Abstract

A diffractive laser cavity mirror is described that can customize the amplitude and phase of a laser mode. The design of this diffractive element is shown for a square, flat-topped fundamental mode. The laser cavity has a theoretical fundamental mode loss of only 0.08% and a second-order mode loss of 48.2%, resulting in high modal discrimination. The fabricated mirror is tested in a Nd:YAG laser system. The resulting square flat-topped mode has an rms variation of 1.5% over the two-dimensional flat-topped region and a large discrimination against higher-order modes.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Kermene, A. Saviot, M. Vampuille, B. Colombeau, C. Froehly, T. Dohnalik, Opt. Lett. 17, 859 (1992).
    [CrossRef] [PubMed]
  2. J. R. Leger, in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 14.
  3. J. R. Leger, G. J. Swanson, U.S. patent5,033,060 (July16, 1991).
  4. J. R. Leger, X. Li, Bull. Am. Phys. Soc. 37, 1212 (1992).
  5. P. A. Bélanger, C. Paré, Opt. Lett. 16, 1057 (1991).
    [CrossRef] [PubMed]
  6. P. A. Bélanger, R. L. Lachance, C. Paré, Opt. Lett. 17, 739 (1992).
    [CrossRef] [PubMed]
  7. C. Paré, P.-A. Bélanger, IEEE J. Quantum Electron. 28, 355 (1992).
    [CrossRef]
  8. J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
    [CrossRef]
  9. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  10. J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

1992 (4)

1991 (1)

1988 (1)

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

1979 (1)

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

1961 (1)

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Auyeung, J.

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Bélanger, P. A.

Bélanger, P.-A.

C. Paré, P.-A. Bélanger, IEEE J. Quantum Electron. 28, 355 (1992).
[CrossRef]

Bundman, P.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

Colombeau, B.

Dohnalik, T.

Fekete, D.

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Froehly, C.

Griswold, M. P.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

Kermene, V.

Lachance, R. L.

Leger, J. R.

J. R. Leger, X. Li, Bull. Am. Phys. Soc. 37, 1212 (1992).

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

J. R. Leger, in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 14.

J. R. Leger, G. J. Swanson, U.S. patent5,033,060 (July16, 1991).

Li, T.

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Li, X.

J. R. Leger, X. Li, Bull. Am. Phys. Soc. 37, 1212 (1992).

Paré, C.

Pepper, D. M.

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Saviot, A.

Scott, M. L.

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

Swanson, G. J.

J. R. Leger, G. J. Swanson, U.S. patent5,033,060 (July16, 1991).

Vampuille, M.

Yariv, A.

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Bell Syst. Tech. J. (1)

A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).

Bull. Am. Phys. Soc. (1)

J. R. Leger, X. Li, Bull. Am. Phys. Soc. 37, 1212 (1992).

IEEE J. Quantum Electron. (2)

C. Paré, P.-A. Bélanger, IEEE J. Quantum Electron. 28, 355 (1992).
[CrossRef]

J. Auyeung, D. Fekete, A. Yariv, D. M. Pepper, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Opt. Lett. (3)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. R. Leger, M. L. Scott, P. Bundman, M. P. Griswold, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 82 (1988).

Other (2)

J. R. Leger, in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 14.

J. R. Leger, G. J. Swanson, U.S. patent5,033,060 (July16, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Phase profile of the mode-selecting mirror with a 16-level phase quantization.

Fig. 2
Fig. 2

Required second-order mode gain to overcome cavity losses as a function of cavity length and mode-selecting mirror size. The insets are modal shapes for mirror sizes 8, 12, and 16 mm at a cavity length of one Rayleigh range.

Fig. 3
Fig. 3

Theoretical fundamental mode shape from the mode-selecting mirror cavity. The effects of phase quantization, finite lithographic linewidths, and mirror apertures are included in the calculation.

Fig. 4
Fig. 4

Effect of output mirror size on the fundamental and the second-order mode loss.

Fig. 5
Fig. 5

Measured fundamental mode profile of the Nd:YAG laser: (a) three-dimensional contour plot, (b) profile slice.

Equations (7)

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

a ( x , y ) = A ( u , υ ) exp [ j 2 π ( xu + y υ ) ] d u d υ ,
b ( x , y ) = A ( u , υ ) exp [ j 2 π ( xu + y υ ) ] × exp { jkl [ 1 ( λ u ) 2 ( λ υ ) 2 ] 1 / 2 } d u d υ .
t 2 ( x , y ) = b * ( x , y ) b ( x , y ) ,
b ( x , y ) t 2 ( x , y ) = b * ( x , y ) = A * ( u , υ ) exp [ j 2 π ( xu + y υ ) ] × exp { jkl [ 1 ( λ u ) 2 ( λ υ ) 2 ] 1 / 2 } d u d υ .
A * ( u , υ ) exp [ j 2 π ( xu + y υ ) ] d u d υ = a * ( x , y ) .
t 1 ( x , y ) = a ( x , y ) a * ( x , y ) ,
a ( x , y ) = exp [ ( x ω 0 ) 20 ] exp [ ( y ω 0 ) 20 ] ,

Metrics