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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21113–21118
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Tuneable Gaussian to flat-top resonator by amplitude beam shaping

Sandile Ngcobo, Kamel Ait-Ameur, Igor Litvin, Abdelkrim Hasnaoui, and Andrew Forbes  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 21113-21118 (2013)
http://dx.doi.org/10.1364/OE.21.021113


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Abstract

We outline a simple laser cavity comprising an opaque ring and a circular aperture that is capable of producing spatially tuneable laser modes, from a Gaussian beam to a Flat-top beam. The tuneability is achieved by varying the diameter of the aperture and thus requires no realignment of the cavity. We demonstrate this principle using a digital laser with an intra-cavity spatial light modulator, and confirm the predicted properties of the resonator experimentally.

© 2013 OSA

1. Introduction

A laser beam with an intensity profile that is flat-top (or top-hat) is desirable in many applications [1

1. F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor and Francis, 2006).

]. Many techniques exist for the creation of flat-top beams external to the laser cavity [2

2. F. M. Dickey and S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, 2000).

4

4. A. Laskin and V. Laskin, “Imaging techniques with refractive beam shaping optics,” Proc. SPIE 8490, 84900J, 84900J-11 (2012), doi:. [CrossRef]

], which can be accomplished with low loss albeit with some complexity in the optical delivery system (e.g., requiring careful alignment and fixed input beam parameters to the shaping elements). There are advantages to having such a beam profile as a direct output from a laser cavity (e.g., optimised energy extraction), however the methods of obtaining such beam shapes as the laser eigenmodes are quite complicated, and often involve custom made (expensive) diffractive optics, aspheric elements, graded phase mirrors or deformable mirrors [5

5. I. A. Litvin and A. Forbes, “Intra-cavity flat-top beam generation,” Opt. Express 17(18), 15891–15903 (2009). [CrossRef] [PubMed]

15

15. 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]

]. Furthermore, all the solutions to date have been designed for a single mode and are not tuneable in the mode selection.

2. Concept and simulation

Our concept is based on the mode selective properties of a cavity comprising both an aperture and a ring obstruction, as illustrated in Fig. 1
Fig. 1 A schematic representation of the concept. An absorbing ring (2) is placed at the plano (1) end of a plano-concave cavity. A standard circular aperture (3) is placed at the opposite end, and the mode is transmitted through the output coupler (4).
. We will show that the desired beams can be obtained by careful selection of the normalized radius Ya = ρa/w0 of the opaque ring of width h, and the normalised radius Yc = ρc/wc of the circular aperture; here w0 and wc are the beam radii of the Gaussian beam in the bare cavity (without the ring of radius ρa and aperture of radius ρc) at the flat and curved mirror, respectively. Single pass studies [17

17. A. Hasnaoui and K. Ait-Ameur, “Properties of a laser cavity containing an absorbing ring,” Appl. Opt. 49(21), 4034–4043 (2010). [CrossRef] [PubMed]

,18

18. A. Hasnaoui, T. Godin, E. Cagniot, M. Fromager, A. Forbes, and K. Ait-Ameur, “Selection of a LGp0-shaped fundamental mode in a laser cavity: phase versus amplitude masks,” Opt. Commun. 285(24), 5268–5275 (2012). [CrossRef]

] on the transmission of radial Laguerre-Gaussian beams through each component (separately) have indicated that when the aperture is “open” (Yc > 2) all the radial modes have similar losses, while as it is closed so the Gaussian mode dominates with the lowest loss; in the latter scenario there is no radial mode selectivity by this element.

This suggests a simple approach to tuneability: if the normalized ring radius is chosen to allow particular Laguerre-Gaussian radial modes to lase simultaneously, then they will do so incoherently. If the aperture is open, so that the ring is the mode determining element, then our Fox-Li analysis predicts a flat-top beam as the output. As the aperture is steadily closed, so it becomes the mode determining element and the Gaussian mode is selected, based on substantially lower round trip losses. Hence only the aperture opening needs to change to control the mode.

