Generation of a train of ultrashort pulses using periodic waves in tapered photonic crystal fibres

We consider a light wave propagation in tapered photonic crystal fibres (PCFs) wherein the wave propagation is described by the variable coefficient nonlinear Schrödinger equation. We solve it directly by means of the theta function identities and Hirota bilinear method in order to obtain the exact periodic waves of sn, cn and dn types. These chirped period waves demand exponential variations in both dispersion and nonlinearity. Besides, we analytically demonstrate the generation of a train of ultrashort pulses using the periodic waves by exploiting the exponentially varying optical properties of the tapered PCFs. As a special case, we discuss the chirped solitary pulses under long wave limit of these periodic waves. In addition, we derive these types of periodic waves using the self-similar analysis and compare the results.