Abstract

Results of two recent studies representing distinct approaches to optimizing laser-diode to single-mode fiber ball-lens coupling efficiency are compared and revealed to be in close agreement. One method is based on a conventional optical analysis–design program combining geometrical and diffraction methods, merged with calculated coupling efficiency in terms of balanced spherical aberration. The other is based on exact solution of Maxwell’s equations for scattering of a beam from a dielectric sphere. The results suggest that optimum coupling efficiency may depend critically on sufficiently fine discretization of the distances of source and fiber from the lens. The studies compared here are synergistic with several other recently reported studies on coupling efficiency, and those studies are appropriately cross referenced. A graphic relationship is developed between coupling efficiency and Strehl ratio as an optical tolerance for the coupling system based on balanced spherical aberration.

© 1998 Optical Society of America

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References

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  1. R. G. Wilson, “Numerical aperture limits on efficient ball lens coupling of laser diodes to single-mode fibers with defocus to balance spherical aberration,” NASA Tech. Memo. 4578 (November1994).
  2. R. P. Ratowsky, L. Yang, R. J. Deri, K. W. Chang, J. S. Kallman, G. Trott, “Laser diode to single-mode fiber ball lens coupling efficiency: full-wave calculation and measurements,” Appl. Opt. 36, 3435–3438 (1997).
    [CrossRef] [PubMed]
  3. M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).
  4. S. Szapiel, J. Cote, “Analysis of coupling efficiency in single-mode fiber components as an optical design problem,” in Optical Design for Photonics, Vol. 9 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 140–142.
  5. M. Cote, R. R. Shannon, “Waveguide coupling optimization using lenses,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 160–166 (1995).
    [CrossRef]
  6. M. Cote, R. R. Shannon, “Optimization of waveguide coupling lenses with optical design software,” Appl. Opt. 35, 6179–6185 (1996).
    [CrossRef] [PubMed]
  7. C. Gaebe, “Analysis and compensation of ball-lens induced pupil distortion and spherical aberration,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 184–193 (1995).
    [CrossRef]
  8. T. D. Milster, Z. Y. Chen, “Combination of ray-trace and diffraction modeling to describe coupling laser diodes to fibers and waveguides,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 194–202 (1995).
    [CrossRef]
  9. G. D. Landry, T. A. Maldonado, “Ray tracing through a two ball uniaxial sapphire lens system in a single mode fiber-to-fiber coupler,” J. Lightwave Technol. 14, 509–512 (1996).
    [CrossRef]
  10. C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
    [CrossRef]
  11. R. E. Wagner, W. J. Tomlinson, “Coupling efficiency of optics in single-mode fiber components,” Appl. Opt. 21, 2671–2688 (1982).
    [CrossRef] [PubMed]
  12. V. N. Mahajan, Aberration Theory Made Simple, Vol. TT 6 of Tutorial Text Series (SPIE, Bellingham, Wash., 1991).
  13. W. J. Smith, Modern Optical Engineering—The Design of Optical Systems. (McGraw-Hill, New York, 1990).
  14. V. N. Mahajan, “Strehl ratio for primary aberrations: some analytical results for circular and annular pupils,” J. Opt. Soc. Am. 72, 1258–1266 (1982).
    [CrossRef]

1997 (1)

1996 (2)

M. Cote, R. R. Shannon, “Optimization of waveguide coupling lenses with optical design software,” Appl. Opt. 35, 6179–6185 (1996).
[CrossRef] [PubMed]

G. D. Landry, T. A. Maldonado, “Ray tracing through a two ball uniaxial sapphire lens system in a single mode fiber-to-fiber coupler,” J. Lightwave Technol. 14, 509–512 (1996).
[CrossRef]

1995 (1)

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

1994 (1)

R. G. Wilson, “Numerical aperture limits on efficient ball lens coupling of laser diodes to single-mode fibers with defocus to balance spherical aberration,” NASA Tech. Memo. 4578 (November1994).

1993 (1)

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

1982 (2)

Chang, K. W.

Chen, Z. Y.

T. D. Milster, Z. Y. Chen, “Combination of ray-trace and diffraction modeling to describe coupling laser diodes to fibers and waveguides,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 194–202 (1995).
[CrossRef]

Cote, J.

S. Szapiel, J. Cote, “Analysis of coupling efficiency in single-mode fiber components as an optical design problem,” in Optical Design for Photonics, Vol. 9 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 140–142.

Cote, M.

M. Cote, R. R. Shannon, “Optimization of waveguide coupling lenses with optical design software,” Appl. Opt. 35, 6179–6185 (1996).
[CrossRef] [PubMed]

M. Cote, R. R. Shannon, “Waveguide coupling optimization using lenses,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 160–166 (1995).
[CrossRef]

Deri, R. J.

Dragone, C.

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

Edwards, C. A.

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

Gaebe, C.

C. Gaebe, “Analysis and compensation of ball-lens induced pupil distortion and spherical aberration,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 184–193 (1995).
[CrossRef]

Goure, J. P.

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

Kallman, J. S.

Landry, G. D.

