SCATTERING METHOD CALCULATION OF THE ELECTROMAGNETIC PROPERTIES OF TWO-DIMENSIONAL PHOTONIC CRYSTAL SLABS AND WAVEGUIDES

摘要

For the past decade photonic crystals (PCs) have been the subject of increasing research owing to the effective control of light they can provide. In particular a growing interest has been devoted to 2D PCs with finite height for two main reasons: firstly, conventional lithography techniques are now well developed to achieve their fabrication and secondly, 2D PC slabs are well adapted to the domain of integrated optics. Here we present theoretical studies on such PC slabs. We have developed a scattering matrix approach, which allows a complete modeling of the electromagnetic properties of structures made of layers of dielectric materials with planar periodicity. This method is shown to constitute a powerful tool for the analysis of guided and quasi-guided (resonant) modes in PC slabs of finite thickness either suspended in air or on a substrate. The use of the scattering matrix formalism in the field of PC slabs was first introduced by Whittaker and Culshaw in order to model the reflection and transmission properties of these slabs [1]. The approach we have developed exploits the determination of the poles of the scattering operator [2,3], which allows us to obtain not only the whole frequency band structure but also to predict the intrinsic radiation losses of the resonant modes, that are due to their interaction with the continuum of the radiation modes.