Research For Leaky Modes Characteristics In Optical Waveguides

With the development of science and technology, optical waveguide devices with its series of advantages has been widely used in the field of communication, sensing, information processing, the research of the optical waveguide mode has theoretical guidance for the design of optical waveguide components. The most important issue of optical waveguide mode research is determining the complete set of the guided modes and radiation modes. Due to the continuous spectrum of radiation modes are hard to measure, the continuous spectrum of radiation modes can be approximated with leaky modes. The transmission constant of leaky modes is plural. Compared with guide modes the solution of leaky modes is relatively more complex. This thesis mainly studies the characteristics of leaky modes in planar optical waveguide.Firstly, this thesis introduces the concept of leaky modes in planar optical waveguide, and analyses and compares existing methods of the leaky modes research. Take W-type planar optical waveguide as an example, the eigen equation of leaky modes is given, three kinds of methods are applicated to analyze features of leaky modes, of which perturbation method is used to solve the eigen equation approximately, loop integral method is used to solve the eigen equation accurately, radiation mode decomposition method is used to directly analyze features of leaky modes.Secondly, the transfer matrix method is used to deduce eigen equation of leaky modes in periodic planar optical waveguide. The results are fitted to get the curve of real part of leaky modes transmission constant alone with the change of the wave number. The perturbation method is used to solve transmission constant imaginary part of leaky modes. The analytical expression of the imaginary part of leaky modes transmission constant is deduced in three different refractive index distribution structure of periodic waveguide. Then, the effect of optical waveguide parameters on the loss of leaky modes is clarified.Finally, eigen equation of leaky modes in the form of integral equation in planar optical waveguide with arbitrary refractive index profile is deduced. The eigen equation is transformed into the issue of matrix eigenvalue solving when it has been discreted. The method of increasing the Gauss-Legendre points, the method of optimizing the integral value near the pole position and the combination of these two methods are used to improve the accuracy of solution of leaky modes eigen equation, and the error reaches 10-2.