Abstract

An entrance surface of a multimode optical fiber with the highest efficiency of coupling radiation from a laser diode is considered. The geometry of the surface is designed with the purpose of keeping a refracted ray inside the fiber with simultaneous minimization of the reflection coefficient in each point of the surface. As a good approximation to the ideal surface, the composite entrance surface of a cylinder–wedge shape is proposed. It has clearly improved the coupling efficiency as compared with that of the purely cylindrical surface. Analysis of the entrance surfaces is based on their transmission coefficients, depending on the incident ray direction.

© 1999 Optical Society of America

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1997 (1)

A. E. Prokofjev, O. V. Sizov, S. O. Chistjakov, “Gradient-optical system for coupling radiation of semiconductor laser diode into single-mode fiber,” J. Opt. Technol. 64, 67–69 (1997).

1996 (1)

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

1995 (4)

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

T. Graf, J. E. Balmer, “Lasing properties of diode-laser-pumped Nd:KGW,” Opt. Eng. 34, 2349–2352 (1995).
[CrossRef]

J. Braat, “Design of beam-shaping optics,” Appl. Opt. 34, 2665–2670 (1995).
[CrossRef] [PubMed]

B. Messerschmidt, T. Possner, R. Goering, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

1994 (3)

1992 (4)

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

M. Oka, H. Masuda, Y. Kaneda, S. Kubota, “Laser-diode-pumped phase-locked Nd:YAG laser arrays,” IEEE J. Quantum Electron. 28, 1142–1147 (1992).
[CrossRef]

F. Brioschi, E. Nava, G. C. Reali, “Gain shaping and beam quality in diode-laser multiarray side-pumped solid-state lasers,” IEEE J. Quantum Electron. 28, 1070–1074 (1992).
[CrossRef]

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

1991 (1)

1990 (3)

1988 (3)

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

J. Berger, D. F. Welch, W. Streifer, D. R. Scifres, N. J. Hoffman, J. J. Smith, D. Radecki, “Fiber-bundle coupled, diode end-pumped Nd:YAG laser,” Opt. Lett. 13, 306–308 (1988).
[CrossRef] [PubMed]

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

1986 (1)

1982 (2)

1981 (1)

1977 (1)

1974 (2)

C. A. Brackett, “On the efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
[CrossRef]

J. K. Butler, J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. 10, 809–815 (1974).
[CrossRef]

1973 (4)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

H. C. Casey, M. B. Panish, J. L. Merz, “Beam divergence of the emission from double-heterostructure lasers,” J. Appl. Phys. 44, 5470–5475 (1973).
[CrossRef]

G. A. Hockam, “Radiation from a solid-state laser,” Electron. Lett. 9, 389–391 (1973).
[CrossRef]

D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
[CrossRef]

1972 (1)

L. G. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573–594 (1972).
[CrossRef]

Albrecht, G. F.

Baer, T. M.

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

J. J. Snyder, P. Reichert, T. M. Baer, “Fast diffraction-limited cylindrical microlenses,” Appl. Opt. 30, 2743–2749 (1991).
[CrossRef] [PubMed]

Balmer, J. E.

T. Graf, J. E. Balmer, “Lasing properties of diode-laser-pumped Nd:KGW,” Opt. Eng. 34, 2349–2352 (1995).
[CrossRef]

H. Zbinden, J. E. Balmer, “Q-switched Nd:YLF laser end pumped by a diode-laser bar,” Opt. Lett. 15, 1014–1016 (1990).
[CrossRef] [PubMed]

Beach, R. J.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Benner, A. F.

Berger, J.

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

J. Berger, D. F. Welch, W. Streifer, D. R. Scifres, N. J. Hoffman, J. J. Smith, D. Radecki, “Fiber-bundle coupled, diode end-pumped Nd:YAG laser,” Opt. Lett. 13, 306–308 (1988).
[CrossRef] [PubMed]

Braat, J.

Brackett, C. A.

