Time-frequency analysis of chirped femtosecond pulses using Wigner distribution function

A time-frequency analysis of chirped fetmosecond pulses using the Wigner distribution function is presented. We graphically obtain the instantaneous carrier frequency and the group delay of the chirped pulse using a peak-detection method. After confirming that the instantaneous carrier frequency of an ultra-short laser pulse defined by the derivative of the temporal phase is not generally supported by the optical frequency, we use the Wigner distribution to decompose the optical frequencies that mainly contribute to the pulse at a certain time. For this purpose, a chirped pulse with a double-peaked spectrum and one whose phase is distorted by third-order dispersion are analyzed with the peak-detection method. The Wigner distribution along with this graphical method successfully resolves the multicomportent frequencies that cannot be seen in the standard Fourier analysis.