Abstract

We study the problem of coupling an electromagnetic beam of any state of coherence and polarization into a multimode optical fiber. Using the well-known concept of the cross-spectral density matrix, we derive a general expression for the coupling efficiency of a stochastic electromagnetic beam into a multimode fiber in terms of the cross-spectral density matrix of the incident beam and another matrix representing field distributions of fiber modes. We apply this result to a specific case in which the incident beam belongs to a broad class of so-called electromagnetic Gaussian Schell-model beams and obtain a simple analytical expression for the coupling efficiency in the case of single-mode fibers. We use this expression to study how coupling efficiency depends on the coherence and polarization properties of the incident beam.

© 2009 Optical Society of America

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  1. L. C. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573-594 (1972).
  2. E. Weidel, “New coupling method for GaAs laser-fibre coupling,” Electron. Lett. 11, 436-437 (1975).
    [CrossRef]
  3. L. G. Cohen and M. V. Schneider, “Microlenses for coupling junction lasers to optical fibers,” Appl. Opt. 13, 89-94 (1974).
    [CrossRef]
  4. J. Sakai and T. Kimura, “Design of miniature lens for semiconductor laser to single-module fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059-1067 (1980).
    [CrossRef]
  5. M. Saruwatari and T. Sugie, “Efficient laser diode to single-mode fiber coupling using a combination of two lenses in confocal condition,” IEEE J. Quantum Electron. QE-17, 1021-1027 (1981).
    [CrossRef]
  6. V. Shah, L. Curtis, R. Vodhanel, D. Bour, and W. Young, “Efficient power coupling from a 980-nm, broad-area laser to a single-mode fiber using a wedge-shaped fiber endface,” J. Lightwave Technol. 8, 1313-1318 (1990).
    [CrossRef]
  7. K. Barrell and C. Pask, “Optical fibre excitation by lenses,” Opt. Acta 26, 91-108 (1979).
  8. M. Lazzaroni and F. Zocchi, “Optical coupling from plane wave to step-index single-mode fiber,” Opt. Commun. 237, 37-43 (2004).
    [CrossRef]
  9. R. Wagner and W. Tomlinson, “Coupling efficiency of optics in single-mode fiber components,” Appl. Opt. 21, 2671-2688 (1982).
    [CrossRef]
  10. S. Shaklan and F. Roddier, “Coupling starlight into single-mode fiber optics,” Appl. Opt. 27, 2334-2338 (1988).
    [CrossRef]
  11. D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
    [CrossRef]
  12. K. Chen and D. Kerps, “Coupling efficiency of surface LED's to single-mode fibers,” J. Lightwave Technol. 5, 1600-1604 (1987).
    [CrossRef]
  13. P. Winzer and W. Leeb, “Fiber coupling efficiency for random light and its applications to lidar,” Opt. Lett. 23, 986-988 (1998).
    [CrossRef]
  14. Y. Dikmelik and F. Davidson, “Fiber-coupling for free-space optical communication through atmospheric turbulence,” Appl. Opt. 44, 4946-4952 (2005).
    [CrossRef]
  15. S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
    [CrossRef]
  16. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).
  17. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
    [CrossRef]
  18. E. Wolf, “Correlation induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28, 1078-1080 (2003).
    [CrossRef]
  19. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991), Chap. 2.
  20. B. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390-1398 (1979).
    [CrossRef]
  21. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
    [CrossRef]
  22. D. Marcuse, “Gaussian approximation of the fundamental modes of graded-index fibers,” J. Opt. Soc. Am. 68, 103-109 (1978).
    [CrossRef]
  23. J. Buck, Fundamentals of Optical Fibers (Wiley, 2004).
  24. S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
    [CrossRef]
  25. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Vol. 99 of SPIE Press Monograph Series (SPIE, 2001).
  26. G. P. Agarwal, Fiber-Optic Communication Systems, 3rd ed., (Wiley, 2002).
  27. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM152 of SPIE Press Monograph Series (SPIE, 1998).
  28. G. N. Watson, A Treatise on the Theory of Bessel Functions, (Cambridge, Univ. Press, 1962).
  29. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, 1965).

