Abstract

We report a 1.055-µm microchip VECSEL array which uses a microlens-patterned diamond both as a heatspreader and as an array of concave output mirrors. This configuration, which is suitable for laser array operation, is here exploited to perform a systematic study of a set of microchip lasers with the same semiconductor structure but different cavity properties. The transverse mode selection of individual VECSELs is found to depend on the mode-matching conditions and on the microlens aperture size. Mode-matched single-device emission in the fundamental mode (M2~1.1) with pump-limited output power of 70 mW is demonstrated.

© 2007 Optical Society of America

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  1. J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
    [CrossRef]
  2. J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
    [CrossRef]
  3. S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
    [CrossRef]
  4. A.J. Kemp, A.J. Maclean, J.E. Hastie, S.A. Smith, J.M. Hopkins, S. Calvez, G.J. Valentine, M.D. Dawson, D. Burns, "Thermal lensing, thermal management and transverse mode control in microchip VECSELs," Appl. Phys. B-Laser O. 83 (2006) 189-194.
    [CrossRef]
  5. R.I. Aldaz, M.W. Wiemer, D.A.B. Miller, J.S. Harris, "Monolithically-integrated long vertical cavity surface emitting laser incorporating a concave micromirror on a glass substrate," Opt. Express 12 (2004) 3967-3971.
    [CrossRef] [PubMed]
  6. K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
    [CrossRef]
  7. A.M. Sarangan, G.M. Peake, "Enhancement of lateral mode discrimination in broad-area VCSELs using curved Bragg mirrors," J. Lightwave Technol. 22 (2004) 543-549.
    [CrossRef]
  8. G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
    [CrossRef]
  9. H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
    [CrossRef]
  10. K.F. Riley, S.J. Hobson, S.J. Bence, Mathematical methods for physics and engineering (Cambridge University Press, 2006).

2005 (2)

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

2004 (3)

2003 (2)

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

2002 (1)

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Abram, R.

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Aldaz, R.I.

Alford, W.J.

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Allerman, A.A.

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Burns, D.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

Calvez, S.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

Choi, H.W.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Dawson, M.D.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

Ferguson, A.I.

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Geib, K.M.

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

Girkin, J.M.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Griffin, C.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Gu, E.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Harris, J.S.

Hastie, J.E.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Hopkins, J.M.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

Hwangbo, C.K.

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Jeon, C.W.

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Jouhti, T.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

Jung, B.Y.

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Keeler, G.A.

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

Kim, K.S.

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Kontinnen, J.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

Lee, Y.H.

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Liu, C.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Mar, A.

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

Miller, D.A.B.

Peake, G.M.

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

A.M. Sarangan, G.M. Peake, "Enhancement of lateral mode discrimination in broad-area VCSELs using curved Bragg mirrors," J. Lightwave Technol. 22 (2004) 543-549.
[CrossRef]

Pessa, M.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

Raymond, T.D.

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

Riis, E.

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

Sarangan, A.M.

Serkland, D.K.

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

Smith, S.A.

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

Watson, I.M.

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Wiemer, M.W.

Electron. Lett. (2)

J.E. Hastie, J.M. Hopkins, C.W. Jeon, S. Calvez, D. Burns, M.D. Dawson, R. Abram, E. Riis, A.I. Ferguson, W.J. Alford, T.D. Raymond, A.A. Allerman, "Microchip vertical external cavity surface emitting lasers," Electron. Lett. 39 (2003) 1324-1326.
[CrossRef]

S.A. Smith, J.M. Hopkins, J.E. Hastie, D. Burns, S. Calvez, M.D. Dawson, T. Jouhti, J. Kontinnen, M. Pessa, "Diamond-microchip GaInNAs vertical external-cavity surface-emitting laser operating CW at 1315 nm," Electron. Lett. 40 (2004) 935-937.
[CrossRef]

IEEE Photonic. Technol. Lett. (2)

J.E. Hastie, J.M. Hopkins, S. Calvez, C.W. Jeon, D. Burns, R. Abram, E. Riis, A.I. Ferguson, M.D. Dawson, "0.5-W single transverse-mode operation of an 850-nm diode-pumped surface-emitting semiconductor laser," IEEE Photonic. Technol. Lett. 15 (2003) 894-896.
[CrossRef]

G.A. Keeler, D.K. Serkland, K.M. Geib, G.M. Peake, A. Mar, "Single transverse mode operation of electrically pumped vertical-external-cavity surface-emitting lasers with micromirrors," IEEE Photonic. Technol. Lett. 17 (2005) 522-524.
[CrossRef]

J. Lightwave Technol. (1)

J. Vac. Sci. Technol. B (1)

H.W. Choi, E. Gu, C. Liu, C. Griffin, J.M. Girkin, I.M. Watson, M.D. Dawson, "Fabrication of natural diamond microlenses by plasma etching," J. Vac. Sci. Technol. B 23 (2005) 130-132.
[CrossRef]

Jpn. J. Appl. Phys. (1)

K.S. Kim, Y.H. Lee, B.Y. Jung, C.K. Hwangbo, "Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector," Jpn. J. Appl. Phys. 241 (2002) L827-L829.
[CrossRef]

Opt. Express (1)

Other (2)

A.J. Kemp, A.J. Maclean, J.E. Hastie, S.A. Smith, J.M. Hopkins, S. Calvez, G.J. Valentine, M.D. Dawson, D. Burns, "Thermal lensing, thermal management and transverse mode control in microchip VECSELs," Appl. Phys. B-Laser O. 83 (2006) 189-194.
[CrossRef]

K.F. Riley, S.J. Hobson, S.J. Bence, Mathematical methods for physics and engineering (Cambridge University Press, 2006).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of an individual µ-VECSEL.

Fig. 2.
Fig. 2.

Picture of the µ-VECSEL array.

Fig. 3.
Fig. 3.

Left: Experimental set-up. Right: schematic of the single µ-VECSEL probing.

Fig. 4.
Fig. 4.

Plane-plane µ VECSEL (a): Output power transfer function (b): M2 measurements.

Fig. 5.
Fig. 5.

(a): Devices’ power transfer functions, (b): summary of M2values, (c): Examples of M2 measurements for the 90 µm device. Inset: beam image at full power, (d): Spectrum at full power of the 90-µm, 50-µm and 42-µm devices.

Fig. 6.
Fig. 6.

Fundamental mode (2ω0) and pump (2ωp) diameter evolution as a function of the lens diameter d (bottom axis) and of the radius of curvature R (top axis).

Fig. 7.
Fig. 7.

Aperture losses of a few Hermite-Gaussian modes reflecting on concave micro-mirrors.

Equations (2)

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ω 0 = [ t λ n π n R 1 ] 1 2
L = aperture [ H m ( 2 x ω ) ] 2 [ H n ( 2 y ω ) ] 2 exp ( 2 x 2 y 2 ω 2 ) dxdy + + [ H m ( 2 x ω ) ] 2 [ H n ( 2 y ω ) ] 2 exp ( 2 x 2 y 2 ω 2 ) dxdy

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