Transcript High Harmonic Generation
High Harmonic Generation in Gases
Muhammed Sayrac Texas A&M University
Short laser pulse with carrier frequency ω 1
HHG
Gas q ω 1 7 ω 1 5 ω 1 3 ω 1 1 ω 1
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 when a higher intensity is passing the crystal. 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
iknz
n
0
n I
2 So the pulse develops a phase change f
(t)
proportional to the pulse intensity
I(t)
.
E t
p
ikn
2
I z
Pulse intensity vs. time where f (
t
)
kn
2
I
(
t
)
z
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 3 Step 1 Step 2 Tunnel ionization Acceleration in laser field 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
37 th 27 th 25 th 21 st 19 th 17 th 15 th 13 th 11 th Argon refractive index for the wavelengths of high harmonics from 11 th to 65 th
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
𝜆
nm
H2, 950 ms Ar, 105 ms Ne, 30 s
High harmonics
30
W
Spectrum of the HH for Argon
17 th 27 th 23 th 25 47 th 45 th 20 39 th 33 th 45 Lamda Lamda nm 20 25 30 35 40
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.