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Propagation of ultrashort pulses in multimode fiber in space and time

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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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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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