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Space-time analogy

Space-time analogy. True for all pulse/beam shapes. Paraxial approximation (use of Fourier transforms). Gaussian beams (q parameters and matrices). Geometric optics. SPACE. TIME. Fourier transform in time. Fourier transform in space. Space-time analogy. Geometric optics. d 1. d 2.

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Space-time analogy

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  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

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