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.