Abstract

Equilateral 3 × 3 tapered couplers made from single-mode fiber are found to behave in a less-than-ideal manner. This behavior is due to twist and can be corrected by twisting the coupler after its fabrication. A small amount of twist causes only a redistribution of output power between the two nonlaunch fibers, whereas a larger twist can restore the original response but with a cyclic change of fiber identity. An analysis of local mode coupling between the two degenerate LP11 modes in the waist of the coupler leads to equations that successfully account for the twist-tuning effect.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. K. Sheem, T. G. Giallorenzi, “Single-mode fiber multiterminal star directional coupler,” Appl. Phys. Lett. 35, 131–133 (1979).
    [Crossref]
  2. R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
    [Crossref]
  3. W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
    [Crossref]
  4. M. Kawachi, “Fabrication of polarisation-maintaining [3 × 3] single-mode-fibre couplers,” Electron. Lett. 19, 781–782 (1983).
    [Crossref]
  5. M. H. Slonecker, J. C. Williams, “Recent advances in single-mode fused taper coupler technology,” in Fiber Optic and Laser Sensors I, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.412, 50–53 (1983).
  6. K. O. Hill, D. C. Johnson, R. G. Lamont, “Wavelength dependence in fused biconical taper splitters: measurement and control,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.
  7. A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
    [Crossref]
  8. K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
    [Crossref]
  9. H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
    [Crossref]
  10. D. B. Mortimore, J. W. Arkwright, “Performance tuning of 1 × 7 wavelength-flattened fused fibre couplers,” Electron. Lett. 26, 1442–1443 (1990).
    [Crossref]
  11. T. A. Birks, “Power equalisation in 3 × 3 fibre couplers by twist tuning,” Electron. Lett. 27, 1087–1088 (1991).
    [Crossref]
  12. T. A. Birks, “Twist-induced tuning in tapered fibre couplers,” Appl. Opt. 28, 4226–4233 (1989).
    [Crossref] [PubMed]
  13. F. P. Payne, C. D. Hussey, M. S. Yataki, “Modelling fused single-mode-fibre couplers,” Electron. Lett. 21, 461–462 (1985).
  14. C. Vassallo, “Extension de la representation scalaire du champ aux fibres optiques à gaine finie,” Opt. Quantum Electron. 15, 349–353 (1983).
    [Crossref]
  15. W. J. Stewart, J. D. Love, “Design limitation on tapers and couplers in single mode fibres,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.
  16. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  17. W. K. Li, S. M. Blinder: “Solution of the Schrödinger equation for a particle in an equilateral triangle,” J. Math. Phys. N.Y. 26, 2784–2786 (1985).
    [Crossref]

1991 (2)

T. A. Birks, “Power equalisation in 3 × 3 fibre couplers by twist tuning,” Electron. Lett. 27, 1087–1088 (1991).
[Crossref]

K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
[Crossref]

1990 (2)

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

D. B. Mortimore, J. W. Arkwright, “Performance tuning of 1 × 7 wavelength-flattened fused fibre couplers,” Electron. Lett. 26, 1442–1443 (1990).
[Crossref]

1989 (1)

1986 (2)

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

1985 (2)

W. K. Li, S. M. Blinder: “Solution of the Schrödinger equation for a particle in an equilateral triangle,” J. Math. Phys. N.Y. 26, 2784–2786 (1985).
[Crossref]

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

1983 (2)

C. Vassallo, “Extension de la representation scalaire du champ aux fibres optiques à gaine finie,” Opt. Quantum Electron. 15, 349–353 (1983).
[Crossref]

M. Kawachi, “Fabrication of polarisation-maintaining [3 × 3] single-mode-fibre couplers,” Electron. Lett. 19, 781–782 (1983).
[Crossref]

1982 (1)

W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
[Crossref]

1979 (1)

S. K. Sheem, T. G. Giallorenzi, “Single-mode fiber multiterminal star directional coupler,” Appl. Phys. Lett. 35, 131–133 (1979).
[Crossref]

Arkwright, J. W.

D. B. Mortimore, J. W. Arkwright, “Performance tuning of 1 × 7 wavelength-flattened fused fibre couplers,” Electron. Lett. 26, 1442–1443 (1990).
[Crossref]

Bdhler, W.

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

Birks, T. A.

T. A. Birks, “Power equalisation in 3 × 3 fibre couplers by twist tuning,” Electron. Lett. 27, 1087–1088 (1991).
[Crossref]

T. A. Birks, “Twist-induced tuning in tapered fibre couplers,” Appl. Opt. 28, 4226–4233 (1989).
[Crossref] [PubMed]

Black, R. J.

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

Blinder, S. M.

W. K. Li, S. M. Blinder: “Solution of the Schrödinger equation for a particle in an equilateral triangle,” J. Math. Phys. N.Y. 26, 2784–2786 (1985).
[Crossref]

Burns, W. K.

W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
[Crossref]

Davis, A. W.

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

Gagnon, L.

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

Giallorenzi, T. G.

S. K. Sheem, T. G. Giallorenzi, “Single-mode fiber multiterminal star directional coupler,” Appl. Phys. Lett. 35, 131–133 (1979).
[Crossref]

Gunther, M. F.

