Abstract

The temporal coherence effect of a light source on a fiber-optic Fabry-Perot interferometer is described. The ratio of the end-mirror separation h to the coherence length Lc of a single-frequency laser source gives an important parameter to specify the transmission characteristics of the interferometer. A criterion to determine the largest permissible mirror separation, hc, is discussed and given by hc = (0.1/2π) Lc. The peak transmission and finesse are heavily dependent on the ratio h/Lc. The sensing sensitivity is also discussed in association with the ratio h/Lc.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. R. Tebo, Electro. Opt. Syst. Des., Feb.19 (1982).
  2. T. G. Giallorenzi, Opt. Laser Technol. 23, 73 (1981).
    [Crossref]
  3. D. L. Franzen, E. M. Kim, Appl. Opt. 20, 3991 (1981).
    [Crossref] [PubMed]
  4. P. G. Cielo, Appl. Opt. 18, 2933 (1979).
    [Crossref] [PubMed]
  5. T. Yoshino, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WL2.
  6. S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
    [Crossref]
  7. F. T. Arecchi, Phys. Rev. Lett. 15, 912 (1965).
    [Crossref]
  8. H. Z. Cummins, Prog. Opt. 8, 133 (1970).
    [Crossref]
  9. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p.182.
  10. See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p.324.

1982 (1)

A. R. Tebo, Electro. Opt. Syst. Des., Feb.19 (1982).

1981 (3)

T. G. Giallorenzi, Opt. Laser Technol. 23, 73 (1981).
[Crossref]

D. L. Franzen, E. M. Kim, Appl. Opt. 20, 3991 (1981).
[Crossref] [PubMed]

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

1979 (1)

1970 (1)

H. Z. Cummins, Prog. Opt. 8, 133 (1970).
[Crossref]

1965 (1)

F. T. Arecchi, Phys. Rev. Lett. 15, 912 (1965).
[Crossref]

Arecchi, F. T.

F. T. Arecchi, Phys. Rev. Lett. 15, 912 (1965).
[Crossref]

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p.324.

Cielo, P. G.

Cummins, H. Z.

H. Z. Cummins, Prog. Opt. 8, 133 (1970).
[Crossref]

Franzen, D. L.

Giallorenzi, T. G.

T. G. Giallorenzi, Opt. Laser Technol. 23, 73 (1981).
[Crossref]

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Kim, E. M.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p.182.

Petuchowski, S. J.

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Sheem, S. K.

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Tebo, A. R.

A. R. Tebo, Electro. Opt. Syst. Des., Feb.19 (1982).

Wolf, E.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p.324.

Yoshino, T.

T. Yoshino, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WL2.

Appl. Opt. (2)

Electro. Opt. Syst. Des. (1)

A. R. Tebo, Electro. Opt. Syst. Des., Feb.19 (1982).

IEEE J. Quantum Electron. (1)

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Opt. Laser Technol. (1)

T. G. Giallorenzi, Opt. Laser Technol. 23, 73 (1981).
[Crossref]

Phys. Rev. Lett. (1)

F. T. Arecchi, Phys. Rev. Lett. 15, 912 (1965).
[Crossref]

Prog. Opt. (1)

H. Z. Cummins, Prog. Opt. 8, 133 (1970).
[Crossref]

Other (3)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965), p.182.

See, for example, M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), p.324.

T. Yoshino, in Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), paper WL2.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Transmission characteristics dependent on 2πh/Lc. The curves from a to d are plotted, respectively, with 2πh/Lc = 0, 0.05, 0.1, and 0.2.

Fig. 2
Fig. 2

Peak transmission as a function of 2πh/Lc.

Fig. 3
Fig. 3

Degradation of the finesse as a function of 2πh/Lc.

Fig. 4
Fig. 4

Highest phase sensitivity as a function of 2πh/Lc.

Equations (40)

