Parabolic temporal lensing and spectrotemporal imaging: a femtosecond optical oscilloscope

We introduce a self-reference method of parabolic temporal lensing and aberration-free spectrotemporal imaging for the direct measurements of femtosecond waveforms, with the goal of designing an ultrafast optical oscilloscope. Our method is based on dispersive stretching of the signal pulse and afterwards cancellation of the dispersion-induced phase in a quadratic nonlinear process by adding a reference parabolic phase (instead of Kerr lensing of traditional spectral compression). We have implemented the method through sum-frequency generation using the self-shaped nonlinear-dispersive similariton as a reference pulse and have demonstrated it experimentally for the direct measurements of amplitude- and phase-modulated pulses on a femtosecond time scale.