Abstract

We describe experimental results and a theoretical analysis for propagation in graded-index multimode fiber when diode laser light is launched into the lowest-order propagation modes and the fiber undergoes severe bending perturbations. Experimentally, near-field modal interference images and transmission loss measurements were obtained for different loop diameters. The data indicate that, when the fundamental mode is excited, the light remains in lowest-order modes even for small bend diameters. This is consistent with analysis which predicts that, in a parabolic-index multimode fiber subject to constant diameter bending, the light tends to oscillate between lowest-order modes and remains trapped therein rather than diffusing to high-order modes. Implications of these results for an intrusion-resistant communication system with graded-index multimode fiber are discussed.

© 2000 Optical Society of America

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References

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  1. C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).
  2. D. Marcuse, “Losses and impulse response of a parabolic index fiber with random bends,” Bell Syst. Tech. J. 52, 1423–1437 (1973).
    [CrossRef]
  3. F. Dubois, Ph. Emplit, O. Hugon, “Selective mode excitation in graded-index multimode fiber by a computer-generated optical mask,” Opt. Lett. 19, 433–435 (1994).
    [CrossRef] [PubMed]
  4. J. Saijonmaa, S. J. Halme, “Reduction of modal noise by using reduced spot excitation,” Appl. Opt. 20, 4302–4306 (1981).
    [CrossRef] [PubMed]
  5. Z. Haas, M. A. Santoro, “A mode filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems,” J. Lightwave Technol. 11, 1125–1130 (1993).
    [CrossRef]
  6. G. C. Papen, G. M. Murphy, “Modal noise in multimode fibers under restricted launch conditions,” J. Lightwave Technol. 17, 817–822 (1999).
    [CrossRef]
  7. D. Donlagic, M. Zavrsnik, “Fiber-optic microbend sensor structure,” Opt. Lett. 22, 837–839 (1997).
    [CrossRef]
  8. D. Donlagic, B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded-index multimode fiber,” J. Lightwave Technol. 17, 1856–1868 (1999).
    [CrossRef]
  9. L. Faustini, G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671–679 (1997).
    [CrossRef]
  10. J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.
  11. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chap. 2.
  12. H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
    [CrossRef]

1999

1997

L. Faustini, G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671–679 (1997).
[CrossRef]

D. Donlagic, M. Zavrsnik, “Fiber-optic microbend sensor structure,” Opt. Lett. 22, 837–839 (1997).
[CrossRef]

1994

1993

Z. Haas, M. A. Santoro, “A mode filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems,” J. Lightwave Technol. 11, 1125–1130 (1993).
[CrossRef]

1984

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
[CrossRef]

1981

1973

D. Marcuse, “Losses and impulse response of a parabolic index fiber with random bends,” Bell Syst. Tech. J. 52, 1423–1437 (1973).
[CrossRef]

Arnaud, J. A.

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.

Asawa, C. K.

C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).

Asawa, J. K.

C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).

Asawa, M.

C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).

Asawa, M. H.

C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).

Culshaw, B.

Donlagic, D.

Dubois, F.

Emplit, Ph.

Faustini, L.

L. Faustini, G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671–679 (1997).
[CrossRef]

Haas, Z.

Z. Haas, M. A. Santoro, “A mode filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems,” J. Lightwave Technol. 11, 1125–1130 (1993).
[CrossRef]

Halme, S. J.

Hugon, O.

Marcuse, D.

D. Marcuse, “Losses and impulse response of a parabolic index fiber with random bends,” Bell Syst. Tech. J. 52, 1423–1437 (1973).
[CrossRef]

Martini, G.

L. Faustini, G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671–679 (1997).
[CrossRef]

Murphy, G. M.

Papen, G. C.

Saijonmaa, J.

Santoro, M. A.

Z. Haas, M. A. Santoro, “A mode filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems,” J. Lightwave Technol. 11, 1125–1130 (1993).
[CrossRef]

Taylor, H. F.

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chap. 2.

Zavrsnik, M.

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Losses and impulse response of a parabolic index fiber with random bends,” Bell Syst. Tech. J. 52, 1423–1437 (1973).
[CrossRef]

J. Lightwave Technol.

Z. Haas, M. A. Santoro, “A mode filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems,” J. Lightwave Technol. 11, 1125–1130 (1993).
[CrossRef]

L. Faustini, G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671–679 (1997).
[CrossRef]

H. F. Taylor, “Bending effects in optical fibers,” J. Lightwave Technol. LT-2, 617–628 (1984).
[CrossRef]

G. C. Papen, G. M. Murphy, “Modal noise in multimode fibers under restricted launch conditions,” J. Lightwave Technol. 17, 817–822 (1999).
[CrossRef]

D. Donlagic, B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded-index multimode fiber,” J. Lightwave Technol. 17, 1856–1868 (1999).
[CrossRef]

Opt. Lett.

Other

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976), Chap. 2.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), Chap. 2.

