High Harmonic Generationin Gases

Muhammed Sayrac

Texas A&M University

HHG

Short laser pulse with carrier

frequency ω1

q ω1

 

7 ω1

 

5 ω1

 

3 ω1

 1 ω1

 

Gas

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 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.

The refractive index  increases according to                                    when a higher intensity is passing the crystal.  

Kerr lens:  fs pulses

0 2( )n I n n I

 The refractive index is changing with intensity.

( , ) (0, ) expE z t E t iknz

So the pulse develops a phase change (t) proportional to the pulse intensity I(t).

2( , ) (0, ) ex ( )pE z t E t ikn I zt Pulse intensity vs. time

where 

2( )) (knt I zt

Generating short pulses = Mode-lockingLocking vs. not locking the phases of the laser modes (frequencies)

Random phases

Light bulb

Intensity vs. time

Ultrashort pulse!

Locked phases

Time

Time

Intensity vs. time

Factors influencing HHG

Three step modelThe 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.

 

Step 1 Step 2 Step 3

Recombination Acceleration in laser field Tunnel ionization

Illustration to the three step model

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

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 turnsthe medium into a mixture of plasma and neutral atoms

Phase relations in HHG

dispersion in the neutral gas:

Ref. Tadas Balciunas, June 2009 “Design and Implementation of an XUV-pump IR-probe Transient Grating

Experiment”

Argon refractive index for the wavelengths of high harmonics from 11th to 65th

Refractive index of Argon

11th 13th 15th 17th 19th 21st 25th 27th 37th 

The second phase mismatch contribution is caused by the generated plasma. 

Phase relations in HHG

Phase relations in HHGThe 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.

Then we calculate the total phase mismatch for several harmonics

Results of the phase mismatching

Absorption of XUV radiation in the gas jet medium

.

 

Transm

issio

n

𝑒−𝐿𝜅2ൗ�

𝜆 nm

Ar, 105 ms

Ne,30 s

H2, 950 ms

High harmonics

Spectrum of the HH for Argon

 

20 25 30 35 40 45L amda nm

20

25

30

P ow er WPower

Lamda

47th 

45th 39th 

33th 27th  23th 

17th 

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.

THANK YOU