Abstract

In a multimode step-index fiber the propagation angle of a beam is conserved over short distances even if the fiber is bent slightly. This behavior can be exploited for a multiplexed signal transmission by the assignment of different channels to different propagation angles [angle-division multiplexing (ADM)]. Thus parallel transmission can be achieved. Because each channel occupies only a subrange of the fiber’s numerical aperture, modal dispersion is reduced compared with single-channel transmission through the same fiber. The transmission properties of an ADM-based transmission line are analyzed for short propagation distances. Passive all-optical setups for multiplexing and demultiplexing operations are proposed. Cross-talk measurements are shown for a transmission with a length of 8 m and 13 multiplexed channels.

© 2000 Optical Society of America

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References

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    [Crossref]
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  6. K.-H. Brenner, R. Klug, U. W. Krackhardt, “Angular multiplexing for optical board to board interconnection,” in Digest of the Topical Meeting Optics in Computing (Optical Society of America, Washington, D.C., 1999), pp. 118–120.
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    [Crossref] [PubMed]
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  9. J. Bähr, K.-H. Brenner, “Realization and optimization of planar refractive microlenses by Ag–Na ion-exchange techniques,” Appl. Opt. 35, 5102–5107 (1996).
    [Crossref] [PubMed]
  10. S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
    [Crossref]

1996 (2)

1983 (1)

G. J. Herskowitz, H. Kobrinsky, U. Levy, “Angular division multiplexing in optical fibers,” Laser Focus 19, 83–88 (1983).

1981 (1)

U. Levy, H. Kobrinsky, A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron. QE-17, 2215–2224 (1981).
[Crossref]

1975 (1)

1974 (1)

1972 (1)

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

Bähr, J.

Brenner, K.-H.

J. Bähr, K.-H. Brenner, “Realization and optimization of planar refractive microlenses by Ag–Na ion-exchange techniques,” Appl. Opt. 35, 5102–5107 (1996).
[Crossref] [PubMed]

K.-H. Brenner, R. Klug, U. W. Krackhardt, “Angular multiplexing for optical board to board interconnection,” in Digest of the Topical Meeting Optics in Computing (Optical Society of America, Washington, D.C., 1999), pp. 118–120.

Feely, C. A.

S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992), p. 236.

Friesem, A.

U. Levy, H. Kobrinsky, A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron. QE-17, 2215–2224 (1981).
[Crossref]

Gambling, W. A.

Gloge, G.

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

Herskowitz, G. J.

G. J. Herskowitz, H. Kobrinsky, U. Levy, “Angular division multiplexing in optical fibers,” Laser Focus 19, 83–88 (1983).

Kasahara, K.

Kawai, S.

Keck, D. B.

Klug, R.

K.-H. Brenner, R. Klug, U. W. Krackhardt, “Angular multiplexing for optical board to board interconnection,” in Digest of the Topical Meeting Optics in Computing (Optical Society of America, Washington, D.C., 1999), pp. 118–120.

Kobrinsky, H.

G. J. Herskowitz, H. Kobrinsky, U. Levy, “Angular division multiplexing in optical fibers,” Laser Focus 19, 83–88 (1983).

U. Levy, H. Kobrinsky, A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron. QE-17, 2215–2224 (1981).
[Crossref]

Kosaka, H.

Krackhardt, U. W.

K.-H. Brenner, R. Klug, U. W. Krackhardt, “Angular multiplexing for optical board to board interconnection,” in Digest of the Topical Meeting Optics in Computing (Optical Society of America, Washington, D.C., 1999), pp. 118–120.

Levy, U.

G. J. Herskowitz, H. Kobrinsky, U. Levy, “Angular division multiplexing in optical fibers,” Laser Focus 19, 83–88 (1983).

U. Levy, H. Kobrinsky, A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron. QE-17, 2215–2224 (1981).
[Crossref]

Li, Y.

Martin, S.

S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
[Crossref]

Matsumura, H.

Payne, D. H.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992), p. 236.

Sheridan, J. T.

S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
[Crossref]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992), p. 236.

Toal, V.

S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992), p. 236.

Wang, T.

