Abstract

A laser-diode–optical-fiber coupling scheme that uses aspherically ended thermally overexpanded fiber is proposed. The scheme is verified by both an analytical formalism and a wide-angle beam-propagation method analysis in cylindrical coordinates.

© 1998 Optical Society of America

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References

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  1. J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
    [CrossRef]
  2. J. Sakai, T. Kimura, “Design of a miniature lens for semiconductor laser to single-mode fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059–1066 (1980).
    [CrossRef]
  3. H. Presby, C. Giles, “Asymmetric fiber microlenses for efficient coupling to elliptical laser beams,” IEEE Photon. Technol. Lett. 5, 184–186 (1993).
    [CrossRef]
  4. C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
    [CrossRef]
  5. K. Shiraishi, “New scheme of coupling from laser diodes to single-mode fibers: a beam expanding fiber with a hemispherical end,” Appl. Opt. 29, 3469–3470 (1990).
    [CrossRef] [PubMed]
  6. K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
    [CrossRef]
  7. H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
    [CrossRef]
  8. M. Saruwatari, K. Nawata, “Semiconductor laser to single-mode fiber coupler,” Appl. Opt. 18, 1847–1856 (1979).
    [CrossRef] [PubMed]
  9. J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
    [CrossRef]
  10. G. R. Hadley, “Wide-angle beam propagation using padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
    [CrossRef] [PubMed]
  11. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).
  12. K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
    [CrossRef]
  13. J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
    [CrossRef]
  14. Y. Takeuchi, J. Noda, “Novel fiber coupler tapering process using a microheater,” IEEE Photon. Technol. Lett. 4, 465–467 (1992).
    [CrossRef]
  15. J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
    [CrossRef]
  16. M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
    [CrossRef]
  17. K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
    [CrossRef]
  18. C. P. Botham, “Theory of tapering single-mode optical fibres by controlled core diffusion,” Electron. Lett. 24, 243–245 (1988).
    [CrossRef]
  19. N. Amitay, H. M. Presby, “Optical fiber up-tapers modeling and performance analysis,” J. Lightwave Technol. 7, 131–137 (1989).
    [CrossRef]
  20. G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

1996 (1)

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

1995 (1)

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

1993 (3)

K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
[CrossRef]

H. Presby, C. Giles, “Asymmetric fiber microlenses for efficient coupling to elliptical laser beams,” IEEE Photon. Technol. Lett. 5, 184–186 (1993).
[CrossRef]

C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

1992 (3)

Y. Takeuchi, J. Noda, “Novel fiber coupler tapering process using a microheater,” IEEE Photon. Technol. Lett. 4, 465–467 (1992).
[CrossRef]

M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
[CrossRef]

G. R. Hadley, “Wide-angle beam propagation using padé approximant operators,” Opt. Lett. 17, 1426–1428 (1992).
[CrossRef] [PubMed]

1991 (2)

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
[CrossRef]

1990 (2)

K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
[CrossRef]

K. Shiraishi, “New scheme of coupling from laser diodes to single-mode fibers: a beam expanding fiber with a hemispherical end,” Appl. Opt. 29, 3469–3470 (1990).
[CrossRef] [PubMed]

1989 (1)

N. Amitay, H. M. Presby, “Optical fiber up-tapers modeling and performance analysis,” J. Lightwave Technol. 7, 131–137 (1989).
[CrossRef]

1988 (2)

C. P. Botham, “Theory of tapering single-mode optical fibres by controlled core diffusion,” Electron. Lett. 24, 243–245 (1988).
[CrossRef]

J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
[CrossRef]

1980 (2)

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

J. Sakai, T. Kimura, “Design of a miniature lens for semiconductor laser to single-mode fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059–1066 (1980).
[CrossRef]

1979 (1)

Aizawa, Y.

K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
[CrossRef]

Akimoto, Y.

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

Amitay, N.

N. Amitay, H. M. Presby, “Optical fiber up-tapers modeling and performance analysis,” J. Lightwave Technol. 7, 131–137 (1989).
[CrossRef]

Botham, C. P.

C. P. Botham, “Theory of tapering single-mode optical fibres by controlled core diffusion,” Electron. Lett. 24, 243–245 (1988).
[CrossRef]

J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
[CrossRef]

Burrus, C. A.

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

Centanni, J. C.

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

Dragone, C.

C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Edwards, C.

C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Giles, C.

H. Presby, C. Giles, “Asymmetric fiber microlenses for efficient coupling to elliptical laser beams,” IEEE Photon. Technol. Lett. 5, 184–186 (1993).
[CrossRef]

Hadley, G. R.

Hanafusa, H.

H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
[CrossRef]

Harper, J. S.

J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
[CrossRef]

Horiguchi, M.

