement of the TEM01 mode beam can be verified by measuring both an intensity distribution and an interference fringe pattern with a reference beam. The fringe pattern of one lobe will alternate with that of the other lobe because of the π phase shift. The intensity distribution and the interference fringe pattern were observed by a CCD camera.

Fig. 1. Schematic for generating cylindrically symmetric, polarized beams by use of an external cavity diode laser (ECDL) and a two mode optical fiber.

2.2 Conversion of a TEM01 mode beam into a cylindrically symmetric, polarized mode beam

Fig. 2. Transverse mode combinations in an optical fiber.

3. Results

Figure 3(a) shows the intensity distribution of the laser beam generated from the ECDL in which a phase adjustment plate was inserted in order to produce a TEM01 mode beam. As seen in the figure, the intensity distribution was a two-lobe pattern with intensity null along the vertical center line. Figure 3(b) shows the intensity profile in the horizontal direction and a curve fitting to a theoretical TEM10 mode profile. The curve fitting showed a good agreement with the theoretical profile. Figure 3(c) shows the interference fringe pattern with a reference beam. The reference beam was prepared by splitting a fraction of the two-lobe pattern beam generated and selecting only one lobe with an appropriate magnification. The horizontal fringe pattern in the right hand side alters with that in the left hand side. This clearly means that the phase shift between the right and left lobes was π. Figures 3(d)–3(f) show the results obtained when the phase adjustment plate was inserted in the vertical direction. From these results, the generated laser beams can be verified to be a TEM10 and a TEM01 mode beams. It is noted that the transverse mode transformation from TEM00 to TEM10 mode as shown in Fig. 3(a) was not observed if we simply insert a thin wire inside the laser cavity that will scatter small amount of light along the wire. Thus, not only attenuation of the light along the central crossing line of the laser beam but also phase adjustment between two lobes is necessary to induce the mode transformation to TEM10 mode. Although the phase adjustment plate we used here is very similar to the discontinuous phase element (DPE) used for generating both the TEM01 and TEM10 modes inside the laser cavity [8

8. 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, 3322–3324 (2000). [CrossRef]

], our plate is much simpler and easier to fabricate that than the DPE.

Fig. 3. Higher order transverse modes from the ECDL with a phase adjustment plate. (a). The intensity distribution, (b). the horizontal intensity profile and the fitting to the theoretical one and (c). the interference pattern of the TEM10 mode beam generated. (d). The intensity distribution, (e). the vertical intensity profile and the fitting to the theoretical one and (f). the interference pattern of the TEM01 mode beam generated.

The TEM01 or TEM10 mode beam generated from the ECDL was focused into a two mode optical fiber. Mechanical stress was applied on the optical fiber by making a single circular loop of the fiber. By carefully adjusting the loop diameter and slightly twisting the fiber, the intensity distribution of the output was finely controlled. The radius of the loop was about 25 cm and the twist angle was 45 degrees in maximum. Figure 4 shows the intensity distributions of the doughnut shaped beam obtained when a horizontally polarized TEM10 mode beam was focused into the optical fiber. Figure 4(b) shows the total intensity distribution as well as the horizontal and the vertical intensity profiles with curve fittings to TEM10 and TEM01 mode, respectively. It is seen that the intensity distribution is doughnut shaped with a null on the center and both the horizontal and the vertical profiles show excellent agreement with the theoretical one of a TEM10 or a TEM01 mode. Figures 4(c)–4(f) show the intensity distributions after passing through a linear polarizer for different directions. Each arrow indicates the direction of the polarizer. This variation of the polarization distribution means that the beam was radially polarized as shown in Fig. 4(a). The output power was about 15 mW when the input power into the optical fiber was about 32 mW.

Fig. 4. (a). Schematic drawing of conversion from a TEM10 mode beam to a radially polarized beam. (b). Observed total intensity distribution and the intensity profile. (c).–(f). Intensity distributions after passing through a linear polarizer. Each arrow indicates the direction of the polarizer.