3. Experimental setup and results

In order to test the simulated results we used the laser set–up shown in Fig. 3(a)
Fig. 3 (a) Schematic setup of an intra-cavity SLM with diagnostic and control equipment. The High Reflectors (HR) were used to reflect the 808 nm or 1064 nm wavelengths. (b) SLM phase screen acted as a flat-end mirror containing an opaque ring of 100 μm width.
. The cavity was arranged in a Z-shape to allow the high power pump (808 nm) to pass through the gain medium (Nd:YAG) without interference from the aperture and ring mask. The stable plano-concave cavity had an effective length of 252 mm, with the circular aperture placed directly in front of the curved (R = 500 mm) output coupler of reflectivity 80%. The output mode could be measured in both the near field and far field with imaging or Fourier transforming optics. Care was taken to separate the lasing wavelength (1064 nm) from the pump light (808 nm) with suitable filters.

An additional novel aspect of this experiment was the use of a “digital laser” [16

16. S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013), doi:. [CrossRef] [PubMed]

]. One of the cavity mirrors in the digital laser setup is a rewritable phase-only spatial light modulator (SLM), forming a holographic end-mirror. The SLM was programmed with a digital hologram representing both the flat mirror and the opaque ring, as shown in Fig. 3(b). The digital laser allowed for easy optimisation of the ring radius as well as the ring thickness. To vary these parameters with lithographically produced rings of varying thickness and radius would be time consuming, and would require a realignment of the cavity for each setting. In the digital laser, a new ring could be created by merely changing an image on the control PC representing the desired digital hologram, without any realignment. The amplitude modulation employed to realise the ring was achieved by complex amplitude modulation [19

19. V. Arrizón, “Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,” Opt. Lett. 28(24), 2521–2523 (2003). [CrossRef] [PubMed]

,20

20. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24(11), 3500–3507 (2007). [CrossRef] [PubMed]

] using high spatial frequency gratings in the form of so-called “checker boxes”. On the other side of the cavity we had a variable circular aperture which was controlled manually in order to find the optimal value of Yc. This standard aperture provided the tuneability of the mode.

The output from the digital laser is shown in Fig. 4
Fig. 4 Experimentally obtained near field and far field images of the Gaussian beam and Flat-top beam for ring width settings of (a-b): 20 μm and (c-d): 100 μm. Gaussian beam (a and a*) and Flat-top beam (b and b*) for Ya = 1.4, a ring width of 20 μm, and Yc = 2.0 (Gaussian) and 2.3 (FT). Gaussian beam (c and c*) and Flat-top beam (d and d*) for Ya = 1.4, a ring width of 100 μm, and Yc = 2.0 (Gaussian), 2.3 (FT). These values are in good agreement with theory.
, where the near field and the far field intensity profiles of the quasi-Gaussian (a) and Flat-top (b) beams are shown. In the first four panels (a-b) we have the results for a 20 μm width ring, while in the last four panels (c-d) we have the results for a 100 μm width ring. We note that the spatial intensity distributions are in good agreement with the simulated Fox-Li results in Fig. 2(d). Moreover, as predicted by theory, the desired shapes are found in the far field too. The field patterns are also found at values of Ya and Yc close to those predicted by theory, differing by less than 10%. The small deviation can be attributed to minor mode size errors, e.g., due to small thermal lensing or refractive index errors.

Slope efficiency measurements, Fig. 5
Fig. 5 The slope efficiencies of the FT beam, quasi Gaussian beam and Gaussian beam for (a) 20 μm and (b) 100 μm ring width.
, reveal that the FT beam has the highest slop efficiency but also the highest threshold as compared to the quasi-Gaussian beam selected by the ring cavity. The FT beam slope efficiency is approximately 2 × that of the quasi-Gaussian. This can be explained by the fact that the FT beam has a much larger gain volume than the quasi-Gaussian mode and is better matched to the pump beam in size and shape. For comparison the data for a Gaussian beam without any ring is also shown; this was achieved with no opaque ring programmed on the SLM and a normalized circular aperture set to Ya = 2.0 on the curve mirror (i.e., the standard approach to Gaussian mode selection). The quasi-Gaussian and Gaussian mode show little difference when the ring width is small (20 μm), indicating that indeed the perturbation from the ring is minimal in the case of selecting the quasi-Gaussian, and thus it may indeed be considered as a Gaussian mode, in agreement with the theoretical prediction. It has been suggested previously [18

