Abstract

In this paper we experimentally demonstrate the intracavity generation of selected Laguerre–Gaussian modes of variable radial order, from 0 to 5. Our technique requires only an amplitude mask made up of absorbing rings to be placed inside the cavity, with the ring radii selected to coincide with the zeros of the desired Laguerre–Gaussian mode. We demonstrate high mode purity and a mode volume proportional to the order of the mode. Our results suggest a possible route to high brightness diode-pumped solid-state laser sources.

© 2013 Optical Society of America

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    [CrossRef]
  7. S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
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    [CrossRef]
  16. A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
    [CrossRef]
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    [CrossRef]
  20. D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
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    [CrossRef]
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    [CrossRef]
  26. A. Hasnaoui, T. Godin, E. Cagniot, M. Fromager, A. Forbes, and K. Aït-Ameur, “Selection of a LGp0–shaped fundamental mode in a laser cavity: phase versus amplitude masks,” Opt. Commun. 285, 5268–5275 (2012).
    [CrossRef]
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    [CrossRef]
  28. D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
    [CrossRef]
  29. A. Hasnaoui and K. Aït-Ameur, “Properties of a laser cavity containing an absorbing ring,” Appl. Opt. 49, 4034–4043 (2010).
    [CrossRef]
  30. A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
    [CrossRef]
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    [CrossRef]
  33. F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, 2000).
  34. F. M. Dickey and S. C. Holswade, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).
  35. R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
    [CrossRef]

2012 (4)

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

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

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparre, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2481 (2012).
[CrossRef]

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

2011 (2)

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (1)

2007 (2)

2005 (1)

2003 (2)

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef]

2001 (1)

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72, 167–170 (2001).
[CrossRef]

2000 (1)

1999 (1)

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

1998 (1)

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (1)

F. T. Arecchi, “Optical morphogenesis: pattern formation and competition in nonlinear optics,” Physica D 86, 297–322 (1995).
[CrossRef]

1994 (1)

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72, 2379–2382 (1994).
[CrossRef]

1992 (4)

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, A. V. Larichev, and N. I. Zheleznykh, “Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures,” J. Opt. Soc. Am. B 9, 78–90 (1992).
[CrossRef]

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

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

1991 (1)

1988 (1)

T. Y. Fan and R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

1974 (1)

Abramski, K. M.

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Aït-Ameur, K.

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

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

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

Akhmanov, S. A.

Allen, L.

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

Arecchi, F. T.

F. T. Arecchi, “Optical morphogenesis: pattern formation and competition in nonlinear optics,” Physica D 86, 297–322 (1995).
[CrossRef]

Arrizon, V.

Baker, H. J.

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Beijersbergen, M. W.

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

Bélanger, P. A.

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

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

Bisson, J. F.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

Brunel, M.

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

Bryngdahl, O.

Burger, L.

Byer, R. L.

T. Y. Fan and R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

R. L. Byer, “Diode pumped solid state lasers,” in Conference on Lasers and Electro-Optics/Pacific Rim 2009 (OSA, 2009), paper MD1_1.

Cagniot, E.

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

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

Carrada, R.

Chen, Y. F.

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72, 167–170 (2001).
[CrossRef]

Colley, A. D.

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Danziger, Y.

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Davidson, N.

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Very high-order pure Laguerre-Gaussian mode selection in a passive Q-switched Nd:YAG laser,” Opt. Express 13, 4952–4962 (2005).
[CrossRef]

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Deng, H.

Deng, Q.

Deppe, D. G.

Dickey, F. M.

F. M. Dickey and S. C. Holswade, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).

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

Duparre, M.

Fan, T. Y.

T. Y. Fan and R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

Flamm, D.

Forbes, A.

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

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparre, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2481 (2012).
[CrossRef]

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

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

L. Burger and A. Forbes, “Kaleidoscope modes in large aperture Porro prism resonators,” Opt. Express 16, 12707–12714 (2008).
[CrossRef]

I. A. Litvin, L. Burger, and A. Forbes, “Petal-like modes in Porro prism resonators,” Opt. Express 15, 14065–14077 (2007).
[CrossRef]

Friesem, A. A.

