Complete Optical Field Reconstruction of Gain-Switched Optical Frequency Combs Using the Gerchberg-Saxton Algorithm

This work proposes and characterizes the use of the Gerchberg-Saxton algorithm for the phase retrieval of Optical Frequency Combs (OFC) generated by gain-switched laser diodes, using temporal and spectral measurements obtained with standard instrumentation. A systematic and comprehensive numerical analysis followed by the experimental demonstration and validation of the iterative algorithm is presented here. Critical parameters, such as the initial phase seed, number of samples, and starting point, that may limit the performance of the iterative algorithm are identified and examined. The numerical analysis shows that optimizing these parameters significantly improves the quality of the retrieved phase. Furthermore, this numerical study evaluates the limitations imposed by real-case instrumentation using simulated results, providing valuable insights for the requirements of the necessary equipment for the algorithm experimental implementation of the phase retrieval. Finally, the phase retrieval of an OFC generated by a gain-switched laser was successfully demonstrated using the iterative algorithm. The results demonstrate a strong agreement with those obtained via an experimental approach employing optical differentiation, with multiple similarities between the results using both methodologies. This comparative validation showcases the iterative algorithm as a reliable technique for OFC phase characterisation, while offering significant advantages in terms of simplicity or efficiency.