1. The right tool for a given measurement: An overview
The pulse train
The pulse of a train
The single amplified pulse
The methods
Correlations
Femtonitpicker -- Picasso
Spider
Cross-correlation
Frog

2. The right tool for a given measurement
An overview
THE PULSE TRAIN
TOOLS: Simple analog oscilloscope and frequency doubling crystal.
Electronic Spectrum analyzer
Spectrometer
What to look for?
Both fundamental and second harmonic: a straight line.
No sideband and higher harmonics
Continuous spectrum, central wavelength
MANY OPPORTUNITIES TO CHEAT WITH ANY METHOD
The more sophisticated the instrument, the easier it is for the manufacturer to cheat.
There is no point in taking an autocorrelation, frog of spider if the above conditions are not satisfied.

3. The right tool for a given measurement
An overview
THE PULSE TRAIN
Both fundamental and second harmonic: a straight line.
Electronic Spectrum analyzer

4. The right tool for a given measurement
An overview
THE PULSE TRAIN
What we should not see:
Modulation of the train on a ms scale
Q-switched-mode-locked train
(Shows as a sideband on spectrum
analyzer on a 100 KHz scale)

5. The right tool for a given measurement
An overview
THE PULSE OF A TRAIN
Do you want to tune the laser to get the shortest pulse?
TOOLS: Scanning autocorrelator, Intensity, interferometric, spatially encoded Spider
Tuning a laser oscillator
Tuning a high power
system
Single pulse characterization at high repetiton rate: SPIDER

6. The right tool for a given measurement
An overview
THE SINGLE AMPLIFIED PULSE
Short pulse
Stretched pulse
Complex pulse shapc
Single shot autocorrelations
Cross-correlations
(intensity and interferometric)
Frog
(high dynamic range)
Femtonitpicker (Picasso)
Spider
Spider
1 KHz WOULD NOT WORK WITH FROG
Basic difference between FROG and SPIDER:
FROG: 2D frames
Spider
Frog
SPIDER: 2 x 1D frames
FASTER: pulse reconstruction at 1 kHz

7. The right tool for a given measurement
An overview
THE SINGLE AMPLIFIED PULSE
Ultra-
Short pulse
Complex pulse shapc
Single shot autocorrelations
Cross-correlation
Femtonitpicker (Picasso)
Tadpole
SEA-
SPIDER
1 KHz WOULD NOT WORK WITH FROG
Not so fast as spider:
2D frames
Frog
(high dynamic range)
Spider

8. The choice of the optimum metrology method
for a given problem
Playing with analogies….
More serious stuff: what is a pulse
what is a pulse train?
The right tool for a given measurement: An overview
The pulse train
The pulse of a train
The single amplified pulse
The methods
Correlations
Femtonitpicker -- Picasso
Spider
Frog
Measurement of Carrier to Envelope Offset (CEO)
by “correlation” – next lecture
Measurement of Carrier to Envelope Phase (CEP)

9. t I
Correlations
ref I s t
Phase information: parallel polarization and replace the
polarizing beam splitter by a non-polarizing beam splitter.

10. Interferometric
Intensity
Autocorrelation

11. Interferometric
correlation

12. What do these autocorrelation tell us?
Intensity autocorrelations:
Continuous signal
with100% mod.
Cw + noise
pulse

13. What do these autocorrelation tell us?
Interferometric autocorrelations
Linearly chirped pulse
Bandwidth limited pulse

14. What do these autocorrelation tell us?
How to measure a linear chirp.

15. Single shot interferometric
autocorrelation

16. The choice of the optimum metrology method
for a given problem
Playing with analogies….
More serious stuff: what is a pulse
what is a pulse train?
The right tool for a given measurement: An overview
The pulse train
The pulse of a train
The single amplified pulse
The methods
Correlations
Femtonitpicker -- Picasso
Spider
Frog
Measurement of Carrier to Envelope Offset (CEO)
by “correlation” – next lecture
Measurement of Carrier to Envelope Phase (CEP)

17. b) Apply a transformation to the object, so that it can be observed
How to make a cross correlation
when there is no shorter pulse available?
b) Apply a transformation to the object, so that it can be observed
The
transformed
object
is visible
“Linear
Transformation”
Object
(a flea)
Applying a transformation to the object, so that it can be observed: this is
--- to a certain extent – what one does when labelling molecules,
Viruses with organic dyes. It is never known for certain that the properties of
the object to be observed are not affected by the labeling.

