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Retrieval of the pulse amplitude and phase from cross-phase modulation spectrograms using the simulated annealing method

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Abstract

The simulated annealing method is used for retrieving the amplitude and phase from cross-phase modulation spectrograms. The method allows us to take into account the birefringence of the measurement fiber and resolution of the optical spectrum analyzer. The influence of the birefringence and analyzer resolution are discussed.

©2004 Optical Society of America

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Figures (4)

Fig. 1.
Fig. 1. Schematic set-up for fiber FROG measurement.
Fig. 2.
Fig. 2. Comparison of the numerically generated field and reconstructed field for test pulses. Figures a)–d) correspond to pulses no. 1–4 of Tab. 1, respectively.
Fig. 3.
Fig. 3. a) Noisy spectrogram with contours in decibels. b) Original and reconstructed pulse.
Fig. 4.
Fig. 4. a) Influence of walk-off and OSA resolution on the pulse reconstruction. b) Influence of walk-off between probe and cross-polarized pulse on the mean frequency of spectrogram.

Tables (1)

Tables Icon

Table 1. Summary of test pulses parameters. For all pulses v=0.

Equations (11)

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i z E x , y + β 2 2 tt E x , y ± i σ t E x , y ± κ E x , y + γ [ ( E x , y 2 + 2 3 E y , x 2 ) E x , y + 1 3 E y , x 2 E x , y * ] = 0 ,
E ˜ x = E x e i κ z , E ˜ y = E y e i κ z ,
i z E ˜ x , y + β 2 2 tt E ˜ x , y ± i σ t E ˜ x , y + γ ( E ˜ x , y | 2 + 2 3 E ˜ y , x | 2 ) E ˜ x , y + γ 3 E ˜ y , x 2 E ˜ x , y * e 4 i κ z = 0 ,
i z E ˜ x , y ± i σ t E ˜ x , y + γ ( E ˜ x , y 2 + 2 3 E ˜ y , x | 2 ) E ˜ x , y = 0 .
E x , y ( z , t ) = E x , y ( 0 , t σ z ) exp [ i γ E x , y ( 0 , t σ z ) | 2 z + i γ 3 z z E y , x ( 0 , t σ ξ ) | 2 d ξ ] .
E SIG ( t , τ ) = r E ( 0 , t σ L ) exp [ i γ r 2 E ( 0 , t σ L ) 2 z + i γ ( 1 r 2 ) 3 L L E ( 0 , t τ + σ ξ ) 2 d ξ ] ,
S ( ω , τ ) = E SIG ( t , τ ) exp [ i ω t ] d t 2 .
S ( ω , τ ) = S ( Ω , τ ) K ( ω Ω ) d Ω .
E ( t ) exp [ i ψ ( t ) ] i = 1 n p S i exp [ 2 l n ( 2 ) ( t t i / 2 T ) 2 ] ,
ψ ( t ) = a ( t T ) 2 + b ( t T ) 3 + c ( t T ) 4 + q E ( t ) 2 ,
E ( t ) = 𝓕 1 { exp [ i ξ ( ν ) ] 𝓕 [ E ( t ) ] ( ν ) } ( t ) , ξ ( ν ) = u ( ν T ) 3 + v ( ν T ) 4 + x ( ν T ) 5 .
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