Abstract

We present the numerical and experimental study that we carried out to compare the performances of two hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers. The two resonators are designed to fit a 320 mm × 60 mm × 2 mm rf-discharge channel and are both guided in the narrow transverse direction. They differ in the other transverse direction, consisting of a positive- or a negative-branch unstable resonator scheme. The two solutions have been characterized in terms of modal structure, power extraction, stability, and quality of the extracted beam.

© 1996 Optical Society of America

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References

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  1. S. Yatsiv, “Conductively cooled capacitively coupled rf excited CO2 lasers,” in Gas Flow and Chemical Lasers, S. Rosenwaks, ed. (Springer-Verlag, Berlin, 1987), pp. 252–257.
    [CrossRef]
  2. K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
    [CrossRef]
  3. A. E. Siegman, “Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
    [CrossRef] [PubMed]
  4. O. L. Bourn, P. E. Dyer, “A novel stable-unstable resonator for beam control of rare-gas halides lasers,” Opt. Commun. 31, 193–196 (1979).
    [CrossRef]
  5. J. J. Degnan, D. R. Hall, “Finite-aperture waveguide laser resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
    [CrossRef]
  6. P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
    [CrossRef]
  7. R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
    [CrossRef]
  8. A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
    [CrossRef]
  9. C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
    [CrossRef]
  10. A. E. Siegman, “Stable–unstable resonator design for a wide tuning-range free-electron laser,” IEEE J. Quantum Electron. QE-28, 1243–1247 (1992).
    [CrossRef]
  11. A. Borghese, R. Canevari, V. Donati, L. Garifo, “Unstable–stable resonators with toroidal mirrors,” Appl. Opt. 20, 3547–3552 (1981).
    [CrossRef] [PubMed]
  12. A. Lapucci, S. Mascalchi, F. Rossetti, “Pulse behaviour of a compact R. F. discharge CO2 laser,” Opt. Laser Technol. (1996), to be published.
  13. A. E. Siegman, Lasers (University Science Books, Mill Valley Calif., 1986), Chaps. 22 and 23.
  14. K. D. Laakmann, W. M. Steier, “Waveguides: characteristic modes of hollow rectangular dielectric waveguides,” Appl. Opt. 15, 1334–1340 (1976).
    [CrossRef] [PubMed]
  15. A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  16. See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  17. W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
    [CrossRef]
  18. W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
    [CrossRef]
  19. T. F. Ewanizky, J. M. Craig, “Negative-branch unstable resonator Nd:YAG laser,” Appl. Opt. 15, 1465–1469 (1976).
    [CrossRef] [PubMed]
  20. Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
    [CrossRef]
  21. M. Khelkhal, F. Herlemont, “RF excitation of a flowing gas CO2 waveguide laser,” IEEE J. Quantum Electron. QE-29, 818–821 (1993).
    [CrossRef]
  22. M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, London, 1989), pp. 132–142.
  23. A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
    [CrossRef]
  24. J. F. Perkins, R. W. Jones, “Effects of unstable resonator misalignment in the cusping domain,” Appl. Opt. 23, 358–360 (1984).
    [CrossRef] [PubMed]

1994 (1)

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

1993 (1)

M. Khelkhal, F. Herlemont, “RF excitation of a flowing gas CO2 waveguide laser,” IEEE J. Quantum Electron. QE-29, 818–821 (1993).
[CrossRef]

1992 (4)

Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
[CrossRef]

A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
[CrossRef]

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

A. E. Siegman, “Stable–unstable resonator design for a wide tuning-range free-electron laser,” IEEE J. Quantum Electron. QE-28, 1243–1247 (1992).
[CrossRef]

1989 (2)

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

1984 (1)

1981 (1)

1979 (1)

O. L. Bourn, P. E. Dyer, “A novel stable-unstable resonator for beam control of rare-gas halides lasers,” Opt. Commun. 31, 193–196 (1979).
[CrossRef]

1976 (2)

1974 (1)

1973 (1)

J. J. Degnan, D. R. Hall, “Finite-aperture waveguide laser resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

1969 (1)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

1965 (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

1961 (1)

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

Abramski, K. M.

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

Abramsky, K. M.

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

Baker, H. J.

A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
[CrossRef]

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

Baker, H. M.

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

Borghese, A.

Bourn, O. L.

O. L. Bourn, P. E. Dyer, “A novel stable-unstable resonator for beam control of rare-gas halides lasers,” Opt. Commun. 31, 193–196 (1979).
[CrossRef]

Burlamacchi, P.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Canevari, R.