G. D. Landry, T. A. Maldonado, “Ray tracing through a two ball uniaxial sapphire lens system in a single mode fiber-to-fiber coupler,” J. Lightwave Technol. 14, 509–512 (1996).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, “Strehl ratio for primary aberrations: some analytical results for circular and annular pupils,” J. Opt. Soc. Am. 72, 1258–1266 (1982).
[CrossRef]

V. N. Mahajan, Aberration Theory Made Simple, Vol. TT 6 of Tutorial Text Series (SPIE, Bellingham, Wash., 1991).

Maldonado, T. A.

G. D. Landry, T. A. Maldonado, “Ray tracing through a two ball uniaxial sapphire lens system in a single mode fiber-to-fiber coupler,” J. Lightwave Technol. 14, 509–512 (1996).
[CrossRef]

Milster, T. D.

T. D. Milster, Z. Y. Chen, “Combination of ray-trace and diffraction modeling to describe coupling laser diodes to fibers and waveguides,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 194–202 (1995).
[CrossRef]

Mottier, P.

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

Presby, H. M.

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

Ramos, M.

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

Ratowsky, R. P.

Shannon, R. R.

M. Cote, R. R. Shannon, “Optimization of waveguide coupling lenses with optical design software,” Appl. Opt. 35, 6179–6185 (1996).
[CrossRef] [PubMed]

M. Cote, R. R. Shannon, “Waveguide coupling optimization using lenses,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 160–166 (1995).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering—The Design of Optical Systems. (McGraw-Hill, New York, 1990).

Szapiel, S.

S. Szapiel, J. Cote, “Analysis of coupling efficiency in single-mode fiber components as an optical design problem,” in Optical Design for Photonics, Vol. 9 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 140–142.

Tomlinson, W. J.

Trott, G.

Verrier, I.

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

Wagner, R. E.

Wilson, R. G.

R. G. Wilson, “Numerical aperture limits on efficient ball lens coupling of laser diodes to single-mode fibers with defocus to balance spherical aberration,” NASA Tech. Memo. 4578 (November1994).

Yang, L.

Appl. Opt. (3)

J. Lightwave Technol. (2)

G. D. Landry, T. A. Maldonado, “Ray tracing through a two ball uniaxial sapphire lens system in a single mode fiber-to-fiber coupler,” J. Lightwave Technol. 14, 509–512 (1996).
[CrossRef]

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

J. Opt. Commun. (1)

M. Ramos, I. Verrier, J. P. Goure, P. Mottier, “Efficient ball lens coupling between a single-mode optical fiber and a silica microguide at 1.3 μm,” J. Opt. Commun. 16, 179–185 (1995).

J. Opt. Soc. Am. (1)

NASA Tech. Memo. (1)

R. G. Wilson, “Numerical aperture limits on efficient ball lens coupling of laser diodes to single-mode fibers with defocus to balance spherical aberration,” NASA Tech. Memo. 4578 (November1994).

Other (6)

V. N. Mahajan, Aberration Theory Made Simple, Vol. TT 6 of Tutorial Text Series (SPIE, Bellingham, Wash., 1991).

W. J. Smith, Modern Optical Engineering—The Design of Optical Systems. (McGraw-Hill, New York, 1990).

S. Szapiel, J. Cote, “Analysis of coupling efficiency in single-mode fiber components as an optical design problem,” in Optical Design for Photonics, Vol. 9 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 140–142.

M. Cote, R. R. Shannon, “Waveguide coupling optimization using lenses,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 160–166 (1995).
[CrossRef]

C. Gaebe, “Analysis and compensation of ball-lens induced pupil distortion and spherical aberration,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 184–193 (1995).
[CrossRef]

T. D. Milster, Z. Y. Chen, “Combination of ray-trace and diffraction modeling to describe coupling laser diodes to fibers and waveguides,” in Laser Diode Chip and Packaging Technology, P. C. Chen, T. D. Milster, eds., Proc. SPIE2610, 194–202 (1995).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

LD-to-SMF coupling configuration.

Fig. 2
Fig. 2

Effects of SA (W 40) and focal shift (W 20) on transmission or on CE (Fig. 11 of Ref. 11).

Fig. 3
Fig. 3

Optimum CE for balanced SA.

Fig. 4
Fig. 4

Dependence of NA on ball-lens magnification M of a LD with defocus to balance SA and provide a 0.25λ-OPD wave front: CE, 0.56; λ = 1.3 μm; n = 1.76 (Fig. 4 of Ref. 1).

Fig. 5
Fig. 5

Calculated CE versus D SMF for seven values of LD distance D LD (Fig. 2 of Ref. 2).

Fig. 6
Fig. 6

SR for balanced SA (Fig. 2 of Ref. 14).

Fig. 7
Fig. 7

CE versus SR.

Tables (1)

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Table 1 Symbols and Abbreviations, with Refs. 1 and 2 Equivalents

Equations (2)

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D SMF = D i - R = 0.166 M + 0.163 - 0.150 = 0.166 M + 0.013 ,
D LD = D o - R = D i / M - 0.150 = 0.163 / M + 0.016 .

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