Abstract

We calculate the oscillation conditions and the eigenfrequencies for phase-conjugating-resonator-normal-resonator coupled optical systems. With an eye toward applications to interferometry, we choose specific examples for which it is shown that the conditions for oscillation and the eigenfrequencies depend on the normal-resonator path length. The examples include both linear displacement and rotation sensing (Sagnac) resonant interferometers. Our results suggest that if the distortion-correcting and self-aligning properties of the phase-conjugating resonator are retained in the more complicated system, then these hybrid resonators may offer some advantages over their conventional counterparts.

© 1984 Optical Society of America

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References

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  1. J. F. Lam, W. P. Brown, Opt. Lett. 5, 61 (1980).
    [CrossRef] [PubMed]
  2. J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980);erratum, Opt. Lett. 6, 257 (1981).
    [CrossRef] [PubMed]
  3. R. C. Lind, D. G. Steel, Opt. Lett. 6, 554 (1981).
    [CrossRef] [PubMed]
  4. J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).
  5. J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
    [CrossRef]
  6. P. A. Belanger, Opt. Eng. 21, 266 (1982).
  7. D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1982), pp. 42–48.
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 323–341.
  9. In Eqs. (6), (7), and (13) we have omitted, for clarity, some inconsequential constant phases.
  10. M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
    [CrossRef]
  11. E. J. Post, Rev. Mod. Phys. 39, 475 (1967).
    [CrossRef]
  12. For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]

1983 (1)

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1982 (2)

J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

P. A. Belanger, Opt. Eng. 21, 266 (1982).

1981 (1)

1980 (2)

1979 (1)

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

1972 (1)

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

1967 (1)

E. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

Auyeung, J.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Belanger, P. A.

P. A. Belanger, Opt. Eng. 21, 266 (1982).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 323–341.

Brown, W. P.

Drever, R. W. P.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Feinberg, J.

Fekete, D.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Ford, G. M.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hall, J. L.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hellwarth, R. W.

Hough, J.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kowalski, F. V.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Lam, J. F.

Lamb, W. E.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Lind, R. C.

Munley, A. J.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Pepper, D. M.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1982), pp. 42–48.

Post, E. J.

E. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

Spencer, M. B.

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Steel, D. G.

Ward, H.

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

White, J. O.

J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 323–341.

Yariv, A.

J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1982), pp. 42–48.

Appl. Phys. B (1)

For optical frequency-locking techniques, see, for example, R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Opt. Eng. (2)

P. A. Belanger, Opt. Eng. 21, 266 (1982).

J. O. White, A. Yariv, Opt. Eng. 21, 224 (1982).

Opt. Lett. (3)

Phys. Rev. A (1)

M. B. Spencer, W. E. Lamb, Phys. Rev. A 5, 893 (1972).
[CrossRef]

Rev. Mod. Phys. (1)

E. J. Post, Rev. Mod. Phys. 39, 475 (1967).
[CrossRef]

Other (3)

D. M. Pepper, A. Yariv, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1982), pp. 42–48.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), pp. 323–341.

In Eqs. (6), (7), and (13) we have omitted, for clarity, some inconsequential constant phases.

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Figures (1)

Fig. 1
Fig. 1

Coupled resonator configurations. a, PCR coupled to a Fabry–Perot resonator; b, PCR coupled to a folded Fabry-Perot resonator; c, PCR coupled to a ring resonator; d, PCR coupled to a normal resonator represented as a complex mirror.

Equations (23)

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2 E ( z , t ) z 2 1 c 2 2 E ( z , t ) t 2 = 0
E ( z , t ) = [ A U exp ( i k U z ) + B U exp ( i k U z ) ] × exp [ i ( ν 0 + δ ν ) t ] + [ A L exp ( i k L z ) + B L exp ( i k L z ) ] × exp [ i ( ν 0 δ ν ) t ] ,
A L = g ( δ ν ) B * U ,
A U = g ( δ ν ) B * L .
r ( ν ) = ρ ( ν ) exp [ i φ r ( ν ) ] ,
t ( ν ) = τ ( ν ) exp [ i φ t ( ν ) ] ,
B U = ρ ( ν 0 + δ ν ) A U exp { i [ 2 k U L + φ r ( ν 0 + δ ν ) ] } ,
B L = ρ ( ν 0 δ ν ) A L exp { i [ 2 k L L + φ r ( ν 0 δ ν ) ] } .
g 2 ( δ ν ) ρ ( ν 0 + δ ν ) ρ ( ν 0 δ ν ) = 1
φ ( ν 0 + δ ν ) φ ( ν 0 δ ν ) + 4 δ k L = 2 n π ( n = 0 , ± 1 , ± 2 , ) ,
r 0 ( ν ) = τ 1 2 e i 1 ρ 1 e i ρ 1 ,
= ( ν ω 0 ) ( 2 L 1 / c )
δ ν τ c / 2 L .
r ( ν ) = τ 1 2 1 ρ 1 2 e i ,
t ( ν ) = ρ 1 ( τ 1 2 e i 1 ρ 1 2 e i 1 ) ,
E ( z , t ) = [ A ν exp ( i k ν z ) + B ν exp ( i k ν z ) ] × exp [ i ( ν 0 + δ ν ) t ] + [ A L exp ( i k L z ) + B L × exp ( i k L z ) ] exp [ i ( ν 0 δ ν ) t ] , z > 0 ,
2 δ k L + φ + ( ν 0 + δ ν ) φ ( ν 0 δ ν ) = 2 n π ,
2 δ k L + φ ( ν 0 + δ ν ) φ + ( ν 0 δ ν ) = 2 n π .
ω ± = ω 0 δ ω ,
δ ω = 4 π A λ P Ω ,
φ + ( ν ) = φ 0 ( ν δ ω ) ,
φ ( ν ) = φ 0 ( ν + δ ω ) ,
φ 0 ( ν ) = arg { t } = arg { τ 1 2 1 ρ 1 2 e i }

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