Abstract

Laser beam characteristics are altered during propagation through large-core optical fibers. The distribution of modes excited by the input laser beam is modified by means of mode coupling on transmission through the fiber, leading to spatial dispersion of the profile and, ultimately and unavoidably, to degradation in the quality of the delivered beam unless the beam is spatially filtered with consequent power loss. Furthermore, a mismatch between the intensity profile of a typical focused high-power laser beam and the profile of the step-index fiber gives rise to additional beam-quality degradation. Modern materials processing applications demand ever higher delivered beam qualities (as measured by a parameter such as M 2) to achieve greater machining precision and efficiency, a demand that is currently in conflict with the desire to utilize the convenience and flexibility of large-core fiber-optic beam delivery. We present a detailed experimental investigation of the principal beam-quality degradation effects associated with fiber-optic beam delivery and use numerical modeling to aid an initial discussion of the causes of such degradation.

© 2000 Optical Society of America

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References

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  1. N. Reng, T. Beck, M. Ostermeyer, “Comparison of different types of fibers for high power cw Nd:YAG lasers,” in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc SPIE2206, 443–454 (1994).
  2. B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.
  3. M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).
  4. T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.
  5. A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.
  6. D. P. Hand, J. D. C. Jones, “Single-mode fiber delivery of Nd:YAG light for precision machining applications,” Appl. Opt. 37, 1602–1606 (1998).
    [CrossRef]
  7. D. Gloge, “Propagation effects in optical fibres,” IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
    [CrossRef]
  8. D. Marcuse, Light Transmission Optics (Van Norstrand Reinhold, New York, 1982).
  9. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
    [CrossRef]
  10. J. Saijonmaa, D. Yevik, “Beam-propagation analysis of loss in bent optical waveguides and fibers,” J. Opt. Soc. Am. 73, 1785–1791 (1983).
    [CrossRef]
  11. L. B. Felsen, “Rays, modes and beams in optical fibre waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
    [CrossRef]
  12. W. A. E. Goethals, “Laser beam analysis by geometrical optics,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).
  13. A. Yariv, Optical Electronics, 3rd ed. (Holt-Saunders, New York, 1985).
  14. D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

1998 (1)

1994 (1)

D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

1983 (1)

1977 (1)

L. B. Felsen, “Rays, modes and beams in optical fibre waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
[CrossRef]

1975 (1)

D. Gloge, “Propagation effects in optical fibres,” IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
[CrossRef]

1972 (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

Beck, T.

N. Reng, T. Beck, M. Ostermeyer, “Comparison of different types of fibers for high power cw Nd:YAG lasers,” in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc SPIE2206, 443–454 (1994).

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

Blewett, I. J.

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Boechat, A. A. P.

D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

Bostanjoglo, I. G.

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

Felsen, L. B.

L. B. Felsen, “Rays, modes and beams in optical fibre waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
[CrossRef]

French, P.

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Glesias, R. D.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Gloge, D.

D. Gloge, “Propagation effects in optical fibres,” IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
[CrossRef]

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

Goethals, W. A. E.

W. A. E. Goethals, “Laser beam analysis by geometrical optics,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).

Golden, J. F.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Hand, D. P.

D. P. Hand, J. D. C. Jones, “Single-mode fiber delivery of Nd:YAG light for precision machining applications,” Appl. Opt. 37, 1602–1606 (1998).
[CrossRef]

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Hunter, B. V.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Jones, J. D. C.

D. P. Hand, J. D. C. Jones, “Single-mode fiber delivery of Nd:YAG light for precision machining applications,” Appl. Opt. 37, 1602–1606 (1998).
[CrossRef]

D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Kugler, N.

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

Kuhn, A.

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Laverty, P. J.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Leong, K. H.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Norstrand Reinhold, New York, 1982).

Miller, C. B.

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

Ostermeyer, M.

N. Reng, T. Beck, M. Ostermeyer, “Comparison of different types of fibers for high power cw Nd:YAG lasers,” in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc SPIE2206, 443–454 (1994).

Reng, N.

N. Reng, T. Beck, M. Ostermeyer, “Comparison of different types of fibers for high power cw Nd:YAG lasers,” in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc SPIE2206, 443–454 (1994).

