Abstract

A novel optical coupling scheme that uses a lensed fiber integrated with a long-period fiber grating (LPFG) is proposed. Two experiments are performed to demonstrate the validity of such a scheme in single-mode-fiber–single-mode-fiber (SMF-to-SMF) and laser-diode–single-mode-fiber (LD-to-SMF) coupling setups. The measured results show that for an appropriate lens radius the addition of a LPFG will lead to a higher coupling efficiency over a longer range of working distance than without the LPFG. Coupling efficiencies of ∼78% and 35% are achieved for corresponding working distances of ∼250 and 110 µm, 1-dB longitudinal tolerances of ∼40 and 26 µm, and 1-dB transverse tolerances of ∼7.6 and 2.6 µm for SMF-to-SMF and LD-to-SMF, respectively.

© 2000 Optical Society of America

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  1. A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
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    [CrossRef]
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    [CrossRef] [PubMed]
  4. K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
    [CrossRef]
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    [CrossRef]
  23. T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
    [CrossRef]
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    [CrossRef]
  27. H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long period fiber grating to external index of refraction,” J. Lightwave Technol. 16, 1606–1611 (1998).
    [CrossRef]
  28. B. H. Lee, J. Nishii, “Cladding-surrounding interface insensitive long-period grating,” Electron. Lett. 34, 1129–1130 (1998).
    [CrossRef]
  29. K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper FB2.

1999 (1)

W. T. Chen, L. A. Wang, “Optical coupling between singlemode fibers by utilizing long-period fibre grating,” Electron. Lett. 35, 421–423 (1999).
[CrossRef]

1998 (4)

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
[CrossRef]

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long period fiber grating to external index of refraction,” J. Lightwave Technol. 16, 1606–1611 (1998).
[CrossRef]

B. H. Lee, J. Nishii, “Cladding-surrounding interface insensitive long-period grating,” Electron. Lett. 34, 1129–1130 (1998).
[CrossRef]

1997 (5)

T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

H. J. Patrick, C. G. Askins, R. W. McElhanon, E. J. Friebel, “Amplitude mask patterned on an excimer laser mirror for high intensity writing of long period fiber gratings,” Electron. Lett. 33, 1167–1168 (1997).
[CrossRef]

E. M. Dianove, D. S. Stardubov, S. A. Vasiliev, A. A. Frolov, O. I. Medvedkov, “Refractive-index gratings written by near-ultraviolet radiation,” Opt. Lett. 22, 221–223 (1997).
[CrossRef]

I. Moerman, P. P. Van Daele, P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III–V semiconductor devices,” IEEE J. Sel. Top. Quantum. Electron. 3, 1308–1320 (1997).
[CrossRef]

1996 (4)

A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
[CrossRef]

A. M. Vengsakar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

H. Kuwahara, M. Sasaki, N. Tokoyo, “Efficient coupling from semiconductor lasers into single-mode fibers with tapered hemispherical ends,” J. Lightwave Technol. 14, 58–65 (1996).

1995 (1)

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

1994 (1)

N. Kalonji, J. Semo, “High efficiency long working distance laser diode to singlemode fiber coupling arrangement,” Electron. Lett. 30, 892–893 (1994).
[CrossRef]

1993 (1)

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

1992 (1)

1990 (1)

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

1987 (1)

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

1985 (1)

W. Bludau, R. H. Rosserg, “Low-loss laser-to-fiber coupling with negligible optical feedback,” J. Lightwave Technol. LT-3, 294–302 (1985).
[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.-I. 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]

1969 (1)

1965 (1)

Askins, C. G.

H. J. Patrick, C. G. Askins, R. W. McElhanon, E. J. Friebel, “Amplitude mask patterned on an excimer laser mirror for high intensity writing of long period fiber gratings,” Electron. Lett. 33, 1167–1168 (1997).
[CrossRef]

Auvray, P.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Bhatia, V.

A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
[CrossRef]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

Bilodeau, F.

D. C. Johnson, F. Bilodeau, B. Malo, K. O. Hill, P. G. J. Wigley, G. I. Stegeman, “Long-length, long-period rocking filters fabricated from conventional monomode telecommunications optical fiber,” Opt. Lett. 17, 1635–1637 (1992).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Bludau, W.

W. Bludau, R. H. Rosserg, “Low-loss laser-to-fiber coupling with negligible optical feedback,” J. Lightwave Technol. LT-3, 294–302 (1985).
[CrossRef]

Bucholtz, F.

Caulet, J.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Chanclou, P.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Chen, W. T.

W. T. Chen, L. A. Wang, “Optical coupling between singlemode fibers by utilizing long-period fibre grating,” Electron. Lett. 35, 421–423 (1999).
[CrossRef]

Clavel, B.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Danzuka, T.

T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

Davis, D. D.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
[CrossRef]

Demeester, P. M.

I. Moerman, P. P. Van Daele, P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III–V semiconductor devices,” IEEE J. Sel. Top. Quantum. Electron. 3, 1308–1320 (1997).
[CrossRef]

Dianove, E. M.

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]

Emkey, W. L.

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

Enomoto, T.

T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

Erdogan, T.

