Abstract

Equations are given for reflectance, bandwidth and root gain-bandwidth of an active interference filter having unequal mirror reflectances and operating in the reflecting mode. Gain for various configurations is compared keeping the product of the mirror reflectances constant. It is shown that the reflectance gain of an asymmetric configuration can be greater than the transmittance gain while the bandwidths are identical. Specific examples are treated to show how device gain depends on single-pass gain and input and output mirror reflectances.

© 1966 Optical Society of America

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References

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  1. V. V. Lebedeva, I. V. Lebedev, Opt. Spectry. 15, 221 (1963).
  2. H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
    [Crossref]
  3. K. Tomiyasu, Proc. IEEE 52, 856 (1964).
    [Crossref]
  4. V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
    [Crossref]
  5. V. N. Smiley, Proc. IEEE 51, 120 (1963).
    [Crossref]
  6. J. A. Fleck, J. Appl. Phys. 34, 2997 (1963).
    [Crossref]
  7. V. N. Smiley, A. L. Lewis, D. K. Forbes, J. Opt. Soc. Am. 55, 1552 (1965).
    [Crossref]
  8. A. D. Jacobson, T. R. O’Meara, Proc. IEEE 53, 529 (1965).
    [Crossref]

1965 (3)

V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
[Crossref]

V. N. Smiley, A. L. Lewis, D. K. Forbes, J. Opt. Soc. Am. 55, 1552 (1965).
[Crossref]

A. D. Jacobson, T. R. O’Meara, Proc. IEEE 53, 529 (1965).
[Crossref]

1964 (1)

K. Tomiyasu, Proc. IEEE 52, 856 (1964).
[Crossref]

1963 (4)

V. N. Smiley, Proc. IEEE 51, 120 (1963).
[Crossref]

J. A. Fleck, J. Appl. Phys. 34, 2997 (1963).
[Crossref]

V. V. Lebedeva, I. V. Lebedev, Opt. Spectry. 15, 221 (1963).

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

Brand, F. A.

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

Fleck, J. A.

J. A. Fleck, J. Appl. Phys. 34, 2997 (1963).
[Crossref]

Forbes, D. K.

V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
[Crossref]

V. N. Smiley, A. L. Lewis, D. K. Forbes, J. Opt. Soc. Am. 55, 1552 (1965).
[Crossref]

Hatkin, L.

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

Holmes, D. A.

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

Jacobs, H.

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

Jacobson, A. D.

A. D. Jacobson, T. R. O’Meara, Proc. IEEE 53, 529 (1965).
[Crossref]

Lebedev, I. V.

V. V. Lebedeva, I. V. Lebedev, Opt. Spectry. 15, 221 (1963).

Lebedeva, V. V.

V. V. Lebedeva, I. V. Lebedev, Opt. Spectry. 15, 221 (1963).

Lewis, A. L.

V. N. Smiley, A. L. Lewis, D. K. Forbes, J. Opt. Soc. Am. 55, 1552 (1965).
[Crossref]

V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
[Crossref]

O’Meara, T. R.

A. D. Jacobson, T. R. O’Meara, Proc. IEEE 53, 529 (1965).
[Crossref]

Smiley, V. N.

V. N. Smiley, A. L. Lewis, D. K. Forbes, J. Opt. Soc. Am. 55, 1552 (1965).
[Crossref]

V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
[Crossref]

V. N. Smiley, Proc. IEEE 51, 120 (1963).
[Crossref]

Tomiyasu, K.

K. Tomiyasu, Proc. IEEE 52, 856 (1964).
[Crossref]

Appl. Phys. Letters (1)

V. N. Smiley, D. K. Forbes, A. L. Lewis, Appl. Phys. Letters 7, 1 (1965).
[Crossref]

J. Appl. Phys. (2)

H. Jacobs, D. A. Holmes, L. Hatkin, F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
[Crossref]

J. A. Fleck, J. Appl. Phys. 34, 2997 (1963).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Spectry. (1)

V. V. Lebedeva, I. V. Lebedev, Opt. Spectry. 15, 221 (1963).

Proc. IEEE (3)

A. D. Jacobson, T. R. O’Meara, Proc. IEEE 53, 529 (1965).
[Crossref]

K. Tomiyasu, Proc. IEEE 52, 856 (1964).
[Crossref]

V. N. Smiley, Proc. IEEE 51, 120 (1963).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

A general active interference filter consisting of two parallel planar mirrors, M2 and M1, intracavity active material of length d and index of refraction n1, and intracavity inactive material of length l and index n2 Input, reflected, and transmitted signals are represented, respectively, by Iin, IR, and IT.

Fig. 2
Fig. 2

Qualitative plots of reflectance vs frequency illustrating the evolution of reflected signal as single-pass gain is varied for R2 = R1, R2 < R1, and R2 >R1.

Fig. 3
Fig. 3

Semilog plot of reflectance and transmittance vs single-pass gain for asymmetric and symmetric configurations keeping the feedback factor fixed at 0.85: —, reflectance; —, transmittance. I: R2 = 0.9000, R1 = 0.8027; II: R2 = 0.8027, R1 = 0.9000; III: R2 = R1 = 0.8500; IV: R2 = 0.7225, R1 = 1.0000.

Fig. 4
Fig. 4

Linear plot of reflectance and transmittance vs single-pass gain for the same examples given in Fig. 3.

Fig. 5
Fig. 5

Ratio of root gain-bandwidth for reflectance minus one to that for transmittance keeping R0 = 0.85 is a function of single-pass gain for three configurations given in Fig. 3.

Equations (11)

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R = [ R 2 1 2 - R 1 1 2 e K d ] 2 + 4 R 0 e K d sin 2 β / 2 [ 1 - R 0 e K d ] 2 + 4 R 0 e K d sin 2 β / 2
R max = [ ( R 2 1 2 - R 1 1 2 e K d ) / ( 1 - R 0 e K d ) ] 2 .
R - 1 = ( 1 - R 2 ) ( R 1 G 2 - 1 ) [ 1 - R 0 G ] 2 + 4 R 0 G sin 2 β / 2 ,
( R - 1 ) max = ( 1 - R 2 ) ( R 1 G 2 - 1 ) / [ 1 - R 0 G ] 2 .
T max = ( 1 - R 2 ) ( 1 - R 1 ) G / [ 1 - R 0 G ] 2 .
1 2 β = ± [ ( 2 π γ 0 / c ) ( n 1 d + n 2 l ) - ( 2 π / c ) ( 1 2 δ γ ) ( n 1 d + n 2 l ) ] = ± ( 2 π / c ) ( n 1 d + n 2 l ) ( γ 0 - 1 2 δ γ ) = ± N π ( π δ γ ) ( n 1 d + n 2 l ) ,
δ γ = c π ( n 1 d + n 2 l ) sin - 1 [ 1 - R 0 G 2 ( R 0 G ) 1 2 ] .
δ γ c [ 1 - R 0 G ] 2 π ( n 1 d + n 2 l ) ( R 0 G ) 1 2 [ 1 + ( 1 - R 0 G ) 2 6 R 0 G ] .
δ γ c ( 1 - R 0 G ) / 2 π n 1 d ( R 0 G ) 1 2 ,
R G B ( R - 1 ) = ( R - 1 ) max 1 2 δ γ c 2 π n 1 d [ ( 1 - R 2 ) ( R 1 G 2 - 1 R 0 G ) ] 1 2 .
lim R 0 G 1 R G B ( R - 1 ) = ( c / 2 π n 1 d ) [ ( 1 - R 2 ) / R 2 1 2 ] ,

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