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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 14526–14531
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High power Er:YAG laser with radially-polarized Laguerre-Gaussian (LG01) mode output

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 14526-14531 (2011)
http://dx.doi.org/10.1364/OE.19.014526


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Abstract

A simple method for conditioning the pump beam in an end-pumped solid-state laser to allow direct excitation of the first order Laguerre-Gaussian doughnut (LG01) mode is reported. This approach has been applied to a hybrid (fiber-laser-pumped) Er:YAG laser yielding 13.1 W of continuous-wave output at 1645 nm in a radially-polarized LG01 doughnut beam with beam propagation factor (M2) < 2.4 for 34 W of incident pump power at 1532 nm. The corresponding slope efficiency with respect to incident pump power was 48%. The prospects of further power scaling and improved laser performance are discussed.

© 2011 OSA

1. Introduction

Laser beams with a ring-shaped intensity profile, sometimes referred to as hollow laser beams or doughnut beams, have applications in a number of areas including laser drilling and writing [1

1. R. B. Charters, B. Luther-Davies, and F. Ladouceur, “Improved performance of laser channel written waveguides using a TEM01* beam,” IEEE Photon. Technol. Lett. 11(12), 1617–1619 (1999). [CrossRef]

, 2

2. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18(21), 22305–22313 (2010). [CrossRef] [PubMed]

], optical manipulation of particles [3

3. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

, 4

4. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002). [CrossRef]

], trapping and guiding of atoms [5

5. R. Ozeri, L. Khaykovich, N. Friedman, and N. Davidson, “Large-volume single-beam dark optical trap for atoms using binary phase elements,” J. Opt. Soc. Am. B 17(7), 1113–1116 (2000). [CrossRef]

, 6

6. Y. Song, D. Milam, and W. T. Hill III, “Long, narrow all-light atom guide,” Opt. Lett. 24(24), 1805–1807 (1999). [CrossRef] [PubMed]

] and lithography [7

7. V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(01), 143–154 (2007). [CrossRef]

]. Not surprisingly, methods for generating hollow laser beams have been the subject of much research over the years. Simple beam shaping schemes (e.g. based on axicons [8

8. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000). [CrossRef]

, 9

9. D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998). [CrossRef] [PubMed]

] or hollow-core fibers [10

10. J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, and W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138(4-6), 287–292 (1997). [CrossRef]

]) provide a relatively straightforward route to a doughnut beam, but at the expense of a significant degradation in beam quality and brightness, hence limiting applicability. A more attractive route is to generate a Laguerre-Gaussian mode with a ring-shaped intensity profile (e.g. LG0n mode). This can be achieved using external beam-shaping arrangements (e.g. based on spatial light modulators [11

11. J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000). [CrossRef] [PubMed]

, 12

12. A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004). [CrossRef]

], computer-generated holograms [13

13. C. Paterson, “Higher order Bessel waves produced by axicon-type computer-based holograms,” Opt. Commun. 124(1-2), 121–130 (1996). [CrossRef]

], a pair of cylindrical lenses [14

14. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]

, 15

15. L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]

]) to transform a Hermite-Gaussian mode (TEM0n) into the required Laguerre-Gaussian mode. Scaling to high powers via this route is rather challenging due to power handling limitations of the beam transforming optics and the difficulty in scaling power for single mode TEM0n lasers. Alternatively, hollow Laguerre-Gaussion beams can be generated directly within the laser itself, for example, by exploiting bifocussing [16

16. C. H. Chen, P. T. Tai, and W. F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Opt. 43(32), 6001–6006 (2004). [CrossRef] [PubMed]

, 17

17. M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3 µm bounce laser,” Opt. Express 15(12), 7616–7622 (2007). [CrossRef] [PubMed]

] or via the use of intra-cavity mode discriminating components (e.g. by using diffractive optical elements [18

18. A. J. Caley, M. J. Thomson, J. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15(17), 10699–10704 (2007). [CrossRef] [PubMed]

, 19

19. M. E. Marhic and E. Garmire, “Low-order TE0q operation of a CO2 laser for transmission through circular metallic waveguides,” Appl. Phys. Lett. 38(10), 743–745 (1981). [CrossRef]

]). However, to date these approaches have suffered from rather low efficiency and limited flexibility due to pump-power dependent resonator configurations or the need for additional relatively high-loss intra-cavity components.