18. A. Hasnaoui, T. Godin, E. Cagniot, M. Fromager, A. Forbes, and K. Ait-Ameur, “Selection of a LGp0-shaped fundamental mode in a laser cavity: phase versus amplitude masks,” Opt. Commun. 285(24), 5268–5275 (2012). [CrossRef]

] that in some cases amplitude masks do not lead to higher losses, and this could be the situation here too. When the ring width increases the quasi-Gaussian departs further from the ideal Gaussian mode and the lasing threshold increases.

Finally we point out that while we have used the digital laser to prove the principle, one would not use the intra-cavity SLM approach in a high power system. Rather, one would make use of custom optical elements to implement the ring aperture, thereby increasing the damage threshold and lowering the losses, to produce a more efficient and practical system.

4. Conclusion

In conclusion, we have conceived of and then demonstrated a novel laser cavity that is mode tuneable. We have shown that by simply adjusting the diameter of a standard circular aperture in the cavity, the mode can be selected from the ubiquitous Gaussian to a Flat-top beam. The ring mask was implemented with an intra-cavity holographic mirror for the convenience that this allows in testing the design parameters, but a high power version, optimised for power extract, would necessarily be made with standard optics and lithographic processing techniques to eliminate the SLM losses.

References and links

1.

F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor and Francis, 2006).

2.

F. M. Dickey and S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, 2000).

3.

J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39(30), 5488–5499 (2000). [CrossRef] [PubMed]

4.

A. Laskin and V. Laskin, “Imaging techniques with refractive beam shaping optics,” Proc. SPIE 8490, 84900J, 84900J-11 (2012), doi:. [CrossRef]

5.

I. A. Litvin and A. Forbes, “Intra-cavity flat-top beam generation,” Opt. Express 17(18), 15891–15903 (2009). [CrossRef] [PubMed]

6.

P. A. Bélanger and C. Paré, “Optical resonators using graded-phase mirrors,” Opt. Lett. 16(14), 1057–1059 (1991). [CrossRef] [PubMed]

7.

P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett. 17(10), 739–741 (1992). [CrossRef] [PubMed]

8.

J. R. Leger, D. Chen, and Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19(2), 108–110 (1994). [CrossRef] [PubMed]

9.

I. A. Litvin and A. Forbes, “Gaussian mode selection with intracavity diffractive optics,” Opt. Lett. 34(19), 2991–2993 (2009). [CrossRef] [PubMed]

10.

J. R. Leger, D. Chen, and K. Dai, “High modal discrimination in a Nd:YAG laser resonator with internal phase gratings,” Opt. Lett. 19(23), 1976–1978 (1994). [CrossRef] [PubMed]

11.

J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, “Low-order adaptive deformable mirror,” Appl. Opt. 37(21), 4663–4668 (1998). [CrossRef] [PubMed]

12.

T. Y. Cherezova, L. N. Kaptsov, and A. V. Kudryashov, “Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror,” Appl. Opt. 35(15), 2554–2561 (1996). [CrossRef] [PubMed]

13.

T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001). [CrossRef] [PubMed]

14.

M. Gerber and T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with a graded-phase mirror,” IEEE J. Quantum Electron. 40(6), 741–746 (2004). [CrossRef]

15.

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]

16.

S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013), doi:. [CrossRef] [PubMed]

17.

A. Hasnaoui and K. Ait-Ameur, “Properties of a laser cavity containing an absorbing ring,” Appl. Opt. 49(21), 4034–4043 (2010). [CrossRef] [PubMed]

18.

A. Hasnaoui, T. Godin, E. Cagniot, M. Fromager, A. Forbes, and K. Ait-Ameur, “Selection of a LGp0-shaped fundamental mode in a laser cavity: phase versus amplitude masks,” Opt. Commun. 285(24), 5268–5275 (2012). [CrossRef]

19.

V. Arrizón, “Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,” Opt. Lett. 28(24), 2521–2523 (2003). [CrossRef] [PubMed]

20.

