A very simple self-referenced, linear pulse-characterization technique based on spectral phase reconstruction by frequency-domain signal differentiation is introduced. This technique can be implemented using electro-optic intensity modulation of the pulse under test with a synchronized RF sinusoid. The pulse spectral phase profile can be accurately and unambiguously reconstructed from only two measured energy spectra, i.e., at the input and at the output of the modulator, using a direct analytic equation. The method is experimentally demonstrated by precisely characterizing microwatt-power picosecond pulses after linear dispersion through short sections (50700m) of conventional single-mode fiber.

© 2008 Optical Society of America

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram of the spectral phase reconstruction process. (b) Experimental setup.

Fig. 2
Fig. 2

Input pulse intensity (dashed curve) and modulation signal (solid curve), both measured with a sampling oscilloscope. A linear curve fit of the modulation signal for determining the time modulation coefficient A Ω is also shown (dotted curve).

Fig. 3
Fig. 3

(a) Acquired spectra of the input and the frequency-domain differentiated pulses for the 300 m fiber propagation experiment. Squares show the logarithmic ratio of these measured spectra. (b) Measured energy spectrum (dotted curve) and reconstructed phase profiles (solid curves) of dispersed pulses from FFL for different SMF lengths. Circles show the phase measured at a lower average power ( 17 μ W ) . (c) Reconstructed spectrum (dotted curve) and phase (solid and dashed curves) of dispersed pulses from UOC for different SMF lengths. (d) Dispersion-length products (solid circles) determined from the reconstructed phase profiles in Figs. 3b, 3c and the estimated curve of the SMF dispersion (solid line). The inset shows the recovered (solid circles) and measured (solid curve) autocorrelation of the optical pulse after 100 m of SMF (experiment with FFL).

Equations (2)

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y ̂ ( t ) T 0 2 [ 1 + A Ω t ] x ̂ ( t ) ,
Φ ( ω ) ω = ( 1 A Ω ) [ 1 ( ( 2 T 0 ) Y ̂ ( ω ) 2 ( A Ω ) 2 [ X ̂ ( ω ) ω ] 2 X ̂ ( ω ) 2 ) 1 2 ] .