H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
[CrossRef]

Hornung, S.

J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
[CrossRef]

Kawakami, S.

K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
[CrossRef]

K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
[CrossRef]

Kihara, M.

M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
[CrossRef]

Kimura, T.

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

J. Sakai, T. Kimura, “Design of a miniature lens for semiconductor laser to single-mode fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059–1066 (1980).
[CrossRef]

Kweon, G.

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

Matsumoto, M.

M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
[CrossRef]

Matsumura, K.

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

Murakami, Y.

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

Nakano, H.

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

Nawata, K.

Nibe, M.

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

Noda, J.

Y. Takeuchi, J. Noda, “Novel fiber coupler tapering process using a microheater,” IEEE Photon. Technol. Lett. 4, 465–467 (1992).
[CrossRef]

H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
[CrossRef]

Ohishi, I.

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

Oyama, N.

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

Park, I.

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

Presby, H.

H. Presby, C. Giles, “Asymmetric fiber microlenses for efficient coupling to elliptical laser beams,” IEEE Photon. Technol. Lett. 5, 184–186 (1993).
[CrossRef]

C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Presby, H. M.

N. Amitay, H. M. Presby, “Optical fiber up-tapers modeling and performance analysis,” J. Lightwave Technol. 7, 131–137 (1989).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Sakai, J.

J. Sakai, T. Kimura, “Design of a miniature lens for semiconductor laser to single-mode fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059–1066 (1980).
[CrossRef]

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

Saruwatari, M.

Shim, J.

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

Shiraishi, K.

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
[CrossRef]

K. Shiraishi, “New scheme of coupling from laser diodes to single-mode fibers: a beam expanding fiber with a hemispherical end,” Appl. Opt. 29, 3469–3470 (1990).
[CrossRef] [PubMed]

K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
[CrossRef]

Song, I.

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

Song, J.

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

Stone, J.

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

Stulz, L. W.

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

Suga, S.

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

Takeuchi, Y.

Y. Takeuchi, J. Noda, “Novel fiber coupler tapering process using a microheater,” IEEE Photon. Technol. Lett. 4, 465–467 (1992).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Tomita, S.

M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Yamada, J.

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

Yamauchi, J.

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

Yanagi, T.

K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (3)

H. Hanafusa, M. Horiguchi, J. Noda, “Thermally-diffused expanded core fibres for low-loss and inexpensive photonic components,” Electron. Lett. 27, 1968–1969 (1991).
[CrossRef]

C. P. Botham, “Theory of tapering single-mode optical fibres by controlled core diffusion,” Electron. Lett. 24, 243–245 (1988).
[CrossRef]

J. S. Harper, C. P. Botham, S. Hornung, “Tapers in single-mode optical fibre by controlled core diffusion,” Electron. Lett. 24, 245–246 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Yamada, Y. Murakami, J. Sakai, T. Kimura, “Characteristics of a hemispherical microlens for coupling between a semiconductor laser and single-mode fiber,” IEEE J. Quantum Electron. QE-16, 1067–1072 (1980).
[CrossRef]

J. Sakai, T. Kimura, “Design of a miniature lens for semiconductor laser to single-mode fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059–1066 (1980).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

H. Presby, C. Giles, “Asymmetric fiber microlenses for efficient coupling to elliptical laser beams,” IEEE Photon. Technol. Lett. 5, 184–186 (1993).
[CrossRef]

Y. Takeuchi, J. Noda, “Novel fiber coupler tapering process using a microheater,” IEEE Photon. Technol. Lett. 4, 465–467 (1992).
[CrossRef]

J. Stone, L. W. Stulz, C. A. Burrus, J. C. Centanni, “FiEnd filters: etalon on the beveled facet of a fiber with an out-diffused core,” IEEE Photon. Technol. Lett. 3, 216–218 (1991).
[CrossRef]

M. Kihara, S. Tomita, M. Matsumoto, “Loss characteristics of thermally diffused expanded core fiber,” IEEE Photon. Technol. Lett. 4, 1390–1391 (1992).
[CrossRef]

J. Yamauchi, Y. Akimoto, M. Nibe, H. Nakano, “Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM,” IEEE Photon. Technol. Lett. 8, 236–238 (1996).
[CrossRef]

J. Lightwave Technol. (5)

N. Amitay, H. M. Presby, “Optical fiber up-tapers modeling and performance analysis,” J. Lightwave Technol. 7, 131–137 (1989).
[CrossRef]

K. Shiraishi, T. Yanagi, S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11, 1584–1591 (1993).
[CrossRef]

K. Shiraishi, Y. Aizawa, S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8, 1151–1161 (1990).
[CrossRef]

C. Edwards, H. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

K. Shiraishi, N. Oyama, K. Matsumura, I. Ohishi, S. Suga, “A fiber lens with a long working distance for integrated coupling between laser diodes and single-mode fibers,” J. Lightwave Technol. 13, 1736–1744 (1995).
[CrossRef]

