Abstract

A bundle of monomode fibers can be used for transmission of coherent radiation at power levels beyond the damage threshold of an individual fiber. The coherence at the bundle output can be reestablished by proper correction of the phases at the individual fiber ends. For a phase adjustment that leads to a convergent wave the focusing efficiencies are calculated for various geometric parameters of the fiber bundle. For practical situations concentration of almost 40% of the power into the focal spot seems realistic.

© 1989 Optical Society of America

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References

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  1. H. P. Weber, W. Hodel, “High Power Light-Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).
  2. J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
    [CrossRef]
  3. W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303–305 (1986).
    [CrossRef] [PubMed]
  4. J. R. Leger, G. J. Swanson, M. Holz, “Efficient Side Lobe Suppression of Laser Diode Arrays,” Appl. Phys. Lett. 50, 1044–1046 (1987).
    [CrossRef]
  5. G. J. Swanson, J. R. Leger, M. Holz, “Aperture Filling of Phase-Locked Laser Arrays,” Opt. Lett. 12, 245–247 (1987).
    [CrossRef] [PubMed]
  6. B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
    [CrossRef]
  7. D. A. Jackson, R. Priest, A. Dandridge, A. B. Tveten, “Elimination of Drift in a Single-Mode Optical Fiber Interferometer Using a Piezoelectrically Stretched Coiled Fiber,” Appl. Opt. 19, 2926–2929 (1980).
    [CrossRef] [PubMed]
  8. G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
    [CrossRef]
  9. A. W. Snyder, J. D. Love, Optical Waveguide Theory, (Chapman & Hall, London, 1983), pp. 336ff.
    [CrossRef]
  10. J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
    [CrossRef]
  11. W. Siegmund, “The Fiber Option for Image Transmission,” Photonics Spectra 20, 59–62 (1986).

1988 (1)

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

1987 (4)

J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
[CrossRef]

J. R. Leger, G. J. Swanson, M. Holz, “Efficient Side Lobe Suppression of Laser Diode Arrays,” Appl. Phys. Lett. 50, 1044–1046 (1987).
[CrossRef]

G. J. Swanson, J. R. Leger, M. Holz, “Aperture Filling of Phase-Locked Laser Arrays,” Opt. Lett. 12, 245–247 (1987).
[CrossRef] [PubMed]

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

1986 (4)

W. Siegmund, “The Fiber Option for Image Transmission,” Photonics Spectra 20, 59–62 (1986).

H. P. Weber, W. Hodel, “High Power Light-Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303–305 (1986).
[CrossRef] [PubMed]

1980 (1)

Appleman, H. R.

J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Bobb, L. C.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Dandridge, A.

Davis, J. P.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Eppler, J. E.

J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
[CrossRef]

Heidel, J. R.

J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Hodel, W.

H. P. Weber, W. Hodel, “High Power Light-Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

Holz, M.

G. J. Swanson, J. R. Leger, M. Holz, “Aperture Filling of Phase-Locked Laser Arrays,” Opt. Lett. 12, 245–247 (1987).
[CrossRef] [PubMed]

J. R. Leger, G. J. Swanson, M. Holz, “Efficient Side Lobe Suppression of Laser Diode Arrays,” Appl. Phys. Lett. 50, 1044–1046 (1987).
[CrossRef]

Jackson, D. A.

Josten, G.

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

Krumboltz, H. D.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Larson, D. C.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Leger, J. R.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory, (Chapman & Hall, London, 1983), pp. 336ff.
[CrossRef]

Luethy, W.

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

Paoli, T. L.

J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
[CrossRef]

Priest, R.

Rice, R. R.

J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

Siegenthaler, U.

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

Siegmund, W.

W. Siegmund, “The Fiber Option for Image Transmission,” Photonics Spectra 20, 59–62 (1986).

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory, (Chapman & Hall, London, 1983), pp. 336ff.
[CrossRef]

Swanson, G. J.

Thornton, R. L.

J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
[CrossRef]

Tveten, A. B.

Veldkamp, W. B.

Weber, H. P.

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

H. P. Weber, W. Hodel, “High Power Light-Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

White, B. J.

