1. Ariadna study 13-9202: Space-based femtosecond laser filamentation Vytautas Jukna, Arnaud Couairon, Carles Milián Centre de Physique théorique, CNRS École Polytechnique Palaiseau, France Christophe Praz, Leopold Summerer, Isabelle Dicaire Advanced Concepts Team, European Space Agency December 5th, 2014 ESTEC 1

2. What is a filament? Why it is interesting? It generates white light at km distances from the laser. Suitable for applications to detect pollutants in the atmosphere via LIDAR or LIBS techniques. Filamentation is a nonlinear propagation regime: The beam does not spread due to a competition between self-focusing and plasma defocusing. Length ~ 10’s to 100’s m Diameter ~ 100  m Intensity ~ 10 14 W/cm 2 P. Polynkin at al. Phys.Rev.Lett., 103, 123902 (2009); A. Couairon and A. Mysyrowicz, Phys. Rep., 441, 47 (2007); 2

3. Why filamentation from space? J. Kasparian et al., Science 301, 61 (2003); G. Mechain et al., Opt. Commun. 247, 171 (2005); drawbacks of Femtosecond LIDAR from ground Powerful beam will undergo multifilamentation. The backscattered signal is weak. Only local analysis of the atmosphere is possible. High power beam multifilamentation 3 Conceptual femtosecond LIDAR from the ground

4. Why filamentation from space? Advantages of Femtosecond LIDAR from space: Both the filament and the backscattered signal cross an underdense medium (less distortion and less loss) Global solution to atmospheric monitoring 4

5. Retrieved using MSIS model. Decay of different species density 5 Altitude (km) Species density (cm -3 ) CCMC: community Coordinated Modeling Center ρ 0 exp(-z/(7km))

6. Analytical estimation of beam radius dependence on altitude Propagation equation: Assuming that beam shape stays Gaussian: Propagation equation simplifies to: If nonlinear refractive index versus altitude z: 6 Critical power for self-focusing: Simplified propagation equation has a solution:

7. z(km) zczc Direct numerical simulation results departs from moment formalism 7 Propagation equation: Nonlinear refractive index depends on the density of air: Altitude (km) Species density (cm -3 ) Collapse position z c is higher for direct numerical simulation.

8. Filamentation from space (400 km) is possible at desired heights… …with beam radius R 0 ~ 10 - 60 cm and beam powers P ~ 100 GW - 5 TW 8

9. Scaling law for collapse position vs P and beam radius 9 It very closely matches the collapse height obtained by direct numerical simulations.

10. Filamentation is starting further from the ground when beam power increases. 45 cm 10

11. Filamentation is starting further from the ground when beam power increases. 11 Fixed initial beam curvature of 390 km. Beam radius minimum is 390 km away from the laser. Nonlinear effects starts to act when beam power > 1 P* cr cr To achieve minimum of beam radius at desired length z F from the laser, the beam curvature F min can be retrieved by:

12. Collapse point can be varied changing beam radius 2.1TW 12

13. Collapse point can be varied changing beam radius at P=2.1TW 13 Fixed initial beam curvature of 390 km. Beam radius minimum is 390 km away from the laser. Nonlinear effects starts to act when beam power > 1 P* cr,0 Nonlinear region

14. State of the art numerical simulations 14 Unidirectional pulse propagation equation: Optical Kerr effect is described by nonlinear polarization: Current accounting different species: Evolution equations for the density of species: Monochromatic version of propagation equation: Electron density: s = N 2,O 2, … s+ = N 2 +,O 2 +, …

15. Simulations show beam compression, filamentation from space and high intensities Initial beam radius R 0 = 50 cm; Initial beam power P = 143 GW. 15 R 0 =50cm

16. Simulations show beam compression, filamentation from space and high intensities Initial beam width R 0 = 50 cm; Initial beam power P = 143 GW. 16 R 0 =50cm