Opt. Lett. (1)

Other (2)

G. Kweon, J. Song, I. Park, I. Song, J. Shim, “A new laser to fiber optical coupling scheme with long working distance using thermally over-expanded fiber,” in Second Optoelectronics and Communications Conference, Technical Digest Series II (Optical Society of Korea, Seoul, 1997), p. 10EP-7.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

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Figures (8)

Fig. 1
Fig. 1

Fabrication of the fiber lens by (a)–(c) Shiraishi’s design and by (d), (e) newly proposed design. (a) Thermally expanded core fiber made with localized heating. (b) Coreless fiber spliced to the cleaved end of the TEC fiber. (c) Lens shaping by an arc discharge. (d) Thermally overexpanded fiber made by excessive heating of the fiber. (e) Lens shaping by an arc discharge.

Fig. 2
Fig. 2

Relevant parameters for analysis of optical coupling efficiency between the laser and the lensed fiber. The laser emission is approximated with a Gaussian beam with beam spot size ωLD0 at the beam waist located at the laser facet. The tip of the lensed fiber is located at a distance D from the LD. The lens shape is parabolic, but the shape of the lens tip can be approximated by a hemisphere with radius R. The beam spot size and the radius of curvature of the Gaussian beam from the laser at the location of the fiber tip are ωLD1 and R LD1, respectively, which after passing the lens tip become ωLD2 and R LD2. The length of the coreless region is L, and the beam waist and the radius of curvature of the eigenmode of the fiber are ω F3 and R F3, respectively. ω F3 and R F3 are not necessarily those of SMF, as shown. Once the beam is coupled into the eigenmode at location 3, the beam is adiabatically transformed into the eigenmode of the SMF. Therefore it is necessary to calculate the coupling efficiency only at the end of the TEC region at location 3.

Fig. 3
Fig. 3

Coupling efficiency between a LD and a lensed fiber. The beam spot size of the LD at the beam waist is assumed to be 0.8 μm. The refractive index of the coreless region is taken to be the same as that of the fiber cladding. The lens shape is assumed parabolic. Curves a and b are coupling efficiencies between the LD and the SMF (ω F3 = 5.0 μm). Curve a is for a 1-mm length of coreless region, and curve b is for a 2 mm length. Curves c, d, and e are for TEC fibers (ω F3 = 22.4 μm) for coreless region lengths of 1, 2, and 3 mm, respectively.

Fig. 4
Fig. 4

Coupling efficiency calculated by the wide-angle BPM in cylindrical coordinates. The (1, 1) Padé approximation and an absorbing boundary condition are used. A typical differencing step is 0.16 μm laterally and 0.01 μm longitudinally. Curve a is the butt-coupling efficiency calculated from the analytical formula, and curve b is the butt-coupling efficiency calculated by the wide-angle BPM. The difference at shorter distances is due primarily to a discretization error. Curves c and d are the coupling efficiencies for the hemispherically ended lensed fiber of Sakai and Kimura. Curve c is the analytical result, and curve d is the numerical result. If we compare it with the experimental result, the numerical result is closer to the experimental findings (Fig. 6 of Ref. 1).

Fig. 5
Fig. 5

Coupling efficiency between the LD and the lensed fiber. The length of the coreless region is 1 mm in curves a and b and 0.5 mm in curves c and d. The beam spot size of the fiber eigenmode is 5.0 μm in curves a–d. Curves a and c are the analytical results and curves b and d are the numerical results. Curves e and f show the coupling efficiency between the LD and the lensed fiber when the coreless region is 1 mm long and the beam spot size of the fiber eigenmode is 22.4 μm. Curve e is the analytical result and curve f is the numerical result.

Fig. 6
Fig. 6

Phase of the propagating beam from the LD near the fiber tip. The coreless region is 1 mm long, and the lens shape is parabolic. The radius of curvature at the fiber tip is determined such as to optimize the coupling efficiency for the given coreless region length. The LD-to-fiber distance is also fixed at the position that yields the maximum coupling efficiency. It is clearly seen that beams traveling at larger angles do not convert into the guided mode. The ideal lens shape must be parabolic only near the axis.

Fig. 7
Fig. 7

Core material profile of the GeO2-doped SMF. Curve a is the core material profile of the step-index SMF. Curve b is the same core material profile series expanded by use of first 100 terms in the Bessel function series expansion. The solutions are truncated eigenfunctions of cylindrical diffusion equation. The heating time is taken as 1 h. The heating temperatures are 25, 1100, 1500, and 1700 °C, respectively, for curves b, c, d, and e. The oscillation of the core material profile at low temperature is due to the extremely slow convergence of the series. Curve e shows that 1-h heating at 1700 °C is enough to diffuse the core material profile completely.