Richmond, M.

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

Richter, K.

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

Saijonmaa, J.

Sasnett, M. W.

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).

Su, D.

D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

Weber, H.

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

Yariv, A.

A. Yariv, Optical Electronics, 3rd ed. (Holt-Saunders, New York, 1985).

Yevik, D.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51, 1767–1783 (1972).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

D. Gloge, “Propagation effects in optical fibres,” IEEE Trans. Microwave Theory Tech. 23, 106–120 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lasers Eng. (1)

D. Su, A. A. P. Boechat, J. D. C. Jones, “Curvature induced mode coupling in large core optical fibres with step refractive index profiles,” Opt. Lasers Eng. 20, 193–205 (1994).

Opt. Quantum Electron. (1)

L. B. Felsen, “Rays, modes and beams in optical fibre waveguides,” Opt. Quantum Electron. 9, 189–195 (1977).
[CrossRef]

Other (8)

W. A. E. Goethals, “Laser beam analysis by geometrical optics,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).

A. Yariv, Optical Electronics, 3rd ed. (Holt-Saunders, New York, 1985).

N. Reng, T. Beck, M. Ostermeyer, “Comparison of different types of fibers for high power cw Nd:YAG lasers,” in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc SPIE2206, 443–454 (1994).

B. V. Hunter, K. H. Leong, C. B. Miller, J. F. Golden, R. D. Glesias, P. J. Laverty, “Selecting a high-power fiber-optic laser beam delivery system,” in Proceedings of ICALEO’96 (Laser Institute of America, Orlando, Fla., 1996), pp. 173–182.

M. W. Sasnett, “Propagation of multimode laser beams—the M2 factor,” in The Physics and Technology of Laser Resonators, D. R. Hall, P. E. Jackson, eds. (Hilger, Bristol, UK, 1989).

T. Beck, I. G. Bostanjoglo, N. Kugler, K. Richter, H. Weber, “Laser beam drilling applications in novel materials for the aircraft industry,” in Proceedings of ICALEO’97 (Laser Institute of America, Orlando, Fla., 1997), pp. E93–E102.

A. Kuhn, P. French, D. P. Hand, I. J. Blewett, M. Richmond, J. D. C. Jones, “Fibre optic delivery of high beam quality, high energy Nd:YAG pulses for percussion drilling,” in Proceedings of ICALEO’98 (Laser Institute of America, Orlando, Fla., 1998), Vol. 85, Section B-40.

D. Marcuse, Light Transmission Optics (Van Norstrand Reinhold, New York, 1982).

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Figures (7)

Fig. 1
Fig. 1

General experiment setup to measure beam quality after propagation through a fiber.

Fig. 2
Fig. 2

Arrangement of three-dimensional meshes (input and output faces) and one-dimensional slices (fiber interior) to enable efficient study of beam quality after propagation through a large-core optical fiber.

Fig. 3
Fig. 3

Example of the propagation of a meridional ray in the horizontal plane of a step-index fiber. Note the effective point of refraction at the midplane of the segment when a change of refractive index (core–cladding interface) occurs between two neighboring segments. Graded-index fiber profiles can be dealt with in the same manner.

Fig. 4
Fig. 4

Qualitative comparison of beam profile results from experiment (dotted curve) and modeling (solid curve) for straight fibers with different core diameters for an input laser beam with an M 2 of 80, focused to a spot diameter of 350 µm at the input face of the fiber, resulting in a beam NA of 0.15.

Fig. 5
Fig. 5

Qualitative comparison of beam profile results from experiment (dashed curve) and modeling (solid curve) for 400-µm core-diameter fibers curved to different radii for a low-quality laser beam. The beam diameter at the input face was 350 µm with an M 2 of 80.

Fig. 6
Fig. 6

Comparison of beam-quality results from experiment (error bars) and the empirical relationship (curve) for fibers with different core diameters for a moderate input beam M 2 of 22.

Fig. 7
Fig. 7

Effect on the transmitted beam quality for moderate input beam quality when optical fibers are bent.

Equations (2)

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M2=D0Θ4λ/π,
D=Mout2Min2exp1.1d,

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