Abstract

A complete analysis of symmetric 2 × 2 fused-fiber couplers in terms of supermode beating is made. The tranverse and longitudinal geometry of the couplers has been carefully modeled to take into account the fabrication parameters. The first two scalar supermodes and their polarization corrections have then been calculated for each degree of fusion and taper ratio, resulting in powerful tools for the design of particular couplers. The good agreement between the observed and the predicted responses for slightly and strongly fused couplers confirms the validity of each step of this analysis.

© 1994 Optical Society of America

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References

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  1. J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918–1921 (1983).
    [CrossRef] [PubMed]
  2. F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
    [CrossRef]
  3. W. K. Burns, M. Abebe, “Coupling model for fused fiber couplers with parabolic taper shape,” Appl. Opt. 26, 4190–4192 (1987).
    [CrossRef] [PubMed]
  4. F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).
  5. J. D. Love, M. Hall, “Polarisation modulation in long couplers,” Electron. Lett. 21, 519–520 (1985).
  6. J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
    [CrossRef]
  7. M. Eisenmann, E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol. 6, 113–118 (1988).
    [CrossRef]
  8. J. V. Wright, “Variational analysis of fused taper couplers,” Electron. Lett. 21, 1064–1065 (1985).
    [CrossRef]
  9. X.-H. Zheng, “Finite-element analysis for fused couplers,” Electron. Lett. 22, 804–805 (1986).
    [CrossRef]
  10. F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
    [CrossRef]
  11. J.-L. Zhang, Z.-M. Mao, Z.-Q. Lin, “Measurements and analyses of fields in fused tapered single-mode couplers,” Appl. Opt. 28, 2026–2030 (1989).
    [CrossRef] [PubMed]
  12. J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett. 22, 320–321 (1986).
    [CrossRef]
  13. K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol. 8, 678–683 (1990).
    [CrossRef]
  14. D. Marcuse, Dielectric Optical Waveguides (Academic, San. Diego, Calif., 1991).
  15. C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).
  16. V. J. Tekippe, “Passive fiber-optic components made by the fused biconical taper process,” Fiber. Integrated Opt. 9, 97–123 (1990).
    [CrossRef]
  17. R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
    [CrossRef]
  18. T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
    [CrossRef]
  19. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  20. F. Gonthier, “Conception et réalisation de coupleurs multifibres intégrés à des fibres optiques unimodales,” Ph.D. dissertation (Ecole Polytechnique de Montréal, Montréal, Québec, Canada, 1993).
  21. F. Gonthier, D. Ricard, S. Lacroix, J. Bures, “Wavelength-flattened 2 × 2 splitters made of identical single-mode fibers,” Opt. Lett. 16, 1201–1203 (1991).
    [CrossRef] [PubMed]
  22. F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
    [CrossRef]
  23. J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
    [CrossRef]
  24. F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
    [CrossRef]
  25. M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
    [CrossRef]

1994 (1)

F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
[CrossRef]

1992 (1)

T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

1991 (5)

F. Gonthier, D. Ricard, S. Lacroix, J. Bures, “Wavelength-flattened 2 × 2 splitters made of identical single-mode fibers,” Opt. Lett. 16, 1201–1203 (1991).
[CrossRef] [PubMed]

R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
[CrossRef]

1990 (2)

K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol. 8, 678–683 (1990).
[CrossRef]

V. J. Tekippe, “Passive fiber-optic components made by the fused biconical taper process,” Fiber. Integrated Opt. 9, 97–123 (1990).
[CrossRef]

1989 (1)

1988 (1)

M. Eisenmann, E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol. 6, 113–118 (1988).
[CrossRef]

1987 (1)

1986 (4)

X.-H. Zheng, “Finite-element analysis for fused couplers,” Electron. Lett. 22, 804–805 (1986).
[CrossRef]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett. 22, 320–321 (1986).
[CrossRef]

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

1985 (4)

J. V. Wright, “Variational analysis of fused taper couplers,” Electron. Lett. 21, 1064–1065 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).

