Optical Hilbert Transform Based On Fiber Bragg Gratings

Fiber Bragg grating (FBG) is a novel type of important passive fiber components, which is widely used in optical communication systems and the optical sensing systems owing to its superior characteristics of immune of electromagnetic interference, anti-radiation, surviving in high temperature, small size, light weight, and all-fiber compatibility. Advantages of the FBGs also include polarization insensitive and tuning flexibility of the spectral characteristics. Investigations on FBGs including theory, fabrication and application have been conducted both intensively and extensively and significant progress has been achieved since its emergence of the first fiber grating in 1978. Fiber Bragg gratings have been one of the most promising and representative passive optical fiber devices.With the fast development of the all optical network, one of the key technologies is to achieve the all-optic logic circuits without the resort to conventional electronic processing circuits. Hilbert transform has been widely employed in conventional signal processing and communication field due to its capability of orthogonal decomposition and phase shifting of an input signal. In recent years, with the development of optical signal processing, Hilbert transform has been implemented in all-optical domain, in which either the classical integer or the fractional order Hilbert transform has been investigated.In this thesis, we propose and demonstrate that an arbitrary order (including both integer and fractional orders) Hilbert transform (HT) of an input optical waveform can be implemented by a simple and practical phase-shifted fiber Bragg grating (PSFBG) operated in reflection mode. Based on the space-to-frequency-to-time mapping technique, a design method which employs a simple structure of a phase-shifted FBG (PSFBG) has been proposed. The PSFBG consists of two concatenated identical uniform FBGs with a proper phase shift between them. It is found that both the phase shift of the FBGs and the apodizing profile of the refractive index modulation determine the order of the Hilbert transform. Theoretical simulation results show that the device can perform arbitrary fractional Hilbert transform (FHT) with excellent accuracy for input signals with up to hundreds-of-GHz bandwidth using practically feasible FBG structures.