Colley, A. D.

A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
[CrossRef]

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

Craig, J. M.

Degnan, J. J.

J. J. Degnan, D. R. Hall, “Finite-aperture waveguide laser resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

Donati, V.

Dyer, P. E.

O. L. Bourn, P. E. Dyer, “A novel stable-unstable resonator for beam control of rare-gas halides lasers,” Opt. Commun. 31, 193–196 (1979).
[CrossRef]

Ewanizky, T. F.

Fox, A. G.

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

Garifo, L.

Goodman, J. W.

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hall, D. R.

A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
[CrossRef]

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-aperture waveguide laser resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

Hall, T.

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

Herlemont, F.

M. Khelkhal, F. Herlemont, “RF excitation of a flowing gas CO2 waveguide laser,” IEEE J. Quantum Electron. QE-29, 818–821 (1993).
[CrossRef]

Jackson, P. E.

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

Jones, R. W.

Khelkhal, M.

M. Khelkhal, F. Herlemont, “RF excitation of a flowing gas CO2 waveguide laser,” IEEE J. Quantum Electron. QE-29, 818–821 (1993).
[CrossRef]

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Kuzumoto, M.

Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
[CrossRef]

Laakmann, K. D.

Lapucci, A.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

A. Lapucci, S. Mascalchi, F. Rossetti, “Pulse behaviour of a compact R. F. discharge CO2 laser,” Opt. Laser Technol. (1996), to be published.

Li, T.

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

Mascalchi, S.

A. Lapucci, S. Mascalchi, F. Rossetti, “Pulse behaviour of a compact R. F. discharge CO2 laser,” Opt. Laser Technol. (1996), to be published.

Nowak, R.

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

Opower, H.

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

Perkins, J. F.

Rigrod, W. W.

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Rossetti, F.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

A. Lapucci, S. Mascalchi, F. Rossetti, “Pulse behaviour of a compact R. F. discharge CO2 laser,” Opt. Laser Technol. (1996), to be published.

Sasnett, M. W.

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, London, 1989), pp. 132–142.

Schaefer, U.

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

Shackleton, C.J.

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “Stable–unstable resonator design for a wide tuning-range free-electron laser,” IEEE J. Quantum Electron. QE-28, 1243–1247 (1992).
[CrossRef]

A. E. Siegman, “Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
[CrossRef] [PubMed]

A. E. Siegman, Lasers (University Science Books, Mill Valley Calif., 1986), Chaps. 22 and 23.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Steier, W. M.

Takanaka, Y.

Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
[CrossRef]

Wessel, K.

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

Yasui, K.

Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
[CrossRef]

Yatsiv, S.

S. Yatsiv, “Conductively cooled capacitively coupled rf excited CO2 lasers,” in Gas Flow and Chemical Lasers, S. Rosenwaks, ed. (Springer-Verlag, Berlin, 1987), pp. 252–257.
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (3)

P. E. Jackson, H. J. Baker, D. R. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

A. D. Colley, H. J. Baker, D. R. Hall, “Planar waveguide, 1-kW cw, carbon dioxide laser excited by a single transverse rf discharge,” Appl. Phys. Lett. 61, 136–138 (1992).
[CrossRef]

K. M. Abramsky, A. D. Colley, H. M. Baker, D. R. Hall, “Power scaling of large-area transverse radio frequency discharge CO2 lasers,” Appl. Phys. Lett. 54, 1833–1835 (1989).
[CrossRef]

Bell Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (5)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Y. Takanaka, M. Kuzumoto, K. Yasui, “A 5-kW cw CO2 laser using a novel negative-branch unstable resonator with a phase-unifying output coupler,” IEEE J. Quantum Electron. QE-28, 1855–1858 (1992).
[CrossRef]

M. Khelkhal, F. Herlemont, “RF excitation of a flowing gas CO2 waveguide laser,” IEEE J. Quantum Electron. QE-29, 818–821 (1993).
[CrossRef]

A. E. Siegman, “Stable–unstable resonator design for a wide tuning-range free-electron laser,” IEEE J. Quantum Electron. QE-28, 1243–1247 (1992).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-aperture waveguide laser resonators,” IEEE J. Quantum Electron. QE-9, 901–910 (1973).
[CrossRef]

J. Appl. Phys. (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487–2490 (1965).
[CrossRef]

Opt. Commun. (3)

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an R.F.-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

O. L. Bourn, P. E. Dyer, “A novel stable-unstable resonator for beam control of rare-gas halides lasers,” Opt. Commun. 31, 193–196 (1979).
[CrossRef]

