Abstract

The appropriate combination of spherical and cylindrical mirrors allows one to arrange an unstable laser cavity with asymmetrical magnification and to generate collimated output as well. By introducing two additional cylindrical mirrors into the cavity the aberration problems of tilted mirror systems are avoided. On the other hand, this modification is a low-cost alternative to cavities with diamond-turned mirrors with ellipsoidal surface curvature. In the geometrical-optics limit there exists a unique combination of mirror radii of curvature for a given ratio of magnification at fixed distances between the mirrors.

© 1981 Optical Society of America

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References

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  1. C. Cason, R. W. Jones, J. F. Perkins, “Unstable optical resonators with tilted spherical mirrors,” Opt. Lett. 2, 145 (1978).
    [CrossRef] [PubMed]
  2. W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2-laser system,” IEEE J. Quantum Electron. QE-5, 12 (1969).

1978 (1)

1969 (1)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2-laser system,” IEEE J. Quantum Electron. QE-5, 12 (1969).

Cason, C.

Jones, R. W.

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2-laser system,” IEEE J. Quantum Electron. QE-5, 12 (1969).

Perkins, J. F.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2-laser system,” IEEE J. Quantum Electron. QE-5, 12 (1969).

IEEE J. Quantum Electron. (1)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2-laser system,” IEEE J. Quantum Electron. QE-5, 12 (1969).

Opt. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1

Equivalent lens chain for one round trip in the resonator. Equivalent lenses S are positioned at relative distances a and b. Corresponding focus points are indicated by f.

Fig. 2
Fig. 2

Resonator scheme.

Fig. 3
Fig. 3

Reduced radii of curvature of the cylindrical mirrors versus reduced radius of curvature of the concave mirror. The parameter is the reduced radius of curvature of the coupling mirror.

Fig. 4
Fig. 4

Ratio of magnifications versus reduced radius of curvature of the concave mirror. Parameter as in Fig. 3.

Fig. 5
Fig. 5

Reduced fractional coupling versus reduced radius of curvature of the concave mirror. Parameter as in Fig. 3.

Fig. 6
Fig. 6

Total coupling versus reduced radius of curvature of the concave mirror. Parameter as in Fig. 3.

Fig. 7
Fig. 7

Ratio of fractional couplings versus reduced radius of curvature of the concave mirror for an arbitrary value R1/L = −2. Parameter as indicated in the text.

Equations (13)

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K = 1 1 m x m y
K x = ( 1 + m y ) ( m x 1 ) 2 m x m y ,
K y = ( 1 + m x ) ( m y 1 ) 2 m x m y ,
K = K x + K y .
f 3 = A x B x 2 B x f 2 x 2 = A y B y 2 B y f 2 y 2 ,
L = a x + b x = a y + b y ,
a x a y , b x b y ,
A x = b x f 2 x ,
A y = b y f 2 y ,
B x = b x f 1 + b x f 2 x a x b x + a x f 2 x f 1 f 2 x ,
B y = b y f 1 + b y f 2 y a y b y + a y f 2 y f 1 f 2 y .
m x = B x / f 1 A x ,
m y = B y / f 1 A y .

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