C. K. Asawa, M. H. Asawa, J. K. Asawa, M. Asawa, “Optical waveguide including single-mode waveguide channels coupled to a multimode fiber,” U.S. patent5,712,937 (27January1998).

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Figures (10)

Fig. 1
Fig. 1

Experimental arrangement for examining the near-field for lateral offset of the single-mode fiber with respect to the graded-index multimode fiber. Power measurements were made at the multimode fiber end. Position of the planar small-loop perturbation is indicated by a dotted circle. For other low-order mode launches, the single-mode and multimode fibers were connected with a mechanical splice. DFB, distributed feedback.

Fig. 2
Fig. 2

Near-field image at the output end of a laser single-mode pigtail. The image intensity profile along the vertical line through the image appears to the left. The spot diameter is approximately 10 µm.

Fig. 3
Fig. 3

Near-field images at the output end of the graded-index multimode fiber for lateral displacements of the axis of the light-launching single-mode fiber with respect to that of the multimode fiber. Displacements: (a) 0 µm, (b) 5 µm, (c) 10 µm, (d) 15 µm, (e) 20 µm, and (f) 25 µm.

Fig. 4
Fig. 4

Near-field images at the output end of a graded-index multimode fiber where the lowest-order modes are excited. The near-field images of (a)–(f) were taken after moving, looping, or twisting the fiber at various points. Relative phase changes of the different modes that were due to fiber disturbances result in different patterns. (a) appears to be mostly the fundamental mode, but with some low-order modes added. The spot diameter is approximately 17 µm.

Fig. 5
Fig. 5

Near-field images at the end of a 25-cm length of multimode graded-index fiber. The fiber is axially twisted randomly up to 180 deg for the near-field images of (a)–(f). The fiber output end was held rigidly, while the input fiber end and the attached single-mode fiber were twisted axially.

Fig. 6
Fig. 6

Near-field images at the output end of a graded-index multimode fiber, where the fiber undergoes a planar single-loop perturbation of various small diameters at its midpoint: (a) 8 cm, (b) 5 cm, (c) 3 cm, (d) 2 cm, (e) 1.5 cm, (f) 1.25 cm, (g) 1.0 cm, and (h) 0.75 cm. The fundamental mode appears in all these images, whereas other low-order modes contribute to the patterns.

Fig. 7
Fig. 7

Graph of optical power change when the graded-index (GI) multimode fiber is perturbed by a single planar loop of various diameters. Diode laser light was launched into high-order modes by laterally translating the axis of the single-mode fiber by 15 and 20 µm with respect to the axis of the multimode fiber. Light was launched into low-order modes by aligning the axes coaxially. The transmitted light was noisy for the high-order mode cases. The noise boundaries are indicated for the larger loops; for the smaller loops, the noise boundaries exceed (±) 0.5 dB. Because highly coherent light is launched near the core–cladding boundary, the fluctuations are thought to be modal noise. The transmission changes for a single-mode fiber for the same perturbation are shown for comparison. The small losses for the low-order modes for the larger-diameter loops of the multimode fiber could not be measured because the power-meter resolution was limited to 0.01 dB.

Fig. 8
Fig. 8

Calculated power in the fundamental mode and all guided modes of graded-index fiber as a function of fiber length along a 2-cm-diameter bend. Virtually all the power remains in the guided modes for this bend diameter.

Fig. 9
Fig. 9

Power distribution among fiber modes at a distance of 0.57 mm (corresponding to half of the intermodal beat length) from the start of a 2-cm-diameter bend. This corresponds to the furthest excursion from the fundamental mode that occurs as the power oscillates between the fundamental mode and the first few higher-order modes.

Fig. 10
Fig. 10

Half-tone plots of calculated near-field power density distributions for individual-mode and multimode outputs from the graded-index fiber, with the following mode amplitudes represented: (a) (0 0), (b) (1 0), (c) (1 1), (d) (00) + i (11), (e) (0 0) - (1 1), (f) (0 0) - (1 0), (g) (00) + i(10), (h) (0 0) + (1 1), (i) (0 0) + (2 0), and (j) (00) + i(20).

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

n=n1-Δnx2+y2/a2,
NA=2n1Δn1/2.
uij=uixujy,
uix=NiHiαxexp-α2x2/2,
α=2πNA/λa1/2.
βij=βc-i+j+1Δβ,
βc=2πn1/λ,
Δβ=α2/βc.
i+j+1<πNAa/λ.
i+j<11.1,
ux, y=i,j Aijuijx, y,
uijx, yexp-iβcxϕ=ux, y
x=a++a/α2,
- unaumdx=mδm,n+1,
- una+umdx=m+1δm,n-1.
Ai+1j=iβcϕi+1/2α,
Ai-1j=iβcϕi/2α,
Alm=0 if mj or li-1 or li+1.
dAijdz=iκi,i+1Ai+1jexpiΔz+iκi,i-1Ai-1jexp-iΔz,
κi,i+1=i+1κ1,
κi,i-1=iκ1,
κ1=βc/2αR.

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