The theoretical study of dispersion management in a photonic crystal fiber
Abstract
Photonic crystal fiber is widely used in optical communication and ultrafast optics. In this paper, the nonlinear Schrödinger equation in the photonic crystal fiber is studied analytically. With the Horita method, the bilinear form are derived, and the analytic one-soliton solution for the nonlinear Schrödinger equation are obtained. Through the analytic one-soliton solution obtained, the transmission characteristics of solitons in the photonic crystal fiber are analyzed with the different group velocity dispersion. With the help of the dispersion management technology, we discuss the soliton transmission in the case of different group velocity dispersion functions by changing the group velocity dispersion of the photonic crystal fiber. If the group velocity dispersion function of the photonic crystal fiber is constant, the solitons can keep their velocities and shapes during the transmission. If the group velocity dispersion function of the photonic crystal fiber is the trigonometric one, the solitons show the periodic transmission. While the group velocity dispersion function of the photonic crystal fiber is the Gauss one, the properties of local solitons are demonstrated. Moreover, when the group velocity dispersion function of the photonic crystal fiber is the linear one, the soliton compression and amplification in the photonic crystal fiber can be realized simultaneously. The conclusion of this paper provides a theoretical reference for the corresponding dispersion management technology in the photonic crystal fiber.
