1. Introduction to MOSAIC, SHG-FROG, and GRENOUILLE
Ning Hsu
03/02/2016

2. Modified Spectrum Auto Interferometric Correlation
Interferometric Autocorrelation DC
Intensity Autocorrelation
I.F.T.{SH spectrum}
Delay

3. Modified Spectrum Auto Interferometric Correlation
x 2
MOSAIC Trace
Frequency
FFT
Frequency
x 2
Delay
FFT-1
Delay
1) M. Sheik-Bahae, Opt. Lett. 22, (1997)
2) T. Hirayama and M. Sheik-Bahae, Opt. Lett. 27, (2002)

4. MOSAIC in time
Intensity Autocorrelation
x 2
I.F.T.{SH spectrum}

5. Why MOSAIC? Interferometric Autocorrelation
Not sensitive to pulse’s phase and shape?

6. MOSAIC is pickier on chirp (phase variation)

7. 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
The pulse is chirped, but how much?

8. Spectrum’s phase retrieving from MOSAIC
delay
Computed MOSAIC Trace
delay
experimental
MOSAIC Trace
Second order coefficient a optimizing
Pass keep a and move
on to b
Does not pass change a
and repeat
delay
Computed MOSAIC Trace
Third order coefficient b optimizing
Error function = difference between computed MOSAIC and experimental MOSACI (Using Nelder–Mead method to find the minimum)

9. An example of a pulse taken by GRENOUILLE and MOSAIC

11. Most people think of acoustic waves in terms of a musical score.
It’s a plot of frequency vs. time, with information on top about the intensity.
The musical score lives in the time-frequency domain.

12. Wigner distribution
unchirped
linearly chirped

13. Second-harmonic-generation FROG
SHG FROG is simply a spectrally resolved autocorrelation.
Pulse to be measured
Beam
splitter
E(t–t)
Camera
SHG
crystal
Spec-
trometer
E(t)
Esig(t,t)= E(t)E(t-t)
Variable delay, t
SHG FROG is the most sensitive version of FROG.

14. SHG FROG traces are symmetrical with respect to delay.
Frequency
Time
Delay
Negatively chirped Unchirped Positively chirped
SHG FROG has an ambiguity in the direction of time, but it can be removed.

15. Generalized Projections
A projection maps the current guess for the waveform to the closest point in the constraint set.
The Solution!
Initial guess for Esig(t,)
Set of Esig(t,t) that satisfy the nonlinear-optical constraint: Esig(t,)  E(t)E(t–)
Set of Esig(t,t) that satisfy the data constraint:
Algorithm developed by Rick Trebino and Ken DeLong
Convergence is guaranteed for convex sets, but generally occurs even with non-convex sets and in particular in FROG.

16. Ultrashort pulses measured using FROG
Traces
Retrieved
pulses
Data courtesy of Profs. Bern Kohler and Kent Wilson, UCSD.

17. GRating-Eliminated No-nonsense Observation of Ultrafast Incident Laser Light E-fields (GRENOUILLE)
FROG
2 key innovations: A single optic that replaces the entire delay line,
and a thick SHG crystal that replaces both the thin crystal and spectrometer.
GRENOUILLE
C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, Opt. Comm
P. O’Shea, M. Kimmel, X. Gu and R. Trebino, Optics Letters, 2001.

18. The Fresnel biprism
Crossing beams at a large angle maps delay onto transverse position.
Input pulse
Pulse #1
Pulse #2
t =t(x)
Here, pulse #1 arrives
earlier than pulse #2
Here, the pulses
arrive simultaneously
later than pulse #2 x
Fresnel biprism
Even better, this design is amazingly compact and easy to use, and it never misaligns!

