Investigation of isolated attosecond pulse reconstruction from angular integrated photoelectron streaking spectra

We theoretically investigate the temporal characterization of isolated attosecond pulses from angular integrated photoelectron streaking spectra. In this work, our recently developed `phase retrieval of broadband pulses' (PROBP) algorithm for attosecond pulse retrieval is modified so that photoelectrons emitted over a broad angular range can be used to retrieve the spectral phase of the broadband XUV to x-ray attosecond pulses. Compared to common retrieval methods that utilize photoelectrons only in the forward direction, the inclusion of electrons over a broad angular range has the advantage that stronger signals are analyzed to mitigate the effect of low statistics of photoelectrons for analysis. The present investigation also serves to test the commonly used approximation where the photoelectrons are collected over a finite angular range experimentally, but the theoretical analysis relies on electrons emitted only in the forward direction. Our results show that the extended PROBP method can be used to more accurately retrieve the spectral phase of an attosecond pulse from photoelectrons collected over a wider angular range.