Xing Fu

Multiresolution Dynamic Mode Decomposition

We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multiresolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of multiresolution time-scale components. A one-level separation allows for background (low-rank) and foreground (sparse) separation of dynamical data, or robust principal component analysis. The multiresolution DMD (mrDMD) is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. DMD modes with temporal frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given dynamics, and the terms with temporal frequencies bounded away from the origin are their sparse counterparts. The mrDMD method is demonstrated on several examples involving multiscale dynamical data, showing excellent decomposition results, ...

High-energy mode-locked fiber lasers using multiple transmission filters and a genetic algorithm.

We theoretically demonstrate that in a laser cavity mode-locked by nonlinear polarization rotation (NPR) using sets of waveplates and passive polarizer, the energy performance can be significantly increased by incorporating multiple NPR filters. The NPR filters are engineered so as to mitigate the multi-pulsing instability in the laser cavity which is responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. Engineering of the NPR filters for performance is accomplished by implementing a genetic algorithm that is capable of systematically identifying viable and optimal NPR settings in a vast parameter space. Our study shows that five NPR filters can increase the cavity energy by approximately a factor of five, with additional NPRs contributing little or no enhancements beyond this. With the advent and demonstration of electronic controls for waveplates and polarizers, the analysis suggests a general design and engineering principle that can potentially close the order of magnitude energy gap between fiber based mode-locked lasers and their solid state counterparts.

Extremum-Seeking Control of a Mode-Locked Laser

An adaptive controller is demonstrated that is capable of both obtaining and maintaining high-energy, single-pulse states in a mode-locked fiber laser. In particular, a multi-parameter extremum-seeking control (ESC) algorithm is used on a nonlinear polarization rotation (NPR) based laser using waveplate and polarizer angles to achieve optimal passive mode-locking despite large disturbances to the system. The physically realizable objective function introduced divides the energy output by the kurtosis of the pulse spectrum, thus balancing the total energy with the coherence of the mode-locked solution. In addition, its peaks are high-energy mode-locked states that have a safety margin near parameter regimes where mode-locking breaks down or the multipulsing instability occurs. The ESC is demonstrated by numerical simulations of a single-NPR mode-locked laser and is able to track locally maximal mode-locked states despite significant disturbances to parameters such as the fiber birefringence.

Self-Tuning Fiber Lasers

We demonstrate that the integration of data-driven machine learning strategies with adaptive control are capable of producing an efficient and optimal self-tuning algorithm for mode-locked fiber lasers. The adaptive controller, based upon a multiparameter extremum-seeking control algorithm, is capable of obtaining and maintaining high-energy, single-pulse states in a mode-locked fiber laser while the machine learning characterizes the cavity itself for rapid state identification and improved optimization. The theory developed is demonstrated on a nonlinear-polarization-rotation-based laser using waveplate and polarizer angles to achieve optimal passive mode-locking despite large disturbances to the system. The physically realizable objective function introduced divides the energy output by the fourth moment of the pulse spectrum, thus balancing the total energy with the time duration of the mode-locked solution. Moreover, its peaks are high-energy mode-locked states that have a safety margin near parameter regimes where mode-locking breaks down or the multipulsing instability occurs. The methods demonstrated can be implemented broadly to optical systems, or more generally to any self-tuning complex systems.

Classification of birefringence in mode-locked fiber lasers using machine learning and sparse representation

It has been observed that changes in the birefringence, which are difficult or impossible to directly measure, can significantly affect mode-locking in a fiber laser. In this work we develop techniques to estimate the effective birefringence by comparing a test measurement of a given objective function against a learned library. In particular, a toroidal search algorithm is applied to the laser cavity for various birefringence values by varying the waveplate and polarizer angles at incommensurate angular frequencies, thus producing a time-series of the objective function. The resulting time series, which is converted to a spectrogram and then dimensionally reduced with a singular value decomposition, is then labelled with the corresponding effective birefringence and concatenated into a library of modes. A sparse search algorithm (L(1)-norm optimization) is then applied to a test measurement in order to classify the birefringence of the fiber laser. Simulations show that the sparse search algorithm performs very well in recognizing cavity birefringence even in the presence of noise and/or noisy measurements. Once classified, the wave plates and polarizers can be adjusted using servo-control motors to the optimal positions obtained from the toroidal search. The result is an efficient, self-tuning laser.

Multi-resolution Dynamic Mode Decomposition for Foreground/Background Separation and Object Tracking

We demonstrate that the integration of the recently developed dynamic mode decomposition with a multi-resolution analysis allows for a decomposition of video streams into multi-time scale features and objects. A one-level separation allows for background (low-rank) and foreground (sparse) separation of the video, or robust principal component analysis. Further iteration of the method allows a video data set to be separated into objects moving at different rates against the slowly varying background, thus allowing for multiple-target tracking and detection. The algorithm is computationally efficient and can be integrated with many further innovations including compressive sensing architectures and GPU algorithms.

Self-tuning fiber lasers

We demonstrate that the integration of data-driven machine learning strategies with adaptive control are capable of producing an efficient and optimal self-tuning algorithm for mode-locked fiber lasers. The adaptive controller, based upon a multiparameter extremum-seeking control algorithm, is capable of obtaining and maintaining high-energy, single-pulse states in a mode-locked fiber laser while the machine learning characterizes the cavity itself for rapid state identification and improved optimization. The theory developed is demonstrated on a nonlinear-polarization-rotation-based laser using waveplate and polarizer angles to achieve optimal passive mode-locking despite large disturbances to the system. The physically realizable objective function introduced divides the energy output by the fourth moment of the pulse spectrum, thus balancing the total energy with the time duration of the mode-locked solution. Moreover, its peaks are high-energy mode-locked states that have a safety margin near parameter regimes where mode-locking breaks down or the multipulsing instability occurs. The methods demonstrated can be implemented broadly to optical systems, or more generally to any self-tuning complex systems.

Data Driven Control of Complex Optical Systems

Advances in data science are revolutionizing the characterization and control of complex optical systems, including the ultra-fast laser and the reconfigurable holographic metamaterial antenna. Methods from data science include machine learning, dimensionality reduction, and compressive sensing. We present these techniques on two optical systems.