Abstract

Transmission characteristics of graded-index oval (GIO) core fibers are theoretically analyzed, and basic equations representing the specific properties of the fiber are obtained. Formulas for the propagation constant, the field-profile function, the cutoff condition, and the total number of guided modes are derived in explicit forms. The formula for the change of the Gaussian beam radius as a function of the propagation distance is also given, and the numerical example agrees well with experimental data and agrees completely with that obtained by the beam-propagation method. These explicit expressions are useful for finding optimum structural parameters of GIO fibers to be used in practical fields.

© 2004 Optical Society of America

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References

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  1. L. Cohen, M. Schneider, “Microlenses for coupling junction lasers to optical fibers,” Appl. Opt. 13, 89–94 (1974).
    [CrossRef] [PubMed]
  2. V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
    [CrossRef]
  3. R. A. Modavis, T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling,” IEEE Photon. Technol. Lett. 7, 798–800 (1995).
    [CrossRef]
  4. S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.
  5. A. Ogura, K. Shiraishi, “A field-profile transformer utilizing a graded-index oval-core (GIO) fiber,” IEEE J. Lightwave Technol. 19, 49–53 (2001).
    [CrossRef]
  6. A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
    [CrossRef]
  7. M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
    [CrossRef] [PubMed]
  8. D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).
  9. H. Kogelnik, “Imaging of optical modes-resonators with internal mirrors,” Bell Syst. Tech. J. 44, 455–494 (1965).
  10. R. Kishimoto, M. Koyama, “Coupling characteristics between single-mode fiber and square law medium,” IEEE Trans. Microwave Theory Tech. 30, 882–893 (1982).
    [CrossRef]
  11. W. Emkey, C. Jack, “Analysis and evaluation of graded-index fiber-lenses,” IEEE J. Lightwave Technol. 5, 1156–1164 (1987).
    [CrossRef]

2001

A. Ogura, K. Shiraishi, “A field-profile transformer utilizing a graded-index oval-core (GIO) fiber,” IEEE J. Lightwave Technol. 19, 49–53 (2001).
[CrossRef]

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

1995

R. A. Modavis, T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling,” IEEE Photon. Technol. Lett. 7, 798–800 (1995).
[CrossRef]

1990

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

1987

W. Emkey, C. Jack, “Analysis and evaluation of graded-index fiber-lenses,” IEEE J. Lightwave Technol. 5, 1156–1164 (1987).
[CrossRef]

1982

R. Kishimoto, M. Koyama, “Coupling characteristics between single-mode fiber and square law medium,” IEEE Trans. Microwave Theory Tech. 30, 882–893 (1982).
[CrossRef]

1978

1974

1973

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

1965

H. Kogelnik, “Imaging of optical modes-resonators with internal mirrors,” Bell Syst. Tech. J. 44, 455–494 (1965).

Bouer, D. P.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

Cohen, L.

Curtis, L.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

Emkey, W.

W. Emkey, C. Jack, “Analysis and evaluation of graded-index fiber-lenses,” IEEE J. Lightwave Technol. 5, 1156–1164 (1987).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Gaebe, C. E.

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

Gloge, D.

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

Huang, S. Y.

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

Jack, C.

W. Emkey, C. Jack, “Analysis and evaluation of graded-index fiber-lenses,” IEEE J. Lightwave Technol. 5, 1156–1164 (1987).
[CrossRef]

Kishimoto, R.

R. Kishimoto, M. Koyama, “Coupling characteristics between single-mode fiber and square law medium,” IEEE Trans. Microwave Theory Tech. 30, 882–893 (1982).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Imaging of optical modes-resonators with internal mirrors,” Bell Syst. Tech. J. 44, 455–494 (1965).

Koyama, M.

R. Kishimoto, M. Koyama, “Coupling characteristics between single-mode fiber and square law medium,” IEEE Trans. Microwave Theory Tech. 30, 882–893 (1982).
[CrossRef]

Kuchiki, S.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Marcatili, E. A. J.

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

Miller, K. A.

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

Modavis, R. A.

R. A. Modavis, T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling,” IEEE Photon. Technol. Lett. 7, 798–800 (1995).
[CrossRef]

Ogura, A.

A. Ogura, K. Shiraishi, “A field-profile transformer utilizing a graded-index oval-core (GIO) fiber,” IEEE J. Lightwave Technol. 19, 49–53 (2001).
[CrossRef]

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Ohta, K.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Oishi, I.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

Schneider, M.

Shah, V. S.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

Shiraishi, K.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

A. Ogura, K. Shiraishi, “A field-profile transformer utilizing a graded-index oval-core (GIO) fiber,” IEEE J. Lightwave Technol. 19, 49–53 (2001).
[CrossRef]

Stakelon, T. S.

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

Vodhanel, R. S.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

Webb, T. W.

R. A. Modavis, T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling,” IEEE Photon. Technol. Lett. 7, 798–800 (1995).
[CrossRef]

Wiand, G. T.

