Analytical Analysis Of Complex Coupled Mode Theory And Its Application In Optical Fiber Sensing

Coupled-mode theory is widely applied in the field of optical waveguide.The traditional coupled-mode theory shows the advantages of intuitive physical concepts and concise mathematical form in the analysis of the couplings of discrete guided modes.However,when dealing with problems related to the coupling of continuous radiation modes,it is necessary to solve the problems of solving and normalizing radiation modes.Leaky modes are put forward to solve the problem,but due to the complex propagation constant and non-physical field of leaky modes,the analytical expressions are more complicated,and it also brings about problems of orthogonality and normalization.In order to solve these problems,the coupled-mode theory has been extended to the complex domain based on the expansion of the complex modes obtained from an equivalent closed waveguide model.Then it is possible to deal with the couplings of radiation mode in a similar way to those of guided modes.Compared with traditional coupled mode equations,unavoidable complex propagation constants and complex coupling coefficients will lead to different analytical processes and physical mechanisms in complex coupled mode equations.Therefore,it is necessary to solve the complex coupled mode equations systematically and explore the corresponding physical meaning in order to discover new phenomena,reveal new mechanisms and stimulate new applications.In this paper,a complete analytical analysis of complex coupled modes is established to reveal the relationship between design parameters and transmission characteristics of optical devices under consideration.Furthermore,we apply it to the analysis and design of fiber sensing based on long period fiber grating(LPFG),which provides a clear scheme for the design and optimization of optical devices.Specifically,our main work includes the following four aspects:1)The complex coupled mode equations are solved systematically,and the energy evolution in the process of complex mode couplings is studied.By solving the complex coupled mode equations,both the solution of the equations and its physical insight are explored;the characteristics of mode coupling and energy exchange between complex modes,especially the influence of complex propagation constants and coupling coefficients,are studied;meanwhile,in the case of phase matching,we focus on the energy evolution of the coupling modes under different coupling states,and the relationship between the coupling state and the transmission characteristics is established,which lays the foundation for further study and wide application of complex coupled-mode theory.2)The influence of the change of ambient refractive index on leaky modes is studied,and the feasibility of power detection is demonstrated.In the application of high refractive index sensing,the influence of ambient refractive index on leaky mode is studied by both theoretical and numerical methods,respectively,under the condition of lossless environmental medium;furthermore,the influence of ambient refractive index on leaky mode is discussed when environmental medium is lossy,and the feasibility of using power to analyze the change of sensing physical quantity is verified.3)Optimization of a high refractive index sensor based on LPFG.Firstly,the complex coupled mode equations of LPFG are analyzed,and three coupling states under phase matching condition are defined following those of the damped oscillation equations.Subsequently,two optimizations are done for the requirements of a large measurement range and a higher sensitivity,respectively.For the measurement of the ambient refractive index ranging from 1.47 to 1.72,the theoretical sensing resolution is 10-4.When the measurement ranges from 1.465 to 1.485,the theoretical sensing resolution can reach to 10-6.So it can meet the needs of different sensing applications.4)An experimental system of high refractive index sensing based on LPFG is designed and developed for verifications.We built an experimental system.According to the coupling state,we designed three groups of LPFGs with different grating period,and have three institutions prepare the samples by three different preparation methods.The experimental results were in accordance with the expectations of the theoretical model.