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (1)

U. Levy, H. Kobrinsky, A. Friesem, “Angular multiplexing for multichannel communication in a single fiber,” IEEE J. Quantum Electron. QE-17, 2215–2224 (1981).
[Crossref]

Laser Focus (1)

G. J. Herskowitz, H. Kobrinsky, U. Levy, “Angular division multiplexing in optical fibers,” Laser Focus 19, 83–88 (1983).

Other (3)

K.-H. Brenner, R. Klug, U. W. Krackhardt, “Angular multiplexing for optical board to board interconnection,” in Digest of the Topical Meeting Optics in Computing (Optical Society of America, Washington, D.C., 1999), pp. 118–120.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1992), p. 236.

S. Martin, C. A. Feely, J. T. Sheridan, V. Toal, “Applications of a self-developing photopolymer material: holographic interferometry and high efficiency diffratvie optical elements,” in Holographic Materials IV, J. Trout, ed., Proc. SPIE3296, 60–70 (1998).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1

Operating principles of ADM: conservation of the principal propagation direction.

Fig. 2
Fig. 2

Far-field intensity distribution of an ADM line designed for N = 12 channels. Only every second channel is activated.

Fig. 3
Fig. 3

Relative optical intensity as a function of the propagation angle and the fiber quality D for a propagation distance of 1 m. The solid curve represents Dz = 1 × 10-6 rad2/m, the dashed curve represents Dz = 1 × 10-5 rad2/m, and the long-dashed curve represents Dz = 1 × 10-4 rad2/m.

Fig. 4
Fig. 4

Number of channels N plotted versus the interconnection distance for different values of acceptable cross talk for a fiber with NA = 0.36 and a quality of D = 3 × 10-6 rad2/m. The solid curve represents a cross talk of -10 dB, and the dashed curve represents a cross talk of -26 dB.

Fig. 5
Fig. 5

Bandwidth–distance product (in gigabits per second times meters) for an ADM-based multiplexed fiber transmission for a fiber with NA = 0.39 plotted versus the number of channels N at low (dashed curve) and high (dotted curve) propagation angles. The solid curve indicates the aggregate bandwidth–distance product of the ADM line.

Fig. 6
Fig. 6

Bandwidth gain of an ADM-based fiber transmission compared with a single-channel transmission by the same fiber. The dashed (dotted) curve indicates a low (high) propagation angle. The solid curve indicates the gain in the aggregate bandwidth–distance product.

Fig. 7
Fig. 7

Bandwidth–distance product (in gigabits per second times meters) for the case of parallel and uncompensated processing of all multiplexed channels from interchannel dispersion (skew).

Fig. 8
Fig. 8

Concept for a passive all-optical MUX setup.

Fig. 9
Fig. 9

Concept for a passive all-optical DEMUX setup.

Fig. 10
Fig. 10

Impact of fiber bending on the angular width: The resolution of the measurement setup is ±4 mrad. The fiber has a glass core, a core diameter of 200 µm, and NA = 0.39.

Fig. 11
Fig. 11

Output angle plotted versus the input angle of a multimode step-index fiber with NA = 0.48, d = 200 µm, and a length L of 0.4 m.

Fig. 12
Fig. 12

Schematic diagram of a binary amplitude CGH used in a DEMUX unit for an N = 9 channels ADM line (magnified). The minimum feature size is 1.5 µm.

Fig. 13
Fig. 13

Diffraction pattern of the CGH sketched in Fig. 12. The zero order is at the lower left-hand side, and the +1 orders are lined up along a 45° line.

Fig. 14
Fig. 14

Measured cross talk of an ADM line with N = 13 channels with a multimode glass fiber of NA = 0.39, D = 3 × 10-6 rad2/m, d = 200 µm, and L = 8 m. Contributions from adjacent channels of higher (dark) and lower (light) axial angles are shown.

Equations (7)

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

m=1N δϑmarcsinNA.
pθ, zz=-Aθ2p+Dθθθ pθ,
px, z=exp-x0+x21+exp-bz1-exp-bz×exp-bz/21-exp-bz I0xx01/22 exp-bz/21-exp-bz,
pθ, zexpθm2+θ24Dz14ADz1/2 I0θ0θ2Dz.
I0x12πx1/2expx.
pθ, zexp-θ-θm24Dz2θθm4Dz1/2,
sz, ϑ=n2zn2-sin2 ϑ1/2.

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