Temporal Super-Resolution and Phase Retrieval

Temporal optics is an emerging field in which optical signals are considered similarly to objects in spatial optics, in order to apply techniques from the spatial domain to the temporal domain. Indeed, temporal magnifications, temporal Fourier transform, and temporal signal processing have been demonstrated by adopting optical schemes from space to time. To that end, the concept of a lens in space is adopted to the time-domain for creating the time-lens, which enables to extend and compress optical signals in time, as well as to perform Fourier transform. By integrating the time-lens into the optical system, we are able to extend events in time to investigate them efficiently. However, as in space imaging, also the imaging process in time is subjected to resolution limits imposed by the Rayleigh criterion. Those limitations prevent us from investigating and reconstructing shorter signals than the resolution limit. In order to overcome some of those issues in the space-domain, a new field was established, called “super-resolution”. In this work, we investigated the resolution limitations of time-lenses based on four wave mixing and adopted different super-resolution techniques into the time-domain. That enables us to define in advance the capacities of our temporal imaging system, as well as to increase our temporal resolution by physical and/or numerical techniques. We applied the localization microscopy algorithm - a super-resolution technique from the space-domain - into the time-domain, and were able to reconstruct signals shorter than the resolution limit of our time-lens system. That demonstrates the feasibility of reconstructing ultrafast signals in time with high fidelity, as well as to provide a tool for studying ultrashort phenomena in time, even below the resolution limit of the imaging system. In addition, we developed a method to measure the phase of the input signal. The phase of the light bears the imagery part of the waveform, and by that has an integral role in the physical behavior of the light in the system. The phase has a great importance during light propagation and can lead to constructive and destructive interference. Therefore, methods for retrieving the optical phase are highly important and useful, and can contribute to a wide verity of fields in optical research. One of the most used techniques for phase retrieval in space is a numerical algorithm named Gerchberg-Saxton algorithm. In this research, we adopted the Gerchberg-Saxton algorithm from the spatial domain into the temporal domain, by using an array of overlapping time-lenses. As a result, we were able to retrieve the temporal phase of our signal, and by that to reconstruct the full form of the original signal.