772Pulse Propagation in Optical FiberE.1Propagation of Chirped Gaussian PulsesMathematically, a chirped Gaussian pulse atz=0is described by the equationG(t)=±±A0e−1+iκ2²tT0³2e−iω0t´=A0e−12²tT0³2cosµω0t+κ2¶tT0·2¸.(E.6)The peak amplitude of the pulse isA0. The parameterT0determines the width of thepulse. It has the interpretation that it is the half-width of the pulse at the1/e-intensitypoint. (The intensity of a pulse is the square of its amplitude.) Thechirp factorκdetermines the degree of chirp of the pulse. From (E.4), the phase of this pulse isφ(t)=ω0t+κt22T20.The instantaneous angular frequency of the pulse is the derivative of the phase andis given byddtµω0t+κ2t2T20¸=ω0+κT20t.We deﬁne thechirp factorof a Gaussian pulse asT20times the derivative of itsinstantaneous angular frequency. Thus the chirp factor of the pulse described by(E.6) is
This is the end of the preview. Sign up
access the rest of the document.