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 frontdb
tan g = l dl

4. b = q - q db tan g = l dl q q q q q q r i Tilting at an interface
TAC = L sin qi /c q q
Pulse
n sin = sin r i
TBD = L sin qr n/c
TBD – TAC = -L sin qr /vg + L sin qi /c
= L sin qr (n/c – 1/vg) = L sin qr
l dn
c dl
DC = L cos q 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. Wave front and energy front
Group delay
Wave front and energy front db
tan g = l db
g = tilt of energy front
= angular dispersion dl dl
Group velocity dispersion
There is also a relation between GVD and angular dispersion

8. 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. Q
S0, SW
S’0
S’W a P0 PW rW r0 L

9. Q
S0, SW
S’0
S’W a P0 PW rW r0 L

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.
Indeed, we have assumed in the previous calculation
that the beam started as a plane wave (plane reference surface normal to the
initial beam) and terminates in a plane normal to the ray at a reference
optical frequency $\omega_\ell$. The choice of that terminal plane is as arbitrary
as that of the reference frequency $\omega_\ell$ (cf. Chapter 1, Section~\ref{Fourier-rep}).
After some propagation distance, the various spectral component of the pulse
will have separated, and a finite size detector will only record a portion of
the pulse spectrum. 10

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

12. 2

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

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

15. Interferogram for 2 mm of glass, spectrum and spectral phase.
Reminder White light interferometry was for
dispersion measurement 30 60 90
120
-1.0
-0.5
0.0
0.5
1.0
Normalized Intensity (a.u.)
Relative Delay ( m m)
100
200
300
400
Relative Delay (fs) m
Wavelength ( m)
1.2 1
0.8
0.6 5
1.0
Spectrum
Phase
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. td f(W) Either accurate spectral amplitude OR accurate spectral phase
Cross-correlator td
f(W)