We derived the evolution of an initial (z=0) gaussian wavepacket (in time) with phase=0 in presence of beta1 and beta2. We first made a change of reference frame defining a new time variable dependent on the spatial position inside the material. We moved to frequency domain, where the solution in z is easy to obtain (exponential) Then we evaluated the initial condition in w-space and we finally anti-transformed back in time domain. We found a temporal broadening and a variation of the compex z-dependent phase. This means the pulse acquires some chirp while propagating along z, with different "temporal portions" of the envelope having different frequencies. The bandwidth is unaffected. Hence, the solution at finite Z is no longer Fourier Transform limited.
Nessun commento:
Posta un commento