Complex Mode Expansion Method And Its Applications In Opitcal Fiber Based Devices

Mode expansion method has been successfully used to analyze the transmissions of optical fiber devices. This method is based on the expansion of the unknown field in terms of a complete set of known orthogonal modes of the unknown waveguide or a reference one. Traditionally, the expansion basis consists of discrete guided modes and continuous radiation modes. In spite of its completeness and exactness, the inclusion of radiation modes is usually very complicated, due to the fact that they are difficult to be solved and dealt with. To circumvent this problem, an equivalent closed waveguide model has been proposed and demonstrated in which the open waveguide is enclosed with a properly set perfectly matched layer terminated by a perfect electric conductor. With this model, the radiation fields are well represented by a set of discrete quasi leaky modes, based on which the complex mode expansion method is proposed.In the thesis, the criteria for approximating the continuous radiation modes with discrete leaky modes are investigated firstly, and both the analytically solved leaky modes in the open waveguide and the numerically solved quasi leaky mode in the equivalent closed waveguide are considered, which lays a foundation for applications of complex mode expansion method. Furthermore, the coupled-mode theory based on the complex mode expansion is developed. With an analytically analogical model, the relationships between coupling characteristics and structure parameters are developed in mode coupling and power exchanging. Finally, we apply the complex mode expansion method to the analysis and design of optical fiber devices, and devote to the solving of problems associated with radiation modes. For this part of work, we focus on three kinds of optical fiber devices:optical fiber grating, single-mode-multimode-single-mode fiber structure and the chiral fiber grating, and the main achievement is listed as follows.(1) By applying the complex mode expansion method, a long-period fiber grating refractive index sensor is proposed for the measurements of ambient refractive indices which are higher than that of the fiber cladding. Based on the theoretical analysis, we designed mask plate, prepared fiber grating sample and did experiments. The result indicates that the sensor exhibits a good linear response, and in the measuring range from1.46to1.7, a sensitivity of90dB/RIU is obtained, and in the range from1.465to1.475, a sensitivity of1200dB/RIU is obtained. This sensor is promising in industrial process monitoring and biomedical applications.(2) By applying the complex mode expansion method, the interference of radiation modes in the single-mode-multimode-single-mode fiber structure is analyzed, and a new concept of leaky mode interference is introduced, which makes the transmission characteristics of this structure more intuitive and concise. Based on the theoretical analysis, a refractive index sensor and a liquid level sensor are proposed and experimentally demonstrated, both of which aim at the high refractive index liquid and exhibit high measuring sensitivity. For the refractive index sensor, a measuring sensitivity of400dB/RIU is achieved, and for the liquid level sensor, a measuring sensitivity of0.57dB/mm is achieved for the liquid with refractive index of1.5025. These kinds of sensors are very promising in practical applications for its simple structure and low cost.(3) By applying the complex mode expansion method, we propose an all-fiber broadband circular polarizer formed by twisting a commercially available high-birefringence fiber at a slowly varying twist rate, and coating the fiber with a high refractive index material. This polarizer is only9cm. Its extinction coefficient more than25dB within a bandwidth of60nm. It is promising in practical use owing to its all-fiber structure and ease to be spliced in fiber measurement and sensing systems.