Abstract

The standard equations of thin film optics are applied to multiplate resonant reflectors of the kind used with ruby lasers. The numerical results show considerable disagreement with predictions based on approximate theory. A design is proposed that gives high reflectivity and is insensitive to thickness errors.

© 1968 Optical Society of America

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References

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  1. W. R. Sooy, Appl. Phys. Lett. 7, 36 (1965).
    [CrossRef]
  2. P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
    [CrossRef]
  3. F. J. McClung, D. Weiner, IEEE J. Quantum Electron. QE-1, 94 (1965).
    [CrossRef]
  4. M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1965), p. 69.
  6. G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
    [CrossRef]
  7. F. Frank, H. Weber, Phys. Lett. 11, 34 (1964).
    [CrossRef]
  8. Y. Ohtsuka, Japan. J. Appl. Phys. 5, 74 (1966).
    [CrossRef]
  9. W. Weinstein, Vacuum 4, 3 (1954).
    [CrossRef]

1967 (1)

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[CrossRef]

1966 (1)

Y. Ohtsuka, Japan. J. Appl. Phys. 5, 74 (1966).
[CrossRef]

1965 (3)

W. R. Sooy, Appl. Phys. Lett. 7, 36 (1965).
[CrossRef]

F. J. McClung, D. Weiner, IEEE J. Quantum Electron. QE-1, 94 (1965).
[CrossRef]

M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
[CrossRef]

1964 (2)

P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
[CrossRef]

F. Frank, H. Weber, Phys. Lett. 11, 34 (1964).
[CrossRef]

1954 (1)

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1965), p. 69.

Frank, F.

F. Frank, H. Weber, Phys. Lett. 11, 34 (1964).
[CrossRef]

Hercher, M.

M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
[CrossRef]

Kafalas, P.

P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
[CrossRef]

Magyar, G.

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[CrossRef]

Masters, J. I.

P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
[CrossRef]

McClung, F. J.

F. J. McClung, D. Weiner, IEEE J. Quantum Electron. QE-1, 94 (1965).
[CrossRef]

Murray, E. M. E.

P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
[CrossRef]

Ohtsuka, Y.

Y. Ohtsuka, Japan. J. Appl. Phys. 5, 74 (1966).
[CrossRef]

Sooy, W. R.

W. R. Sooy, Appl. Phys. Lett. 7, 36 (1965).
[CrossRef]

Weber, H.

F. Frank, H. Weber, Phys. Lett. 11, 34 (1964).
[CrossRef]

Weiner, D.

F. J. McClung, D. Weiner, IEEE J. Quantum Electron. QE-1, 94 (1965).
[CrossRef]

Weinstein, W.

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1965), p. 69.

Appl. Phys. Lett. (2)

W. R. Sooy, Appl. Phys. Lett. 7, 36 (1965).
[CrossRef]

M. Hercher, Appl. Phys. Lett. 7, 39 (1965).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. J. McClung, D. Weiner, IEEE J. Quantum Electron. QE-1, 94 (1965).
[CrossRef]

J. Appl. Phys. (1)

P. Kafalas, J. I. Masters, E. M. E. Murray, J. Appl. Phys. 35, 2349 (1964).
[CrossRef]

Japan. J. Appl. Phys. (1)

Y. Ohtsuka, Japan. J. Appl. Phys. 5, 74 (1966).
[CrossRef]

Phys. Lett. (1)

F. Frank, H. Weber, Phys. Lett. 11, 34 (1964).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Magyar, Rev. Sci. Instrum. 38, 517 (1967).
[CrossRef]

Vacuum (1)

W. Weinstein, Vacuum 4, 3 (1954).
[CrossRef]

Other (1)

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1965), p. 69.

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Figures (6)

Fig. 1
Fig. 1

Plot of reflectance against wavelength for two 2-mm plates of Schott SF6 glass, separated by 25-mm of air. (Inset) Showing six pairs of surfaces interacting in this arrangement.

Fig. 2
Fig. 2

As in Fig. 1, but one plate increased by λ/8 in thickness.

Fig. 3
Fig. 3

Reflection characteristic for (x, 2x, 4x, 8x, 16x) system using fused silica plates, the thinnest being 2 mm thick.

Fig. 4
Fig. 4

Proposed design characteristic, glass is Schott BK7, three 2.5-mm thick plates. (Inset) Arrangement of the three plates.

Fig. 5
Fig. 5

As in Fig. 4, but one outer plate increased by λ/8 in thickness.

Fig. 6
Fig. 6

As in Fig. 4, but one air gap increased by λ/8 in thickness.

Equations (4)

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

R max = { [ 1 - ( 1 / n ) 2 N ] / [ 1 + ( 1 / n ) 2 N ] } 2 ,
E j + 1 = E j cos g j + ( i H j / n j ) sin g j ( g j = 2 π n j h j / λ ) , H j + 1 = i n j E j sin g j + H j cos g j ,
( E j + 1 H j + 1 ) = M j ( E j H j ) .
( cos g i , ( i / n i ) sin g i i n j sin g i , cos g i ) .

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