Abstract

We implemented two different experimental setups to probe directly the nonlinear coupling between modes in microchip lasers. We show that, remarkably, the results can be interpreted by use of Lamb’s coupling constant. In an Er, Yb:glass microchip laser, we measured C12=0.80 between longitudinal modes and Cxy=0.95 between orthogonally linearly polarized eigenstates. The high values obtained give some physical insight into the single-frequency operation of such lasers.

© 2000 Optical Society of America

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  1. B. van der Pol, Proc. IRE 22, 1051 (1934).
    [CrossRef]
  2. W. E. Lamb, Phys. Rev. 134, A1429 (1964).
    [CrossRef]
  3. P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
    [CrossRef] [PubMed]
  4. S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, Opt. Lett. 20, 889 (1995).
    [CrossRef] [PubMed]
  5. T. L. Boyd, D. Klemer, P. A. Leilabady, J. Noriega, and M. Pessot, J. Lightwave Technol. 17, 1904 (1999).
    [CrossRef]
  6. M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
    [CrossRef]
  7. M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
    [CrossRef]
  8. G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
    [CrossRef]
  9. M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
    [CrossRef]

1999 (1)

1998 (1)

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

1997 (1)

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

1996 (1)

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

1995 (1)

1994 (1)

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

1993 (1)

1964 (1)

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

1934 (1)

B. van der Pol, Proc. IRE 22, 1051 (1934).
[CrossRef]

Alouini, M.

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

Boyd, T. L.

Bretenaker, F.

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

Brunel, M.

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

Cecchi, S.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

Chiaretti, G.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

Hyodo, M.

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

Klemer, D.

Lamb, W. E.

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

Laporta, P.

S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, Opt. Lett. 20, 889 (1995).
[CrossRef] [PubMed]

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
[CrossRef] [PubMed]

Le Floch, A.

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

Leilabady, P. A.

Longhi, S.

Matsuura, S.

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

Noriega, J.

Onodera, N.

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

Pessot, M.

Randone, G.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

Sacchi, G.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
[CrossRef] [PubMed]

Sakai, K.

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

Salina, F.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

Svelto, C.

Svelto, O.

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
[CrossRef] [PubMed]

Taccheo, S.

S. Taccheo, P. Laporta, S. Longhi, and C. Svelto, Opt. Lett. 20, 889 (1995).
[CrossRef] [PubMed]

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

P. Laporta, S. Taccheo, S. Longhi, O. Svelto, and G. Sacchi, Opt. Lett. 18, 1232 (1993).
[CrossRef] [PubMed]

Tani, M.

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

Vallet, M.

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

van der Pol, B.

B. van der Pol, Proc. IRE 22, 1051 (1934).
[CrossRef]

Appl. Phys. Lett. (1)

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, Appl. Phys. Lett. 70, 2070 (1997).
[CrossRef]

Electron. Lett. (1)

M. Hyodo, M. Tani, S. Matsuura, N. Onodera, and K. Sakai, Electron. Lett. 32, 1589 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

G. Sacchi, G. Chiaretti, S. Cecchi, G. Randone, P. Laporta, S. Taccheo, F. Salina, and O. Svelto, IEEE Photon. Technol. Lett. 6, 276 (1994).
[CrossRef]

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, IEEE Photon. Technol. Lett. 10, 1554 (1998).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (2)

Phys. Rev. (1)

W. E. Lamb, Phys. Rev. 134, A1429 (1964).
[CrossRef]

Proc. IRE (1)

B. van der Pol, Proc. IRE 22, 1051 (1934).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setups. (a) Dispersive feedback scheme: P, polarizer; FR, Faraday rotator (the slit is 10 µm wide); QWP, quarter-wave plate; G, grating (611 grooves/mm); M, plane mirror upon a piezoelectric transducer (PZT); L1, L2, lenses; D1 D2, Ge detectors. (b) Anisotropic feedback scheme: F, dichroic filter; HWP, half-wave plate; PBS, polarizing beam splitter; A, diaphragm; DF, density filter; M, plane mirror upon a piezoelectric transducer (PZT).

Fig. 2
Fig. 2

Experimental results for the dispersive feedback method of Fig. 1(a). (a) Microchip laser spectrum at T=15 C° monitored with an optical spectrum analyzer (resolution, 0.1 nm). Two longitudinal modes oscillate simultaneously. (b), (c) Intensity modulations observed when the loss modulation (equivalent to a 0.005% peak-to-peak variation of the reflection coefficient of the microchip laser output mirror) is applied to the mode shown by the curved arrow (leading to a 10% intensity modulation depth). The variations of I1 and I2 are reproduced on the same scale. (d) Microchip laser spectrum at T=70 C°. Only one longitudinal mode oscillates.

Fig. 3
Fig. 3

Experimental results for the anisotropic feedback method of Fig. 1(b). (a) Microchip laser spectrum monitored with a confocal Fabry–Perot analyzer (free spectral range, 7.5 GHz) at η=1.5. Both eigenstates oscillate simultaneously. (b), (c) Eigenstate modulations observed when the loss modulation (equivalent to a 0.001% peak-to-peak variation of the reflection coefficient of the microchip laser output mirror) is applied to the eigenstate shown by the curved arrow (leading to a 10% intensity modulation depth). The variations of Ix and Iy are represented on the same scale. (d) Microchip laser spectrum at η=1.3. Single-frequency operation is observed.

Equations (3)

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α1-β1I1-θ12I2=0,
α2-β2I2-θ21I1=0,
C12=θ12θ21β1β2.

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