2007 (1)

S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
[CrossRef]

2005 (1)

2004 (2)

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
[CrossRef]

M. Lazzaroni and F. Zocchi, “Optical coupling from plane wave to step-index single-mode fiber,” Opt. Commun. 237, 37-43 (2004).
[CrossRef]

2003 (2)

1998 (1)

1990 (1)

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

1988 (1)

1987 (2)

D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
[CrossRef]

K. Chen and D. Kerps, “Coupling efficiency of surface LED's to single-mode fibers,” J. Lightwave Technol. 5, 1600-1604 (1987).
[CrossRef]

1984 (1)

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

1982 (1)

1981 (1)

M. Saruwatari and T. Sugie, “Efficient laser diode to single-mode fiber coupling using a combination of two lenses in confocal condition,” IEEE J. Quantum Electron. QE-17, 1021-1027 (1981).
[CrossRef]

1980 (1)

J. Sakai and T. Kimura, “Design of miniature lens for semiconductor laser to single-module fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059-1067 (1980).
[CrossRef]

1979 (2)

K. Barrell and C. Pask, “Optical fibre excitation by lenses,” Opt. Acta 26, 91-108 (1979).

B. Rye, “Antenna parameters for incoherent backscatter heterodyne lidar,” Appl. Opt. 18, 1390-1398 (1979).
[CrossRef]

1978 (1)

1975 (1)

E. Weidel, “New coupling method for GaAs laser-fibre coupling,” Electron. Lett. 11, 436-437 (1975).
[CrossRef]

1974 (1)

1972 (1)

L. C. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573-594 (1972).

Agarwal, G. P.

G. P. Agarwal, Fiber-Optic Communication Systems, 3rd ed., (Wiley, 2002).

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Vol. 99 of SPIE Press Monograph Series (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM152 of SPIE Press Monograph Series (SPIE, 1998).

Barrell, K.

K. Barrell and C. Pask, “Optical fibre excitation by lenses,” Opt. Acta 26, 91-108 (1979).

Bour, D.

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

Buck, J.

J. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

Chen, K.

K. Chen and D. Kerps, “Coupling efficiency of surface LED's to single-mode fibers,” J. Lightwave Technol. 5, 1600-1604 (1987).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
[CrossRef]

Cohen, L. C.

L. C. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573-594 (1972).

Cohen, L. G.

Curtis, L.

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

Davidson, F.

Dikmelik, Y.

Gangopadhyay, S.

S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, 1965).

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Vol. 99 of SPIE Press Monograph Series (SPIE, 2001).

Kerps, D.

K. Chen and D. Kerps, “Coupling efficiency of surface LED's to single-mode fibers,” J. Lightwave Technol. 5, 1600-1604 (1987).
[CrossRef]

Kimura, T.

J. Sakai and T. Kimura, “Design of miniature lens for semiconductor laser to single-module fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059-1067 (1980).
[CrossRef]

Korotkova, O.

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
[CrossRef]

Kumar, A.

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

Lazzaroni, M.

M. Lazzaroni and F. Zocchi, “Optical coupling from plane wave to step-index single-mode fiber,” Opt. Commun. 237, 37-43 (2004).
[CrossRef]

Leeb, W.

Marcuse, D.

Mukhopadhyay, S.

S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
[CrossRef]

Pask, C.

K. Barrell and C. Pask, “Optical fibre excitation by lenses,” Opt. Acta 26, 91-108 (1979).

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Vol. 99 of SPIE Press Monograph Series (SPIE, 2001).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM152 of SPIE Press Monograph Series (SPIE, 1998).

Reith, L. A.

D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
[CrossRef]

Roddier, F.

Rye, B.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, 1965).

Saifi, M. A.

D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
[CrossRef]

Sakai, J.

J. Sakai and T. Kimura, “Design of miniature lens for semiconductor laser to single-module fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059-1067 (1980).
[CrossRef]

Salem, M.

