1. Space-time analogy True for all pulse/beam shapes Paraxial approximation (use of Fourier transforms) Gaussian beams (q parameters and matrices) Geometric optics

2. SPACETIME Fourier transform in time Fourier transform in space

3. d1d1 d2d2 DIFFRACTION  (r)  (-r/M) Space-time analogy By matrices: SPACE Geometric optics

4. d1d1 d2d2 DISPERSION  (t)  (--t/M) Space-time analogy By matrices: TIME y length in time T Geometric optics = chirp imposed on the pulse

5. d1d1 d2d2 DIFFRACTION  (r)  (-r/M) Space-time analogy By matrices: SPACE Gaussian optics

6. d1d1 d2d2 DISPERSION  (t)  (--t/M) Space-time analogy By matrices: TIME Gaussian optics = chirp imposed on the pulse Find the image plane:

7. WHAT IS THE MEANING k”d? Fiber Prism L LgLg Gratings b Fabry-Perot at resonance d LfLf

8. TIME LENS d1d1 d2d2 DISPERSION  1 (t)  (t) d1d1 d2d2 DIFFRACTION  (r)  (-r/M) TIME MICROSCOPE

9. 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

10. Other version of the pulse shaper Laser source 10 ns grating Programmable mask grating

11. FOPA: Frequency domain optical parametric amplification (Faux-pas) Where time domain/space domain mix Space-time analogy Laser source grating The principle of the time lens/pulse shaper. y grating L Over the height of the crystal, there is a phase shift:

12. FOPA: Frequency domain optical parametric amplification (Faux-pas) Laser source grating y L Spatial problem Diffraction of a Gaussian beam of finite size by a grating, such that the diffraction of a monochromatic beam at covers  y; the full pulse spectrum covers the crystal; no higher order mode overlap with the first order Temporal problem Pulse broadening by dispersion at each wavelength by the pair of gratings; Fourier transform of the pulse at the entrance of the crystal; Inverse FT of each section  y wide; Propagation of each pulse in each section; Linear approximation of spatial chirp; Difference in group velocity in bottom and top of each crystal; Calculation of the deflection of each beam At the end of each crystal