Abstract

A five-mirror cavity suitable for passively mode-locked dye lasers is analyzed and also modeled on the computer. Simple approaches for constructing a compensated cavity are shown. Experiments are performed confirming the theoretical results.

© 1981 Optical Society of America

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References

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  1. H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
    [Crossref]
  2. Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
    [Crossref]
  3. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [Crossref] [PubMed]
  4. G. H. C. New, IEEE J. Quantum Electron. QE-10, 115 (1974).
    [Crossref]
  5. E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
    [Crossref]

1977 (1)

Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
[Crossref]

1975 (1)

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[Crossref]

1974 (1)

G. H. C. New, IEEE J. Quantum Electron. QE-10, 115 (1974).
[Crossref]

1972 (1)

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

1966 (1)

Dienes, A.

Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
[Crossref]

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

Ippen, E. P.

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[Crossref]

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

Kogelnik, H.

Kogelnik, H. W.

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

Li, T.

New, G. H. C.

G. H. C. New, IEEE J. Quantum Electron. QE-10, 115 (1974).
[Crossref]

Shank, C. V.

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[Crossref]

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

Whinnery, J. R.

Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
[Crossref]

Yasa, Z. A.

Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Z. A. Yasa, A. Dienes, J. R. Whinnery, Appl. Phys. Lett. 30, 24 (1977).
[Crossref]

E. P. Ippen, C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).
[Crossref]

IEEE J. Quantum Electron. (2)

H. W. Kogelnik, E. P. Ippen, A. Dienes, C. V. Shank, IEEE J. Quantum Electron. QE-8, 373 (1972).
[Crossref]

G. H. C. New, IEEE J. Quantum Electron. QE-10, 115 (1974).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Folded three-mirror cavity with internal Brewster-angle cell. Portion enclosed by dashed lines is the basic building block.

Fig. 2
Fig. 2

Examples constructed by the building units of Fig. 1. Dotted straight lines are unit boundaries.

Fig. 3
Fig. 3

Equivalent empty resonator with internal lens of a five-mirror cavity: (a) 2M group; (b) 3M group.

Fig. 4
Fig. 4

Stability plot by approximate analytical solution. Parameters used are: l1 = 7.5 cm; l = 60 cm; l2 = 10 cm; l3 = 60 cm; R1 = 5 cm; R2 = 5 cm; R3 = 10 cm; R4 = 10 cm; and the thicknesses of the dye streams are 125 μm.

Fig. 5
Fig. 5

Stability region of an uncompensated laser cavity from numerical calculation. Solid and broken lines indicate the sagittal and tangential planes, respectively. Intersection is the stable region. Parameters used are the same as in Fig. 4, but in addition the folding angles are 13°.

Fig. 6
Fig. 6

Stability region of a compensated laser cavity. Parameters used are the same as Fig. 5, except dye stream thicknesses are 1.5 and 3 mm.

Fig. 7
Fig. 7

Beam shapes in various regions of stability.

Fig. 8
Fig. 8

Stability regions found by experiment.

Equations (24)

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f = R 3 cos θ / 2 ,
f = R 3 / 2 cos θ ,
d = d 1 - d 2 f d 2 - f ;
R 1 = R 1 ;
R 2 = R 2 f 2 ( d 2 - f ) ( d 2 - R 2 - f ) .
d 1 = R 1 + f + δ ,
d 1 = l 1 f 2 R 1 + δ 2 M ( R 1 + f 2 ) f 2 R 1 = C 1 ,
R 1 = R 1 f 2 2 ( R 1 + δ 2 M ) δ 2 M f 2 2 δ 2 M = C 2 δ 2 M ,
l 1 = R 1 + f 2 + δ 2 M ,
l 2 = f 3 + f 4 + δ 3 M ,
d 2 f 3 2 δ 3 M = C 3 δ 3 M ,
R 2 - f 3 2 f 4 2 l 3 δ 3 M 1 ( δ 3 M + f 4 2 / l 3 ) = C 4 δ 3 M ( δ 3 M + C 5 ) .
0 ( α 1 + β 1 δ 2 M + γ 1 δ 2 M δ 3 M ) ( α 2 + β 2 δ 3 M + γ 2 δ 3 M 2 ) 1 ,
α 1 = 1 ,
α 2 = 1 - C 3 C 5 / C 4 ,
β 1 = - ( l - C 1 ) / C 2 ,
β 2 = [ C 5 ( l - C 1 ) - C 3 ] / C 4 ,
γ 1 = C 3 / C 2 ,
γ 2 = ( l - C 1 ) / C 4 ,
1 q = D - A 2 B + i 1 - ( D + A 2 ) 2 B = 1 R - i λ π ω 2 .
M 0 = M 1 M 2 , , M 11 M 12 M 11 , , M 2 M 1 = ( A 0 B 0 C 0 D 0 ) .
1 - ( D 0 + A 0 2 ) 2 > 0 ,
A 0 = D 0 < 1.
ω = ( λ π ) 1 / 2 B 0 1 / 2 ( 1 - A 0 2 ) 1 / 4 .

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