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
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Physical quantities, Fundamental physics concepts, chirped Gaussian pulse