Abstract

We perform 3D cross-correlation measurements of the optical field distribution resulting from an ultrashort pulse propagating in 6 meters of multimode fiber. Spatial amplitude and phase distributions of the optical field at the output of the fiber are measured using a time-gated spatial heterodyne interferometer as a function of time delay between the signal and the reference optical fields. We show that the measured signal represents an approximation to the optical impulse response of the multimode fiber.

© 2003 Optical Society of America

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References

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    [CrossRef]
  2. G.J. Dunning, R.C. Lind, �??Demonstration of image transmission through fibers by optical phase conjugation,�?? Opt. Lett. 7, 558, (1982)
    [CrossRef] [PubMed]
  3. S.E. Miller, N.J. Locust, �??Mode detection and delay equalization in multimode optical fiber transmission systems,�?? U.S. Patent 3,777,150 (1973)
  4. Teiji Uchida, Atsufumi Ueki, �??Mode separator and delay equalizer for multimode optical fiber transmission systems,�?? U.S. Patent 4,050,782 (1977)
  5. K.M. Patel, S.E. Ralph, �??Enhanced multimode fiber link performance using a spatially resolved receiver,�?? IEEE Phot. Tech. Lett. 14, 393 (2002)
    [CrossRef]
  6. X. Zhao, F.S. Choa, �??Demonstration of 10-Gb/s transmissions over a 1.5-km-long multimode fiber using equalization techniques,�?? IEEE Phot. Tech. Lett. 14, 1187 (2002)
    [CrossRef]
  7. H.R. Stuart, �??Dispersive Multiplexing in Multimode Optical Fiber,�?? Science 289, 281 (2000)
    [CrossRef] [PubMed]
  8. G.J. Foschini and M.J. Gans, �??On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas,�?? Wireless Personal Communications 6, 311 (1998)
    [CrossRef]
  9. R. Rokitski, P. C. Sun, Y. Fainman, �??Study of spatial-temporal characteristics of optical fiber based on ultrashort-pulse interferometry,�?? Opt. Lett. 26, 1125 (2001)
    [CrossRef]
  10. B. Järne, Digital Image Processing (Springer-Verlag, Berlin, 1995)
  11. D.C. Ghiglia, M.D. Pritt, Two-dimensional Phase Unwrapping (John Wiley & Sons, New York, 1998)

Appl. Phys. Lett.

A. Yariv, �??Three-dimensional pictorial transmission in fibers,�?? Appl. Phys. Lett. 28, 88 (1976)
[CrossRef]

IEEE Phot. Tech. Lett.

K.M. Patel, S.E. Ralph, �??Enhanced multimode fiber link performance using a spatially resolved receiver,�?? IEEE Phot. Tech. Lett. 14, 393 (2002)
[CrossRef]

X. Zhao, F.S. Choa, �??Demonstration of 10-Gb/s transmissions over a 1.5-km-long multimode fiber using equalization techniques,�?? IEEE Phot. Tech. Lett. 14, 1187 (2002)
[CrossRef]

Opt. Lett.

G.J. Dunning, R.C. Lind, �??Demonstration of image transmission through fibers by optical phase conjugation,�?? Opt. Lett. 7, 558, (1982)
[CrossRef] [PubMed]

R. Rokitski, P. C. Sun, Y. Fainman, �??Study of spatial-temporal characteristics of optical fiber based on ultrashort-pulse interferometry,�?? Opt. Lett. 26, 1125 (2001)
[CrossRef]

Science

H.R. Stuart, �??Dispersive Multiplexing in Multimode Optical Fiber,�?? Science 289, 281 (2000)
[CrossRef] [PubMed]

Wireless Personal Communications

G.J. Foschini and M.J. Gans, �??On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas,�?? Wireless Personal Communications 6, 311 (1998)
[CrossRef]

Other

S.E. Miller, N.J. Locust, �??Mode detection and delay equalization in multimode optical fiber transmission systems,�?? U.S. Patent 3,777,150 (1973)

Teiji Uchida, Atsufumi Ueki, �??Mode separator and delay equalizer for multimode optical fiber transmission systems,�?? U.S. Patent 4,050,782 (1977)

B. Järne, Digital Image Processing (Springer-Verlag, Berlin, 1995)

D.C. Ghiglia, M.D. Pritt, Two-dimensional Phase Unwrapping (John Wiley & Sons, New York, 1998)

Supplementary Material (1)

» Media 1: AVI (1692 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Formation of the interference pattern between short pulses on the surface of CCD.

Fig. 2.
Fig. 2.

Optical setup for time-gating spatial heterodyne measurements

Fig. 3.
Fig. 3.

(a) Observed interference pattern; (b) spatial spectrum of the interference pattern, shown in logarithmic grayscale; (c) reconstructed amplitude distribution of the signal field; (d) reconstructed spatial phase distribution of the signal field. [Media 1]

Fig. 4.
Fig. 4.

Total optical power at the observation plane as a function of time delay τ.

Fig. 5.
Fig. 5.

Optical power impulse response of the multimode fiber: a) impulse response of 4 pixels randomly selected across the aperture of the fiber b) impulse response of 4 adjacent pixels in the center of the aperture. Total optical power is shown by black line in both graphs. Lines with different colors correspond to optical impulse response at the locations of individual pixels. Location of the pixels inside the CCD matrix is shown approximately by color squares in the top right corner of the graphs.

Equations (6)

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E 1 ( r , t ) = U ( r , t ) exp [ j ( ω t + ϕ ( r , t ) k 1 r ) ]
E 2 ( r , t ) = p ( r , t + τ ) exp [ j ( ω ( t + τ ) k 2 r ) ]
I ( r , t ) = 0 T E 1 ( r , t ) + E 2 ( r , t ) 2 dt
= 0 T [ U ( x , y , t ) 2 + p ( x , y , t + τ ) 2 + U ( x , y , t ) p ( x , y , t + τ ) cos ( ωτ + x k 2 x + y k 2 y + ϕ ( x , y , t ) ) ] dt
U est ( x , y , τ ) = 0 T U ( x , y , t ) p ( x , y , t + τ ) exp [ j ( ω τ + ϕ ( x , y , t ) ) ] dt
U est ( x , y , τ ) U ˜ ( x , y , τ ) exp [ j ( ω τ + ϕ ˜ ( x , y , τ ) ) ] ,

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