Here we report an alternative and very simple strategy for directly generating a high quality LG01 mode in a laser, which is especially well-suited for hybrid (fiber-laser-pumped) bulk solid-state laser architectures [20

20. J. W. Kim, D. Y. Shen, J. K. Sahu, and W. A. Clarkson, “Fiber-Laser-Pumped Er:YAG Lasers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 361–371 (2009). [CrossRef]

, 21

21. M. Eichhorn, “High-power resonantly diode-pumped CW Er3+:YAG laser,” Appl. Phys. B 93(4), 773–778 (2008). [CrossRef]

] and hence offers the prospect of very high average output power in continuous-wave (cw) and pulsed modes of o`peration. Using this approach, we have successfully operated an Er:YAG laser, in-band pumped by an Er,Yb fiber laser, with a high quality radially-polarized LG01 mode output. The laser produced 13.1 W of output at 1645 nm for 34 W of incident pump power at 1532 nm. To the best of our knowledge, this is the first demonstration of a high-power end-pumped Er:YAG laser operating on the LG01 mode.

2. Experiment and results

Our approach makes use of a simple, low-loss fiber-based beam shaping element to re-format the output beam from the cladding-pumped fiber laser pump source into a ring-shaped pump beam whilst maintaining reasonably good beam quality. The ring-shaped pump beam is tailored to spatially-match the intensity distribution for the first-order Laguerre-Gaussian mode (LG01) in the laser medium of a bulk laser resonator with the result that lasing occurs preferentially on the LG01 mode since it has the lowest threshold. The experimental set-up for the hybrid Er:YAG laser is shown schematically in Fig. 1
Fig. 1 Schematic diagram of the Er:YAG laser resonator. The pictures show the cross-section of the capillary fiber (upper-left) and the near-field beam profile for the pump beam exiting the capillary fiber (upper-right).
. The pump beam was provided by a high-power cladding-pumped Er,Yb fiber laser constructed in-house. The latter comprised a ~2.5 m length of double-clad fiber with a 30 μm diameter (0.22 NA) Er,Yb co-doped phospho-silicate core surrounded by a 400 μm diameter D-shaped pure silica inner-cladding. The latter was surrounded by a low refractive index (n≈1.375) polymer coating giving the inner-cladding pump guide a calculated numerical aperture of ~0.49. Operation at the absorption peak in Er:YAG at 1532 nm was achieved with the aid of a wavelength-tunable external cavity with wavelength dependent feedback provided by a Volume Bragg Grating (VBG). The VBG had a peak reflectivity of 95% and a full-width at half-maximum (FWHM) reflection bandwidth of 0.5 nm. The Er,Yb fiber laser yielded a maximum power of 78 W at 1532 nm with a linewidth of ~0.2 nm (FWHM) in a slightly multimode beam with M2 ~5. At this power level, the fiber laser was prone to damage so, in order to ensure reliable operation, the laser was operated at power levels below 50 W. Further details of the Er,Yb fiber laser pump source can be found in Ref. 22

22. J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, “High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating,” Opt. Lett. 33(11), 1204–1206 (2008). [CrossRef] [PubMed]

.

To produce the required ring-shaped pump beam profile, the output from the Er,Yb fiber laser was launched into the solid glass portion (inner-cladding) of a simple capillary (hollow-core) fiber of length, 50 cm. The capillary fiber was fabricated in-house and had pure silica inner-cladding of diameter, 400 µm with a 100 μm diameter air-hole in the center (see the upper-left picture in Fig. 1). The capillary fiber was coated with a low refractive index (n=1.375) fluorinated polymer outer-cladding giving a calculated NA of 0.49 for the inner-cladding waveguide. The launching efficiency was ~94%. The upper-right picture in Fig. 1 shows the transmitted (ring-shaped) near-field output beam profile recorded with a Pyrocam III camera (Spiricon Inc.). The beam propagation factor (M2) for the transmitted pump beam was measured to be ~51 and hence was degraded by a factor of ~10 compared to the incident pump beam in accordance with expectations. The extent to which pump beam quality is degraded by the capillary fiber depends on the input pump beam dimensions and beam divergence, and on the fiber design. Further optimization of the capillary fiber design in conjunction with the use of a single-mode Er,Yb fiber pump laser should yield a substantial improvement in transmitted pump beam quality. One important prerequisite for preferential lasing on LG01 mode is that there should be negligible diffraction spreading of the pump beam over the length of the pump absorption region in the Er:YAG rod to ensure that the ring-shaped pump beam profile is preserved and hence spatial-mode-matching to the LG01 mode is maintained. Therefore, by setting the Rayleigh range of the pump to be equal to the absorption length (1/ αp) for the pump, we obtain the following lower limit for the pump beam radius:
wp(M2λπnαp)
(1)
where αp is the absorption coefficient for the pump. This, in turn, imposes a lower limit on the laser mode size and threshold pump power.