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Very high-order pure Laguerre-Gaussian mode selection in a passive Q-switched Nd:YAG laser,” Opt. Express 13, 4952–4962 (2005).
[CrossRef]

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Fromager, M.

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

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

Godin, T.

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

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

Gonzalez, L. A.

Grynberg, G.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72, 2379–2382 (1994).
[CrossRef]

Hall, D. R.

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

Hasman, E.

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Hasnaoui, A.

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

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

Hodgson, N.

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd ed. (Springer, 2005).

Holswade, S. C.

F. M. Dickey and S. C. Holswade, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996).

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

Ishaaya, A. A.

Ito, A.

Ivanov, V. Yu.

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer, 1999).

Kozawa, Y.

Lan, Y. P.

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72, 167–170 (2001).
[CrossRef]

Larichev, A. V.

Li, J.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

Litvin, I. A.

Machavariani, G.

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

A. A. Ishaaya, G. Machavariani, N. Davidson, and A. A. Friesem, “Conversion of a high-order mode beam into a nearly Gaussian beam by use of a single interferometric element,” Opt. Lett. 28, 504–506 (2003).
[CrossRef]

Maître, A.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72, 2379–2382 (1994).
[CrossRef]

Nadioo, D.

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

Naidoo, D.

D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparre, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2481 (2012).
[CrossRef]

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, and E. Hasman, “Continuous-phase elements can improve laser beam quality,” Opt. Lett. 25, 939–941 (2000).
[CrossRef]

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

Paré, C.

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

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

Passilly, N.

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

E. Cagniot, M. Fromager, T. Godin, N. Passilly, M. Brunel, and K. Aït-Ameur, “Variant of the method of Fox and Li dedicated to intracavity laser beam shaping,” J. Opt. Soc. Am. A 28, 489–495 (2011).
[CrossRef]

Pereira, S. F.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

Petrossian, A.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72, 2379–2382 (1994).
[CrossRef]

Ruiz, U.

Sato, S.

Schulze, C.

Senatsky, Y.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

Shirakawa, A.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science Books, 1986).

Spreeuw, R. J. C.

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

Thirugnansambandam, M.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

van Exter, M. P.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

Vorontsov, M. A.

Wang, S. C.

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72, 167–170 (2001).
[CrossRef]

Weber, H.

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd ed. (Springer, 2005).

Willemsen, M. B.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

Woerdman, J. P.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

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

Zheleznykh, N. I.

Appl. Opt. (1)

Appl. Phys. B (2)

D. Nadioo, K. Aït-Ameur, M. Brunel, and A. Forbes, “Intracavity generation of superpositions of Laguerre-Gaussian beams,” Appl. Phys. B 106, 683–690 (2012).
[CrossRef]

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72, 167–170 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Discontinuous phase elements for transverse mode selection in laser resonators,” Appl. Phys. Lett. 74, 1373–1375 (1999).
[CrossRef]

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73, 2239–2241 (1998).
[CrossRef]

K. M. Abramski, H. J. Baker, A. D. Colley, and D. R. Hall, “Single-mode selection using coherent imaging within a slab waveguide CO2 laser,” Appl. Phys. Lett. 60, 2469–2471 (1992).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. Paré and P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

T. Y. Fan and R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

A. A. Ishaaya, N. Davidson, G. Machavariani, E. Hasman, and A. A. Friesem, “Efficient selection of high-order Laguerre-Gaussian modes in a Q-switched Nd:YAG laser,” IEEE J. Quantum Electron. 39, 74–82 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

D. Naidoo, T. Godin, M. Fromager, E. Cagniot, N. Passilly, A. Forbes, and K. Aït-Ameur, “Transverse mode selection in a monolithic microchip laser,” Opt. Commun. 284, 5475–5479 (2011).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (6)

Opt. Rev. (1)

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, and M. Thirugnansambandam, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19, 201–221 (2012).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (1)

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72, 2379–2382 (1994).
[CrossRef]

Physica D (1)

F. T. Arecchi, “Optical morphogenesis: pattern formation and competition in nonlinear optics,” Physica D 86, 297–322 (1995).
[CrossRef]

Other (5)

R. L. Byer, “Diode pumped solid state lasers,” in Conference on Lasers and Electro-Optics/Pacific Rim 2009 (OSA, 2009), paper MD1_1.

