Numerical Analysis Of Electromagnetic Field In Dielectric Media

Efficient and accurate methods to simulate the electromagnetic field in the dielectric media can promote the design and development of optical components and integrated circuits.Depending on the theoretical basis of computational electromagnetics,we numerically solve Maxwell's equations under given boundary conditions to simulate the response of dielectric structures to the incident electromagnetic waves.More analytical analysis is given to decrease the cost of numerical computation.We mainly study the propagation of light in three-dimensional dielectric waveguides and two-dimensional transverse electric field scattering problems.In the third chapter,we first introduce the mode solver based on vector finite elements method.Next,we utilize the perfect matching layer to solve the modes of dielectric waveguides with finite computational region.After we obtain the modes,we combine the mode-matching method and energy conservation and propose an improved mode-matching method to calculate the reflection and transmission coefficients in the context of a mode-matching method with optimization,which makes the results more reliable and accurate as the number of modes employed in the mode-matching method is increased.Additionally,we deduce the constraints of the scattering matrix of light propagating in three-dimensional dielectric waveguide.Considering the application of the mode solver,we associate the scattering condition with the modes of the waveguide.In the forth chapter,we utilize a domain integral equation formulation to simulate two-dimensional transverse electric scattering in a homogeneous medium.In the spatial representation,we employthe piecewise-linear functions along the x direction and Gabor frame with the Gaussian window along the z direction.Mean-while,the dual Gabor window is approximated by a summation of modulated Gaussian functions.Then we apply Ewald Green's function transformation to separate the integrals related to x and z in the integral equation,which also produce Gaussian items.These Gaussian items in the integrand can be integrated analytically and it greatly simplifies the calculation process.At the last,we discuss the convergence and the selection of the Ewald splitting parametere.In the fifth chapter,we solve the scattering problem of two-dimensional transverse electric field in a layered structure with the similar algorithm described in the forth chapter.The scattering object is located in only one medium and its size is finite.We still use the Gabor frame and piecewise linear functions as discrete functions in the direction of x and z respectively.In this chapter,we use the superposition of reflection and refraction of scattered field in homogeneous medium to represent the total scattered field in layered structure.For the scattered field in homogeneous medium,we still use Ewald Green function transformation to deal with it.This not only simplifies the singularity problem into an integral at infinity,but also avoids the matrix inversion operation in the original recursive formula,which greatly improves the efficiency.