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. SPACE TIME Fourier transform in time Fourier transform in space

3. Space-time analogy Geometric optics d1 d2 SPACE e(-r/M) e(r) DIFFRACTION DIFFRACTION By matrices:

4. Space-time analogy Geometric optics d1 d2 TIME e(--t/M) e(t) DISPERSION DISPERSION By matrices: y length in time T = chirp imposed on the pulse

5. Space-time analogy Gaussian optics d1 d2 SPACE e(-r/M) e(r) DIFFRACTION DIFFRACTION By matrices:

6. Space-time analogy Gaussian optics d1 d2 TIME e(--t/M) e(t) DISPERSION DISPERSION By matrices: = chirp imposed on the pulse Find the image plane:

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

8. TIME MICROSCOPE d1 d2 e(-r/M) e(r) DIFFRACTION DIFFRACTION e(t) d2 DISPERSION d1 e1(t) TIME LENS DISPERSION

9. CHIRPED PUMP ep(t) = eeiat 2 TIME LENS e1(t) DISPERSED INPUT TIME LENS OUTPUT w1 wp w1 + e1(t)eiat 2 wp

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

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

12. Laser source FOPA:Frequency domain optical parametric amplification (Faux-pas) Spatial problem Temporal problem Diffraction of a Gaussian beam of finite size by a grating, such that the diffraction of a monochromatic beam atl covers Dy; the full pulse spectrum covers the crystal; no higher order mode overlap with the first order 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 Dy 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 grating y grating L