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24(11), 3500–3507 (2007). [CrossRef] [PubMed]

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3410) Lasers and laser optics : Laser resonators
(070.3185) Fourier optics and signal processing : Invariant optical fields
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: July 10, 2013
Revised Manuscript: August 19, 2013
Manuscript Accepted: August 23, 2013
Published: September 3, 2013

Citation
Sandile Ngcobo, Kamel Ait-Ameur, Igor Litvin, Abdelkrim Hasnaoui, and Andrew Forbes, "Tuneable Gaussian to flat-top resonator by amplitude beam shaping," Opt. Express 21, 21113-21118 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21113


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References

  1. F. M. Dickey, S. C. Holswade, and D. L. Shealy, Laser Beam Shaping Applications (Taylor and Francis, 2006).
  2. F. M. Dickey and S. C. Holswade, Laser Beam Shaping, Theory and Techniques (Marcel Dekker, 2000).
  3. J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt.39(30), 5488–5499 (2000). [CrossRef] [PubMed]
  4. A. Laskin and V. Laskin, “Imaging techniques with refractive beam shaping optics,” Proc. SPIE8490, 84900J, 84900J-11 (2012), doi:. [CrossRef]
  5. I. A. Litvin and A. Forbes, “Intra-cavity flat-top beam generation,” Opt. Express17(18), 15891–15903 (2009). [CrossRef] [PubMed]
  6. P. A. Bélanger and C. Paré, “Optical resonators using graded-phase mirrors,” Opt. Lett.16(14), 1057–1059 (1991). [CrossRef] [PubMed]
  7. P. A. Bélanger, R. L. Lachance, and C. Paré, “Super-Gaussian output from a CO2 laser by using a graded-phase mirror resonator,” Opt. Lett.17(10), 739–741 (1992). [CrossRef] [PubMed]
  8. J. R. Leger, D. Chen, and Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG laser,” Opt. Lett.19(2), 108–110 (1994). [CrossRef] [PubMed]
  9. I. A. Litvin and A. Forbes, “Gaussian mode selection with intracavity diffractive optics,” Opt. Lett.34(19), 2991–2993 (2009). [CrossRef] [PubMed]
  10. J. R. Leger, D. Chen, and K. Dai, “High modal discrimination in a Nd:YAG laser resonator with internal phase gratings,” Opt. Lett.19(23), 1976–1978 (1994). [CrossRef] [PubMed]
  11. J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, “Low-order adaptive deformable mirror,” Appl. Opt.37(21), 4663–4668 (1998). [CrossRef] [PubMed]
  12. T. Y. Cherezova, L. N. Kaptsov, and A. V. Kudryashov, “Cw industrial rod YAG:Nd3+ laser with an intracavity active bimorph mirror,” Appl. Opt.35(15), 2554–2561 (1996). [CrossRef] [PubMed]
  13. T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt.40(33), 6026–6033 (2001). [CrossRef] [PubMed]
  14. M. Gerber and T. Graf, “Generation of super-Gaussian modes in Nd:YAG lasers with a graded-phase mirror,” IEEE J. Quantum Electron.40(6), 741–746 (2004). [CrossRef]
  15. 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. Express15(17), 10699–10704 (2007). [CrossRef] [PubMed]
  16. S. Ngcobo, I. A. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun.4, 2289 (2013), doi:. [CrossRef] [PubMed]
  17. A. Hasnaoui and K. Ait-Ameur, “Properties of a laser cavity containing an absorbing ring,” Appl. Opt.49(21), 4034–4043 (2010). [CrossRef] [PubMed]
  18. A. Hasnaoui, T. Godin, E. Cagniot, M. Fromager, A. Forbes, and K. Ait-Ameur, “Selection of a LGp0-shaped fundamental mode in a laser cavity: phase versus amplitude masks,” Opt. Commun.285(24), 5268–5275 (2012). [CrossRef]
  19. V. Arrizón, “Optimum on-axis computer-generated hologram encoded into low-resolution phase-modulation devices,” Opt. Lett.28(24), 2521–2523 (2003). [CrossRef] [PubMed]
  20. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A24(11), 3500–3507 (2007). [CrossRef] [PubMed]

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