High Harmonic Generation in Gases

1. High Harmonic Generationin Gases Muhammed Sayrac Texas A&M University

2. Gas Short laser pulse with carrier frequency ω1 q ω1 7 ω1 5 ω1 3 ω1 1 ω1 HHG

3. 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: • by mechanically knocking the laser cavity mirror, • 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.

4. Kerr lens: fs pulses The refractive index is changing with intensity. So the pulse develops a phase change f(t) proportional to the pulse intensity I(t). Pulse intensity vs. time where

5. Random phases Light bulb Locked phases Ultrashort pulse! Time Time Generating short pulses = Mode-locking Locking vs. not locking the phases of the laser modes (frequencies) Intensity vs. time Intensity vs. time

6. Factors influencing HHG

7. 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.

8. Illustration to the three step model

9. Optical setup for HHG

10. Details of the optical setup • Making a phase shift by using SLM

11. Details of the optical setup McPherson Spectrometer

12. 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:

13. Kerr effect in optics

14. Experimental parameters

15. Kerr effect in optics: estimates

16. 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”

17. Refractive index of Argon 11th 37th 27th 25th 21st 19th 17th 15th 13th Argon refractive index for the wavelengths of high harmonics from 11th to 65th

18. Phase relations in HHG The second phase mismatch contribution is caused by the generated plasma.

19. 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.

20. Results of the phase mismatching Then we calculate the total phase mismatch for several harmonics

21. Absorption of XUV radiation in the gas jet medium .

22. High harmonics H2, 950 ms Ar, 105 ms Ne, 30 s

23. Spectrum of the HH for Argon 17th Power 27th 23th 33th 39th 45th 47th Lamda

24. 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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