Multiple plane phase retrieval from temporal lens array

摘要

Phase retrieval is an important eld in communication systems, since detectors are generally able to measureintensity 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 andkeeping the phase, the algorithm iteratively reconstructs the lost phase. It was demonstrated that by adding moreintensity images, one increase the probability to converge to the correct reconstruction. Space time duality statesthat since spatial diffraction and temporal dispersion are described by similar equations, the same methodologiesdeveloped in space are applicable in time. Following this principle, temporal lenses where developed. Sincetemporal imaging systems suu000ber from the same phase loss, phase retrieval methods were applied in this eld aswell. However, as in space, accurate phase retrieval requires multiple intensity images. In this work, we propose atemporal phase retrieval methods based on Gerchberg-Saxton, where the multiple planes are measured by a timelensarray. The temporal lens array is achieved using four-wave mixing interaction between a signal and a chirpedpump wave, resulting in high temporal magnication. The proposed iterative phase reconstruction algorithmtakes advantage of the overlap between nearby lenses, which improves the convergence. We demonstrate howincreasing the number of planes improves the reconstruction. Furthermore, the use of shifted lenses, as opposedto several defocused images, has a practical advantage in regards to additional errors in the system.