Similarly, it was possible to generate an azimuthally polarized beam when a horizontally polarized TEM01 mode beam was focused into the optical fiber as shown in Fig. 5(a). The intensity distribution of the output beam was also doughnut shaped with a null on the center and the intensity profiles were in excellent agreement with the theoretical one as shown in Fig. 5(b). The variation of the polarization distributions for different directions of a linear polarizer was shown in Figs. 5(c)–5(f). Note that the direction of the two-lobe pattern was rotated by an angle of π/2 radians compared to that in the radially polarized beam as shown in Figs. 4(c)–4(f) indicating that the output beam was azimuthally polarized. The output power from optical fiber was about 6 mW when the input power was about 30 mW. The reduction of throughput compared to the radial polarized beam generation was due to mismatching between the convergence of the incident beam and the numerical aperture of the optical fiber. This is because the output beam from the ECDL has different divergences in the horizontal and the vertical directions. If a proper objective is selected, the throughput will be increased. Note that hybrid mode beams were also excited in the two mode optical fiber by controlling the stress-induced birefringence on the fiber but the detail is not shown in this paper because the hybrid mode is out of our scope.

Fig. 5. (a). Schematic drawing of conversion from a TEM01 mode to an azimuthally polarized beam. (b). Observed total intensity distribution and the intensity profile. (c).–(f). Intensity distributions after passing through a linear polarizer. Each arrow indicates the direction of the polarizer.

The spectral linewidth and tunability of the radially and azimuthally polarized beams were also investigated. Figure 6 shows the spectra measured by a Fabry-Perot interferometer. The spectrum of the TEM00 mode beam from the ECDL without any phase element is seen in the top of the figure. The linewidth was less than 20 MHz. The spectra of the TEM10 mode beam generated by using a phase adjustment plate and of the radially polarized beam are shown in the middle and the bottom of the figure, respectively. It is clearly seen that the TEM10 mode and the radially polarized beam keep the narrow linewidth less than 20 MHz.

Fig. 6. (from top to bottom) Spectra of a TEM00 mode beam from the ECDL, a TEM10 mode beam from the ECDL with a phase adjustment plate and a radially polarized beam after propagating an optical fiber.

Because the ECDL can tune the wavelength by tilting the grating used as a cavity mirror, the wavelength of the radially or the azimuthally polarized beam generated in this experiment is expected to be also tunable with the narrow linewidth. The tunability of the beam was verified by observing resonant emission from a cesium vapor cell. The resonant emission from the cesium vapor cell through which a radially polarized beam was passed is shown in Fig. 7. The laser beam was coming from the right to the left and the transmitted beam was stopped by a screen in the figure. The laser wavelength was tuned to around 852.11 nm that is the resonant wavelength of cesium atom.

Fig. 7. (840 KB) Video image of resonant emission from a cesium vapor cell through which a radially polarized beam passed. The wavelength was tuned around the resonant wavelength of cesium atom. When the wavelength was in resonance, the emission was strong and vice versa. Note that the doughnut shape of the beam was preserved even if the wavelength was changed.

When the wavelength was resonant with the cesium atom, the broad two-line emission image as shown on the right hand side of Fig. 7 was observed. Because the beam was doughnut shaped, both the emission image and the transmitted image on the screen were hollow. When the wavelength was tuned out of the resonance, the emission became gradually weak while the doughnut shape on the screen was kept (see video). Note that the intensity of the doughnut shaped light on the screen was inverse to that of the emission from the vapor cell because of the absorption.

4. Discussion

Direct generation of the higher order transverse mode beam from an ECDL is demonstrated for the first time to our best knowledge. We believe that this achievement made the conversion of the TEM01 or TEM10 mode beam into cylindrically symmetric, polarized beams possible.

As shown in Figs. 4(b) and 5(b), the curve fittings of the radially and azimuthally polarized beams were in excellent agreement with the theoretical intensity profile of the lowest order doughnut mode beam. Because the mechanical stress on the optical fiber was manually added in this experiment, further improvement can be expected by more precise control using precision actuators. It was found that the intensity distribution was maintained as long as the ECDL was stable. The experimental result shown in Fig. 6 implied that the spectral property strongly depends on that of the original ECDL because this technique has no mechanism that changes the wavelength and the linewidth. Furthermore, the output power will be increased with increasing the input power up to propagation limit of an optical fiber.

