Thin-film theorems are well developed and so are the fabrication processes. Yet under some special conditions, traditional methods (such as the ABCD matrix and the transmission matrix methods) will lead to a serious numerical error. In this thesis, we propose a new method called Couple E/H field formulation, which will overcome this numerical problem in simulating characteristics of complex multi-layered structures. We have verified both the algorithm and its results with the traditional techniques. By extending the impedance matching principle, we came out with a multi-layer anti-reflection coating design optimized for a time-harmonic plane wave incidence with any incident angle. Such a design allows for more plane waves with adjacent angles to pass through the coating layers with minimal reflection. Furthermore, we apply this AR coating design to facets of semiconductor lasers. Our calculation shows that multi-layer coating does a better job than a single layer coating. The reflectivity of a laser diode from single layer coating 0.085% to 5 layer coating 0.056%, which is a 33% improvement.

Numerical analysis of periodic structures in layered media is usually accomplished by using Method of Moments which requires the formation of the impedance matrix of the structure. The construction of this impedance matrix requires the evaluation of the periodic Green&rsquo / s function in layered media which is expressed as an infinite series in terms of the spectral domain Green&rsquo / s function. The slow converging nature of this series make these kinds of analysis computationally expensive. Although some papers have proposed methods to accelerate the computation of these series successfully for a single frequency point, it is still very computation intensive to obtain the frequency response of the structure over a band of frequencies. In this thesis, Discrete Complex Image Method (DCIM) is utilized for the efficient computation of the periodic Green&rsquo / s function. First, the spectral domain Green&rsquo / s function in layered media is approximated by complex exponentials through the use of DCIM. During the application of the DCIM, three-level approximation scheme is employed to improve accuracy. Then, Ewald&rsquo / s transformation is applied to accelerate the computation of the infinite series involved in the periodic Green&rsquo / s functions. The accuracy and the efficiency of the method is demonstrated through numerical examples.