Abstract

A time-dependent analysis of an all-single-mode fiber-optic resonator is presented in which the input field is allowed to exhibit an arbitrary dependence on time. In particular, the transmissivity of the resonator is evaluated for an input field possessing an arbitrary temporal coherence, which allows one to consider the role of the source coherence time as compared with the fiber time delay.

© 1986 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. L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
    [CrossRef]
  3. Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985); see also M. Tur, B. Moslehi, J. W. Goodman, J. Lightwave Technol. LT-3, 20 (1985).
    [CrossRef]
  4. See, for example, G. Korn, T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

1985 (1)

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985); see also M. Tur, B. Moslehi, J. W. Goodman, J. Lightwave Technol. LT-3, 20 (1985).
[CrossRef]

1983 (1)

L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
[CrossRef]

1982 (1)

Chodorow, M.

L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
[CrossRef]

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

Korn, G.

See, for example, G. Korn, T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

Korn, T.

See, for example, G. Korn, T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

Ohtsuka, Y.

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985); see also M. Tur, B. Moslehi, J. W. Goodman, J. Lightwave Technol. LT-3, 20 (1985).
[CrossRef]

Shaw, H. J.

L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
[CrossRef]

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

Stokes, L. F.

L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
[CrossRef]

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

J. Lightwave Technol. (2)

L. F. Stokes, M. Chodorow, H. J. Shaw, J. Lightwave Technol. LT-1, 110 (1983).
[CrossRef]

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985); see also M. Tur, B. Moslehi, J. W. Goodman, J. Lightwave Technol. LT-3, 20 (1985).
[CrossRef]

Opt. Lett. (1)

Other (1)

See, for example, G. Korn, T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961).

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Figures (3)

Fig. 1
Fig. 1

Fiber-optic passive loop resonator.

Fig. 2
Fig. 2

Transmissivity T as a function of βL for k = 0.95, γ0 = 0.05, M ≃ 1 − γ0, and δ = 0.7. Curve a, exact solution; curve b, approximate solution (n = 5).

Fig. 3
Fig. 3

Transmissivity T as a function of βL for k = 0.95, γ0 = 0.05, M ≃ 1 − γ0, and δ = 0.7. Curve a, G(τ) = exp(−Δωτ); curve b, G(τ) = exp[−(Δωτ)2 ].

Equations (16)

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E 1 ( z , t ) = exp ( i β z - i ω t ) 1 ( t )
E ( t ) = E 0 exp [ - i ω t + i ϕ ( t ) ]
G ( τ ) = 1 ( t ) 1 * ( t - τ ) 1 ( t ) 2
3 ( t ) = ( 1 - γ 0 ) 1 / 2 [ ( 1 - k ) 1 / 2 1 ( t ) + i k 1 / 2 × exp ( - α 0 L + i β L ) 3 ( t - τ ) ] , 4 ( t ) = ( 1 - γ 0 ) 1 / 2 [ i k 1 / 2 1 ( t ) + ( 1 - k ) 1 / 2 × exp ( - α 0 L + i β L ) 3 ( t - τ ) ] ,
2 ( t ) = exp ( - α 0 L + i β L ) 3 ( t - τ ) ,
4 ( t ) - λ 4 ( t - τ ) = a 1 ( t ) + b 1 ( t - τ ) ,
4 ( t ) - λ K ( t , t ) 4 ( t ) d t = F ( t ) ,
4 ( t ) = a 1 ( t ) + h n = 0 λ n 1 [ t - ( n + 1 ) τ ] ,
4 ( t ) 2 = a 2 1 ( t ) 2 + a h * × n = 0 λ * n 1 ( t ) 1 * [ t - ( n + 1 ) τ ] + a * h n = 0 λ n 1 * ( t ) 1 [ t - ( n + 1 ) τ ] + h 2 n = 0 m = 0 λ n λ * m 1 [ t - ( n + 1 ) τ ] × 1 * [ t - ( m + 1 ) τ ] .
4 ( t ) 2 = ( a 2 + h 2 n = 0 λ 2 n ) 1 ( t ) 2 + [ a h * + a * h + h 2 ( n = 0 λ n λ * n + 1 + n = 0 λ n + 1 λ * n ) ] 1 ( t ) 1 * ( t - τ ) + [ a h * λ * + a * h λ + h 2 ( n = 0 λ n λ * n + 2 + n = 0 λ n + 2 λ * n ) ] 1 ( t ) 1 * ( t - 2 τ ) + .
T = 4 ( t ) 2 1 ( t ) 2 = [ a 2 + h 2 / ( 1 - λ 2 ) ] × { G ( 0 ) + n = 0 ( λ n + 1 + λ * n + 1 ) G [ ( n + 1 ) τ ] } + n = 0 ( a b * λ * n + a * b λ n ) G [ ( n + 1 ) τ ] .
T ( t c τ ) = a 2 + h 2 / ( 1 - λ 2 ) = ( 1 - γ 0 ) × [ 1 - ( 1 - k ) ( 1 - M ) / ( 1 - k M ) ] ,
T ( t c τ ) = a + b 2 / 1 - λ 2 = ( 1 - γ 0 ) × k + M + 2 k 1 / 2 M 1 / 2 sin ( β L ) 1 + k M + 2 k 1 / 2 M 1 / 2 sin ( β L ) .
T = { ( 1 - λ 2 δ 2 ) ( a 2 + b 2 ) + a b * [ δ ( 1 - λ 2 ) + λ ( 1 - δ 2 ) ] + a * b [ δ ( 1 - λ 2 ) + λ * ( 1 - δ 2 ) ] } / 1 - λ δ 2 ( 1 - λ 2 ) ,
F ( 1 - k ) ( 1 - M ) ( 1 - k M δ 2 ) / ( 1 - k M ) ( 1 + δ k 1 / 2 M 1 / 2 ) 2 , H 4 δ k 1 / 2 M 1 / 2 / ( 1 + δ k 1 / 2 M 1 / 2 ) 2 ,             θ = β L - π / 2 , T = ( 1 - γ 0 ) [ 1 - F 1 - H sin 2 ( θ / 2 ) ] .
T = ( 1 - γ 0 ) ( 1 - ( 1 - k ) ( 1 - M ) 1 - k M { 1 + 2 n = 0 × ( k M ) ( n + 1 ) / 2 G [ ( n + 1 ) τ ] × cos [ ( n + 1 ) ( β L + π / 2 ) ] } ) ,

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