Multiple plane phase retrieval from temporal lens array

Phase retrieval is an important field in communication systems, since detectors are generally able to measure intensity while the phase is lost. One of the most common phase retrieval methods is the Gerchberg-Saxton (GS). This algorithm uses two intensity images, while imposing the amplitudes known from the intensities and keeping the phase, the algorithm iteratively reconstructs the lost phase. It was demonstrated that by adding more intensity images, one increase the probability to converge to the correct reconstruction. Space time duality states that since spatial diffraction and temporal dispersion are described by similar equations, the same methodologies developed in space are applicable in time. Following this principle, temporal lenses where developed. Since temporal imaging systems suffer from the same phase loss, phase retrieval methods were applied in this field as well. However, as in space, accurate phase retrieval requires multiple intensity images. In this work, we propose a temporal phase retrieval methods based on Gerchberg-Saxton, where the multiple planes are measured by a timelens array. The temporal lens array is achieved using four-wave mixing interaction between a signal and a chirped pump wave, resulting in high temporal magnification. The proposed iterative phase reconstruction algorithm takes advantage of the overlap between nearby lenses, which improves the convergence. We demonstrate how increasing the number of planes improves the reconstruction. Furthermore, the use of shifted lenses, as opposed to several defocused images, has a practical advantage in regards to additional errors in the system.