19. The thick crystal
Suppose white light with a large divergence angle impinges on an SHG crystal. The SH generated depends on the angle. And the angular width of the SH beam created varies inversely with the crystal thickness.
Very thin crystal creates broad SH spectrum in all directions.
Standard autocorrelators and FROGs use such crystals.
Thin crystal creates narrower SH spectrum in
a given direction and so can’t be used
for autocorrelators or FROGs.
Thin
SHG
crystal
Very
Thin
SHG
crystal
Thick crystal begins to
separate colors.
Thick
SHG crystal
Very thick crystal acts like
a spectrometer! Why not replace the
spectrometer in FROG with a very thick crystal?
Very
thick crystal

20. GRENOUILLE Beam Geometry
Top
view
Lens images position in crystal
(i.e., delay, t) to horizontal
position at camera
Imaging Lens
Camera
Cylindrical
lens
Fresnel
Biprism
Thick
SHG
Crystal
FT Lens
Side
view
Lens maps angle (i.e.,
wavelength) to vertical
position at camera
Yields a complete single-shot FROG. Uses the standard FROG algorithm. Never misaligns. Is more sensitive. Measures spatio-temporal distortions!

21. GVM is usually much greater than GVD
GRENOUILLE requires a large GVM to spectrally resolve the pulse.
But it requires a small GVD, or the pulse will spread.
For all but near-single-cycle pulses (which are very broadband), GVM >> GVD, allowing us to satisfy both conditions simultaneously.

22. The GRENOUILLE operating range varies with wavelength.80
3.5-mm BBO 70 60
Flat-phase pulse expands due to GVD 50
GVM constraint
(2.5 x device spectral resolution)
Bandwidth (nm) 40 30 20 10
500
600
700
800
900
1000
1100
1200
Wavelength (nm)
Operation outside these limits is possible with corrections.

23. GRENOUILLE and crystal thickness
A = ratio of pulse length or bandwidth and resolution limit
The crystal must be thick and/or dispersive enough to frequency-resolve the pulse spectral structure (the GVM condition).
Yet, the crystal must be thin and/or non-dispersive enough, or the pulse will spread in time (the GVD condition).

24. Read more about GRENOUILLE in the cover story of OPN, June 2001
Testing GRENOUILLE
GRENOUILLE
FROG
Measured
Retrieved
Compare a GRENOUILLE measurement of a pulse with a tried-and-true FROG measurement of the same pulse:
Read more about GRENOUILLE in the cover story of OPN, June 2001
Retrieved pulse in the time and frequency domains

25. Spatio-temporal distortions in pulses
Prism pairs and simple tilted windows cause “spatial chirp.”
Prism pair
Input pulse
Spatially chirped output pulse
Spatially chirped output pulse
Input pulse
Tilted window
Gratings and prisms cause both spatial chirp and “pulse-front tilt.”
Angularly dispersed pulse with spatial chirp and pulse-front tilt
Prism
Angularly dispersed pulse with spatial chirp and pulse-front tilt
Input pulse
Input pulse
Grating

26. GRENOUILLE measures spatial chirp.

Fresnel biprism



Signal pulse frequency
SHG
crystal
Spatially chirped pulse

 
-t0 
+t0
Delay
Frequency
2w+dw
2wdw
+t0
-t0
Tilt in the otherwise symmetrical SHG FROG trace indicates spatial chirp!


27. GRENOUILLE accurately measures spatial chirp.
Measurements confirm GRENOUILLE’s ability to measure spatial chirp.
Positive spatial chirp
Spatio-spectral plot slope (nm/mm)
Negative spatial chirp

28. GRENOUILLE measures pulse-front tilt
Fresnel biprism
Tilted pulse front
Zero relative delay is off to side of the crystal
SHG
crystal
Zero relative delay is in the crystal center
Untilted pulse front
An off-center trace indicates the pulse front tilt!
Delay
Frequency

29. GRENOUILLE accurately measures pulse-front tilt.
Varying the incidence angle of the 4th prism in a pulse-compressor allows us to generate variable pulse-front tilt.
Negative PFT
Zero PFT
Positive PFT

30. Disadvantages of GRENOUILLE
Its low spectral resolution limits its use to pulse lengths between ~ 20 fs and ~ 1 ps.
Like other single-shot techniques, it requires good spatial beam quality.
Improvements on the horizon:
Inclusion of GVD and GVM in FROG code to extend the range of operation to shorter and longer pulses.

31. Reference
[1] D. A. Bender, Precision Optical Caracterization on Nanometer Length and Femtosecond Time Scales. Ph.D dissertation, University of New Mexico, 2002
[2] J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time scale. Academic Press, 1996.