The laser output power as a function of incident pump power is shown in Fig. 2(a)
Fig. 2 (a) Er:YAG laser output power and measured beam propagation factor (M2) as a function of incident pump power and (b) the output beam profiles monitored by a Pyrocam III camera. (c) The calculated and measured transverse intensity distributions for the LG01.
. The laser yielded 13.1 W of output at 1645 nm at the maximum available incident pump power of 34 W. The corresponding slope efficiency with respect to incident pump power was 48%. The threshold pump power was measured to be 5.8 W, which is in close agreement with the calculated value of 5.2 W. It should be pointed out that the threshold pump power for the LG01 mode is ~2.2 times larger than for the TEM00 mode with a spatially-matched ‘top-hat’ pump beam due to the larger pump beam area for the ring-shaped pump beam required to excite the LG01 mode. The output beam profile was monitored as a function of laser power with the aid of a pyroelectric detector 2D array (Pyrocam III). Figure 2(b) shows the beam profiles at low power (3 W) and high power (13 W) confirming the axially-symmetric ring-shaped nature of the output beam. The measured beam propagation factor (M2) for the output beam increased slightly from ~1.9 to ~2.4 with increasing pump power indicating that there is very little thermally-induced beam distortion. The calculated M2 parameter for a perfect LG01 mode is 2 [23

23. R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22(5), 643–644 (1983). [CrossRef] [PubMed]

] and hence is in close agreement with our measured values for M2 confirming that laser mode excited was indeed the LG01 mode. Further confirmation was obtained by noting that the measured transverse intensity as a function of radial position is in close agreement with the theoretical transverse intensity profile (Fig. 2(c)).

The polarization state of the output beam was investigated with the aid of the Glan-Taylor calcite polarizer on a rotation stage. Figure 3(a)
Fig. 3 (a) Relay-imaged output beam profiles for different angular positions of the polarizer. The arrow shows the polarizer transmission direction. (b) The normalized azimuthal intensity as a function of polarizer angle.
shows that the magnified (relay-imaged) output beam profile for different angular positions of the polarizer indicating that the laser output was radially-polarized. The polarization purity was investigated by measuring the intensity as a function azimuthal angle. The results (plotted in Fig. 3(b)) show a cosine-squared dependence of measured intensity as expected for radially-polarized light. The extinction ratio (i.e. radial polarization / azimuthal polarization) was found to be >98%. The underlying mechanism for preferential lasing with radial polarization is attributed to thermally-induced bifocussing. This results in slightly different thermal lens focal lengths [24

24. W. Koechner, “Solid state laser engineering,” Springer-Verlag, Sixth edition, 442–445 (2006).

] and hence slightly different laser mode sizes for radial and azimuthal polarization states. As a consequence, one polarization state (in this case the radial polarization state) has a slightly larger mode radius and a better spatial overlap with the ring-shaped inversion distribution. The net result is that the radial polarization has a lower threshold and hence reaches threshold first, saturating the inversion and preventing the azimuthal polarization state from lasing. In this way, the resonator can be designed to select either the radial or azimuthal polarization without having to resort to using a resonator design that is unstable for one polarization.

In the present arrangement the output power was limited by the maximum available pump power and there was no evidence of thermally-induced roll-over in output power. Thus, scaling to higher powers should be possible via the use of a higher power Er,Yb fiber pump laser in combination with a better optimized and lower-loss capillary fiber.