T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760–1773 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
[CrossRef]

Friebel, E. J.

H. J. Patrick, C. G. Askins, R. W. McElhanon, E. J. Friebel, “Amplitude mask patterned on an excimer laser mirror for high intensity writing of long period fiber gratings,” Electron. Lett. 33, 1167–1168 (1997).
[CrossRef]

Frolov, A. A.

Gaylord, T. K.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
[CrossRef]

Glytsis, E. N.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
[CrossRef]

Hill, K. O.

D. C. Johnson, F. Bilodeau, B. Malo, K. O. Hill, P. G. J. Wigley, G. I. Stegeman, “Long-length, long-period rocking filters fabricated from conventional monomode telecommunications optical fiber,” Opt. Lett. 17, 1635–1637 (1992).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Himeno, K.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper FB2.

Ishikawa, S.

T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

Jack, C. A.

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

Johnson, D. C.

D. C. Johnson, F. Bilodeau, B. Malo, K. O. Hill, P. G. J. Wigley, G. I. Stegeman, “Long-length, long-period rocking filters fabricated from conventional monomode telecommunications optical fiber,” Opt. Lett. 17, 1635–1637 (1992).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Joulié, G.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Judkins, J. B.

A. M. Vengsakar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef]

A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
[CrossRef]

Kalonji, N.

N. Kalonji, J. Semo, “High efficiency long working distance laser diode to singlemode fiber coupling arrangement,” Electron. Lett. 30, 892–893 (1994).
[CrossRef]

Kanamori, H.

T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

Kersey, A. D.

Kimura, T.

J.-I. 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]

Kogelnik, H.

Kuwahara, H.

H. Kuwahara, M. Sasaki, N. Tokoyo, “Efficient coupling from semiconductor lasers into single-mode fibers with tapered hemispherical ends,” J. Lightwave Technol. 14, 58–65 (1996).

Lee, B. H.

B. H. Lee, J. Nishii, “Cladding-surrounding interface insensitive long-period grating,” Electron. Lett. 34, 1129–1130 (1998).
[CrossRef]

Lemaire, P. J.

A. M. Vengsakar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 4, 58–65 (1996).
[CrossRef]

A. M. Vengsakar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996).
[CrossRef]

Lostec, J.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Malo, B.

D. C. Johnson, F. Bilodeau, B. Malo, K. O. Hill, P. G. J. Wigley, G. I. Stegeman, “Long-length, long-period rocking filters fabricated from conventional monomode telecommunications optical fiber,” Opt. Lett. 17, 1635–1637 (1992).
[CrossRef] [PubMed]

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26, 1270–1272 (1990).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, Boston, Mass., 1991), Chaps. 2 and 3.

Massey, G. A.

McElhanon, R. W.

H. J. Patrick, C. G. Askins, R. W. McElhanon, E. J. Friebel, “Amplitude mask patterned on an excimer laser mirror for high intensity writing of long period fiber gratings,” Electron. Lett. 33, 1167–1168 (1997).
[CrossRef]

Medvedkov, O. I.

Mettle, S. C.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. C. Mettle, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarisation independence,” Electron. Lett. 34, 1416–1417 (1998).
[CrossRef]

Moerman, I.

I. Moerman, P. P. Van Daele, P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III–V semiconductor devices,” IEEE J. Sel. Top. Quantum. Electron. 3, 1308–1320 (1997).
[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]

Nishii, J.

B. H. Lee, J. Nishii, “Cladding-surrounding interface insensitive long-period grating,” Electron. Lett. 34, 1129–1130 (1998).
[CrossRef]

Okude, S.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper FB2.

Patrick, H. J.

H. J. Patrick, A. D. Kersey, F. Bucholtz, “Analysis of the response of long period fiber grating to external index of refraction,” J. Lightwave Technol. 16, 1606–1611 (1998).
[CrossRef]

H. J. Patrick, C. G. Askins, R. W. McElhanon, E. J. Friebel, “Amplitude mask patterned on an excimer laser mirror for high intensity writing of long period fiber gratings,” Electron. Lett. 33, 1167–1168 (1997).
[CrossRef]

Pedrazzani, J. R.

Poudoulec, A.

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

Presby, H.

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

Rosserg, R. H.

W. Bludau, R. H. Rosserg, “Low-loss laser-to-fiber coupling with negligible optical feedback,” J. Lightwave Technol. LT-3, 294–302 (1985).
[CrossRef]

Sakai, 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]

Sakai, J.-I.

J.-I. 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]

Sakai, T.

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T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

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K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper FB2.

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[CrossRef]

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Appl. Opt. (2)

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[CrossRef]

P. Chanclou, M. Thual, J. Lostec, P. Auvray, J. Caulet, G. Joulié, A. Poudoulec, B. Clavel, “Highly efficient collective coupling between laser diode array and lensed fiber ribbon,” Electron. Lett. 34, 273–274 (1998).
[CrossRef]

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[CrossRef]

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[CrossRef]

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I. Moerman, P. P. Van Daele, P. M. Demeester, “A review on fabrication technologies for the monolithic integration of tapers with III–V semiconductor devices,” IEEE J. Sel. Top. Quantum. Electron. 3, 1308–1320 (1997).
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Opt. Lett. (4)

Other (4)

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A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1983), Chap. 11.

