Abstract

For large-core optical fibers of a few meters length, which are typical of those used in beam delivery systems for high-power Nd:YAG lasers, it is shown that the near-field profile of the output beam is a strong function of the launching conditions. The output profile depends on both the input spot size and its alignment relative to the fiber axis. A simple theoretical model is developed for step-index fiber that shows that the output profile depends on the distribution of guided power between meridional modes and groups of skew modes. A relationship is hence derived between the launching conditions and the output profile. The predictions of the theoretical model are consistent with experiment.

© 1992 Optical Society of America

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References

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  1. H. P. Weber, W. Hockel, “High power light transmission in optical waveguides,” in High Power Lasers and their Industrial Application, S. Schuocker, ed., Proc. Soc. Photo-Opt. Instrum. Eng.650, 102–110 (1986).
  2. H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
    [CrossRef]
  3. H. Miura, K. Okino, “The transmission characteristics of high power cw YAG laser light through optical fibers,” Rev. Laser Eng. Jpn. 16(6), 310–317 (1988).
    [CrossRef]
  4. A. A. P. Boechat, D. Su, D. R. Hall, J. D. C. Jones, “Bend loss in large core multimode optical fiber beam delivery systems,” Appl. Opt. 30, 321–327 (1991).
    [CrossRef] [PubMed]
  5. G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibers: perturbative solution of the time dependent power flow equation,” Opt. Quantum Electron. 15, 119–123 (1983).
    [CrossRef]
  6. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 2.
  7. M. Ikeda, A. Sugimura, T. Ikegami, “Multimode optical fibers: steady-state mode exciter,” Appl. Opt. 15, 2116–2120 (1976).
    [CrossRef] [PubMed]
  8. W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988).

1991

1988

H. Miura, K. Okino, “The transmission characteristics of high power cw YAG laser light through optical fibers,” Rev. Laser Eng. Jpn. 16(6), 310–317 (1988).
[CrossRef]

1984

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

1983

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibers: perturbative solution of the time dependent power flow equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

1976

Asakura, T.

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

Boechat, A. A. P.

Cancellieri, G.

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibers: perturbative solution of the time dependent power flow equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Fantini, P.

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibers: perturbative solution of the time dependent power flow equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Fujii, H.

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

Hall, D. R.

Hockel, W.

H. P. Weber, W. Hockel, “High power light transmission in optical waveguides,” in High Power Lasers and their Industrial Application, S. Schuocker, ed., Proc. Soc. Photo-Opt. Instrum. Eng.650, 102–110 (1986).

Ikeda, M.

Ikegami, T.

Jones, J. D. C.

Koechner, W.

W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988).

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 2.

Matsumoto, T.

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

Miura, H.

H. Miura, K. Okino, “The transmission characteristics of high power cw YAG laser light through optical fibers,” Rev. Laser Eng. Jpn. 16(6), 310–317 (1988).
[CrossRef]

Ohura, T.

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

Okino, K.

H. Miura, K. Okino, “The transmission characteristics of high power cw YAG laser light through optical fibers,” Rev. Laser Eng. Jpn. 16(6), 310–317 (1988).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 2.

Su, D.

Sugimura, A.

Weber, H. P.

H. P. Weber, W. Hockel, “High power light transmission in optical waveguides,” in High Power Lasers and their Industrial Application, S. Schuocker, ed., Proc. Soc. Photo-Opt. Instrum. Eng.650, 102–110 (1986).

Appl. Opt.

IEEE J. Lightwave Technol.

H. Fujii, T. Asakura, T. Matsumoto, T. Ohura, “Output power distribution of a large core optical fiber,” IEEE J. Lightwave Technol. LT-2, 1057–1062 (1984).
[CrossRef]

Opt. Quantum Electron.

G. Cancellieri, P. Fantini, “Mode coupling effects in optical fibers: perturbative solution of the time dependent power flow equation,” Opt. Quantum Electron. 15, 119–123 (1983).
[CrossRef]

Rev. Laser Eng. Jpn.

H. Miura, K. Okino, “The transmission characteristics of high power cw YAG laser light through optical fibers,” Rev. Laser Eng. Jpn. 16(6), 310–317 (1988).
[CrossRef]

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 2.

