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Supported by NSF and Georgia Institute of Technology
Numerical Simulations of an UltrasimpleUltrashort-Laser-Pulse Measurement
Device─GRENOUILLE
Xuan Liu and R. TrebinoSchool of Physics, Georgia Institute of
Technology, GA 30332 USAArlee V. Smith
Sandia National Laboratories, Albuquerque, NM 87185, USA
Outline
Measure ultrashortpulses using the FROG technique
NumericalSimulations of GRENOUILLE
Simplification of FROG set up: the
GRENOUILLE device
Frequency Resolved Optical Gating (FROG)
SHGcrystal
Pulse to be measured
Variable delay, τ
CameraSpec-
trometer
Beamsplitter
E(t)
E(t–τ)
Esig(t,τ)
FROG measures the full-intensity-and-phase of the pulse.
FROG involves gating the pulse with a variably delayed replica of itself in an instantaneous nonlinear-optical medium and then spectrally resolving the gated pulse vs. delay.
The FROG trace is a spectrogram of E(t). The mathematical expressionfor the FROG trace:
2( , ) ( ) ( ) exp( )FROGI E t g t i t dtω τ τ ω∝ − −∫
g(t–τ) = E(t–τ)
We must invert this integral equation and solve for the unknown pulse.Thisintegral-inversion problem is the 2D phase-retrieval problem, for which the solution exists and is (essentially) unique. And simple algorithms exist for finding it.
Run FROGretrieval program
The FROG Technique
Where is the gate function.
Outline
Measure ultrashortpulses using the FROG technique
NumericalSimulations of GRENOUILLE
Simplification of FROG set up: the
GRENOUILLE device
GRating-Eliminated No-nonsense Observationof Ultrafast Incident Laser Light E-fields
(GRENOUILLE)
FROG:Frequency-
ResolvedOpticalGating
GRENOUILLE:GRating-
EliminatedNo-nonsense
Observation ofUltrafastIncident
LaserLight
E-fields
A single optic (a Fresnel biprism) replaces the entire delay line, anda thick SHG crystal replaces both the thin crystal and spectrometer.
Crossing beams at a large angle maps delay onto transverse position.
Even better, this design is amazingly compact and easy to use, and it never misaligns!
Here, pulse #1 arrivesearlier than pulse #2
Here, the pulsesarrive simultaneously
Here, pulse #1 arriveslater than pulse #2
Fresnel biprism
τ =τ(x)
x
Input pulse
Pulse #1
Pulse #2
The Fresnel Biprism
Very thin crystal creates broad SH spectrum in all directions.Standard autocorrelators and FROGs use such crystals.
VeryThinSHG
crystal
Thin crystal creates narrower SH spectrum ina given direction and so can’t be used
for autocorrelators or FROGs.
ThinSHG
crystal
Thick crystal begins to separate colors.
ThickSHG crystalVery thick crystal acts like
a spectrometer! Why not replace the spectrometer in FROG with a very thick crystal? Very
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.
Crystal Thickness
Yields a complete single-shot FROG. Uses the standard FROG algorithm. Never misaligns. Is more sensitive. Measures spatio-temporal distortions*
Lens images position in crystal (i.e., delay, τ) to horizontal
position at camera
Topview
Sideview
Cylindricallens
FresnelBiprism
ThickSHG
Crystal
Imaging Lens
FT Lens
Camera
Lens maps angle (i.e.,wavelength) to vertical
position at camera
GRENOUILLE Beam Geometry
*Akturk, S., et al., Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE. Opt. Expr., 2003. 11(5): p. 491-501.Akturk, S., et al., Measuring spatial chirp in ultrashort pulses using single-shot Frequency-Resolved Optical Gating. Opt. Expr.,
2003. 11(1): p. 68-78
Testing GRENOUILLE
GRENOUILLE FROG
Mea
sure
dR
etrie
ved
Retrieved pulse in the time and frequency domains
Read more about
GRENOUILLE in the cover
story of OPN, June 2001
Compare a GRENOUILLE measurement of a pulse with a tried-and-true FROG measurement of the same pulse:
Outline
Measure ultrashortpulses using the FROG technique
NumericalSimulations of GRENOUILLE
Simplification of FROG set up: the
GRENOUILLE device
Nonlinear Process in GRENOUILLE
1 2 3ω ω ω+ =
All the plane wave pairs have to satisfy:
1 2 3y y yk k k+ =
3ω1ω
2ω
3k1k
2k
GRENOUILLE uses the second-order nonlinearities of a thick crystal withrelatively tightly focused and broadband pulses. We must allow not only SHGprocesses, but also all possible sum-frequency-generation processes, both collinear and non-collinear.
Sum Frequency Generation
No pump depletion:
3θ2θ
qkr1Pk
r
2Pkr Z
1θ3 3 3
3
1 1 2 21 2
( , ) cos
( ) ( )cos cos
eqz
o o
nkc
n nc c
ω ω θ θ
ω ω ω ωθ θ
Δ = −
−
Phase mismatch:
3 3 3 3
3
1 1 1 2 3 1 3 1 1 1
( , , )exp( )
( , , ) ( , , )
y effz
y y y y
E k z di i k z
z cnE k z E k k z dk d
ω ω
ω ω ω ω
∂= − Δ ×
∂− −
∫∫ %
Zero Delay Spectrum at Different Angles
The deviation angle vs. spectrum plot confirmed that the crystaldoes work like a spectrometer.
Wavelength (nm)
Deviation angle (Rad)
Simulated GRENOUILLE Trace and Its Retrieval
200 fs chirped pulse, The FROG (rms) error was 0.001148.
Conclusion
We numerically simulated the performance of GRENOUILLE, which involves the sum frequency generation of tightly focusedbroadband input beams.
Using the full Sellmeier equation, we can take into account all of the dispersion effects.
In order to improve GRENOUILLE’s spectral resolution when high accuracy is required, we numerically deconvolve the spectralresponse of the device with a efficiency curve that we derive fromour simulations. We show that accurate measurements are easily obtained for properly designed device.