K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
[Crossref]

Hart, E.

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

Hill, K. O.

K. O. Hill, D. C. Johnson, R. G. Lamont, “Wavelength dependence in fused biconical taper splitters: measurement and control,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

Hussey, C. D.

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

Johnson, D. C.

K. O. Hill, D. C. Johnson, R. G. Lamont, “Wavelength dependence in fused biconical taper splitters: measurement and control,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

Kawachi, M.

M. Kawachi, “Fabrication of polarisation-maintaining [3 × 3] single-mode-fibre couplers,” Electron. Lett. 19, 781–782 (1983).
[Crossref]

King, J. P.

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

Lamont, R. G.

K. O. Hill, D. C. Johnson, R. G. Lamont, “Wavelength dependence in fused biconical taper splitters: measurement and control,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

Li, W. K.

W. K. Li, S. M. Blinder: “Solution of the Schrödinger equation for a particle in an equilateral triangle,” J. Math. Phys. N.Y. 26, 2784–2786 (1985).
[Crossref]

Love, J. D.

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

W. J. Stewart, J. D. Love, “Design limitation on tapers and couplers in single mode fibres,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

Moeller, R. P.

W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
[Crossref]

Mortimore, D. B.

D. B. Mortimore, J. W. Arkwright, “Performance tuning of 1 × 7 wavelength-flattened fused fibre couplers,” Electron. Lett. 26, 1442–1443 (1990).
[Crossref]

Müller, R.

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

Murphy, K. A.

K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
[Crossref]

Payne, F. P.

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

Pettitt, M. J.

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

Poisel, H.

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

Richards, K.

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

Sheem, S. K.

S. K. Sheem, T. G. Giallorenzi, “Single-mode fiber multiterminal star directional coupler,” Appl. Phys. Lett. 35, 131–133 (1979).
[Crossref]

Slonecker, M. H.

M. H. Slonecker, J. C. Williams, “Recent advances in single-mode fused taper coupler technology,” in Fiber Optic and Laser Sensors I, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.412, 50–53 (1983).

Snyder, A. W.

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

Stewart, W. J.

W. J. Stewart, J. D. Love, “Design limitation on tapers and couplers in single mode fibres,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

Trommer, G. F.

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

Vassallo, C.

C. Vassallo, “Extension de la representation scalaire du champ aux fibres optiques à gaine finie,” Opt. Quantum Electron. 15, 349–353 (1983).
[Crossref]

Vengsarkar, A. M.

K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
[Crossref]

Villarruel, C. A.

W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
[Crossref]

Wentworth, R. H.

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

Williams, J. C.

M. H. Slonecker, J. C. Williams, “Recent advances in single-mode fused taper coupler technology,” in Fiber Optic and Laser Sensors I, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.412, 50–53 (1983).

Wright, S.

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

Yataki, M. S.

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

Youngquist, R. C.Youngquist

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. K. Sheem, T. G. Giallorenzi, “Single-mode fiber multiterminal star directional coupler,” Appl. Phys. Lett. 35, 131–133 (1979).
[Crossref]

Electron. Lett. (9)

R. J. Black, L. Gagnon, R. C.Youngquist Youngquist, R. H. Wentworth, “Modes of evanescent 3 × 3 couplers and three-core fibres,” Electron. Lett. 22, 1311–1313 (1986).
[Crossref]

W. K. Burns, R. P. Moeller, C. A. Villarruel, “Observation of low noise in a passive fibre gyroscope,” Electron. Lett. 18, 648–650 (1982).
[Crossref]

M. Kawachi, “Fabrication of polarisation-maintaining [3 × 3] single-mode-fibre couplers,” Electron. Lett. 19, 781–782 (1983).
[Crossref]

A. W. Davis, S. Wright, M. J. Pettitt, J. P. King, K. Richards, “Coherent optical receiver for 680 Mbit/s using phase diversity,” Electron. Lett. 22, 9–11 (1986).
[Crossref]

K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, “Variable-ratio, polarisation-insensitive, 3 × 3 fused biconical tapered couplers,” Electron. Lett. 27, 1336–1337 (1991).
[Crossref]

H. Poisel, G. F. Trommer, W. Bdhler, E. Hart, R. Müller, “Low-cost fibre-optic gyroscope,” Electron. Lett. 26, 69–70 (1990).
[Crossref]

D. B. Mortimore, J. W. Arkwright, “Performance tuning of 1 × 7 wavelength-flattened fused fibre couplers,” Electron. Lett. 26, 1442–1443 (1990).
[Crossref]

T. A. Birks, “Power equalisation in 3 × 3 fibre couplers by twist tuning,” Electron. Lett. 27, 1087–1088 (1991).
[Crossref]

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

J. Math. Phys. N.Y. (1)

W. K. Li, S. M. Blinder: “Solution of the Schrödinger equation for a particle in an equilateral triangle,” J. Math. Phys. N.Y. 26, 2784–2786 (1985).
[Crossref]

Opt. Quantum Electron. (1)

C. Vassallo, “Extension de la representation scalaire du champ aux fibres optiques à gaine finie,” Opt. Quantum Electron. 15, 349–353 (1983).
[Crossref]

Other (4)

W. J. Stewart, J. D. Love, “Design limitation on tapers and couplers in single mode fibres,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

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

M. H. Slonecker, J. C. Williams, “Recent advances in single-mode fused taper coupler technology,” in Fiber Optic and Laser Sensors I, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.412, 50–53 (1983).