Compared with other techniques for generating cylindrically symmetric, polarized beam using an optical fiber [19–21

19. 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, 12–21 (2005). [CrossRef]

], our technique has some advantages. TE01 and TM01 mode beams were generated by finely adjusting the coupling between single- and multi-mode optical fibers with the input beam of a TEM00 mode beam [20

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

]. In this case, the residual of unwanted HE21 mode was reported. When a Laguerre-Gaussian (LG01) mode beam was applied as an input beam to an optical fiber [21

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

], the output beam was not single transverse mode but a superposition of doughnut shaped modes because the LG01 mode is a superposition of TEM01 and TEM10 modes. Application of a pseudo TEM01 or TEM10 mode beam generated by inserting a π phase plate outside a laser cavity was also reported [19

19. 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, 12–21 (2005). [CrossRef]

]. Although intensity profiles were shown in the paper, fitting was not performed. Judging from the profiles in the figures, the profiles might be in poor agreement with the theoretical one. Especially, the intensity around peripheral area is relatively strong. By contrast, real TEM01 and TEM10 mode beams were used in our experiment. The output beam was single transverse mode of a cylindrically symmetric, polarized beam. Furthermore, the intensity profiles were in excellent agreement with the theoretical one. It should be emphasized that the beams reported in this paper have the narrow linewidth and the fine tunability while a pulsed dye laser with radially or azimuthally polarization has been reported by using a birefringent crystal inside the laser cavity [22

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

].

5. Conclusion

High order transverse mode (TEM01 and TEM10 mode) beams were generated by inserting a phase adjustment plate in an ECDL cavity. These beams were converted into cylindrically symmetric, polarized beams by stress-induced birefringence in an optical fiber. By controlling the direction of the polarization and the transverse mode (TEM01 or TEM10) of the incident laser beam and mechanical stress, a single transverse mode (radial, azimuthal and hybrid) was selected. The narrow linewidth and the fine tunability of the ECDL were faithfully preserved even after the conversion. The intensity profiles of the beams were in excellent agreement with the theoretical one.

Compared to the conventional Laguerre-Gaussian beam, an azimuthally polarized beam with narrow linewidth and fine tunability is a promising beam when used as an atom lens because of the complete cylindrical symmetry in the intensity distribution and the complete null on the beam axis even under tight focusing.

References and links

1.

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

2.

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beam,” Opt. Express 10, 324–331 (2002). [PubMed]

3.

A. V. Nestrov and V. G. Niziev, “Laser beam with axially symmetric polarization,” J. Phys. D 33, 1817–1822 (2000). [CrossRef]

4.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001). [CrossRef] [PubMed]

5.

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004). [CrossRef] [PubMed]

6.

Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31, 1726–1728 (2006). [CrossRef] [PubMed]

7.

E. G. Churin, J. Hosfeld, and T. Tschudi, “Polarization configuration with singular point formed by computer generated holograms,” Opt. Commun. 99, 13–17 (1993). [CrossRef]

8.

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, 3322–3324 (2000). [CrossRef]

9.

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

10.

M. A. A Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wavefronts,” Opt. Lett. 27, 1929–1931 (2002). [CrossRef]

11.

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, 807–809 (2003). [CrossRef] [PubMed]

12.

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

13.

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, 2151–2153 (2006). [CrossRef] [PubMed]

14.

D. P. Rhodes, G. P. T. Lancster, J. Livesey, D. McGloin, J. Arlt, and K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002). [CrossRef]

15.

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

16.

J. J. McClelland and M. R. Scheinfein, “Laser focusing of atoms: a particle-optics approach” J. Opt. Soc. Am. B 8, 1974–1986 (1991). [CrossRef]

17.

G. M. Gallatin and P. L. Gould, “Laser focusing of atomic beams,” J. Opt. Soc. Am. B 8, 502–508 (1991). [CrossRef]

18.

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003). [CrossRef] [PubMed]

19.