T. Enomoto, M. Shigehara, S. Ishikawa, T. Danzuka, H. Kanamori, “Long-period fiber grating in a pure-silica-core fiber written by residual stress relaxation,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThG2.

K. Shima, K. Himeno, T. Sakai, S. Okude, A. Wada, R. Yamauchi, “A novel temperature-insensitive long-period fiber grating using a boron-codoped-germanosilicate-core fiber,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper FB2.

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of the proposed novel optical coupling scheme. Abbreviations are defined throughout the text.

Fig. 2
Fig. 2

Evolution of transmission spectra of a LPFG at exposure times (a) 120 s, (b) 180 s, and (c) 210 s.

Fig. 3
Fig. 3

Coupling efficiency versus working distance for a lensed fiber with (solid curve) and without (dashed curve) the LPFG.

Fig. 4
Fig. 4

Coupling efficiency versus transverse displacement for a lensed fiber with (solid curve) and without (dashed curve) the LPFG.

Fig. 5
Fig. 5

Microphotograph showing optical coupling between a Fabry–Perot LD and a LPFG lensed fiber.

Fig. 6
Fig. 6

Spectra of (a) a LPFG and (b) a Fabry–Perot LD.

Fig. 7
Fig. 7

Measured coupling efficiency versus working distance for lensed fibers with various radii R f .

Fig. 8
Fig. 8

Simulated coupling efficiency versus working distance for a lensed fiber with various radii R f . Also shown is the measured result for R f = 120 µm.

Fig. 9
Fig. 9

Simulated coupling efficiency versus transverse displacement for a lensed fiber with various radii R f . Also shown is the measured result for R f = 120 µm.

Fig. 10
Fig. 10

Variation of optimal working distance with radii of a lensed fiber.

Fig. 11
Fig. 11

Transmission spectrum of the LPFG used for coupling of the HE11 and HE13 modes.

Fig. 12
Fig. 12

Measured and simulated coupling efficiencies of HE11 and HE13 modes versus working distance.

Fig. 13
Fig. 13

Evolution of transmission spectra at various bend radii R B .

Fig. 14
Fig. 14

Measured dependence of coupling efficiency and loss of LPFG (dashed curve) on wavelength.

Fig. 15
Fig. 15

Simulated coupling efficiencies and their sum versus working distance for various cladding and core modes.

Equations (29)

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θ4=sin-11nconcl sin θ3+mλΛ>sin-1nclnco
Wx2=W01+ZsZ021/2,
Rx2=Zs1+Z0Zs2,
ϕ1x1, y1, z1=ϕRxR, yR, zR,
ϕixi, yi, zi=kizi+ki2xiqxi+yiqyi,
1qi=1Ri-j λ0niπWi2,  ki=2πni/λ0,
Mx=cos θ2cos θ1+Lfn1 cos θ1-n2 cos θ2n2Rf cos θ1 cos θ2Lfn1 cos θ1n2 cos θ2n1 cos θ1-n2 cos θ2n2Rf cos θ1 cos θ2n1 cos θ1n2 cos θ2=AxBxCxDx,
My=1+Lfn1 cos θ1-n2 cos θ2n2RfLfn1n2n1 cos θ1-n2 cos θ2n2Rfn1n2=AyByCyDy,
θ1=sin-1dx/Rf,
Lf=PQ¯=Df-Rf1-cos θ1cos θ12.
Wx3=Wx2Ax+BxRx22+λ1BxπWx2221/2,
Rx3=Ax+BxRx22+λ1BxπWx222Ax+BxRx2Cx+DxRx2+BxDxλ1πWx222.
Es=1π1/21Wx3Wy31/2 exp-X-dxf2Wx32+Y2Wy32-jk3X-dxf22Rx3+Y22Ry3+θ12X-dxf,
Esr, ϕ=-jEs expjϕrˆ+Es expjϕϕˆ.
Es=i aiEico+v bvEvcl,
ηvs-cl=power carried by the vth excited cladding modepower carried by the Gaussian beam=12 Re|bv|2  Evcl×Hvcl*zˆdA12 Re Es×Hs*zˆdA.
 Em·En*dA=δmn.
i |ai|2+v |bv|2=1,
ηvs-cl= Es·Evcl*dA2=|bv|2.
ηis-co= Es·Eico*dA2=|ai|2.
λi=λvnco-nvclΛ1-κ01-01co-coΛ2π,
κv-01cl-co2+δ+κ01-01co-co221/2Lπ2,
ηtotal= Piv1-Sv,iηis-co+v Sv,iηv,is-cldλi Pidλi,
ηtotal=1-Svηs-co+Svηvs-cl.
Rx3=nclRfR2n1Rf-R2ncl-n1,  Wx3=Wx2.
Zs,optmvRfncl-n1n1±πW0nclθvclλi,
Zs,optm1n1Rfncl-n1.
W3,optm=Crmaxcl,
Rf,optm11=CπW0rmaxclncl-n1n1λ1,

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