Optical Networks - _E_1 Propagation of Chirped Gaussian Pulses_155

Optical Networks - _E_1 Propagation of Chirped Gaussian Pulses_155

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772 Pulse Propagation in Optical Fiber E.1 Propagation of Chirped Gaussian Pulses Mathematically, a chirped Gaussian pulse at z = 0 is described by the equation G(t) ± A 0 e 1 + 2 ² t T 0 ³ 2 e 0 t ´ = A 0 e 1 2 ² t T 0 ³ 2 cos µ ω 0 t + κ 2 t T 0 · 2 ¸ . (E.6) The peak amplitude of the pulse is A 0 . The parameter T 0 determines the width of the pulse. It has the interpretation that it is the half-width of the pulse at the 1 /e -intensity point. (The intensity of a pulse is the square of its amplitude.) The chirp factor κ determines the degree of chirp of the pulse. From (E.4), the phase of this pulse is φ(t) = ω 0 t + κt 2 2 T 2 0 . The instantaneous angular frequency of the pulse is the derivative of the phase and is given by d dt µ ω 0 t + κ 2 t 2 T 2 0 ¸ = ω 0 + κ T 2 0 t. We define the chirp factor of a Gaussian pulse as T 2 0 times the derivative of its instantaneous angular frequency. Thus the chirp factor of the pulse described by (E.6) is
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