Approximate analytical solutions for nonlinear photonic crystal fibers

Abstract

SUMMARYThis paper proposes an analytical approximation theory for evaluation of the transmission characteristics of a nonlinear photonic crystal fiber. A photonic crystal fiber with a complex cross-sectional structure is replaced equivalently with a conventional step-index fiber so that an analytical approximation theory developed for the conventional nonlinear optical fiber can be applied directly to the nonlinear photonic crystal fiber. In order to derive an effective index of refraction of the clad region of the photonic crystal fiber with holes, an empirical formula for the normalized frequency of the photonic crystal fiber proposed recently is introduced. Hence, the fundamental quantities describing the transmission characteristics of the nonlinear photonic crystal fiber, specifically the effective index of refraction and the effective core cross section, can easily be derived without numerical calculations. By using the proposed method, the optical power dependence of the transmission characteristics of the nonlinear photonic crystal fiber is analyzed. Validity of the proposed method is verified by comparison of the results with those by calculations based on the full-vectorial finite element method.