W. Koechner, Solid State Laser Engineering, 2nd ed. (Springer-Verlag, Berlin, 1988).

H. P. Weber, W. Hockel, “High power light transmission in optical waveguides,” in High Power Lasers and their Industrial Application, S. Schuocker, ed., Proc. Soc. Photo-Opt. Instrum. Eng.650, 102–110 (1986).

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Figures (7)

Fig. 1
Fig. 1

Core cross section of a step-index multimode fiber showing the projections of loci of a skew mode.

Fig. 2
Fig. 2

Coordinate system used for the theoretical model: ds is an area element on the entrance face of the fiber at a distance r from the axis OO′, with azimuth θ; the line AA′ is parallel to the axis and passes through ds. The family of rays R1 R2, … are coplanar with AA′ and R, and R is on the entrance face of the fiber at a distance rφ from the axis and makes an angle φ with the radial direction r. The projection of R1, R2, … on the entrance face thus defines R.

Fig. 3
Fig. 3

Diagram of the experimental arrangement: W optical wedge; PM, partial-reflectivity mirror; L1, launching lens; F, optical fiber; L2 and L3, imaging optics; CID, charge-injection-device camera of beam profiler; CCD, camera used to view the input face of the fiber; IBM, computer.

Fig. 4
Fig. 4

Output NFP with the input spot launched to the center of the core as a function of launching lens focal lengths (top to bottom) of 40, 60, 80, and 100 mm, which produce spot sizes of 210, 262, 302, and 410 μm, respectively.

Fig. 5
Fig. 5

Cross section of the output NFP obtained by launching the beam at the center of the core (solid curve) and with a lateral displacement of 100 μm (dashed curve), by using launching lenses of (a) 40-mm focal length (w = 210 μm) and (b) 80-mm focal length (w = 302 μm).

Fig. 6
Fig. 6

Cross section of the output NFP showing the theoretical (solid) and experimental (dashed) curves, for the following launching conditions: (a) center launch, w = 210 μm; (b) 100-μm lateral displacement, w = 210 μm; (c) center launch, w = 262 μm; (d) 100-μm lateral displacement, w = 262 μm; (e) center launch, w = 302 μm; (f) 100-μm lateral displacement, w = 302 μm.

Fig. 7
Fig. 7

Cross section of output NFP with the fiber coiled around a spool with a diameter of 280 mm. The launching lens has a 60-mm focal length.

Equations (12)

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P φ = 2 π r φ R 0 p r 0 d r 0 = 2 π α ( R 0 - r φ ) .
2 π α ( R 0 - r φ ) = ( 1 / 2 π ) f ( r , θ ) d s d φ .
α = 1 4 π 2 f ( r , θ ) R 0 - r φ d s d φ ,
p = 1 4 π 2 f ( r , θ ) r 0 ( R 0 - r φ ) d s d φ ,             r φ r 0 R 0 .
P ( r 0 ) = 1 4 π 2 f ( r , θ ) r r 0 ( R 0 - r sin φ ) d r d θ d φ .
P ( r 0 ) = 1 π 2 r 0 0 2 π d θ 0 R 0 r f ( r , θ ) d r 0 φ ( r ) d φ R 0 - r sin φ ,
φ ( r ) = π / 2 for 0 r r 0 , φ ( r ) = sin - 1 ( r 0 / r ) for r 0 < r R 0 ,
P ( r 0 ) = 1 π 2 r 0 0 2 π d θ 0 r 0 r f ( r , θ ) d r 0 π / 2 d φ R 0 - r sin φ + 1 π 2 r 0 0 2 π d θ r 0 R 0 r f ( r , θ ) d r × 0 sin - 1 ( r 0 / r ) d φ R 0 - r sin φ .
P ( r 0 ) = A r 0 0 2 π d θ 0 r 0 r f ( r , θ ) d r 0 π / 2 d φ R 0 - r sin φ + A r 0 0 2 π d θ r 0 R 0 r f ( r , θ ) d r × 0 sin - 1 ( r 0 / r ) d φ R 0 - r sin φ .
f ( r , θ ) = { a + b r 2 , r < R 0 ,
r 2 r 2 + x 2 - 2 r x cos θ
f ( r , θ ) = { a + b ( r 2 + x 2 - 2 r x cos θ ) , r 2 + x 2 - 2 r x cos θ < R 2 0 elsewhere .

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