3. Conclusions

In summary, we have demonstrated a novel method for selectively exciting lasing on the Laguerre-Gaussian LG01 doughnut mode in an end-pumped solid-state laser. This approach has been applied to a hybrid Er:YAG laser, in-band pumped by an Er,Yb fiber laser, yielding 13.1 W of cw output at 1645 nm in a high quality, radially-polarized LG01 mode with slope efficiency of 48%. Further optimization of the laser design and pump delivery fiber in combination with the use of a higher power Er,Yb fiber pump laser is expected to yield a significant increase in output power. This approach for generating hollow (LG01) beams offers many attractions over existing techniques and is particularly well-suited to low quantum defect hybrid (fiber-laser-pumped-bulk-laser) configurations operating in the wavelength regimes around 1.6 µm and 2 µm [25

25. J. W. Kim, J. I. Mackenzie, D. Parisi, S. Veronesi, M. Tonelli, and W. A. Clarkson, “Efficient in-band pumped Ho:LuLiF4 2 microm laser,” Opt. Lett. 35(3), 420–422 (2010). [CrossRef] [PubMed]

]. The combination of high efficiency, power scalability and flexibility in mode of operation afforded by this technique should benefit a range of applications requiring high power hollow laser beams.

Acknowledgements

This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) and by the Electro-Magnetic Remote Sensing Defence Technology Centre (EMRS DTC), established by the UK Ministry of Defence.

References and links

1.

R. B. Charters, B. Luther-Davies, and F. Ladouceur, “Improved performance of laser channel written waveguides using a TEM01* beam,” IEEE Photon. Technol. Lett. 11(12), 1617–1619 (1999). [CrossRef]

2.

M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18(21), 22305–22313 (2010). [CrossRef] [PubMed]

3.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

4.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002). [CrossRef]

5.

R. Ozeri, L. Khaykovich, N. Friedman, and N. Davidson, “Large-volume single-beam dark optical trap for atoms using binary phase elements,” J. Opt. Soc. Am. B 17(7), 1113–1116 (2000). [CrossRef]

6.

Y. Song, D. Milam, and W. T. Hill III, “Long, narrow all-light atom guide,” Opt. Lett. 24(24), 1805–1807 (1999). [CrossRef] [PubMed]

7.

V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(01), 143–154 (2007). [CrossRef]

8.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000). [CrossRef]

9.

D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998). [CrossRef] [PubMed]

10.

J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, and W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138(4-6), 287–292 (1997). [CrossRef]

11.

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000). [CrossRef] [PubMed]

12.

A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004). [CrossRef]

13.

C. Paterson, “Higher order Bessel waves produced by axicon-type computer-based holograms,” Opt. Commun. 124(1-2), 121–130 (1996). [CrossRef]

14.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]

15.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]

16.

C. H. Chen, P. T. Tai, and W. F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Opt. 43(32), 6001–6006 (2004). [CrossRef] [PubMed]

17.

M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3 µm bounce laser,” Opt. Express 15(12), 7616–7622 (2007). [CrossRef] [PubMed]

18.

A. J. Caley, M. J. Thomson, J. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15(17), 10699–10704 (2007). [CrossRef] [PubMed]

19.

M. E. Marhic and E. Garmire, “Low-order TE0q operation of a CO2 laser for transmission through circular metallic waveguides,” Appl. Phys. Lett. 38(10), 743–745 (1981). [CrossRef]

20.

J. W. Kim, D. Y. Shen, J. K. Sahu, and W. A. Clarkson, “Fiber-Laser-Pumped Er:YAG Lasers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 361–371 (2009). [CrossRef]

21.

M. Eichhorn, “High-power resonantly diode-pumped CW Er3+:YAG laser,” Appl. Phys. B 93(4), 773–778 (2008). [CrossRef]

22.

J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, “High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating,” Opt. Lett. 33(11), 1204–1206 (2008). [CrossRef] [PubMed]

23.

R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22(5), 643–644 (1983). [CrossRef] [PubMed]

24.

W. Koechner, “Solid state laser engineering,” Springer-Verlag, Sixth edition, 442–445 (2006).

25.

