Abstract
In this thesis, we concentrate on the perturbation method as the numerical model in the analysis of electromagnetic fields one-dimensional photonic band gap（PBG） structures. Approximating that the electric fields is in the form of scalar Floquet-Bloch waves, the Maxwell’s equation in the corrugated region is a second-order inhomogeneous coupled differential equation and can be analytically solved by the first-order perturbation method that involves usually massive numerical iterative calculations. We suggest an approximated analytic solution for the electric field in the corrugated region instead of the numerical iterative results. After that, the radiated power with various geometrical parameters are presented. Also, we study the implementation of mode determination inside one-dimensional PBG. The allowed modes, including guided modes and leaky modes, are obtained by finding zeros of the complex multi-valued dispersion equation. With conformal mapping, the four-valued dispersion equation is transformed into a single-valued equation with another new variable. We solve this single-valued equation by applying argument principle method（APM）. APM is a rigorous mathematical technique based on the complex number theory but not merely numerical iterative process. It is capable of finding all the zeros of any analytic function in the complex plane. With APM algorithms, the roots-finding of dispersion equation with PBG structure is more effective and accurate.