Analysis And Synthesis Of Power/Field Distribution Of Fiber Bragg Gratings Along The Propagation Axis (Spatial Characteristics)

Advantages of fiber Bragg gratings(FBGs) include their flexible filtering capability, all-fiber configuration, low insertion loss, and low cost. Therefore, FBGs have been widely used in optical communications, signal processing, microwave photonics, and optical sensing systems. In different scenarios, the requirements on the FBG characteristics are also different. In addition to the well-known spectral characteristics(i.e., the amplitude or the phase spectral responses), the spatial characteristics of the FBG (i.e., axial optical power distribution) is also one of the key properties. To date, a number of investigations and applications on the spectral characteristics have been reported, but very few for the spatial characteristics. Therefore, there are still many problems and methods to be solved for the spatial characteristics. In this thesis, the spatial characteristics analysis of FBGs and the synthesis of FBG with arbitrary power/field distribution are mainly discussed.Firstly, based on the refractive index characteristics of FBGs, the simplified coupled mode equations are derived. Meanwhile, the transfer matrix method is used to analyze filter characteristics of uniform/phase-shifted and chirped FBGs by using the proposed coupled mode equation. Besides, the layer peeling algorithm on the basis of causality argument is discussed in detail, wherein the FBG can be reconstructed from the arbitrary spectral response, such as the rectangular spectral response.Secondly, the spectral and spatial characteristics of FBGs are analyzed. For the spectral characteristics, the spectral response and the group delay of chirped FBGs are firstly emphasized, and then, the corresponding group delay ripples (GDRs) are analyzed in detailed. At the same time, the influences of GDRs on the filter process of microwave signals are investigated, and a theoretical model is established to evaluate the influences on the characteristics of microwave-photonic filters. For the coherent and incoherent light source based filters, the GDRs result in a frequency shift to the notches of the amplitude-frequency response, and the linear phase with distortions are observed due to the existence of GDRs. In addition, for the multi-tap microwave filters, the side-band suppression ratio and the extinction ratio are degraded under the influence of GDRs. For the spatial characteristics, the stationary power/field distribution along the grating length of uniform/apodized and chirped FBG based on the transfer matrix method are studied. The optical power distribution mainly concentrates in the starting of the grating for the uniform FBG. While for chirped FBG, the optical powers at different wavelengths are reflected at different positions.Finally, a synthesis method for the design of FBGs with arbitrary power/field distribution at the Bragg wavelength is proposed and numerically demonstrated. The method starting from the desired power/field distribution for FBGs consisting of a number of grating pieces, the amplitude of the forward and the backward propagation modes at the Bragg wavelength are derived by the low of conservation of energy, and their phases are also can be obtained at the Bragg wavelength. Using the transfer matrix method, the local reflection coefficient is calculated from the two derived propagation modes. Then, the corresponding coupling coefficients and the refractive index modulation are derived from the local reflection coefficients, with the proposed synthesis method realized. The proposed synthesis method is numerically verified by using a uniform/Gaussian-apodized and a phase-shifted FBGs as the target, showing an excellent agreement between the structure parameters of the reconstructed FBG and target FBG.Next, the FBGs with several user-defined power distributions, such as the flat-top shape in differential form, Gaussian shape, the Lorentz shape, the saddle shape, and the ladder shape, are synthesized.