18. How to make a cross correlation
when there is not shorter pulse available?
Ideal for the range 100 fs to 1 ps.
Reference
pulse
The prism transforms
the transverse coordinate
into a delay
Applying a transformation to the object, so that it can be observed---

19. How to make a cross correlation
when there is not shorter pulse available?
Reconstruction by iterative
deconvolution
Ideal for the range 100 fs to 1 ps.
Example

20. How to make a cross correlation
when there is no shorter pulse available?
Advantages: Fast convergence (small number of iterations)
Disadvantage: Small dynamic range, unless the pulse deformation is adjustable
Uncertainty principle (should apply to all methods).
The larger the temporal contrast between original and “transformed” pulse:
References
The better the amplitude reconstruction
Femtonitpicker: Chi Yan and J.-C. Diels,
J. of the Opt.~Soc.~Am.~B, 8:
(1991)
The smaller the interference contrast
Reduced phase accuracy
Picaso J.~W.~Nicholson and W.~Rudolph,
J. of the Opt.~Soc.~Am.~B, 19:
(2002)

21. Femtonitpicker and Picasso
Reconstruction
Pulse 1 short

22. Interferometric correlation
Case of autocorrelation: the last term is the IFT of the second harmonic spectrum

23. MOSAIC : a treatment derived from the interferometric autocorrelation
MOSAIC Trace
Delay
x 2
FFT
FFT-1
Frequency
Frequency
Delay
1) M. Sheik-Bahae, Opt. Lett. 22, (1997)
2) T. Hirayama and M. Sheik-Bahae, Opt. Lett. 27, (2002)

24. Less information leads to … more info?
By eliminating the middle term, we get more sensitivity to chirp
Unchirped
Chirped
-200
-100
100
200
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Delay (fs)
Interferometric
Auto
Correlation
MOdified
Spectrum
Auto
Interferometric
Correlation

25. *D. A. Bender and M. Sheik-Bahae, Opt. Lett. 32, 2822 (2007).15 1
pt. by pt. line search
R-MOSAIC 10 5
Signal (a. u.)
0.5
Phase (rad) -5
-10
-15 -1 -1
-0.5
0.5
0.5 1 1 13
Frequency (Hz)
x 10
x 10
*D. A. Bender and M. Sheik-Bahae, Opt. Lett. 32, 2822 (2007).

26. The choice of the optimum metrology method
for a given problem
Playing with analogies….
More serious stuff: what is a pulse
what is a pulse train?
The right tool for a given measurement: An overview
The pulse train
The pulse of a train
The single amplified pulse
The methods
Correlations
Femtonitpicker -- Picasso
Spider
Cross-correlation
Frog

27. Spectral Phase Interferometry for Direct Electric-field Reconstruction
SPIDER
Spectral Phase Interferometry for Direct Electric-field Reconstruction
Basic principle: Pulse to be measured shifted in frequency and delayed,
and made to interfere with the original pulse in a spectrometer.
Measure:
where
Inverse Fourier transform:
2 one-dimentional measurements:
Fourier transform
The spectrum
The sheared spectrum
Extract

28. Spectral Phase Interferometry for Direct Electric-field Reconstruction
SPIDER
Spectral Phase Interferometry for Direct Electric-field Reconstruction
Basic technique:
Chirp generator
Sum
frequency
pulse
sequencer t
Spectro-
meter
The two pulses are “spectrally sheared” by the product with the chirped pulse

29. SPIDER t Ideal for high (kHz) repetition rate Chirp generator Sum
frequency
pulse
sequencer t
Spectro-
meter
Advantage: 2 x 1D therefore fast (kHz) reconstruction
Disadvantages:
1. Raw data not informative
2. Shear and delay not independent
Spatially encoded arrangement for SPIDER
SEA-SPIDER
2D data but ideal for ultrashort pulses

30. SEA-SPIDER Ideal for few cycle pulses
Spectrum and shear along x, delay along y.
Reference: Webb site of Ian Walmsley, thesis of Adam S. Wyatt (2007)

31. SEA-SPIDER
The experimental setup

32. The FROG Frequency Resolved Optical Gating
It is a time gated spectrum, measuring a two D function:
References:
Advantage: the raw data give a nice representation
Disadvantage: considerable iterations
FROG Trebino,
Kluwer, 2002
Adam S. Wyat
PhD Thesis
University of Oxford
(2007)

33. Spectrograms for Linearly Chirped Pulses
Negatively chirped Unchirped Positively chirped
Frequency
Time
Frequency
Delay
Like a musical score, the spectrogram visually displays the frequency vs. time (and the intensity, too).

34. The uncertainty principle applies – as in any other method
Algorithms exist to retrieve E(t) from its spectrogram.
The spectrogram essentially uniquely determines the waveform intensity, I(t), and phase, (t).
There are a few ambiguities, but they’re “trivial.”
The gate need not be—and should not be—much shorter than E(t).
Suppose we use a delta-function gate pulse:
= The Intensity.
No phase information!

35. The choice of the optimum metrology method
for a given problem
Playing with analogies….
More serious stuff: what is a pulse
what is a pulse train?
The right tool for a given measurement: An overview
The pulse train
The pulse of a train
The single amplified pulse
The methods
Correlations
Femtonitpicker -- Picasso
Spider
Frog