Ultrafast All-Optical Wavelet Transform Based on Temporal Pulse Shaping Incorporating a 2-D Array of Cascaded Linearly Chirped Fiber Bragg Gratings

An all-optical wavelet transformer used to analyze a high-speed and broadband electrical signal is proposed and demonstrated for the first time to our knowledge. The wavelet transform is implemented based on a temporal pulse shaping system incorporating a 2-D array of cascaded linearly chirped fiber Bragg gratings (LCFBGs). An electrical signal to be analyzed is applied to a Mach-Zehnder modulator to modulate the optical spectrum of a time-stretched optical pulse from a mode-locked laser. Each individual LCFBG in the 2-D array functions as a wavelet filter to filter a specific range of the spectrum, which is equivalent to applying a window function to the corresponding section of the temporal signal, and at the same time, as a dispersive element to perform real-time Fourier transform. A Mexican Hat wavelet is employed to implement the optical wavelet transform, which can be achieved based on a specially designed LCFBG. A theoretical analysis is performed which is verified by a proof-of-concept experiment. The key feature of this technique is that it can perform multiresolution time-frequency analysis of an ultrahigh-speed electrical signal, which can give good time resolution for high-speed signals, and good frequency resolution for low-speed signals.