Abstract

Optical resonators using graded-phase mirrors are analyzed with the help of the generalized ABCD propagation law for a real optical beam. This analysis gives the second-order moment gross characteristics of the eigenmode and indicates a design procedure. An example of a super-Gaussian output beam shows that this type of optical resonator might have large transverse-mode discrimination that could provide operation in a large fundamental-mode beamwidth.

© 1991 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23.
  2. P. Lavigne, N. McCarthy, J.-G. Demers, Appl. Opt. 24, 2581 (1985).
    [CrossRef] [PubMed]
  3. G. Duplain, National Optics Institute, Quebec, Canada (personal communication).
  4. Yu. A. Anan’ev, Résonateurs optiques et problème de divergence du rayonnement laser (Editions Mir, Moscow, 1982).
  5. E. F. Ishchenko, E.F. Reshetin, Opt. Spectrosc. (USSR) 51, 581 (1981).
  6. P. A. Bélanger, Opt. Lett. 16, 196 (1991).
    [CrossRef] [PubMed]
  7. A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).
  8. A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” submitted to IEEE J. Quantum Electron.
  9. A. E. Siegman, P.-A. Bélanger, A. Hardy, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 465.
  10. C. Paré, P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” submitted to IEEE J. Quantum. Electron.

1991 (1)

1990 (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

1985 (1)

1981 (1)

E. F. Ishchenko, E.F. Reshetin, Opt. Spectrosc. (USSR) 51, 581 (1981).

Anan’ev, Yu. A.

Yu. A. Anan’ev, Résonateurs optiques et problème de divergence du rayonnement laser (Editions Mir, Moscow, 1982).

Bélanger, P. A.

P. A. Bélanger, Opt. Lett. 16, 196 (1991).
[CrossRef] [PubMed]

C. Paré, P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” submitted to IEEE J. Quantum. Electron.

Bélanger, P.-A.

A. E. Siegman, P.-A. Bélanger, A. Hardy, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 465.

Demers, J.-G.

Duplain, G.

G. Duplain, National Optics Institute, Quebec, Canada (personal communication).

Hardy, A.

A. E. Siegman, P.-A. Bélanger, A. Hardy, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 465.

Ishchenko, E. F.

E. F. Ishchenko, E.F. Reshetin, Opt. Spectrosc. (USSR) 51, 581 (1981).

Lavigne, P.

McCarthy, N.

Paré, C.

C. Paré, P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” submitted to IEEE J. Quantum. Electron.

Reshetin, E.F.

E. F. Ishchenko, E.F. Reshetin, Opt. Spectrosc. (USSR) 51, 581 (1981).

Siegman, A. E.

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” submitted to IEEE J. Quantum Electron.

A. E. Siegman, P.-A. Bélanger, A. Hardy, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 465.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23.

Appl. Opt. (1)

Opt. Lett. (1)

Opt. Spectrosc. (USSR) (1)

E. F. Ishchenko, E.F. Reshetin, Opt. Spectrosc. (USSR) 51, 581 (1981).

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

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

Other (6)

A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” submitted to IEEE J. Quantum Electron.

A. E. Siegman, P.-A. Bélanger, A. Hardy, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 465.

C. Paré, P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” submitted to IEEE J. Quantum. Electron.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 23.

G. Duplain, National Optics Institute, Quebec, Canada (personal communication).

Yu. A. Anan’ev, Résonateurs optiques et problème de divergence du rayonnement laser (Editions Mir, Moscow, 1982).

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of a symmetrical resonator with graded-phase mirrors (GPM’s). Φ0(x) describes the shape of the mirror.

Fig. 2
Fig. 2

Graded-phase-mirror resonator with finite apertures and a super-Gaussian output beam. The figure is approximately scaled and corresponds to N1 = 1.

Fig. 3
Fig. 3

Round-trip eigenvalues of the first two modes for the custom resonator of Fig. 2 (solid curves) and a semi-confocal resonator (dashed curves). The diffractional losses are given by 1 − |γ|2.

Tables (1)

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Table 1 Characteristics of a Super-Gaussian Beam

Equations (19)

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u ( x ) = ψ ( x ) exp [ i 2 π λ Φ ( x ) ] ,
W 2 = 4 + x 2 ψ 2 ( x ) d x ,
1 R = x ( d Φ d x ) ψ 2 ( x ) d x x 2 ψ 2 ( x ) d x .
1 Q = 1 R i λ M 2 π W 2 ,
Q 2 = A Q 1 + B C Q 1 + D ,
1 Q 0 = i λ M 2 π W 0 2 .
Q 1 = Q 0 + L 2 .
Φ 2 ( x ) = Φ 1 ( x ) 2 Φ 0 ( x ) ,
W 2 = W 1
1 R 2 = 1 R 1 2 x [ d Φ 0 ( x ) d x ] ψ 1 2 ( x ) d x x 2 ψ 1 2 ( x ) d x .
Q 3 = Q 2 + L 2 .
Q 3 = Q 0 .
1 R 2 = 1 R 1 .
W 1 4 1 R 1 ( 2 L 1 R 1 ) = ( λ π M 2 ) 2 .
G = 1 L R 1 ,
W 1 2 = ( M 2 λ L π ) 1 ( 1 G 2 ) 1 / 2 ,
W 0 2 = ( M 2 λ L 2 π ) ( 1 + G 1 G ) 1 / 2 .
x ( d Φ 1 d x ) ψ 1 2 ( x ) d x = x ( d Φ 0 d x ) ψ 1 2 ( x ) d x .
Φ 0 ( x ) = Φ 1 ( x ) Φ 1 ( 0 ) .

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