1. Gaussian pulses Bandwidth limited: Pulse duration FWHM Fourier transform Bandwidth duration product Chirped Gaussian Fourier Transform

2. Pulse duration, Spectral width Two-D representation of the field: Wigner function

3. Gaussian Chirped Gaussian Wigner Distribution

4. Wigner function: What is the point? Uncertainty relation: Equality only holds for a Gaussian pulse (beam) shape free of any phase modulation, which implies that the Wigner distribution for a Gaussian shape occupies the smallest area in the time/frequency plane. Only holds for the pulse widths defined as the mean square deviation

5. linear propagation of Gaussian pulses

6. Pulse propagation through 2 mm of BK7 glass

7. A Bandwidth limited pulse Some (experimental) displays of electric field versus time -20-1001020

8. Space-time Analogy

9. d1d1 d2d2 DIFFRACTION  (r)  (-r/M) DIFFRACTION TIME LENS d1d1 d2d2 DISPERSION  1 (t)  (t) Space-time Analogy

10. DISPERSED INPUT  1 (t) TIME LENS OUTPUT  1 (t) e iat 2 pp  1 + 11 pp CHIRPED PUMP  p (t) =  e iat 2 TIME LENS d1d1 DISPERSION  1 (t)

12. A Bandwidth limited pulse Some (experimental) displays of electric field versus time -20-1001020