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer, 1999).

N. Hodgson and H. Weber, Laser Resonators and Beam Propagation, 2nd ed. (Springer, 2005).

A. Siegman, Lasers (University Science Books, 1986).

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

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Figures (10)

Fig. 1.
Fig. 1.

Diode-pumped Nd:YAG laser resonator with internal mask (DOE). Resonator mirrors were configured such that the output beam could be observed from both ends with various beam diagnostic tools. Inset shows the actual setup in the laboratory.

Fig. 2.
Fig. 2.

Numerically simulated lowest-loss eigenmodes, shown as intensity cross-sections, for p = 1 –5, when the appropriate mask with p rings is placed inside the cavity. Such a mask example is shown for the p = 4 , with the high-loss rings of the mask coinciding with the intensity nulls of the p = 4 Laguerre–Gaussian mode.

Fig. 3.
Fig. 3.

Variations of the fundamental mode losses as a function of p the number of absorbing rings which is at the same time the order of the LG mode.

Fig. 4.
Fig. 4.

Near-field (left column) and far-field (right column) intensity patterns for modes p = 0 –5 (top to bottom rows).

Fig. 5.
Fig. 5.

(a) Beam width at the output coupler end as a function of mode order. (b) Beam propagation factor as a function of mode order. Solid line in both cases is the theoretical prediction from Eqs. (3) and (4), respectively.

Fig. 6.
Fig. 6.

Modal decomposition results for modes p = 1 –5. Correlation between the desired mode ( p laser ) and the measured mode ( p decomposition ) is very high, degrading slightly at high values of p .

Fig. 7.
Fig. 7.

(a) Change in beam radius as a function of a changing pump power, for the p = 0 mode, measured at both ends of the cavity. (b) Change in beam radius as a function of a changing pump power, for the p = 5 mode, measured at flat mirror.

Fig. 8.
Fig. 8.

(a) Beam radius and (b) beam quality factor changes for mode p = 1 when the ring thickness of the DOE is changed.

Fig. 9.
Fig. 9.

(a) Threshold and (b) slope efficiency as a function of the mode order p . Both increase approximately linearly with mode index.

Fig. 10.
Fig. 10.

Above a certain critical pump power, the higher-order mode extracts more power (compared to the p = 0 mode) due to its significantly increased mode volume, as shown here for the p = 5 mode.

Tables (2)

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Table 1. Laguerre Polynomials

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Table 2. Roots of Laguerre Polynomials

Equations (7)

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

B = π 2 P λ 2 M 4 .
u p , l = 2 p ! π ( p + | l | ) ! 1 w ( z ) ( 2 r w ( z ) ) | l | L p | l | ( 2 r 2 w ( z ) 2 ) × exp ( r 2 w ( z ) 2 i k r 2 2 R ( z ) ) exp ( i ( 2 p + | l | + 1 ) arctan ( z z R ) ) exp ( i l ϕ ) ,
W p ( z ) = w ( z ) 2 p + 1 .
M p 2 = 2 p + 1 .
θ p = θ 0 2 p + 1 .
V p = 0 l 0 π W 2 ( z ) d z = ( 2 p + 1 ) π w 0 2 l 0 ( 1 + l 0 2 3 z r 2 ) = M 2 V 0 ( 1 + l 0 2 3 z r 2 ) ,
P p P 0 = ( 2 p + 1 ) δ 0 δ p ,

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