New Physics on the Femtosecond Time Scale

1. New Physics on the Femtosecond Time Scale Bernd Hüttner CphysFInstP DLR Stuttgart

2. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary

3. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary

4. 1. What are the distinctions between ns and fs laser pulse interaction? 1. Local thermal equilibrium vs. Nonequilibrium, Tel  Tph vs. Tel >> Tph 2.Electron-electron scattering time smaller than electron-phonon one 3. Changing of optical and thermal properties, e.g. time dependent 4. Relaxation time is in the order or above the laser pulse duration, PHCE HHCE or diffusive ballistic behavior 5. Intensity, ns: F = 1-10J/cm2, fs: F = 1-10mJ/cm2 → I0(fs)  103·I0(ns)

5. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. New thermal and optical properties 4. Hyperbolic heat conduction equation (HHCE) 5. Summary

6. Experimental result: L=180fs, Fabs=(300±90)J/cm2, EL=1.84eV, d=30nm≈2·dopt 2. Nonequilibrium of electron system Au FD Figure 1: Experimental electron energy distribution function taken from Fann et al.

7. Boltzmann equation Theoretical approach with the photon operator for Gaussian laser pulse development small parameter

8. The first order reads and the 2nd order For the one photon distribution function we find

10. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary

11. Fermi liquid theory: 2. Enhanced importance of electron-electron scattering time Au total ph (300K)= 30fs (fs) e-e Te (K)

12. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary

13. 3. New thermal and optical properties 3.1 Thermal conductivity where the scattering time is given as The integration yields

14. λe= λ0·Te/T0 λ1+ λ2 Wiedemann-Franz λ2 Thermal conductivity of Au for the case of nonlocal thermal equilibrium at fixed Tph=300K: Solid upper curve 1+2, dashed ~Te, dashed-dotted curve 2, and for the local thermal equilibrium Te=Tph=T: solid curve 1, dotted curve LTE, à experimental data taken from Weast

15. But there is more Time dependence of thermal conductivity ballistic behavior t/ << 1: diffusive behavior t/ >> 1:

16. Solid: Al • Dasded-dotted: Ag • = -1 Vertical lines: Electron temperature relaxation time T Al Ag Summary:

17. Molecular dynamics and fluctuation-dissipation theorem Volz – Physical Review Letters 87 (2001) 74301

18. with the specific heat of NFE 3.2 Thermal diffusivity Few examples:

22. What is with ballistic behavior? Einstein relation: Sample thickness vs time of flight for various Au films 50, 100, 150, 200, and 300nm thick. Brorson et al. – Phys. Rev. Lett. 59 (1987) 1962

23. Dielectric function Optical properties We find the electrical current by multiplying the BE with –e·v

24. The integration reads for the first order contribution with the abbreviations

25. Complex refractive index Relations between the optical functions Optical penetration depth and absorption An example: hat-top profile with =1eV, L=500fs, Iabs=10GW/cm2, Iabs=20GW/cm2

26. Surface temperature distributions of gold

27. Optical penetration depth

28. Absorption

29. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary

30. Multiply BE by the product of the energy difference (E - ) times the velocity 4. Hyperbolic heat conduction equation (HHCE) Solving the integrals leads to Cattaneo’s equation with

31. Cattaneo equation Energy conservation Extended two temperature model with

32. Electron temperature as a function of time for a Au-film with thickness of d=30nm ..\..\..\Mathematics\FlexPDE5\Files\Archiv\Different laser profiles.pg5

33. Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. Enhanced importance of electron-electron scattering time 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6.Summary

34. 5. Summary The essential new points on the femtosecond time scale • Nonequilibrium distribution of electrons – deviations from FD distribution • Nonequilibrium between electrons and phonons – Te >> Tph • Changed dependence of temperature of the thermal and electrical conductivity • due to electron-electron scattering time • Both conductivities become implicit and explicit time dependent • Change of optical properties (partly drastic) • Extended two temperature model (HHCE) must be used for the determination of • the electron temperature leading to temperature waves • Ballistic electron transport -

35. Thank you for your attention