Transcript High Harmonic Generation

High Harmonic Generation
in Gases
Muhammed Sayrac
Texas A&M University
HHG
Gas
Short laser pulse
with carrier
frequency ω1
q ω1
7 ω1
5 ω1
3 ω1
1 ω1
Generating femtosecond pulses with Kerr-lens
mode-locking
Ti: sapphire crystal was discovered as an appropriate laser medium with a sufficient
broad gain bandwidth to support the generation of femtosecond pulses.
The refractive index increases according to
intensity is passing the crystal.
when a higher
The switching from the CW operation to a mode-locking regime is achieved:
1. by mechanically knocking the laser cavity mirror,
2. by clicking of the prisms in the prism pair that is used inside the laser cavity
for compensation of the light dispersion as we do in our laser.
Kerr lens: fs pulses
The refractive index is changing with
intensity.
E( z, t )  E(0, t ) exp iknz 
n( I )  n0  n2 I
So the pulse develops a phase change f(t) proportional to the pulse intensity I(t).
E( z, t )  E(0, t ) exp ikn2 I (t ) z 
where
f (t )  kn2 I (t ) z
Pulse intensity
vs. time
Generating short pulses = Mode-locking
Locking vs. not locking the phases of the laser modes (frequencies)
Intensity vs. time
Random
phases
Light bulb
Time
Intensity vs. time
Locked
phases
Ultrashort
pulse!
Time
Factors influencing HHG
Three step model
The High harmonic generation is readily explained by three step model.
Initially, the electrons are confined by the Coulomb potential of the
nucleus.
1. When the intensity high enough, electrons can tunnel through the
barrier into the continuum. This is called first step.
2. The laser field accelerates the electron away from the parent ion and
drives it back when the electric field sign is changed. During this
process the electron gains kinetic energy from the laser electric field.
This is step two.
3. In step three, the electron re-combines again to parent ion and emits
its kinetic energy as a high energy photon.
Illustration to the three step model
Step 1
Tunnel ionization
Step 2
Acceleration in laser field
Step 3
Recombination
Optical setup for HHG
Details of the optical setup
•Making a phase shift by using SLM
Details of the optical setup
McPherson Spectrometer
Determination of the experimental parameters: beam
size and intensity
To determine the radius of the beam we used an aperture and measured the power of
the beam limited by this aperture set to different sizes. Beam power passing through a
circle with a radius r is:
Kerr effect in optics
Experimental parameters
Kerr effect in optics: estimates
Phase relations in HHG
The coherence length that is propagation distance of initial wave and the high
harmonic wave of the HHG process is
where Δk is the wave vector mismatch between the fundamental radiation and HH. In
high-harmonic generation, ionization of gas is unavoidable, which turns
the medium into a mixture of plasma and neutral atoms
dispersion in the neutral gas:
Ref. Tadas Balciunas, June 2009 “Design and Implementation of an XUV-pump IR-probe Transient Grating
Experiment”
Refractive index of Argon
37th 27th 25th 21st 19th 17th 15th
13th
11th
Argon refractive index for the wavelengths of high harmonics from 11th to 65th
Phase relations in HHG
The second phase mismatch contribution is caused by the generated plasma.
Phase relations in HHG
The last term is occurring during focusing of the
fundamental Gaussian beam called the Gouy
phase shift, which is the phase difference between
a Gaussian beam and a plane wave. The phase
value changes from -π/2 to π/2.
Results of the phase mismatching
Then we calculate the total phase mismatch for several harmonics
Absorption of XUV radiation in the gas jet medium
Transmission
𝑒
−𝐿𝜅
2
.
𝜆 nm
High harmonics
H2,
950 ms
Ar,
105 ms
Ne,
30 s
Spectrum of the HH for Argon
17th
Power
P ower W
30
27th
39th
25
23th
33th
45th
47th
20
Lamda
Lamda nm
20
25
30
35
40
45
Conclusions
• High harmonic generation in Ar and H2 was
observed.
• The role of absorption, Kerr effect and phase
matching was discussed.
• Experimental parameters of this process were
determined.
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