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
[CrossRef]

Sarkar, S.

S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
[CrossRef]

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

Saruwatari, M.

M. Saruwatari and T. Sugie, “Efficient laser diode to single-mode fiber coupling using a combination of two lenses in confocal condition,” IEEE J. Quantum Electron. QE-17, 1021-1027 (1981).
[CrossRef]

Schneider, M. V.

Shah, V.

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

Shaklan, S.

Sugie, T.

M. Saruwatari and T. Sugie, “Efficient laser diode to single-mode fiber coupling using a combination of two lenses in confocal condition,” IEEE J. Quantum Electron. QE-17, 1021-1027 (1981).
[CrossRef]

Thyagarajan, K.

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

Tomlinson, W.

Vodhanel, R.

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

Wagner, R.

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions, (Cambridge, Univ. Press, 1962).

Weidel, E.

E. Weidel, “New coupling method for GaAs laser-fibre coupling,” Electron. Lett. 11, 436-437 (1975).
[CrossRef]

Winzer, P.

Wolf, E.

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
[CrossRef]

E. Wolf, “Correlation induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation,” Opt. Lett. 28, 1078-1080 (2003).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

Young, W.

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

Zocchi, F.

M. Lazzaroni and F. Zocchi, “Optical coupling from plane wave to step-index single-mode fiber,” Opt. Commun. 237, 37-43 (2004).
[CrossRef]

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

L. C. Cohen, “Power coupling from GaAs injection lasers into optical fibers,” Bell Syst. Tech. J. 51, 573-594 (1972).

Electron. Lett. (1)

E. Weidel, “New coupling method for GaAs laser-fibre coupling,” Electron. Lett. 11, 436-437 (1975).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Sakai and T. Kimura, “Design of miniature lens for semiconductor laser to single-module fiber coupling,” IEEE J. Quantum Electron. QE-16, 1059-1067 (1980).
[CrossRef]

M. Saruwatari and T. Sugie, “Efficient laser diode to single-mode fiber coupling using a combination of two lenses in confocal condition,” IEEE J. Quantum Electron. QE-17, 1021-1027 (1981).
[CrossRef]

J. Lightwave Technol. (3)

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

D. N. Christodoulides, L. A. Reith, and M. A. Saifi, “Theory of LED coupling to single-mode fibers,” J. Lightwave Technol. 5, 1623-1629 (1987).
[CrossRef]

K. Chen and D. Kerps, “Coupling efficiency of surface LED's to single-mode fibers,” J. Lightwave Technol. 5, 1600-1604 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

K. Barrell and C. Pask, “Optical fibre excitation by lenses,” Opt. Acta 26, 91-108 (1979).

Opt. Commun. (3)

M. Lazzaroni and F. Zocchi, “Optical coupling from plane wave to step-index single-mode fiber,” Opt. Commun. 237, 37-43 (2004).
[CrossRef]

S. Sarkar, K. Thyagarajan, and A. Kumar, “Gaussian approximation of the fundamental mode in single mode elliptic core fibers,” Opt. Commun. 49, 178-183 (1984).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225-230 (2004).
[CrossRef]

Opt. Eng. (1)

S. Mukhopadhyay, S. Gangopadhyay, and S. Sarkar, “Coupling of a laser diode to monomode elliptic-core fiber via a hyperbolic microlens on the fiber tip: efficiency computation with the ABCD matrix,” Opt. Eng. 46, 025008 (2007).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263-267 (2003).
[CrossRef]

Other (8)

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications, Vol. 99 of SPIE Press Monograph Series (SPIE, 2001).

G. P. Agarwal, Fiber-Optic Communication Systems, 3rd ed., (Wiley, 2002).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, Vol. PM152 of SPIE Press Monograph Series (SPIE, 1998).

G. N. Watson, A Treatise on the Theory of Bessel Functions, (Cambridge, Univ. Press, 1962).

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, 1965).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991), Chap. 2.

J. Buck, Fundamentals of Optical Fibers (Wiley, 2004).

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