Abstract

An analysis of the dynamic response of a single-mode all-fiber ring resonator is presented in which a time-varying phase shift is induced in the ring by a phase modulator. In particular, the deviation of the response from that expected from the steady-state analysis is discussed.

© 1988 Optical Society of America

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References

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  1. L. F. Stokes, M. Chodorow, H. J. Shaw, Opt. Lett. 7, 288 (1982).
    [CrossRef] [PubMed]
  2. M. J. F. Digonnet, H. J. Shaw, IEEE J. Quantum Electron. QE-18, 746 (1982).
    [CrossRef]
  3. B. Crosignani, A. Yariv, P. Di Porto, Opt. Lett. 11, 251 (1986).
    [CrossRef] [PubMed]
  4. M. Nazarathy, S. A. Newton, Appl. Opt. 25, 1051 (1986),
    [CrossRef] [PubMed]
  5. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964), p. 299.

1986 (2)

1982 (2)

M. J. F. Digonnet, H. J. Shaw, IEEE J. Quantum Electron. QE-18, 746 (1982).
[CrossRef]

L. F. Stokes, M. Chodorow, H. J. Shaw, Opt. Lett. 7, 288 (1982).
[CrossRef] [PubMed]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964), p. 299.

Chodorow, M.

Crosignani, B.

Di Porto, P.

Digonnet, M. J. F.

M. J. F. Digonnet, H. J. Shaw, IEEE J. Quantum Electron. QE-18, 746 (1982).
[CrossRef]

Nazarathy, M.

Newton, S. A.

Shaw, H. J.

L. F. Stokes, M. Chodorow, H. J. Shaw, Opt. Lett. 7, 288 (1982).
[CrossRef] [PubMed]

M. J. F. Digonnet, H. J. Shaw, IEEE J. Quantum Electron. QE-18, 746 (1982).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964), p. 299.

Stokes, L. F.

Yariv, A.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. J. F. Digonnet, H. J. Shaw, IEEE J. Quantum Electron. QE-18, 746 (1982).
[CrossRef]

Opt. Lett. (2)

Other (1)

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1964), p. 299.

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Figures (4)

Fig. 1
Fig. 1

All-fiber ring resonator.

Fig. 2
Fig. 2

Dynamic (solid line) and steady-state (dashed line) response of an optical-fiber resonator.

Fig. 3
Fig. 3

Normalized magnitude (solid lines) and phase deviation (dotted-dashed lines) of optical signal as a function of the number of transients in the ring.

Fig. 4
Fig. 4

Experimental results of the dynamic response of an optical-fiber resonator: rate of phase shift (a) 3.35 × 103 rad/sec; (b), (c) 2.1 × 106 rad/sec; (d) 0.72 × 106 rad/sec.

Tables (1)

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Table 1 Experimental, Numerical [Using Eq. (2)], and Theoretical [Using Eq. (6)] Results for the Half-Periods of Ringinga

Equations (6)

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E 4 ( z , t ) = j T 14 E 1 ( z , t ) + T 13 T 24 j T 23 n = 1 ( j T 23 T L ) n × E 1 ( z + n L , t ) exp [ j m = 1 n ϕ ( t m τ ) ] ,
e 4 ( t ) e 1 = j T 14 + T 13 T 24 j T 23 n = 1 ( T 23 T L ) n × exp { j [ n ( π 2 + β L ) + n α t n ( n + 1 ) 2 α τ ] } ,
e 4 ( t ) e 1 = j T 14 + T 13 T 24 T L exp [ j ( π / 2 + β L + α t ) ] 1 j T 23 T L exp [ j ( π / 2 + β L + α t ) ] ,
I = 0 b x exp [ j ( x α t x 2 α τ / 2 ) d x ] = 0 exp ( j x 2 α τ / 2 λ x ) d x ,
I = π j 2 α τ exp ( j λ 2 2 α τ ) [ 1 erf ( λ j 2 α τ ) ] .
t hp = ( 2 m τ π / α ) 1 / 2 , m = 1 , 2 ,

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