1. + applications

2. Femtosecond Optics 1. Dispersion 2. Interferometer to measure linear dispersion 3. Wave front and energy front A general rule Grating Interface Pair of prisms Applications { Traveling wave amplifier Single shot autocorrelator Femtonitpicker Other diagnostic with pair of prisms

3. Wave front and energy front db tan g = l dl

4. b = q - q l dn c dl db r tan g = l i dl Tilting at an interface TAC = L sin qi/c q q Pulse n sin = sin i r TBD = L sin qrn/c TBD – TAC = -L sin qr/vg + L sin qi/c = L sin qr (n/c – 1/vg) = L sin qr q DC = L cos r A q i q i B C D’ g q r D

5. Consequences of an energy front tilt Focusing: expanded focal region, less intensity Cavity – pulse stretching across the transverse direction. Remedies: image reversal pairs of elements

6. Energy front & Phase front Fermat’s principle  OPL  Phase velocity Energy front (pulse propagation)  Group velocity

7. Group delay Wave front and energy front db tan g = l db = angular dispersion g = tilt of energy front dl dl Group velocity dispersion There is also a relation between GVD and angular dispersion

8. S’W Q S0, SW PW rW a L r0 P0 S’0 Whether considering group delays or group velocity dispersion (GVD), we will consider sufficiently broad beams, and sufficiently short propagation distances Lp behind the element, such that diffraction effects can be neglected.

9. S’W Q S0, SW PW rW a L r0 P0 S’0

10. The most widely used optical devices for angular dispersion are prisms and gratings. To determine the dispersion introduced by them we need to specify not only a(W), but also the optical surfaces between which the path is being calculated. The ``dispersion'' of an element has only meaning in the context of a particular application, that will associate reference surfaces to that element.

11. a h L A B L g C (R)

12. 2

13. INTERFEROMETER TO MEASURE DISPERSION No dispersion Pulse  zero delay group velocity Fringes phase velocity CW interference Phase velocity

14. Delay (fs) -20 -10 0 10 20 1 0 -1 -6 -4 -2 0 2 4 6 Interferogram without sample, and its Fourier Transform

15. Relative Delay (fs) 0 100 200 300 400 1.0 0.5 Normalized Intensity (a.u.) 0.0 -0.5 -1.0 0 30 60 90 120 m Relative Delay ( m) Interferogram for 2 mm of glass, spectrum and spectral phase. Reminder White light interferometry was for dispersion measurement m m) Wavelength ( 1.2 1 0.8 0.6 5 1.0 Spectrum Phase 0 0.8 Polynomial Fit -5 Spectral Amplitude (a.u.) 0.6 Spectral Phase (rad) -10 0.4 -15 0.2 -20 0.0 -0.5 0.0 0.5 1.0 W (1/fs)

19. Femtosecond Optics 1. Dispersion 2. Interferometer to measure linear dispersion 3. Wave front and energy front A general rule Grating Interface Pair of prisms Applications { Traveling wave amplifier Single shot autocorrelator Femtonitpicker Other diagnostic with pair of prisms

20. I don’t have a fs detector… There’s a hole in my bucket, dear Liza, dear Liza There’s a hole in my bucket, dear Liza, a hole Then fix it, dear Henry, dear Henry, dear Henry Then fix it, dear Henry, dear Henry, then fix it With what shall I fix it, dear Liza, dear Liza? With some straw… The straw is too long, dear Liza, dear Liza Then cut it…. In what shall I get it, dear Liza, in what? In a bucket dear Goofy, dear Henry, dear Henry

21. E(W)eif(W)

22. Either accurate spectral amplitude OR accurate spectral phase Cross-correlator td f(W)