Phase retrieval approach for an accurate reconstruction of an arbitrary optical waveform in the petahertz optical oscilloscope

An arbitrary optical waveform can be measured using the technique called the 'petahertz optical oscilloscope' in which an electron trajectory in the process of high harmonic generation is used as a fast temporal gate. In the petahertz optical oscilloscope, a signal laser pulse that needs to be measured is superposed on a fundamental laser pulse that generates high harmonic radiation. The addition of the signal laser pulse slightly modifies the amplitude and phase of the harmonic radiation, which have information on the signal field. While these changes are imposed in the generation medium, the harmonic radiation is measured at the detector. Thus, one needs a special technique to find the phase modulation in the medium using the variation of the spatially-resolved harmonic spectrum measured at the far field. We find that a simple estimation using the deflection angle of the harmonic radiation is not accurate enough for a broadband signal pulse. Here we introduce a phase retrieval approach for the reconstruction of the broadband signal pulse. Our calculations show that the broadband signal pulse can be accurately reconstructed using the phase retrieval approach. (paper)