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, 12–21 (2005). [CrossRef]

20.

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

21.

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

22.

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

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(140.2020) Lasers and laser optics : Diode lasers
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3600) Lasers and laser optics : Lasers, tunable
(260.5430) Physical optics : Polarization

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 6, 2006
Revised Manuscript: December 15, 2006
Manuscript Accepted: December 15, 2006
Published: December 22, 2006

Citation
Toru Hirayama, Yuichi Kozawa, Takahiro Nakamura, and Shunichi Sato, "Generation of a cylindrically symmetric, polarized laser beam with narrow linewidth and fine tunability," Opt. Express 14, 12839-12845 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-26-12839


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References

  1. K. Youngworth and T. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7,77-87 (2000). [CrossRef] [PubMed]
  2. Q. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beam," Opt. Express 10, 324-331 (2002). [PubMed]
  3. A. V. Nestrov and V. G. Niziev, "Laser beam with axially symmetric polarization," J. Phys. D 33, 1817-1822 (2000).Q1 [CrossRef]
  4. L. Novotny, M. R. Beversluis, K. S. Youngworth and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett. 86, 5251-5254 (2001). [CrossRef] [PubMed]
  5. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004). [CrossRef] [PubMed]
  6. Q. Zhan, "Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam," Opt. Lett. 31, 1726-1728 (2006). [CrossRef] [PubMed]
  7. E. G. Churin, J. Hosfeld and T. Tschudi, "Polarization configuration with singular point formed by computer generated holograms," Opt. Commun. 99,13-17 (1993). [CrossRef]
  8. 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, 3322-3324 (2000). [CrossRef]
  9. A. Bomzon, G. Biener, V. Kleiner and E. Hasman, "Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings," Opt. Lett. 27, 285-287 (2002). [CrossRef]
  10. M. A. A Neil, F. Massoumian, R. Juskaitis and T. Wilson, "Method for the generation of arbitrary complex vector wavefronts," Opt. Lett. 27,1929-1931 (2002). [CrossRef]
  11. 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, 807-809 (2003). [CrossRef] [PubMed]
  12. Y. Kozawa and S. Sato, "Generation of a radially polarized laser beam by use of a conical Brewster prism," Opt. Lett. 30, 3063-3065 (2005). [CrossRef] [PubMed]
  13. 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, 2151-2153 (2006). [CrossRef] [PubMed]
  14. D. P. Rhodes, G. P. T. Lancster, J. Livesey, D. McGloin, J. Arlt and K. Dholakia, "Guiding a cold atomic beam along a co-propagating and oblique hollow light guide," Opt. Commun. 214,247-254 (2002). [CrossRef]
  15. S. M. Iftiquar, "A tunable doughnut laser beam for cold-atom experiment," J. Opt. B: Quantum Semiclass. Opt. 5, 40-43 (2003).Q2 [CrossRef]
  16. J. J. McClelland and M. R. Scheinfein, "Laser focusing of atoms: a particle-optics approach " J. Opt. Soc. Am. B 8, 1974-1986 (1991). [CrossRef]
  17. G. M. Gallatin and P. L. Gould, "Laser focusing of atomic beams," J. Opt. Soc. Am. B 8, 502-508 (1991). [CrossRef]
  18. D. Ganic, X. Gan and M. Gu, "Focusing of doughnut laser beams by a high numerical-aperture objective in free space," Opt. Express 11, 2747-2752 (2003). [CrossRef] [PubMed]
  19. 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, 12-21 (2005). [CrossRef]
  20. T. Grosjean, D. Courjon and M. Spajer, "An all-fiber device for generating radially and other polarized light beams," Opt. Commun. 203, 1-5 (2002). [CrossRef]
  21. G. Volpe and D. Petrov, "Genertion of cylindrical vector beams with few-mode fibers by Laguerre-Gaussian beams," Opt. Commun. 237, 89-95 (2004). [CrossRef]
  22. J. J. Wynne, "Generation of the rotationally symmetric TE01 and TM01 modes from a wavelength-tunable laser," IEEE J. Quantum Electron. 10, 125-127 (1974). [CrossRef]

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