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. R. Leger, G. J. Swanson, M. Holz, “Efficient Side Lobe Suppression of Laser Diode Arrays,” Appl. Phys. Lett. 50, 1044–1046 (1987).
[CrossRef]

Electron. Lett. (1)

J. E. Eppler, R. L. Thornton, T. L. Paoli, “Dependence of Central-Lobe Output Power on Fill Factor of an In-Phase Laser Array,” Electron. Lett. 23, 754–755 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. R. Heidel, R. R. Rice, H. R. Appleman, “Use of a Phase Corrector Plate to Generate a Single-Lobed Phased Array Far Field Pattern,” IEEE J. Quantum Electron. QE-22, 749–752 (1986).
[CrossRef]

IEEE/OSAJ. Lightwave Technol. (1)

B. J. White, J. P. Davis, L. C. Bobb, H. D. Krumboltz, D. C. Larson, “Optical-Fiber Thermal Modulator,” IEEE/OSAJ. Lightwave Technol. LT-5, 1169–1175 (1987).
[CrossRef]

Opt. Lett. (2)

Photonics Spectra (1)

W. Siegmund, “The Fiber Option for Image Transmission,” Photonics Spectra 20, 59–62 (1986).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. P. Weber, W. Hodel, “High Power Light-Transmission in Optical Waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 650, 102–108 (1986).

Z. Angew. Math. Phys. (1)

G. Josten, U. Siegenthaler, W. Luethy, H. P. Weber, “Phase Modulation in an Optical Fiber by Transverse Pressure,” Z. Angew. Math. Phys. 39, 328–333 (1988).
[CrossRef]

Other (1)

A. W. Snyder, J. D. Love, Optical Waveguide Theory, (Chapman & Hall, London, 1983), pp. 336ff.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Intensity distribution across the x-z directions in the beam. The intensity is shown from z = 0 to z = 4000 μm along the propagation axis and for x = 0 to x = ±150 μm along the x-direction in the output of a hexagonal array of 127 parallel fibers. The beam waist is 3 μm, the fiber diameter is 12 μm and the focal length is 1 mm for λ = 0.633 μm.

Fig. 2
Fig. 2

Intensity distribution across the beam in the x-y planes situated at different positions between 0 and 1600 μm of a hexagonal array of 127 parallel fibers. x ranges from 0 to ±80 μm, y ranges from 0 to ±100 μm.

Fig. 3
Fig. 3

Distance of highest intensity as a function of the number of fibers. The dots indicate the values for hexagonal arrangements of 1,7,19, 37, 61, 91, 127, and 169 fibers, all with 3-μm beam waist and 12-μm diam fiber.

Fig. 4
Fig. 4

Comparison of the intensity distribution in the focal plane of (a) 127 parallel fibers and (b) 127 inclined fibers with 3-μm beam waist and 12-μm diam fiber.

Fig. 5
Fig. 5

Fraction of energy in the focus as a function of distance d between 37, 91, and 127 fibers. The dashed lines give the results for a hexagonal parallel array. The solid line shows the result for a hexagonal inclined array.

Fig. 6
Fig. 6

Fraction of energy in the focus as a function of focal distance for fiber diameters of 10, 12, 15, and 20 μm. The dashed lines give the results for a hexagonal parallel array of 127 fibers. The solid line shows the result for the corresponding hexagonal inclined arrays.

Fig. 7
Fig. 7

Intensity distribution across the beam in the x-y focal plane of a hexagonal array of 127 parallel fibers. With the point of zero phase difference at x = 20 μm, y = 20 μm, z = 1000 μm, the focus is shifted off the z-axis. x and y range from 0 to ± 150 μm. The beam waist is 3 μm, the fiber diameter is 12 μm, and the focal length is 1 mm for λ = 0.633 μm.

Tables (1)

Tables Icon

Table I Focal Energy, Peak Intensity, and Spot Size for a Lens, a Quadratic Parallel Bundle of 121 Fibers, and a Hexagonal Parallel and a Hexagonal Inclined Bundle of 127 Fibers with 3-μm Beam Waist and 12 μm Diam Fiber; the Spot Size is Given at 1/e2 (Upper Value) and at the Point of Zero Intensity (Lower Value)

Equations (1)

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E ( x , y , z ) = E 0 1 i ( z λ / π w 0 2 ) × exp { x 2 + y 2 / [ w 0 2 i ( z λ / π ) ] } × exp ( i 2 π z / λ ) ,

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