Abstract

An interferometric model is proposed to estimate the phase differences in lossless, strongly coupled biconical fiber couplers. This approximate method is simpler than the traditional s-parameter network theory-based analysis technique and minimizes the number of unknowns. The phase difference between the transmitted and coupled light fields is directly related to the field interaction and can be estimated by employing the energy conservation and mode orthogonality principles. The maximum coupling coefficient and dependence of phase difference on coupling conditions can be analyzed for multiport single-mode fiber couplers.

© 1996 Optical Society of America

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References

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  1. S. K. Sheem, “Fiber-optic gyroscope with 3×3 directional coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
    [CrossRef]
  2. K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
    [CrossRef]
  3. R. Hereth, G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7, 925–930 (1989).
    [CrossRef]
  4. G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
    [CrossRef]
  5. J. Pietzsch, “Scattering matrix analysis of 3×3 fiber couplers,” J. Lightwave Technol. 7, 3030–3037 (1989).
    [CrossRef]
  6. H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
    [CrossRef]
  7. T. A. Birks, “Effect of twist in 3×3 fused tapered couplers,” Appl. Opt. 31, 3004–3014 (1992).
    [CrossRef] [PubMed]
  8. A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).
  9. D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
    [CrossRef]

1992 (2)

T. A. Birks, “Effect of twist in 3×3 fused tapered couplers,” Appl. Opt. 31, 3004–3014 (1992).
[CrossRef] [PubMed]

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

1991 (1)

D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
[CrossRef]

1990 (1)

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

1989 (2)

J. Pietzsch, “Scattering matrix analysis of 3×3 fiber couplers,” J. Lightwave Technol. 7, 3030–3037 (1989).
[CrossRef]

R. Hereth, G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7, 925–930 (1989).
[CrossRef]

1985 (1)

G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
[CrossRef]

1982 (1)

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

1980 (1)

S. K. Sheem, “Fiber-optic gyroscope with 3×3 directional coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
[CrossRef]

Abbas, G. L.

G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
[CrossRef]

Adnams, R. M.

D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
[CrossRef]

Arkwright, J. W.

D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
[CrossRef]

Birks, T. A.

T. A. Birks, “Effect of twist in 3×3 fused tapered couplers,” Appl. Opt. 31, 3004–3014 (1992).
[CrossRef] [PubMed]

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

Buhler, W.

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

Chan, V. W. S.

G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
[CrossRef]

Dandridge, A.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Fitzgerald, C. M.

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

Hartl, E.

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

Hereth, R.

R. Hereth, G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7, 925–930 (1989).
[CrossRef]

Hussey, C. D.

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

Koo, K. P.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Mortimore, D. B.

D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
[CrossRef]

Muller, R.

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

Niu, A.

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

Pietzsch, J.

J. Pietzsch, “Scattering matrix analysis of 3×3 fiber couplers,” J. Lightwave Technol. 7, 3030–3037 (1989).
[CrossRef]

Poisel, H.

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

Schiffner, G.

R. Hereth, G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7, 925–930 (1989).
[CrossRef]

Sheem, S. K.

S. K. Sheem, “Fiber-optic gyroscope with 3×3 directional coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
[CrossRef]

Trommer, G. F.

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

Tveten, A. B.

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Yee, T. K.

G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. K. Sheem, “Fiber-optic gyroscope with 3×3 directional coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
[CrossRef]

K. P. Koo, A. B. Tveten, A. Dandridge, “Passive stabilization scheme for fiber interferometers using 3×3 fiber directional couplers,” Appl. Phys. Lett. 41, 616–618 (1982).
[CrossRef]

Electron. Lett. (3)

A. Niu, C. M. Fitzgerald, T. A. Birks, C. D. Hussey, “1×3 linear array singlemode fiber couplers,” Electron. Lett. 28, 2330–2332 (1992).