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

Young, W. C.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge, E. A. J. Marcatili, “Multimode theory of graded-core fibers,” Bell Syst. Tech. J. 52, 1563–1578 (1973).

H. Kogelnik, “Imaging of optical modes-resonators with internal mirrors,” Bell Syst. Tech. J. 44, 455–494 (1965).

IEEE J. Lightwave Technol.

V. S. Shah, L. Curtis, R. S. Vodhanel, D. P. Bouer, W. C. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” IEEE J. Lightwave Technol. 8, 1313–1318 (1990).
[CrossRef]

A. Ogura, K. Shiraishi, “A field-profile transformer utilizing a graded-index oval-core (GIO) fiber,” IEEE J. Lightwave Technol. 19, 49–53 (2001).
[CrossRef]

W. Emkey, C. Jack, “Analysis and evaluation of graded-index fiber-lenses,” IEEE J. Lightwave Technol. 5, 1156–1164 (1987).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Ogura, S. Kuchiki, K. Shiraishi, K. Ohta, I. Oishi, “Efficient coupling between laser diodes with a highly elliptic field and single-mode fibers by means of GIO fibers,” IEEE Photon. Technol. Lett. 13, 1191–1193 (2001).
[CrossRef]

R. A. Modavis, T. W. Webb, “Anamorphic microlens for laser diode to single-mode fiber coupling,” IEEE Photon. Technol. Lett. 7, 798–800 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

R. Kishimoto, M. Koyama, “Coupling characteristics between single-mode fiber and square law medium,” IEEE Trans. Microwave Theory Tech. 30, 882–893 (1982).
[CrossRef]

Other

S. Y. Huang, C. E. Gaebe, K. A. Miller, G. T. Wiand, T. S. Stakelon, “High coupling optical design for laser diodes with large aspect ratio,” in Proceedings of the IEEE Electronic Components Technology Conference (Institute of Electrical and Electronic Engineers Service Center, Piscataway, N.J., 1999), pp. 912–915.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram illustrating the field transformation of the GIO fiber.

Fig. 2
Fig. 2

Structural parameters of the fiber used in the analysis.

Fig. 3
Fig. 3

Amplitude (absolute value) distributions of some lower-order modes in the GIO fiber. The x- and y-directional mode numbers are denoted by m and n, respectively, and the number is represented in the form (m, n) under each distribution.

Fig. 4
Fig. 4

Mode orders and the cutoff condition for the GIO fiber, where filled and empty circles represent guided and radiation modes, respectively.

Fig. 5
Fig. 5

Coupling efficiency η m between the input Gaussian field and each eigenmode as a function of mode number m. Figures by the curves represent w fx /w gx or w gx /w fx .

Fig. 6
Fig. 6

A cross-sectional microphotograph of the GIO fiber used in the experiment. The other end of the fiber was illuminated by a Lambertian light source.

Fig. 7
Fig. 7

Spot radii as a function of the propagation length. Calculated values based on the formulas agree completely with those obtained by the BPM.

Equations (25)

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

n2x, y=n02-n02-n12x/ax2+y/ay2=n021-x/Agx2+y/Agy2,
2ψx2+2ψy2+k02n2x, y-β2ψ=0,
ψmnx, y=ψmxψny  m, n=0, 1, 2,.
ψmx=Hm2/wfxxexp-x/wfx2,
ψny=Hn2/wfyyexp-y/wfy2,
β2=n0k02-n0k02m+1/Agx+2n+1/Agy.
wfx=λAgx/πn01/2,wfy=λAgy/πn01/2.
2m+sn+s+1=Vx,
NVx2/4s.
βn0k0-m+1/2/Agx+n+1/2/Agy,
ϕ=exp-x/wgx2-y/wgy2.
amn=- ϕ*ψmndxdy- ψmn2dxdy,
amn=aman
amn=0,
am=wgx2m-1/2m/2!wgx2-wfx2m/2wgx2+wfx2m+1/2,
ηmn=- ϕ*ψmn2- ϕ2- ψmn2.
ηmn=ηmηn
ηmn=0,
ηm=m!wgxwfxwgx2-wfx2m2m-1m/2!2wgx2+wfx2m+1,
Ez=n=0m=0 amnψmn expjzβmn.
Ezexp jzn0k0-12Agx-12Agxn=0 Ynm=0 Xm,
Xmamψm exp-jzm/Agx,
m=0 Xm=m=0 X2m.
m=0 X2m=2wgxwgx2+wfx2wgx2+wfx2+wgx2-wfx2exp-j2z/Agx1/2exp-1wfx2×wgx2+wfx2-wgx2-wfx2exp-j2z/Agxwgx2+wfx2+wgx2-wfx2exp-j2z/Agx x2.
wx2z=wfx4wgx2sin2z/Agx+wgx2cos2z/Agx.

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