J. D. Love, M. Hall, “Polarisation modulation in long couplers,” Electron. Lett. 21, 519–520 (1985).

F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
[CrossRef]

1983 (1)

Abebe, M.

Archambault, J. L.

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

Bilodeau, F.

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

Birks, T. A.

T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Black, R. J.

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

Bures, J.

F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
[CrossRef]

F. Gonthier, D. Ricard, S. Lacroix, J. Bures, “Wavelength-flattened 2 × 2 splitters made of identical single-mode fibers,” Opt. Lett. 16, 1201–1203 (1991).
[CrossRef] [PubMed]

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918–1921 (1983).
[CrossRef] [PubMed]

Burns, W. K.

Eisenmann, M.

M. Eisenmann, E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol. 6, 113–118 (1988).
[CrossRef]

Faucher, S.

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

Finegan, T.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

Gazey, B. K.

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

Gonthier, F.

F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
[CrossRef]

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

F. Gonthier, D. Ricard, S. Lacroix, J. Bures, “Wavelength-flattened 2 × 2 splitters made of identical single-mode fibers,” Opt. Lett. 16, 1201–1203 (1991).
[CrossRef] [PubMed]

F. Gonthier, “Conception et réalisation de coupleurs multifibres intégrés à des fibres optiques unimodales,” Ph.D. dissertation (Ecole Polytechnique de Montréal, Montréal, Québec, Canada, 1993).

Hall, M.

J. D. Love, M. Hall, “Polarisation modulation in long couplers,” Electron. Lett. 21, 519–520 (1985).

Hill, K. O.

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

Hussey, C. D.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).

F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
[CrossRef]

Johnson, D. C.

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

Kenny, R. P.

R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Lacroix, S.

F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
[CrossRef]

F. Gonthier, D. Ricard, S. Lacroix, J. Bures, “Wavelength-flattened 2 × 2 splitters made of identical single-mode fibers,” Opt. Lett. 16, 1201–1203 (1991).
[CrossRef] [PubMed]

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

J. Bures, S. Lacroix, J. Lapierre, “Analyse d’un coupleur bidirectionnel à fibres optiques monomodes fusionnées,” Appl. Opt. 22, 1918–1921 (1983).
[CrossRef] [PubMed]

Lapierre, J.

Li, Y. W.

T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

Lin, Z.-Q.

Love, J. D.

J. D. Love, M. Hall, “Polarisation modulation in long couplers,” Electron. Lett. 21, 519–520 (1985).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Maclean, T. S. M.

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

Mao, Z.-M.

Marcuse, D.

D. Marcuse, Dielectric Optical Waveguides (Academic, San. Diego, Calif., 1991).

Marlin, H. R.

M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
[CrossRef]

McLandrich, M. N.

M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
[CrossRef]

Mears, R. J.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

Miller, J. F.

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

Oakley, K. P.

R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Okamoto, K.

K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol. 8, 678–683 (1990).
[CrossRef]

Orazi, R. J.

M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
[CrossRef]

Payne, F. P.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).

Ricard, D.

Rodriguez, J. M. P.

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

Saravanos, C.

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Tekippe, V. J.

V. J. Tekippe, “Passive fiber-optic components made by the fused biconical taper process,” Fiber. Integrated Opt. 9, 97–123 (1990).
[CrossRef]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

Weidel, E.

M. Eisenmann, E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol. 6, 113–118 (1988).
[CrossRef]

Wright, J. V.

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett. 22, 320–321 (1986).
[CrossRef]

J. V. Wright, “Variational analysis of fused taper couplers,” Electron. Lett. 21, 1064–1065 (1985).
[CrossRef]

Yataki, M. S.

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).

F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
[CrossRef]

Zhang, J.-L.

Zheng, X.-H.

