Study On The Periodic Structure FDFD Method With PML And Its Application

With the rapid development of modern science and technology, information need higher transfer rate and capacity. Faster communication of larger amounts of data need to be solved urgently. Because photonics uses electromagnetic waves as information carriers, efficient numerical solution of Maxwell’s equations, which govern all electromagnetic phenomena, has become a new solution. This transmission method has a high speed, wide band, high accuracy, etc. Efficient method of numerical solution of Maxwell’s equations has become the key to solve this problem. Common numerical method has finite element method, method of moments and finite-difference method. This dissertation used Finite Difference Frequency Domain (FDFD) numerical method to solve Maxwell’s equations. Theoretically analyzed the condition number of different perfectly matched layer (PML), plasma coaxial waveguide transmission characteristics and absorption of graphene-based critical coupler.FDFD is an algorithm to calculate the frequency domain Maxwell’s equations. Iterative algorithm is used to solve the matrix. FDFD is easier to programming, requires little memory and efficiency in parallel computing environment. However, in the calculation of three-dimensional Maxwell’s equations, FDFD algorithm has not been widely used due to FDFD algorithm has a slow convergence speed in solving large linear matrix equation.In the FDFD algorithm, different PML result in different coefficient matrices A in the linear systems. In general, it is empirically known that the use of any PML leads to an ill-conditioned matrix and slows down the convergence of iterative method to solve the coefficient matrix A. This paper has theoretically analyzed the condition number of coefficient matrix A with SC-PML and UPML. It shows that the condition number of SC-PML is better than UPML that under the same conditions. It also means that SC-PML leads to far faster convergence than UPML in general. Although it is recommended to use SC-PML to solve Maxwell’s equations in the frequency domain based on the iterative algorithm, but there are cases where one would like to use UPML for practical reasons. In order to effectively improve UPML convergence speed in the FDFD algorithm, the coefficient matrix A must have a preconditioning scheme. The key is to reduce condition number of coefficient matrix A that FDFD algorithm constructed with PML, this can make a better convergence speed. We use the diagonal preconditioning scheme for coefficient matrix A and then solve the resulting matrix can greatly improve UPML convergence speed.Research in any direction of the incident light to submicrometer-scale volume is one of the most basic functions in nanophotonics. Metal plasma waveguide has intrinsically ohmic losses, but still as an important part of nanophotonics devices. This is due to their capability of guiding light through deep-subwavelength mode areas is greater than other materials. We studied a relatively unique plasma waveguide which has broadband transmission characteristics, namely coaxial waveguide. The waveguide has been optimized on this basis to obtain the high transmission characteristics. Because of the high transmission characteristics, the crosstalk can be suppressed effectively. It has provided basic theory to design the optical circuits and photodetector.Graphene is one of the popular materials which has excellent optical and electrical properties. High mobility and transparency, good flexibility and stability are the nature of its excellent features. This paper studies the absorption of graphene-based critical coupler in near-infrared wavelength and critical coupling effect (near-perfect light absorption) can be achieved at the near-infrared wavelength. In addition, we also studied the position and amplitude of the critical coupling frequency can be tuned by adjusting the electrical parameters of graphene and the parameters of the structure.