D. B. Mortimore, J. W. Arkwright, R. M. Adnams, “Monolithic wavelength-flattened 1×4 singlemode fused fiber coupler,” Electron. Lett. 27, 2252–2253 (1991).
[CrossRef]

H. Poisel, G. F. Trommer, W. Buhler, E. Hartl, R. Muller, “Low-cost fiber-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[CrossRef]

J. Lightwave Technol. (3)

R. Hereth, G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7, 925–930 (1989).
[CrossRef]

G. L. Abbas, V. W. S. Chan, T. K. Yee, “A dual-detector optical hyterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110–1122 (1985).
[CrossRef]

J. Pietzsch, “Scattering matrix analysis of 3×3 fiber couplers,” J. Lightwave Technol. 7, 3030–3037 (1989).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Dependence of the phase difference between transmission and coupling coefficients on the magnitude of the coupling coefficient in a symmetric 3×3 fiber coupler.

Fig. 2
Fig. 2

Fiber configurations of the symmetric 1×4 and 1×7 fiber couplers.

Fig. 3
Fig. 3

Dependence of the phase difference between transmission and coupling coefficients on the magnitude of the coupling coefficient in the symmetric 1×4 and 1×7 fiber couplers.

Fig. 4
Fig. 4

Two other possible fiber configurations of a 1×4 fiber coupler.

Fig. 5
Fig. 5

Dependence of phase ϕ2 on coupling coefficient C 1 for different values of C 2 (see text for definitions).

Fig. 6
Fig. 6

Dependence of phase ϕ1 on coupling coefficient C 1 for different values of C 2 (see text for definitions).

Equations (16)

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I taper ( r , x ) = | T ˜ ( r , x ) + C ˜ ( r , x ) | 2 = T 2 ( r , x ) + C 2 ( r , x ) + 2 Re [ T ˜ ( r , x ) C ˜ * ( r , x ) ] ,
P output = P fiber 1 + P fiber 2 = P taper = T 2 ( r , x ) d s + C 2 ( r , x ) d s 2 T ( r , x ) C ( r , x ) cos ϕ d s = P fiber 1 + P fiber 2 + 2 T ( r , x ) C ( r , x ) cos ϕ d s ,
cos ϕ = 0 , or ϕ = π / 2 .
P total = ( T 2 + C 2 ) d s = P taper = [ | α T ˜ + α C ˜ | 2 + ( 1 α ) T 2 + ( 1 α ) C 2 ] d s ,
| T ˜ + 2 C ˜ | 2 = T 2 + 2 C 2 = 1 .
cos ϕ = C 2 T .
I taper = 2 | T ˜ / 2 + C ˜ | 2 = T 2 + 2 C 2 = 1 ,
| T ˜ + ( N 1 ) C ˜ | 2 = T 2 + ( N 1 ) C 2 = 1 ,
cos ϕ = ( N 2 ) C 2 T ( N > 2 ) ,
| T ˜ + ( N 1 ) α C ˜ | 2 + ( N 1 ) ( 1 α ) C 2 = T 2 + ( N 1 ) C 2 = 1 ,
cos ϕ = ( N 2 ) α C 2 T .
S = [ T ˜ C ˜ 2 C ˜ 1 C ˜ 1 C ˜ 2 T ˜ C ˜ 1 C ˜ 1 C ˜ 1 C ˜ 1 T ˜ C ˜ 2 C ˜ 1 C ˜ 1 C ˜ 2 T ˜ ]
T C 2 cos ϕ 2 + C 1 2 = 0 ,
T cos ϕ 1 + C 2 cos ( ϕ 1 ϕ 2 ) = 0 ,
| T ˜ + 2 C ˜ 1 + C ˜ 2 | 2 = T 2 + 2 C 1 2 + C 2 2 = 1 ,
C 1 2 + T C 2 cos ϕ 2 + 2 T C 1 cos ϕ 1 + 2 C 1 C 2 × cos ( ϕ 1 ϕ 2 ) = 0 ,

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