Fig. 8
Fig. 8

Coupling efficiency calculated with the analytical formula (curve a) and the BPM analysis (curves b–d). In curve b the peak temperature is taken as T 0, which is 1400 °C in this example. This structure is effectively a lensed fiber without the diffused core. In curve c, peak temperature T 1 is taken as 1500 °C, and T 1 is taken as 1700 °C in curve d. The length of the transition region is taken as 1 mm, and the length of the coreless region, which is defined as the length from the tip of the lens to the middle of the transition region, is also taken as 1 mm. The lens tip is parabolic in shape. The other parameters are the same as in the previous numerical calculations.

Equations (35)

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E LD 1 x ,   z 2 π 1 ω LD 1 1 / 2 exp - x 2 ω LD 1 2 exp - ikx 2 2 R LD 1 ,
ω LD 1 = ω LD 0 1 + λ D π ω LD 0 2 2 1 / 2
R LD 1 = D 1 + π ω LD 0 2 λ D 2 .
E F 2 x ,   z 2 π 1 ω F 2 1 / 2 exp - x 2 ω F 2 2 exp + inkx 2 2 R F 2 ,
ω F 2 = ω F 3 1 + λ L n π ω F 3 2 2 1 / 2 ,
R F 2 = L 1 + π ω F 3 2 λ L n 2 ,
D opt = L nM .
R = n - 1 D opt M M + 1 .
η 2 = η x η y 2 = 4 ω LD 1 2 ω F 2 2 1 ω LD 1 2 + 1 ω F 2 2 2 + π λ 2 1 R LD 2 + n R F 2 2 ,
R LD 2 = RR LD 1 R - n - 1 R LD 1 .
η 2 = 4 ω LD 1 2 ω F 2 2 1 ω LD 1 2 + 1 ω F 2 2 2 + π λ 2 1 R LD 1 + 1 R F 2 2 .
2 E z 2 + 2 E r 2 + 1 r E r + 1 r 2 2 E ϕ 2 + k 2 n 2 r ,   z E = 0 ,
E r ,   ϕ ,   z = E r ,   z exp - ikn 0 z exp i ν ϕ ,
2 ikn 0 E z - 2 E z 2 = PE ,
P 2 r 2 + 1 r r - ν 2 r 2 + k 2 n 2 r ,   z - n 0 2 ,
E z = - i   P 2 kn 0 1 + i 2 kn 0 z   E .
E z = - i   P 2 kn 0 1 + P 4 k 2 n 0 2   E .
E z E n + 1 - E n Δ z ,
E E n + 1 + E n 2
PE I 1 Δ 2 + 1 2 Δ r I E I + 1 + 1 Δ 2 - 1 2 Δ r I E I - 1 + - 2 Δ 2 - ν 2 r I 2 + k 2 n I 2 - n 0 2 E I .
E I n + 1 + aPE I n + 1 = E I n + bPE I n ,
a 1 + ikn 0 Δ z 4 k 2 n 0 2 ,
b 1 - ikn 0 Δ z 4 k 2 n 0 2 .
E r ,   ϕ ,   z = E r exp - i β z exp i ν ϕ ,
2 E r 2 + 1 r E r + k 2 n 2 E - ν 2 r 2   E HE = β 2 E .
1 Δ 2 + 1 2 Δ r I E I + 1 + 1 Δ 2 - 1 2 Δ r I E I - 1 + - 2 Δ 2 - ν 2 r I 2 + k 2 n I 2 E I = β 2 E I ,
HE 1 = 2 - ν 2 2 1 Δ 2 1 + - 1 ν E 2 - 2 E 1 + k 2 n 1 2 E 1 = β 2 E 1 .
η =   E 1 * r E 2 r r d r 2   | E 1 r | 2 r d r     | E 2 r | 2 r d r ,
2 u r ,   ϕ ,   t - 1 D u r ,   ϕ ,   t t = 0 ,
u r ,   t = a 2 b 2 + i = 1 2 a b 2 J 1 α i a α i J 0 2 α i b   J 0 α i r exp - α i 2 Dt ,
J 1 α i b = 0 .
D = D 0 exp - Q RT ,
n 2 r ,   t = n core 2 u r ,   t + n cladding 2 1 - u r ,   t ,
u r ,   t     1 Dt exp - r 2 4 Dt .
T = T 1 z < z 1 T 0 + T 1 - T 0 cos 2 π 2 z - z 1 z 2 - z 1 z 1 z z 2 T 0 z > z 2 ,

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