K. O. Hill, D. C. Johnson, R. G. Lamont, “Wavelength dependence in fused biconical taper splitters: measurement and control,” presented at the IOOC–ECOC ’85 meeting, Venice, 1985.

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 (10)

Fig. 1
Fig. 1

Schematic equilateral 3 × 3 coupler, showing the system of fiber nomenclature (the numbers in the coupler cross section) used in the text.

Fig. 2
Fig. 2

Schematic diagram illustrating how three fibers are twisted together to form an equilateral array. The convention for positive twist angle is indicated.

Fig. 3
Fig. 3

Wavelength variation of the normalized output powers of a typical short 3 × 3 coupler, in fibers 1, 2, and 3 for light launched into fiber 1.

Fig. 4
Fig. 4

Wavelength responses of another short coupler, for light launched into (a) fiber 1 and (b) fiber 2.

Fig. 5
Fig. 5

Cleaved cross sections of typical (a) short and (b) long 3 × 3 couplers.

Fig. 6
Fig. 6

Wavelength responses of the coupler of Fig. 3 after being subjected to an imposed twist angle of (a) −40°, (b) +185°, and (c) +6°.

Fig. 7
Fig. 7

Variation of the output powers of the coupler of Figs. 3 and 6, for input light with a wavelength of 1290 nm, as a function of net-twist angle.

Fig. 8
Fig. 8

Wavelength responses of a typical long 3 × 3 coupler for net-twist angles of (a) 0°, (b) 26°, (c) 56°, (d) 116°, (e) 176°, and (f) 239°.

Fig. 9
Fig. 9

Three lowest-order scalar normal modes of a weakly interacting equilateral array of fibers. The numbers in the cross sections indicate modal field amplitudes in each fiber.

Fig. 10
Fig. 10

Theoretical wavelength response of a 3 × 3 coupler, calculated (a) using the conventional analysis for an untwisted coupler, with N(λ) assumed linear and fitted to the experimental curves in Fig. 8(a); and (b)–(f) using the analysis for a twisted coupler, with κ = 1/2 and the same N(λ) as (a), with net-twist angles Θ equal to those for the corresponding curves in Figs. 8(b)–8(f).

Equations (27)

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

b a = 3 / 3 u o ,
b b = 6 / 3 u o ,
b c = 0 ,
P 1 = [ 5 + 4 cos ( 2 π N ) ] / 9 P o ,
P 2 = [ 2 - 2 cos ( 2 π N ) ] / 9 P o ,
P 3 = P 2 ,
N = coupler ( β a - β b ) 2 π d z .
N = α L λ n o A ,
b b ( z ) ψ b ( z ) + b c ( z ) ψ c ( z ) = b b ( z + δ z ) ψ b ( z + δ z ) + b c ( z + δ z ) ψ c ( z + δ z ) .
0 = d b b d z ψ b + b b ψ b z + d b c d z ψ c + b c ψ c z ,
d b b d z - κ ( z ) d θ d z b c = 0 ,
d b c d z + κ ( z ) d θ d z b b = 0 ,
C a b = A ψ c ψ b z d A = d θ d z A ψ c ψ b θ d A d θ d z κ ( z ) ,
b a = 3 / 3 u o ,
b b = 6 / 3 cos ( κ Θ ) u o ,
b c = - 6 / 3 sin ( κ Θ ) u o ,
κ = 1 Θ 0 Θ κ [ z ( θ ) ] d θ = 1 Θ - κ ( z ) ( d θ d z ) d z .
u 1 = [ exp ( 2 π N i ) + 2 cos ( κ Θ ) ] / 3 u o ,
u 2 = [ exp ( 2 π N i ) + 2 cos ( κ Θ + 2 π / 3 ) ] / 3 u o ,
u 3 = [ exp ( 2 π N i ) + 2 cos ( κ Θ - 2 π / 3 ) ] / 3 u o .
P 1 = [ 1 + 4 cos 2 ( κ Θ ) + 4 cos ( κ Θ ) cos ( 2 π N ) ] / 9 P o ,
P 2 = [ 1 + 4 cos 2 ( κ Θ + 2 π / 3 ) + 4 cos ( κ Θ + 2 π / 3 ) cos ( 2 π N ) ] / 9 P o ,
P 3 = [ 1 + 4 cos 2 ( κ Θ - 2 π / 3 ) + 4 cos ( κ Θ - 2 π / 3 ) cos ( 2 π N ) ] / 9 P o ,
P 1 = 1 / 3 P o ,
P 2 = [ 1 + 3 κ Θ ] / 3 P o ,
P 3 = [ 1 - 3 κ Θ ] / 3 P o .
N = N o - 9 32 N o ( Θ 2 π ) 2 ,

Metrics