Accuracy of Holographic Real-Time Mode Decomposition Methods Used for Multimode Fiber Laser Emission

Mode decomposition is a powerful tool for analyzing the modal content of optical multimode radiation. There are several basic principles on which this tool can be implemented, including near-field intensity analysis, machine learning, and spatial correlation filtering (SCF). The latter is meant to be applied to a spatial light modulator and allows one to obtain information on the mode amplitudes and phases of temporally stable beams by only analyzing experimental data. As a matter of fact, techniques based on SCF have already been successfully used in several studies, e.g., for investigating the Kerr beam self-cleaning effect and determining the modal content of Raman fiber lasers. Still, such techniques have a major drawback, i.e., they require acquisition times as long as several minutes, thus being unfit for the investigation of fast mode distribution dynamics. In this paper, we numerically study three types of digital holograms, which permits us to determine, at the same time, the parameters of a set of modes of multimode beams. Because all modes are simultaneously characterized, the processing speed of these real-time mode decomposition methods in experimental realizations will be limited only by the acquisition rate of imaging devices, e.g., state-of-the-art CCD camera performance may provide decomposing rates above 1 kHz. Here, we compare the accuracy of conjugate symmetric extension (CSE), double-phase holograms (DPH), and phase correlation filtering (PCF) methods in retrieving the mode amplitudes of optical beams composed of either three, six, or ten modes. In order to provide a statistical analysis of the outcomes of these three methods, we propose a novel algorithm for the effective enumeration of mode parameters, which covers all possible beam modal compositions. Our results show that the best accuracy is achieved when the amplitude-phase mode distribution associated with multiple frequency PCF techniques is encoded by Jacobi-Anger expansion.