Abstract

Unstable resonators show an intense discrimination of undesired higher order modes but a high beam quality cannot be obtained with conventional resonators composed of spherical mirrors. In the present paper we demonstrate the possibility to tailor the fundamental mode by inserting diffractive elements into the resonator to generate a desirable output beam profile even for unstable resonators. We show a concept to design such surface structured elements for customizing the amplitude shape of the outcoupled beam. Further we demonstrate the first experimental realization of an unstable diffractive resonator with a Gaussian shaped amplitude profile of the laser beam for a vertical external cavity surface emitting laser (VECSEL).

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References

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  1. P. A. Bélanger and C. Pare, “Optical resonators using graded phase mirrors,” Opt. Lett. 16(14), 1057–1059 (1991).
    [CrossRef] [PubMed]
  2. A. Siegman, Lasers (University Science Books, Mill Valley, California, 1986).
  3. H. Zucker, “Optical resonators with variable reflective mirrors,” Bell Syst. J. 49, 2349–2376 (1970).
  4. P. A. Belanger and C. Pare, “Unstable laser resonators with a specified output profile using a graded-reflectivity mirror: Geometrical optics limit,” Opt. Commun. 109, 553–555 (1985).
  5. U. D. Zeitner and F. Wyrowski, “Design of Unstable Laser Resonators with User-Defined Mode Shape,” IEEE J. Quantum Electron. 37,(12), 1594–1599 (2001).
    [CrossRef]
  6. A. Büttner, Untersuchung Experimenteller Verfahren zur resonatorinternen Modenformung. PhD Thesis, Friedrich Schiller Universität Jena, 2005.
  7. U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
    [CrossRef]
  8. U. Zeitner, Optimierung von Lasereigenschaften durch generalisierte Konzepte im Resonatordesign. PhD Thesis, Friedrich Schiller Universität Jena, 1999.
  9. A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. 40, 453–488 (1961).
  10. D. Radtke and U. D. Zeitner, “Laser-lithography on non-planar surfaces,” Opt. Express 15(3), 1167–1174 (2007).
    [CrossRef] [PubMed]
  11. R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
    [CrossRef]

2007 (2)

D. Radtke and U. D. Zeitner, “Laser-lithography on non-planar surfaces,” Opt. Express 15(3), 1167–1174 (2007).
[CrossRef] [PubMed]

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

2001 (1)

U. D. Zeitner and F. Wyrowski, “Design of Unstable Laser Resonators with User-Defined Mode Shape,” IEEE J. Quantum Electron. 37,(12), 1594–1599 (2001).
[CrossRef]

2000 (1)

U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
[CrossRef]

1991 (1)

1985 (1)

P. A. Belanger and C. Pare, “Unstable laser resonators with a specified output profile using a graded-reflectivity mirror: Geometrical optics limit,” Opt. Commun. 109, 553–555 (1985).

1970 (1)

H. Zucker, “Optical resonators with variable reflective mirrors,” Bell Syst. J. 49, 2349–2376 (1970).

Belanger, P. A.

P. A. Belanger and C. Pare, “Unstable laser resonators with a specified output profile using a graded-reflectivity mirror: Geometrical optics limit,” Opt. Commun. 109, 553–555 (1985).

Bélanger, P. A.

Fox, A.

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. 40, 453–488 (1961).

Hartke, R.

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

Heumann, E.

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

Huber, G.

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

Kühnelt, M.

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

L, T.

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. 40, 453–488 (1961).

Pare, C.

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

P. A. Belanger and C. Pare, “Unstable laser resonators with a specified output profile using a graded-reflectivity mirror: Geometrical optics limit,” Opt. Commun. 109, 553–555 (1985).

Radtke, D.

Steegmüller, U.

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

Wyrowski, F.

U. D. Zeitner and F. Wyrowski, “Design of Unstable Laser Resonators with User-Defined Mode Shape,” IEEE J. Quantum Electron. 37,(12), 1594–1599 (2001).
[CrossRef]

U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
[CrossRef]

Zeitner, U.

