Abstract

We present in detail a simple analysis of the coupling efficiency and possible transverse and angular misalignment losses of a laser diode to single-mode, step-index fiber excitation with an upside-down tapered lens (UDTL) end, drawn by molding the end of a step-index fiber. The analysis employs our recently formulated ABCD matrix for an UDTL and has the advantage of simplicity compared with complicated methods involving cumbersome numerical integrations. Both the analysis and the results should be useful in designing coupling optics that use such lenses in the context of probable misalignments.

© 1999 Optical Society of America

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  1. C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
    [CrossRef]
  2. H. M. Presby, C. A. Edward, “Near 100% eficient fiber microlenses,” Electron. Lett. 6, 582–584 (1992).
    [CrossRef]
  3. J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
    [CrossRef]
  4. S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
    [CrossRef]
  5. L. B. Yuan, R. L. Shou, “Formation and power distribution properties of an upside-down taper lens at the end of an optical fiber,” Sens. Actuators A 23, 1158–1161 (1990).
    [CrossRef]
  6. L. Yuan, A. Qui, “Analysis of a single-mode fiber with taper lens end,” J. Opt. Soc. Am. A 9, 950–952 (1992).
    [CrossRef]
  7. S. K. Mondal, S. Gangopadhyay, S. N. Sarkar, “Analysis of an upside-down taper lens end from a single-mode, step-index fiber,” Appl. Opt. 37, 1006–1009 (1998).
    [CrossRef]
  8. S. Gangopadhyay, S. N. Sarkar, “ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip,” Appl. Opt. 36, 8582–8586 (1997).
    [CrossRef]
  9. S. Gangopadhayay, S. N. Sarkar, “Misalignment considerations in the laser diode to single-mode fiber excitation via hyperbolic lens on the fiber tip,” Opt. Commun. 146, 104–108 (1998).
    [CrossRef]
  10. S. J. S. Brown, “Geometrical optics of tapered gradient-index rods,” Appl. Opt. 19, 1056–1060 (1980).
    [CrossRef] [PubMed]
  11. J. N. McMullin, “The ABCD matrix in arbitrarily tapered quadratic-index waveguides,” Appl. Opt. 25, 2184–2187 (1986).
    [CrossRef] [PubMed]
  12. J. Linares, C. Gomez-Reino, “Arbitrary single-mode coupling by tapered and nontapered GRIN fiber lenses,” Appl. Opt. 29, 4003–4007 (1990).
    [CrossRef] [PubMed]
  13. M. Saruwatari, K. Nawata, “Semiconductor laser to single-mode fiber coupler,” Appl. Opt. 18, 1847–1856 (1979).
    [CrossRef] [PubMed]
  14. S. Sarkar, K. Thyagarajan, A. Kumar, “Gaussian approximation of the fundamental mode in single-mode elliptic core fibers,” Opt. Commun. 49, 178–183 (1984).
    [CrossRef]
  15. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
    [CrossRef]
  16. A. K. Ghatak, K. Thyagarajan, “Optical fiber waveguides,” in Optical Electronics (Cambridge U. Press, London, 1994), Chap. 13, pp. 411–415.

1998

S. K. Mondal, S. Gangopadhyay, S. N. Sarkar, “Analysis of an upside-down taper lens end from a single-mode, step-index fiber,” Appl. Opt. 37, 1006–1009 (1998).
[CrossRef]

S. Gangopadhayay, S. N. Sarkar, “Misalignment considerations in the laser diode to single-mode fiber excitation via hyperbolic lens on the fiber tip,” Opt. Commun. 146, 104–108 (1998).
[CrossRef]

1997

1994

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

1993

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
[CrossRef]

1992

H. M. Presby, C. A. Edward, “Near 100% eficient fiber microlenses,” Electron. Lett. 6, 582–584 (1992).
[CrossRef]

L. Yuan, A. Qui, “Analysis of a single-mode fiber with taper lens end,” J. Opt. Soc. Am. A 9, 950–952 (1992).
[CrossRef]

1990

L. B. Yuan, R. L. Shou, “Formation and power distribution properties of an upside-down taper lens at the end of an optical fiber,” Sens. Actuators A 23, 1158–1161 (1990).
[CrossRef]

J. Linares, C. Gomez-Reino, “Arbitrary single-mode coupling by tapered and nontapered GRIN fiber lenses,” Appl. Opt. 29, 4003–4007 (1990).
[CrossRef] [PubMed]

1986

J. N. McMullin, “The ABCD matrix in arbitrarily tapered quadratic-index waveguides,” Appl. Opt. 25, 2184–2187 (1986).
[CrossRef] [PubMed]

S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
[CrossRef]

1984

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

1980

1979

1977

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Brown, S. J. S.