X.-H. Zheng, “Finite-element analysis for fused couplers,” Electron. Lett. 22, 804–805 (1986).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (9)

J. V. Wright, “Wavelength dependence of fused couplers,” Electron. Lett. 22, 320–321 (1986).
[CrossRef]

R. P. Kenny, T. A. Birks, K. P. Oakley, “Control of optical fiber taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett. 21, 524–526 (1985).
[CrossRef]

J. V. Wright, “Variational analysis of fused taper couplers,” Electron. Lett. 21, 1064–1065 (1985).
[CrossRef]

X.-H. Zheng, “Finite-element analysis for fused couplers,” Electron. Lett. 22, 804–805 (1986).
[CrossRef]

F. P. Payne, T. Finegan, M. S. Yataki, R. J. Mears, C. D. Hussey, “Dependence of fused taper couplers on external refractive index,” Electron. Lett. 22, 1207–1209 (1986).
[CrossRef]

F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).

J. D. Love, M. Hall, “Polarisation modulation in long couplers,” Electron. Lett. 21, 519–520 (1985).

J. M. P. Rodriguez, T. S. M. Maclean, B. K. Gazey, J. F. Miller, “Completely fused tapered couplers: comparison of theoretical and experimental results,” Electron. Lett. 22, 402–403 (1986).
[CrossRef]

Fiber. Integrated Opt. (1)

V. J. Tekippe, “Passive fiber-optic components made by the fused biconical taper process,” Fiber. Integrated Opt. 9, 97–123 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. L. Archambault, R. J. Black, J. Bures, F. Gonthier, S. Lacroix, C. Saravanos, “Fiber core profile characterization by measuring group velocity equalization wavelengths,” IEEE Photon. Technol. Lett. 3, 351–353 (1991).
[CrossRef]

J. Lightwave Technol. (5)

F. Bilodeau, K. O. Hill, S. Faucher, D. C. Johnson, “Low-loss highly overcoupled fused couplers: fabrication and sensitivity to external pressure,” J. Lightwave Technol. 6, 1476–1482 (1991).
[CrossRef]

M. N. McLandrich, R. J. Orazi, H. R. Marlin, “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 μm,” J. Lightwave Technol. 9, 442–447 (1991).
[CrossRef]

M. Eisenmann, E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol. 6, 113–118 (1988).
[CrossRef]

T. A. Birks, Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
[CrossRef]

K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol. 8, 678–683 (1990).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

F. Gonthier, S. Lacroix, J. Bures, “Numerical calculations of modes of optical waveguides with two-dimensional refractive index profiles by a field correction method,” Opt. Quantum Electron. 26, 5135–5136 (1994).
[CrossRef]

Other (4)

D. Marcuse, Dielectric Optical Waveguides (Academic, San. Diego, Calif., 1991).

C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

F. Gonthier, “Conception et réalisation de coupleurs multifibres intégrés à des fibres optiques unimodales,” Ph.D. dissertation (Ecole Polytechnique de Montréal, Montréal, Québec, Canada, 1993).

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Figures (14)

Fig. 1
Fig. 1

Model of fusion. The tangent arcs are calculated so that the hatched area is equal to the cross-hatched area. For large degrees of fusion, the position of the cores is corrected so that the dotted area remains constant.

Fig. 2
Fig. 2

Cross section of a 2 × 2 coupler for degrees of fusion ranging from 0 to 1. The dimensions are normalized to the fiber-cladding radius.

Fig. 3
Fig. 3

Photograph of an actual 2 × 2 coupler cross section. The degree of fusion has been determined through the measurement of the ratio of the height to the width of the cross section to be f = 0.83.

Fig. 4
Fig. 4

Simulation of the longitudinal profile (i.e., the normalized transverse dimension τ as a function of z) of the coupler shown in Fig. 12, below.

Fig. 5
Fig. 5

(a) LP01 and (b) LP11 modal fields of a slightly fused (f = 0.1) 2 × 2 coupler made of identical fibers for τ = 0.3. The untapered fiber core and cladding diameters are ρco = 4.5 μm and ρcl = 62.5 μm, respectively, with respective indices n co = 1.451813 and n cl = 1.447313 at the calculation wavelength λ = 1.3 μm; the external medium is air with a refractive index n ex = 1.