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

E ( t ) = E 0 exp { i [ 2 π ν 0 t + ϕ ( t ) ] } ,
C E ( τ ) = E ( t ) E * ( t + τ ) ¯ / | E ( t ) | 2 ¯ = [ exp ( 2 π i ν 0 τ ) ] [ exp i ϕ ( t ) ] [ exp i ϕ ( t + τ ) ] ¯ ,
C E ( τ ) = [ exp  ( 2 π i ν 0 τ ) ] exp  ( γ | τ | ) ,
I ( ν ) = + C E ( τ ) [ exp  ( 2 π i ν τ ) ] d τ = 2 γ γ 2 + 4 π 2 ( ν 0 ν ) 2 ,
[ exp  i ϕ ( t ) ] [ exp  i ϕ ( t + τ ) ] ¯ = exp  ( 2 π Δ ν τ ) for τ 0
ϕ ( t ) = ϕ 0 + Δ ϕ ( t ) ,
[ Δ ϕ ( t ) ] 2 = [ Δ ϕ ( t + τ ) ] 2 ,
x 1 = Δ ϕ ( t ) x 2 = Δ ϕ ( t + τ ) X 1 = X 2 = 0 σ 2 = x 1 2 = x 2 2 } ,
P ( x 1 , x 2 ) = 1 2 π σ 2 1 ρ 2 exp  [ x 1 2 2 ρ x 1 x 2 + x 2 2 2 σ 2 ( 1 ρ 2 ) ]  ,
ρ = x 1 x 2 σ 2 .
{ exp  i [ ϕ ( t ) ϕ ( t + τ ) ] } ¯ = { exp  i [ Δ ϕ ( t ) Δ ϕ ( t + τ ) ] } ¯ = exp  [ i ( x 1 x 2 ) ] .
exp  [ i ( x 1 x 2 ) ] = + + P ( x 1 , x 2 ) × { exp  [ i ( x 1 x 2 ) ] } d x 1 d x 2 = exp  [ σ 2 ( 1 ρ ) ] .
{ exp  [ i Δ Φ ( t ) ] } { exp  [ i Δ ϕ ( t + τ ) ] } = exp  ( [ Δ ϕ ( t ) ] 2 { 1 Δ ϕ ( t ) Δ ϕ ( t + τ ) [ Δ ϕ ( t ) ] 2 } ) .
Δ ϕ ( t ) Δ ϕ ( t + τ ) = [ Δ ϕ ( t ) ] 2 ( 1 τ / τ 0 )    for τ 0 ,
{ exp  [ i ϕ ( t ) ] } { exp  [ i ϕ ( t + τ ) ] } = exp  { [ Δ ϕ ( t ) ] 2 ( τ / τ 0 ) } = exp  ( 2 π Δ ν τ )   for  τ 0 ,
[ Δ ϕ ( t ) ] 2 / τ 0 = 2 π Δ ν .
q = 2 h / υ ,
V ( t ) = E 0 a a exp i [ 2 π ν 0 t + ϕ ( t ) ] + E 0 a a r 2 × exp  i [ 2 π ν 0 ( t q ) + ϕ ( t q ) ] + + E 0 a a r 2 ( m 1 ) × exp  i { 2 π ν 0 [ t ( m 1 ) q ] + ϕ ( t ( m 1 ) q ] } + = TE 0 [ exp  ( 2 π i ν 0 t ) ] m  =  1 R ( m 1 ) { exp  [ 2 π i ν 0 ( m 1 ) q ] } × { exp  i ϕ [ t ( m 1 ) q ] } ,
I = | V ( t ) | 2 ¯ = T 2 | E 0 | 2 m  =  1 n  =  1 R ( m 1 ) R ( n 1 ) × { exp  [ 2 π i ν 0 q ( n m ) ] } × { exp  i ϕ [ t ( m 1 ) q ] } { exp  i ϕ ( t ( n 1 ) q ] } , ¯
I = T 2 I 0 ( m  = n  = 1 + m  >  n + m  <  n ) ,
m = n = 1 = m = 1 R 2  ( m 1 ) = 1 / ( 1 R 2 ) ,
m > n = m = 2 n = 1 R ( m + n 2 ) { exp  [ 2 π i ν 0 q ( m n ) ] } × { exp  i ϕ [ t ( m 1 ) q ] } [ exp  i ϕ [ t ( n 1 ) q ] } . ¯
m  >  n = s  =  1 n  =  1 R 2 ( n 1 ) R s [ exp  ( 2 π i ν 0 q s ) ] × { exp  i ϕ [ t ( n 1 ) q s q ] } { exp  i ϕ [ t ( n 1 ) q ] } .
m > n = s = 1 n = 1 R 2 ( n 1 ) R 2 [ exp  ( 2 π i ν 0 q s ) ] × [ exp  i ϕ ( t s q ) ] [ exp  i ϕ ( t ) ] . ¯
m > n = s = 1 m = 1 R 2 ( m 1 ) R s [ exp  ( 2 π i ν 0 q s ) ] × [ exp  i ϕ ( t s q ) ] [ exp  i ϕ ( t ) ] . ¯
[ exp  i ϕ ( t s q ) ] [ exp  i ϕ ( t ) ] ¯ = exp  { [ Δ ϕ ( t ) ] 2 s q / τ 0 } = exp  ( 2 π Δ ν s q ) .
m   > n = n = 1 R 2 ( n 1 ) s = 1 [ R exp  ( 2 π i ν 0 q 2 π Δ ν q ) ] s = [ 1 / ( 1 R 2 ) ] R exp  ( 2 π i ν 0 q 2 π Δ ν q ) 1 R exp  ( 2 π i ν 0 q 2 π Δ ν q ) ,
m < n = [ 1 / ( 1 R 2 ) ] R exp  ( 2 π i ν 0 q 2 π Δ ν q ) 1 R exp  ( 2 π i ν 0 q 2 π Δ ν q ) .
I / I 0 = T 2 [ 1 R 2 exp  ( 4 π Δ ν q ) ] ( 1 R 2 ) { [ 1 R exp  ( 2 π Δ ν q ) ] 2 + 4 R sin 2 ( π ν 0 q ) exp  ( 2 π Δ ν q ) } .
Δ ν q = h / L c .
I / I 0 = G 1 + M sin 2 θ ,
G = ( 1 R 1 + R ) [ 1 + R exp  ( 2 π h / L c ) 1 R exp  ( 2 π h / L c ) ] ,
M = 4 R exp  ( 2 π h / L c ) [ 1 R exp  ( 2 π h / L c ) ] 2 ,
θ = π ν 0 q = k h ,
lim L c G = 1 and lim L c M = 4 R / ( 1 R ) 2 ,
I / I 0 = 1 1 + [ 4 R / ( 1 R ) 2 ] sin 2 ( k h ) .
F = ( π / 2 ) M = π R exp  ( 2 π h / L c ) 1 R exp  ( 2 π h / L c ) .
d I d θ = I 0 G M sin ( 2 θ ) ( 1 + M sin 2 θ ) 2 .
θ 0 = ( 1 / 2 ) cos 1 [ ( 1 / 2 ) ( 2 / M + 1 ) 2 + 8 ( 1 + 2 / M ) ]   .
d I d θ | max = ( I 0 / M ) cos 2   ( 2 θ 0 ) sin 3   ( 2 θ 0 ) .

Metrics