Modeling and band structure calculations in 2-dimensional nonlinear photonic crystals

ABSTRACT MODELING AND BAND STRUCTURE CALCULATIONS İN 2-DIMENSIONAL NONLINEAR PHOTONIC CRYSTALS Ahmet ÇİÇEK Master's Thesis in Physics Advisor: Prof. Dr. Bülent ULÜ? May 2006,106 Pages in this study, band structures of 2-dimensional square photonic crystals comprising Kerr-type nonlinear dielectric material are calculated and compared to those exhibited by the same structures in linear regime. Position and width of the observed band gaps are taken into account for comparison. Band structures for linear photonic crystals are obtained via the Plane Wave Expansion (PWE) and Finite-Difference Time-Domain (FDTD) methods, respectively. The FDTD method is utilized for band structure calculations of nonlinear photonic crystals. The obtained results reveal that the band structures obtained through both methods converge rapidly not only within themselves but also to each other for grid configurations composed of the same number of mesh points. Investigations of the modification of the band structures exhibited by nonlinear photonic crystals with the power carried by the applied electromagnetic (EM) field show that the whole band structure shifts towards lower frequencies (redshift) for a positive Kerr dielectric susceptibility, while shifting towards higher frequencies (blueshift) for a negative susceptibility. Besides, depending on the sign of tiıe Kerr susceptibility, broadening (positive) ör contraction (negative) of band gaps are determined. KEY WORDS: Photonic crystal, band structure, nonlinearity, Kerr-type material, redshift, blueshift, switching. COMMTTTEE: Prof. Dr. Bülent ULU? (Advisor) Assoc. Prof. Dr. Mustafa DEMiRCi Asst Prof. Dr. Şerafettin YALTKAYA *. 11