U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
[CrossRef]

Zeitner, U. D.

D. Radtke and U. D. Zeitner, “Laser-lithography on non-planar surfaces,” Opt. Express 15(3), 1167–1174 (2007).
[CrossRef] [PubMed]

U. D. Zeitner and F. Wyrowski, “Design of Unstable Laser Resonators with User-Defined Mode Shape,” IEEE J. Quantum Electron. 37,(12), 1594–1599 (2001).
[CrossRef]

Zellmer, H.

U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
[CrossRef]

Zucker, H.

H. Zucker, “Optical resonators with variable reflective mirrors,” Bell Syst. J. 49, 2349–2376 (1970).

Appl. Phys. B (1)

R. Hartke, E. Heumann, G. Huber, M. Kühnelt, and U. Steegmüller, “Efficient green generation by intracavity frequency doubling of an optical pumped semiconductor disk laser,” Appl. Phys. B 87(1), 95–99 (2007).
[CrossRef]

Bell Syst. J. (1)

H. Zucker, “Optical resonators with variable reflective mirrors,” Bell Syst. J. 49, 2349–2376 (1970).

Bell Syst. Tech. (1)

A. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. 40, 453–488 (1961).

IEEE J. Quantum Electron. (2)

U. D. Zeitner and F. Wyrowski, “Design of Unstable Laser Resonators with User-Defined Mode Shape,” IEEE J. Quantum Electron. 37,(12), 1594–1599 (2001).
[CrossRef]

U. Zeitner, F. Wyrowski, and H. Zellmer, “External Design Freedom for Optimization of Resonator Originated Beam Shaping,” IEEE J. Quantum Electron. 36(10), 1105–1109 (2000).
[CrossRef]

Opt. Commun. (1)

P. A. Belanger and C. Pare, “Unstable laser resonators with a specified output profile using a graded-reflectivity mirror: Geometrical optics limit,” Opt. Commun. 109, 553–555 (1985).

Opt. Express (1)

Opt. Lett. (1)

Other (3)

A. Siegman, Lasers (University Science Books, Mill Valley, California, 1986).

U. Zeitner, Optimierung von Lasereigenschaften durch generalisierte Konzepte im Resonatordesign. PhD Thesis, Friedrich Schiller Universität Jena, 1999.

A. Büttner, Untersuchung Experimenteller Verfahren zur resonatorinternen Modenformung. PhD Thesis, Friedrich Schiller Universität Jena, 2005.

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the diffractive unstable resonator. (1) Backcoupling mirror (BCM) with amplifying VECSEL disk and optical pumped region (2), (3) Outcoupling mirror (OCM) with diffractive surface profile (4) and eccentric outcoupling of a Gaussian beam (5).

Fig. 2
Fig. 2

A schematic comprehension of the two step design algorithm

Fig. 3
Fig. 3

Calculated phase function of the outcoupling mirror (OCM). (a) phase function as calculated by the design algorithm, (b) spherical part of the appropriate substrate curvature subtracted. (1) circular outcoupling region.

Fig. 4
Fig. 4

Intensity distribution of the resonator mode on the diffractive mirror (b). (a) Normalized intensity in the outcoupling region (eccentric hole marked red)

Fig. 5
Fig. 5

Microscopic images of two mirror samples. The simulated intensity in the outcoupling region is painted into the graphics. The same false color representation than in Fig. 4 is used. (1) diffractive mirror structure, (2) outcoupling region, (3) diffractive lens structure

Fig. 6
Fig. 6

Near-field (a) and far-field (b) images of the laser mode. The amplifier is operating at the highest possible gain and a high beam quality of the outcoupled field is observed.

Tables (1)

Tables Icon

Table 1 Description of symbols used in the algebraic formulation

Equations (3)

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Z^Un(x,y)=λnUn(x,y)
R^iU(x,y,zRi)=U(x,y,zRi)=U(x,y,zRi+)
R^i=2·arg(U(x,y,zRi))

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