C.J. Shackleton, K. M. Abramski, H. J. Baker, D. R. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

Other (6)

S. Yatsiv, “Conductively cooled capacitively coupled rf excited CO2 lasers,” in Gas Flow and Chemical Lasers, S. Rosenwaks, ed. (Springer-Verlag, Berlin, 1987), pp. 252–257.
[CrossRef]

R. Nowak, H. Opower, U. Schaefer, K. Wessel, T. Hall, “High power CO2 waveguide laser of the 1-kW category,” in CO2Lasers and Applications II, H. Opower, ed., Proc. SPIE1276, 18–23 (1990).
[CrossRef]

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, London, 1989), pp. 132–142.

See, for example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

A. Lapucci, S. Mascalchi, F. Rossetti, “Pulse behaviour of a compact R. F. discharge CO2 laser,” Opt. Laser Technol. (1996), to be published.

A. E. Siegman, Lasers (University Science Books, Mill Valley Calif., 1986), Chaps. 22 and 23.

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Figures (15)

Fig. 1
Fig. 1

Schematic view of the two hybrid resonators investigated: (a) positive-branch resonator, (b) negative-branch resonator.

Fig. 2
Fig. 2

Unstable-direction intensity profile on the output mirror of the positive-branch resonator, generated by numerical simulation.

Fig. 3
Fig. 3

Numerical x-direction profiles of the beam emerging from the positive-branch resonator for different mirror misalignments: a, 0 μrad; b, 10 μrad; c, 30 μrad; d, 40 μrad; e, 50 μrad; f, 60 μrad.

Fig. 4
Fig. 4

Positive-branch resonator losses obtained with the numerical simulations for four different cavity lengths: a, 334 mm; b, 340 mm; c, 350 mm; d, 353 mm. The solid curves correspond to total diffraction losses and the dashed curves to the outcoupling losses of the main aperture.

Fig. 5
Fig. 5

Positive-branch resonator power extraction for different mirror alignments and different cavity lengths.

Fig. 6
Fig. 6

Negative-branch resonator power extraction obtained as in Fig. 5.

Fig. 7
Fig. 7

Near-field burn pattern of the beam emerging from the positive-branch hybrid resonator.

Fig. 8
Fig. 8

Experimental x-direction near-field profiles of the positive-branch resonator beam detected with a scanning mirror. The cavity-mirror misalignment increases by ∼100 μrad from a to f.

Fig. 9
Fig. 9

Comparison of numerical and experimental far-field distributions of the beam emerging from the positive-branch resonator: a, numerical, 0-μrad misalignment; b, numerical, 60-μrad misalignment; c, experimental, aligned; d, experimental, misaligned (less than 100 μrad).

Fig. 10
Fig. 10

Comparison of numerical and experimental near-field distributions of the beam emerging from the negative-branch resonator: a, experimental; b, numerical.

Fig. 11
Fig. 11

Comparison of numerical and experimental far-field distributions of the beam emerging from the negative-branch resonator: a, experimental; b, numerical.

Fig. 12
Fig. 12

Comparison of the calculated and measured extracted power versus cavity length for the negative-branch resonator. The 0 length difference indicates a perfectly confocal resonator. Negative (positive) differences indicate a shorter (longer) cavity.

Fig. 13
Fig. 13

Optical output power versus average rf input power obtained in the same experimental conditions for the two resonators.

Fig. 14
Fig. 14

Typical measure of the propagation properties of the beam emerging from the positive-branch resonator. The vertical dashed line indicates the laser output plane, the arrowed line the position of the focusing lens.

Fig. 15
Fig. 15

Encircled energy versus a far-field half-angle calculated for the distributions shown in Figs. 9 and 11. In the inset a comparison between the calculated and the measured encircled energy is shown for the positive-branch resonator.

Tables (1)

Tables Icon

Table 1 Quality-Factor Mx 2 Values Calculated for the Negative- and Positive-Branch Resonator Beams by Using Various Integration Domains and Two Different Equivalent Gaussians a

Equations (6)

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

δ = 1 1 | M | .
E n m ( x , y ) = F n [ π ( n y ) 2 b ] u m ( x ) ,
u ( x , L ) = h ( x , L ) u ( x , 0 ) ,
h ( x , z ) = exp ( jkz ) ( j λ z ) 1 / 2 exp ( j k x 2 2 z )
N eq = M 1 2 M 2 N o ,
positive branch resonator : N o = 243 , N eq = 11 , negative branch resonator : N o = 196 , N eq = 167 .

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