Degeneration of One-dimensional Photonic Crystal by Random Layer Thickness Imperfections

We demonstrate a simple statistical method which allows to analyze the influence of random layer thickness imperfections in a one-dimensional photonic crystal on the properties of the photonic crystal. Our method is based on effective resonator model, which is purely analytical and, as a result, this method does not require a significant computational power to be employed. We show that random defects of width make narrower the frequency region in which a photonic band gap is expected to exist and provide a method to determine required precision of fabrication of the photonic crystal.