C. A. Brackett, “On the efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
[CrossRef]

Brioschi, F.

F. Brioschi, E. Nava, G. C. Reali, “Gain shaping and beam quality in diode-laser multiarray side-pumped solid-state lasers,” IEEE J. Quantum Electron. 28, 1070–1074 (1992).
[CrossRef]

Browder, G. S.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Butler, J. K.

J. K. Butler, J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. 10, 809–815 (1974).
[CrossRef]

Byer, R. L.

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

Casey, H. C.

H. C. Casey, M. B. Panish, J. L. Merz, “Beam divergence of the emission from double-heterostructure lasers,” J. Appl. Phys. 44, 5470–5475 (1973).
[CrossRef]

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), Chap. 2.

Chai, B. H. T.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Cherng, C.-P.

Chistjakov, S. O.

A. E. Prokofjev, O. V. Sizov, S. O. Chistjakov, “Gradient-optical system for coupling radiation of semiconductor laser diode into single-mode fiber,” J. Opt. Technol. 64, 67–69 (1997).

Cohen, L. G.

L. G. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573–594 (1972).
[CrossRef]

Comaskey, B.

DeVito, M.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Edwards, C. A.

Eisenstein, G.

Emanuel, M. A.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Endriz, J. G.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Fan, T. Y.

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

Goering, R.

Gooding, P.

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

Graf, T.

T. Graf, J. E. Balmer, “Lasing properties of diode-laser-pumped Nd:KGW,” Opt. Eng. 34, 2349–2352 (1995).
[CrossRef]

Haden, J. M.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Harnagel, G. L.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

Head, D. F.

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

Hockam, G. A.

G. A. Hockam, “Radiation from a solid-state laser,” Electron. Lett. 9, 389–391 (1973).
[CrossRef]

Hoffman, N. J.

Hunsperger, R. G.

Hutchison, S.

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

Kaneda, Y.

M. Oka, H. Masuda, Y. Kaneda, S. Kubota, “Laser-diode-pumped phase-locked Nd:YAG laser arrays,” IEEE J. Quantum Electron. 28, 1142–1147 (1992).
[CrossRef]

Kato, D.

D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
[CrossRef]

Kawano, K.

Kintz, G. J.

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

Kozlov, V. A.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Kubodera, K.

Kubota, S.

M. Oka, H. Masuda, Y. Kaneda, S. Kubota, “Laser-diode-pumped phase-locked Nd:YAG laser arrays,” IEEE J. Quantum Electron. 28, 1142–1147 (1992).
[CrossRef]

Lee, A.

Marshall, C. D.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Masuda, H.

M. Oka, H. Masuda, Y. Kaneda, S. Kubota, “Laser-diode-pumped phase-locked Nd:YAG laser arrays,” IEEE J. Quantum Electron. 28, 1142–1147 (1992).
[CrossRef]

McInerney, J. G.

Merz, J. L.

H. C. Casey, M. B. Panish, J. L. Merz, “Beam divergence of the emission from double-heterostructure lasers,” J. Appl. Phys. 44, 5470–5475 (1973).
[CrossRef]

Messerschmidt, B.

Mitomi, O.

Moran, B. D.

Nava, E.

F. Brioschi, E. Nava, G. C. Reali, “Gain shaping and beam quality in diode-laser multiarray side-pumped solid-state lasers,” IEEE J. Quantum Electron. 28, 1070–1074 (1992).
[CrossRef]

Nemoto, S.

Nicia, A.

Noda, J.

Oka, M.

M. Oka, H. Masuda, Y. Kaneda, S. Kubota, “Laser-diode-pumped phase-locked Nd:YAG laser arrays,” IEEE J. Quantum Electron. 28, 1142–1147 (1992).
[CrossRef]

Osinski, M.

Panish, M. B.

H. C. Casey, M. B. Panish, J. L. Merz, “Beam divergence of the emission from double-heterostructure lasers,” J. Appl. Phys. 44, 5470–5475 (1973).
[CrossRef]

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), Chap. 2.