Dragone, C.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
[CrossRef]

Edward, C. A.

H. M. Presby, C. A. Edward, “Near 100% eficient fiber microlenses,” Electron. Lett. 6, 582–584 (1992).
[CrossRef]

Edwards, C. A.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
[CrossRef]

Gangopadhayay, S.

S. Gangopadhayay, S. N. Sarkar, “Misalignment considerations in the laser diode to single-mode fiber excitation via hyperbolic lens on the fiber tip,” Opt. Commun. 146, 104–108 (1998).
[CrossRef]

Gangopadhyay, S.

Ghafouri-Shiraz, H.

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

Ghatak, A. K.

A. K. Ghatak, K. Thyagarajan, “Optical fiber waveguides,” in Optical Electronics (Cambridge U. Press, London, 1994), Chap. 13, pp. 411–415.

Gomez-Reino, C.

John, J.

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

Kumar, A.

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

Linares, J.

Maclean, T. S. M.

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

McMullin, J. N.

Mondal, S. K.

Nawata, K.

Niblett, J.

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

Pal, B. P.

S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
[CrossRef]

Presby, H. M.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
[CrossRef]

H. M. Presby, C. A. Edward, “Near 100% eficient fiber microlenses,” Electron. Lett. 6, 582–584 (1992).
[CrossRef]

Qui, A.

Sarkar, S.

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

Sarkar, S. N.

S. K. Mondal, S. Gangopadhyay, S. N. Sarkar, “Analysis of an upside-down taper lens end from a single-mode, step-index fiber,” Appl. Opt. 37, 1006–1009 (1998).
[CrossRef]

S. Gangopadhayay, S. N. Sarkar, “Misalignment considerations in the laser diode to single-mode fiber excitation via hyperbolic lens on the fiber tip,” Opt. Commun. 146, 104–108 (1998).
[CrossRef]

S. Gangopadhyay, S. N. Sarkar, “ABCD matrix for reflection and refraction of Gaussian light beams at surfaces of hyperboloid of revolution and efficiency computation for laser diode to single-mode fiber coupling by way of a hyperbolic lens on the fiber tip,” Appl. Opt. 36, 8582–8586 (1997).
[CrossRef]

S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
[CrossRef]

Saruwatari, M.

Shou, R. L.

L. B. Yuan, R. L. Shou, “Formation and power distribution properties of an upside-down taper lens at the end of an optical fiber,” Sens. Actuators A 23, 1158–1161 (1990).
[CrossRef]

Thyagarajan, K.

S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
[CrossRef]

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

A. K. Ghatak, K. Thyagarajan, “Optical fiber waveguides,” in Optical Electronics (Cambridge U. Press, London, 1994), Chap. 13, pp. 411–415.

Yuan, L.

Yuan, L. B.

L. B. Yuan, R. L. Shou, “Formation and power distribution properties of an upside-down taper lens at the end of an optical fiber,” Sens. Actuators A 23, 1158–1161 (1990).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).
[CrossRef]

Electron. Lett.

H. M. Presby, C. A. Edward, “Near 100% eficient fiber microlenses,” Electron. Lett. 6, 582–584 (1992).
[CrossRef]

IEE Proc. Optoelectron.

J. John, T. S. M. Maclean, H. Ghafouri-Shiraz, J. Niblett, “Matching of single-mode fiber to laser diode by microlenses at 1.5-µm wavelength,” IEE Proc. Optoelectron. 3, 178–184 (1994).
[CrossRef]

J. Lightwave Technol.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 2, 252–257 (1993).
[CrossRef]

J. Opt. Commun.

S. N. Sarkar, B. P. Pal, K. Thyagarajan, “Lens coupling of laser diodes to monomode elliptic core fibers,” J. Opt. Commun. 7, 92–96 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. Gangopadhayay, S. N. Sarkar, “Misalignment considerations in the laser diode to single-mode fiber excitation via hyperbolic lens on the fiber tip,” Opt. Commun. 146, 104–108 (1998).
[CrossRef]

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

Sens. Actuators A

L. B. Yuan, R. L. Shou, “Formation and power distribution properties of an upside-down taper lens at the end of an optical fiber,” Sens. Actuators A 23, 1158–1161 (1990).
[CrossRef]

Other

A. K. Ghatak, K. Thyagarajan, “Optical fiber waveguides,” in Optical Electronics (Cambridge U. Press, London, 1994), Chap. 13, pp. 411–415.

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