Fig. 6
Fig. 6

(a) LP01 and (b) LP11 modal fields of a strongly fused (f = 0.7) 2 × 2 coupler made of identical fibers for τ = 0.3. The calculation parameters are the same as in Fig. 5.

Fig. 7
Fig. 7

LP01 − LP11 beat length z b of a 2 × 2 coupler for different degrees of fusion f as a function of the normalized transverse dimension τ. The calculation parameters are the same as in Fig. 5.

Fig. 8
Fig. 8

Normalized wavelength period around λ = 1.3 μm as a function of the normalized transverse dimension τ for different degrees of fusion of a 2 × 2 coupler. The calculation parameters are the same as in Fig. 5.

Fig. 9
Fig. 9

Effect of the birefringence on the power versus elongation curve of a 2 × 2 coupler. The larger the quantity Q z , the more polarization dependent the coupler response. The inverse quantity 1/Q z = 2n z represents twice the number n z of rapid oscillations between two consecutive nodes in the elongation response. The calculation parameters are the same as in Fig. 5.

Fig. 10
Fig. 10

Effect of the birefringence on the power versus wavelength curve of a 2 × 2 coupler. The larger the quantity Q λ, the more polarization dependent the coupler response. The inverse quantity 1/Q λ = 2n λ represents twice the number n λ of rapid oscillations between two consecutive nodes in the wavelength response. The calculation parameters are the same as in Fig. 5.

Fig. 11
Fig. 11

Comparison between the experimental and the theoretical elongation responses of a strongly fused (f = 0.7) 2 × 2 coupler. The signal was recorded with a linearly polarized laser diode at λ = 1.3 μm. To reproduce this signal with same modulation amplitude, the polarization angle of the exciting field had to be adjusted with respect to the coupler axis.

Fig. 12
Fig. 12

Comparison between the experimental and theoretical wavelength responses of the coupler shown in Fig. 11. The signal was recorded with a white light source coupled with a monochromator so that both polarizations were equally excited, thus explaining the large modulation amplitude.

Fig. 13
Fig. 13

Comparison between the experimental and theoretical elongation responses of a slightly fused (f = 0) 2 × 2 coupler. The experimental conditions of excitation were the same as in Fig. 11.

Fig. 14
Fig. 14

Comparison between the experimental and theoretical wavelength responses of the coupler shown in Fig. 13. The experimental conditions of excitation were the same as in Fig. 12.

Equations (17)

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T 2 × 2 ( α ) = exp ( i α ¯ ) [ cos α i sin α i sin α cos α ] ,
α ¯ = 0 L B ¯ ( z ) d z             with B ¯ ( z ) = B 01 ( z ) + B 11 ( z ) 2 ,
α = 0 L B 01 ( z ) - B 11 ( z ) 2 d z ,
( 1 0 )
T 1 = cos 2 α = ( 1 + cos 2 α ) / 2.
f 2 × 2 = 2 r cl - d 2 ( 2 - 2 ) r cl ,
z b = 16 π 2 n cl ρ cl 2 λ ( U 11 2 - U 01 2 ) τ 2 ,
z b = ( 2 λ ) 5 / 2 π 4 n cl ( n cl 2 - 1 ) 3 / 4 ρ cl 7 / 2 U 01 2 τ 7 / 2 .
1 Λ = 1 π d α d λ ,
1 Λ = L π d δ B d λ = N z b π d δ B d λ ,
T 2 × 2 ( α t ) = exp i α t ¯ [ cos α t i sin α t i sin α t cos α t ] ,
α t ¯ = 0 L B t ¯ d z             with B t ¯ = B 01 t + B 11 t 2 ,
α t = 0 L B 01 t - B 11 t 2 d z ,
T 1 = η cos 2 α x + ( 1 - η ) cos 2 α y ,
T 1 = [ 1 + cos ( α x - α y ) cos ( α x + α y ) ] / 2 ,
Q z = z b y - z b x z b y + z b x = δ B x - δ B y δ B x + δ B y ,
Q λ = Λ y - Λ x Λ y + Λ x ,

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