Payne, S. A.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Plano, W. E.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Possner, T.

Presby, H. M.

Prokofjev, A. E.

A. E. Prokofjev, O. V. Sizov, S. O. Chistjakov, “Gradient-optical system for coupling radiation of semiconductor laser diode into single-mode fiber,” J. Opt. Technol. 64, 67–69 (1997).

Radecki, D.

Reali, G. C.

F. Brioschi, E. Nava, G. C. Reali, “Gain shaping and beam quality in diode-laser multiarray side-pumped solid-state lasers,” IEEE J. Quantum Electron. 28, 1070–1074 (1992).
[CrossRef]

Reichert, P.

Sakamoto, M.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

Salvi, T. C.

Schaffers, K. I.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Scifres, D. R.

Scrifres, D. R.

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

Shcherbakov, I. A.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Sizov, O. V.

A. E. Prokofjev, O. V. Sizov, S. O. Chistjakov, “Gradient-optical system for coupling radiation of semiconductor laser diode into single-mode fiber,” J. Opt. Technol. 64, 67–69 (1997).

Skidmore, J.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Smith, J. J.

Smith, L. K.

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

Snyder, J. J.

Streifer, W.

J. Berger, D. F. Welch, W. Streifer, D. R. Scifres, N. J. Hoffman, J. J. Smith, D. Radecki, “Fiber-bundle coupled, diode end-pumped Nd:YAG laser,” Opt. Lett. 13, 306–308 (1988).
[CrossRef] [PubMed]

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

Studenikin, P. A.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Ter-Mikirtychev, V. V.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Vakili, M.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Velsko, S. P.

Vitello, D.

Vlasenko, O. A.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Welch, D. F.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

J. Berger, D. F. Welch, W. Streifer, D. R. Scifres, N. J. Hoffman, J. J. Smith, D. Radecki, “Fiber-bundle coupled, diode end-pumped Nd:YAG laser,” Opt. Lett. 13, 306–308 (1988).
[CrossRef] [PubMed]

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

Willing, S.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Worland, D. P.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Yao, H. C.

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

Yariv, A.

R. G. Hunsperger, A. Yariv, A. Lee, “Parallel end-butt coupling for optical integrated circuits,” Appl. Opt. 16, 1026–1032 (1977).
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A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

Zagumennyi, A. I.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Zavartsev, Yu. D.

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Zbinden, H.

Zenteno, L. A.

Zoroofchi, J.

J. K. Butler, J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. 10, 809–815 (1974).
[CrossRef]

Appl. Opt. (13)

R. G. Hunsperger, A. Yariv, A. Lee, “Parallel end-butt coupling for optical integrated circuits,” Appl. Opt. 16, 1026–1032 (1977).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

J. J. Snyder, P. Reichert, T. M. Baer, “Fast diffraction-limited cylindrical microlenses,” Appl. Opt. 30, 2743–2749 (1991).
[CrossRef] [PubMed]

B. Comaskey, G. F. Albrecht, S. P. Velsko, B. D. Moran, “24-W average power at 0.537 µm from an externally frequency-doubled Q-switched diode-pumped Nd:YOS laser oscillator,” Appl. Opt. 33, 6377–6382 (1994).
[CrossRef] [PubMed]

S. Nemoto, “Experimental evaluation of a new expression for the far field of a diode laser beam,” Appl. Opt. 33, 6387–6392 (1994).
[CrossRef] [PubMed]

L. A. Zenteno, “Design of a device for pumping a double-clad fiber laser with a laser-diode bar,” Appl. Opt. 33, 7282–7287 (1994).
[CrossRef] [PubMed]

J. Braat, “Design of beam-shaping optics,” Appl. Opt. 34, 2665–2670 (1995).
[CrossRef] [PubMed]

B. Messerschmidt, T. Possner, R. Goering, “Colorless gradient-index cylindrical lenses with high numerical apertures produced by silver-ion exchange,” Appl. Opt. 34, 7825–7830 (1995).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

