Pulse compression in dispersive strontium barium niobate crystal with a random size and distribution of the anti-parallel orientated nonlinear domains is observed via transverse second harmonic generation. The dependence of the transverse width of the second harmonic trace along the propagation direction allows for the determination of the initial chirp and duration of pulses in the femtosecond regime. This technique permits a real-time analysis of the pulse evolution and facilitates fast in-situ correction of pulse chirp acquired in the propagation through an optical system.

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