17. Simulations show beam compression, filamentation from space and high intensities Initial beam width R 0 = 50 cm; Initial beam power P = 143 GW. 17 R 0 =50cm

18. Simulations show beam compression, filamentation from space and high intensities Initial beam radius R 0 = 50 cm; Initial beam power P = 143 GW. Beam compresses 5000 times: from 50 cm to 100 μm radius! R 0 =50cm 18

19. Simulations show beam compression, filamentation from space and high intensities Initial beam radius R 0 = 50 cm; Initial beam power P = 143 GW. Beam compresses 5000 times: from 50 cm to 100 μm radius! Reaches 10 TW/cm 2 over 30 m at 10 km above sea level. 19 Intensity and propagation distance large enough to generate a broadband supercontinuum.

20. 20 Space coordinate Intensity R=50cm R=100μm Space coordinate needs very fine discretization! N=10^5 Space coordinate Intensity z=0 km z=X km R=R 0 R=R 0 /2 N=2N 0 N=N 0 Propagation equation was solved by constantly monitoring beam radius and increasing resolution and reducing box size when needed. Numerical technique to accommodate drastic beam compression

21. Beam-pulse transformation in propagation through atmosphere 21 Spatio-temporal (r,t) intensity profileAngle wavelength (θ,λ) representation Wavelength (nm) Time (ps) Radial coordinate (mm) Transverse wavevector (1/mm) Near field Far field Transverse wavevector and angle relation:

22. Supercontinuum generation is associated to pulse splitting event 22 Spectrum (a), pulse (b) and beam fluence (c) transformations during filamentation. White line in (c) depicts the beam radius.

23. Simulations show the generation of a broadband supercontinuum Initial beam radius R 0 = 50 cm; Initial pulse duration FWHM = 500 fs; Energy = 76 mJ. 23 (B) M. Kolesik et.al, Opt. Express, 13, 10729 (2005).

24. Supercontinuum covers spectral lines for monitoring atmospheric composition, pollutants GOME-2 Newsletter #31 August-October 2012 Numerically calculated filament spectrum 24

25. Ionization of different species 25 Plasma density vs altitude when pulse duration T FWHM 500 fs. The majority of electrons originate from oxygen and nitrogen molecules. The contribution of other species is negligible.

26. Perspectives Control of the collapse via pre-chirp of the pulse, and initial beam curvature. Turbulence effects on filamentation. Filamentation with different initial wavelengths. Full (3+1)D (x,y,t;z) simulations. Different beam shapes. Lab scale experiments. LIDAR and LIBS application analysis. 26

27. Conclusions 1. Laser filamentation from space is possible. 27

28. Conclusions 1. Laser filamentation from space is possible. 2. Numerical techniques were developed: - to accommodate drastic beam changes; - to account for air density profile vs molecule types and altitude. 28

29. Conclusions 1. Laser filamentation from space is possible. 2. Numerical techniques were developed: - to accommodate drastic beam changes; - to account for air density profile vs molecule types and altitude. 3. Conditions for filamentation from orbit: - beam radius R ~ 10 - 60 cm; - beam powers P ~ 100 GW - 5 TW. 29

30. Conclusions 1. Laser filamentation from space is possible. 2. Numerical techniques were developed: - to accommodate drastic beam changes; - to account for air density profile vs molecule types and altitude. 3. Conditions for filamentation from orbit: - beam radius R ~ 10 - 60 cm; - beam powers P ~ 100 GW - 5 TW. 4. Supercontinuum generation from orbit demonstrated. 30

31. Conclusions 1. Laser filamentation from space is possible. 2. Numerical techniques were developed: - to accommodate drastic beam changes; - to account for air density profile vs molecule types and altitude. 3. Conditions for filamentation from orbit: - beam radius R ~ 10 - 60 cm; - beam powers P ~ 100 GW - 5 TW. 4. Supercontinuum generation from orbit demonstrated. 5. Application: multispectral (fs-LIDAR) analysis of the atmosphere. 31