L. G. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573–594 (1972).
[CrossRef]

Electron. Lett. (1)

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[CrossRef]

IEEE J. Quantum Electron. (9)

J. K. Butler, J. Zoroofchi, “Radiation fields of GaAs-(AlGa)As injection lasers,” IEEE J. Quantum Electron. 10, 809–815 (1974).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

F. Brioschi, E. Nava, G. C. Reali, “Gain shaping and beam quality in diode-laser multiarray side-pumped solid-state lasers,” IEEE J. Quantum Electron. 28, 1070–1074 (1992).
[CrossRef]

T. M. Baer, D. F. Head, P. Gooding, G. J. Kintz, S. Hutchison, “Performance of diode-pumped Nd:YAG and Nd:YLF lasers in a tightly folded resonator configuration,” IEEE J. Quantum Electron. 28, 1131–1138 (1992).
[CrossRef]

C. D. Marshall, L. K. Smith, R. J. Beach, M. A. Emanuel, K. I. Schaffers, J. Skidmore, S. A. Payne, B. H. T. Chai, “Diode-pumped ytterbium-doped Sr5(PO4)3F laser performance,” IEEE J. Quantum Electron. 32, 650–656 (1996).
[CrossRef]

W. Streifer, D. R. Scrifres, G. L. Harnagel, D. F. Welch, J. Berger, M. Sakamoto, “Advances in diode laser pumps,” IEEE J. Quantum Electron. 24, 883–893 (1988).
[CrossRef]

J. G. Endriz, M. Vakili, G. S. Browder, M. DeVito, J. M. Haden, G. L. Harnagel, W. E. Plano, M. Sakamoto, D. F. Welch, S. Willing, D. P. Worland, H. C. Yao, “High power diode laser arrays,” IEEE J. Quantum Electron. 28, 952–965 (1992).
[CrossRef]

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[CrossRef]

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J. Opt. Technol. (1)

A. E. Prokofjev, O. V. Sizov, S. O. Chistjakov, “Gradient-optical system for coupling radiation of semiconductor laser diode into single-mode fiber,” J. Opt. Technol. 64, 67–69 (1997).

Opt. Eng. (1)

T. Graf, J. E. Balmer, “Lasing properties of diode-laser-pumped Nd:KGW,” Opt. Eng. 34, 2349–2352 (1995).
[CrossRef]

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Quantum Electron. (1)

O. A. Vlasenko, Yu. D. Zavartsev, A. I. Zagumennyi, V. A. Kozlov, P. A. Studenikin, V. V. Ter-Mikirtychev, I. A. Shcherbakov, “Diode pumped GdVO4:Nd3+ laser with fiber pump input,” Quantum Electron. 22, 788–790 (1995).

Other (1)

H. C. Casey, M. B. Panish, Heterostructure Lasers, Part A: Fundamental Principles (Academic, New York, 1978), Chap. 2.

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Figures (8)

Fig. 1
Fig. 1

Schematic of an ES showing incident and refracted rays and variables used in the calculations.

Fig. 2
Fig. 2

Geometry of optimum (solid curves) and cylinder–wedge (dotted curves) ES’s. The edge angles β are 55.2° (curve 1), 55.4° (curve 2), 56.2° (curve 3), and 57.6° (curve 4). The acceptance angles ϑmax are 54°, 50°, 45°, and 40° respectively. The diameter of fiber core is 120 µm; refractive index, n c = 1.465; and critical angle for total internal reflection, α = 8.2°.

Fig. 3
Fig. 3

Maximum ϑmax (ψ = α) and minimum ϑmin (ψ = -α) boundaries of allowable range of angles ϑ for a plane surface, depending on the inclination angle β.

Fig. 4
Fig. 4

Angle ψ for refracted ray versus angle ϑ of incident ray for the cylindrical ES. The m = R/ L ratios are 0.54 (curve 1), 0.583 (curve 2), and 0.63 (curve 3). The dashed lines show the boundaries of allowable values ψ (-α < ψ < α).