J. W. Kim, J. I. Mackenzie, D. Parisi, S. Veronesi, M. Tonelli, and W. A. Clarkson, “Efficient in-band pumped Ho:LuLiF4 2 microm laser,” Opt. Lett. 35(3), 420–422 (2010). [CrossRef] [PubMed]

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.3500) Lasers and laser optics : Lasers, erbium
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3580) Lasers and laser optics : Lasers, solid-state

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 13, 2011
Revised Manuscript: July 1, 2011
Manuscript Accepted: July 4, 2011
Published: July 13, 2011

Citation
J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, "High power Er:YAG laser with radially-polarized Laguerre-Gaussian (LG01) mode output," Opt. Express 19, 14526-14531 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14526


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References

  1. R. B. Charters, B. Luther-Davies, and F. Ladouceur, “Improved performance of laser channel written waveguides using a TEM01* beam,” IEEE Photon. Technol. Lett. 11(12), 1617–1619 (1999). [CrossRef]
  2. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express 18(21), 22305–22313 (2010). [CrossRef] [PubMed]
  3. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]
  4. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002). [CrossRef]
  5. R. Ozeri, L. Khaykovich, N. Friedman, and N. Davidson, “Large-volume single-beam dark optical trap for atoms using binary phase elements,” J. Opt. Soc. Am. B 17(7), 1113–1116 (2000). [CrossRef]
  6. Y. Song, D. Milam, and W. T. Hill III, “Long, narrow all-light atom guide,” Opt. Lett. 24(24), 1805–1807 (1999). [CrossRef] [PubMed]
  7. V. Sizyuk, A. Hassanein, and T. Sizyuk, “Hollow laser self-confined plasma for extreme ultraviolet lithography and other applications,” Laser Part. Beams 25(01), 143–154 (2007). [CrossRef]
  8. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000). [CrossRef]
  9. D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998). [CrossRef] [PubMed]
  10. J. Yin, H. Noh, K. Lee, K. Kim, Y. Wang, and W. Jhe, “Generation of a dark hollow beam by a small hollow fiber,” Opt. Commun. 138(4-6), 287–292 (1997). [CrossRef]
  11. J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000). [CrossRef] [PubMed]
  12. A. Shevchenko, S. C. Buchter, N. V. Tabiryan, and M. Kaivola, “Creation of a hollow laser beam using self-phase modulation in a nematic liquid crystal,” Opt. Commun. 232(1-6), 77–82 (2004). [CrossRef]
  13. C. Paterson, “Higher order Bessel waves produced by axicon-type computer-based holograms,” Opt. Commun. 124(1-2), 121–130 (1996). [CrossRef]
  14. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]
  15. L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
  16. C. H. Chen, P. T. Tai, and W. F. Hsieh, “Bottle beam from a bare laser for single-beam trapping,” Appl. Opt. 43(32), 6001–6006 (2004). [CrossRef] [PubMed]
  17. M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3 µm bounce laser,” Opt. Express 15(12), 7616–7622 (2007). [CrossRef] [PubMed]
  18. A. J. Caley, M. J. Thomson, J. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15(17), 10699–10704 (2007). [CrossRef] [PubMed]
  19. M. E. Marhic and E. Garmire, “Low-order TE0q operation of a CO2 laser for transmission through circular metallic waveguides,” Appl. Phys. Lett. 38(10), 743–745 (1981). [CrossRef]
  20. J. W. Kim, D. Y. Shen, J. K. Sahu, and W. A. Clarkson, “Fiber-Laser-Pumped Er:YAG Lasers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 361–371 (2009). [CrossRef]
  21. M. Eichhorn, “High-power resonantly diode-pumped CW Er3+:YAG laser,” Appl. Phys. B 93(4), 773–778 (2008). [CrossRef]
  22. J. W. Kim, P. Jelger, J. K. Sahu, F. Laurell, and W. A. Clarkson, “High-power and wavelength-tunable operation of an Er,Yb fiber laser using a volume Bragg grating,” Opt. Lett. 33(11), 1204–1206 (2008). [CrossRef] [PubMed]
  23. R. L. Phillips and L. C. Andrews, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22(5), 643–644 (1983). [CrossRef] [PubMed]
  24. W. Koechner, “Solid state laser engineering,” Springer-Verlag, Sixth edition, 442–445 (2006).
  25. J. W. Kim, J. I. Mackenzie, D. Parisi, S. Veronesi, M. Tonelli, and W. A. Clarkson, “Efficient in-band pumped Ho:LuLiF4 2 microm laser,” Opt. Lett. 35(3), 420–422 (2010). [CrossRef] [PubMed]

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