Space-time analogy True for all pulse/beam shapes Paraxial approximation (use of Fourier transforms) Gaussian beams (q parameters and matrices) Geometric optics
SPACETIME Fourier transform in time Fourier transform in space
d1d1 d2d2 DIFFRACTION (r) (-r/M) Space-time analogy By matrices: SPACE Geometric optics
d1d1 d2d2 DISPERSION (t) (--t/M) Space-time analogy By matrices: TIME y length in time T Geometric optics = chirp imposed on the pulse
d1d1 d2d2 DIFFRACTION (r) (-r/M) Space-time analogy By matrices: SPACE Gaussian optics
d1d1 d2d2 DISPERSION (t) (--t/M) Space-time analogy By matrices: TIME Gaussian optics = chirp imposed on the pulse Find the image plane:
WHAT IS THE MEANING k”d? Fiber Prism L LgLg Gratings b Fabry-Perot at resonance d LfLf
TIME LENS d1d1 d2d2 DISPERSION 1 (t) (t) d1d1 d2d2 DIFFRACTION (r) (-r/M) TIME MICROSCOPE
DISPERSED INPUT 1 (t) TIME LENS OUTPUT 1 (t) e iat 2 pp 1 + 11 pp CHIRPED PUMP p (t) = e iat 2 TIME LENS
Other version of the pulse shaper Laser source 10 ns grating Programmable mask grating
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:
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