Fig. 5
Fig. 5

Transmission coefficients T(ϑ): flat ES, curve 1; purely cylindrical ES (m = 0.583, ϑmax = 36°), curve 2; cylinder–wedge ES (β = 56.2°, ϑmax = 45°) - 3, (β = 55.2°, ϑmax = 53°), curve 4; optimum ES (β = 55.15°, ϑmax = 55.15°), curve 5. The dotted curve shows an intensity profile for a double-heterostructure (DH) LD with the beam divergence ϑFWHM = 47°.

Fig. 6
Fig. 6

Efficiency of coupling η a lowest-order TE mode into the fiber with different ES’s (m = 0.583 for a cylindrical ES, β = 55.4° for a cylinder–wedge ES, and β = 55.15° for an optimum ES). The LD beam divergence is measured as the full angle ϑFWHM between the half-intensity points.

Fig. 7
Fig. 7

Ratio R/ d for an optimized cylinder–wedge ES versus the inclination angle β of a wedge section.

Fig. 8
Fig. 8

Fragments of a far-field intensity pattern for a DH LD in a plane normal to the junction plane. The curves follow from Eqs. (A3) (dashed and dotted) and (A6) (solid) for a lowest-order TE mode.

Equations (25)

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tan χ=nc cos ψ-cos ϑsin ϑ-nc sin ψ.
ϑlim=βlim=α+arccos1/nc.
Tϑ, χ, ψ=1-sinϑ-ψsin2χ-ϑ-ψ2,
|ψ|<|α|,
P=-90°90° Iϑdϑ.
η=1PES IϑTϑdϑ,
ES IϑTϑdϑ=ES Irrcos90°-χ+ψdlr.
ϑmaxβ=arcsinnc sin β cosβ-α-cos β1-nc2 cos2β-α1/2.
χϑ=arctannc cos α-cos ϑsin ϑ-nc sin α,α<ϑ<ϑmaxϑ+90°,0<ϑ<α.
d ln rdϑ=nc cos α sin ϑ-nc sin α cos ϑnc cos α cos ϑ+nc sin α sin ϑ-1.
rϑ=d2 sin ϑmaxnc cos α cos ϑmax+nc sin α sin ϑmax-1nc cos α cos ϑ+nc sin α sin ϑ-1,α<ϑ<ϑmaxβd2 sin ϑmaxnc cos α cos ϑmax+nc sin α sin ϑmax-1nc-1,0<ϑ<α.
ψβ, ϑ=arcsinsin β cosβ-ϑnc-cos β1-cos2β-ϑnc21/2.
tan ϑ=m 1-cos2 φ1-m cos φ,
Tϑ=1-nc2-sin2ϑ+φϑ1/2-cosϑ+φϑnc2-sin2ϑ+φϑ1/2+cosϑ+φϑ2,
φ=arccossin2 ϑm+sin4 ϑm2-sin2 ϑm2+cos2 ϑ1/2.
ϑ<arcsinm,
tan ψ=tan φϑa-b cos φϑ-tan2 φϑa-b cos φϑ-tan φϑa-b cos φϑsin2 φϑ-11/2,
ϑc=arctanm 1-sin2 β1/21-m sin β.
R=d2sin ϑcsinϑmaxβsinβ-ϑmaxβcos β sinβ-ϑc,
IϑI0=|gϑ|2|g0|2|Fϑ|2|F0|2.
Fϑ=- Eyx, 0expjσϑxdx,
|Fϑ||F0|=γκ2γ cosσϑW2-σϑsinσϑW2κ2-σ2ϑγ2+σ2ϑ.
tanκW2=γκ.
gϑ=2 cos ϑcos ϑ+n2-sin2 ϑn2-sin2 ϑ+ξκ0,
|Fϑ||F0|=γκ22γ2+σ2ϑcosκW2×sinκ+σϑ2 Wκ+σϑ+sinκ-σϑ2 Wκ-σϑ.

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