Abstract

The concept of a phase-conjugate etalon mirror consisting of one flat and one aspheric surface is introduced. This new element can be used as an end mirror of a conventional resonator to promote spatial-mode selection and mode shaping. A phase-conjugate etalon designed for the fundamental Gaussian mode is experimentally implemented and tested with a single-mode He-Ne laser.

© 2004 Optical Society of America

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References

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  1. M. A. Rob, J. R. Izatt, “Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO2 laser,” IEEE J. Quantum Electron. 28, 56–59 (1992).
    [CrossRef]
  2. N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
    [CrossRef]
  3. G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
    [CrossRef]
  4. D. A. King, R. J. Pittaro, “Simple diode pumping of a power-buildup cavity,” Opt. Lett. 23, 774–776 (1998).
    [CrossRef]
  5. P. A. Belanger, C. Pare, “Optical resonators using graded-phase mirrors,” Opt. Lett. 16, 1057–1059 (1991).
    [CrossRef] [PubMed]
  6. J. R. Leger, D. Chen, G. Mowry, “Design and performance of diffractive optics for custom laser resonators,” Appl. Opt. 34, 2498–2509 (1995).
    [CrossRef] [PubMed]
  7. U. D. Zeitner, F. Wyrowski, “Design of unstable laser resonators with user-defined mode shape,” IEEE J. Quantum Electron. 37, 1594–1599 (2001).
    [CrossRef]
  8. W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

2001 (1)

U. D. Zeitner, F. Wyrowski, “Design of unstable laser resonators with user-defined mode shape,” IEEE J. Quantum Electron. 37, 1594–1599 (2001).
[CrossRef]

1999 (1)

G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
[CrossRef]

1998 (1)

1995 (1)

1992 (1)

M. A. Rob, J. R. Izatt, “Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO2 laser,” IEEE J. Quantum Electron. 28, 56–59 (1992).
[CrossRef]

1991 (1)

1985 (1)

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Anthony, P. J.

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Belanger, P. A.

Chen, D.

Chen, G.

G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
[CrossRef]

Dutta, N. K.

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Flannery, B. P.

W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Gopinath, A.

G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
[CrossRef]

Gordon, E. I.

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Izatt, J. R.

M. A. Rob, J. R. Izatt, “Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO2 laser,” IEEE J. Quantum Electron. 28, 56–59 (1992).
[CrossRef]

King, D. A.

Leger, J. R.

G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
[CrossRef]

J. R. Leger, D. Chen, G. Mowry, “Design and performance of diffractive optics for custom laser resonators,” Appl. Opt. 34, 2498–2509 (1995).
[CrossRef] [PubMed]

Mowry, G.

Pare, C.

Pittaro, R. J.

Press, W. H.

W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Rob, M. A.

M. A. Rob, J. R. Izatt, “Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO2 laser,” IEEE J. Quantum Electron. 28, 56–59 (1992).
[CrossRef]

Shen, T.

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Teukolsky, S. A.

W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Vetterling, W. T.

W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

Wyrowski, F.

U. D. Zeitner, F. Wyrowski, “Design of unstable laser resonators with user-defined mode shape,” IEEE J. Quantum Electron. 37, 1594–1599 (2001).
[CrossRef]

Zeitner, U. D.

U. D. Zeitner, F. Wyrowski, “Design of unstable laser resonators with user-defined mode shape,” IEEE J. Quantum Electron. 37, 1594–1599 (2001).
[CrossRef]

Zydzik, G.

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Chen, J. R. Leger, A. Gopinath, “Angular filtering of spatial modes in a vertical-cavity surface-emitting laser by a Fabry-Perot etalon,” Appl. Phys. Lett. 74, 1069–1071 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

U. D. Zeitner, F. Wyrowski, “Design of unstable laser resonators with user-defined mode shape,” IEEE J. Quantum Electron. 37, 1594–1599 (2001).
[CrossRef]

M. A. Rob, J. R. Izatt, “Intermodal tuning behavior of an etalon-tuned three-mirror TEA CO2 laser,” IEEE J. Quantum Electron. 28, 56–59 (1992).
[CrossRef]

N. K. Dutta, E. I. Gordon, T. Shen, P. J. Anthony, G. Zydzik, “Single-longitudinal mode operation of semiconductor laser using a metal film reflection filter,” IEEE J. Quantum Electron. 21, 559–562 (1985).
[CrossRef]

Opt. Lett. (2)

Other (1)

W. H. Press, W. T. Vetterling, B. P. Flannery, S. A. Teukolsky, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1992).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the phase-conjugate etalon.

Fig. 2
Fig. 2

Experimental setup for testing the phase-conjugate reflection.

Fig. 3
Fig. 3

Simulated phase profile of mirror 2.

Fig. 4
Fig. 4

Irradiance of different beams measured at 60 cm in front of mirror MC: (a) incident Gaussian beam measured at the first etalon mirror (MC), equivalent to the measurement at 60 cm in front of MC; (b) the beam reflected from the phase-conjugate etalon measured at 60 cm in front of MC; (c) the beam reflected from the flat MC alone; (d) the beam reflected from the aspheric mirror alone (MC was removed in this case).

Fig. 5
Fig. 5

Beam divergence measurement of the reflected beam from the phase-conjugate etalon.

Equations (7)

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E2=E1×RC1+O2E1×TC×TC+O2(O2E1×TC×RC2)×TC+,
PEexp-E/kT,
E=C=aϕerr+bAerr+cD,
ϕerr=MC |ϕE1x, y-ϕE2x, y|IE1normx, ydxdy,
Aerr=MC |AE1normx, y-AE2normx, y|dxdy,
D=MCIE1x, y-IE2x, ydxdy,
ω2=ω02+M2z2ω0/ZR2,

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