1. ZAKHAROV-70 Chernogolovka, 3 August 2009 1 Collapsing Femtosecond Laser Bullets Vladimir Mezentsev, Holger Schmitz Mykhaylo Dubov, and Tom Allsop Photonics Research Group Aston University Birmingham, United Kingdom The Fifth International Conference SOLITONS COLLAPSES AND TURBULENCE

2. ZAKHAROV-70 Chernogolovka, 3 August 2009 2

3. 3 Where we are Birmingham

4. ZAKHAROV-70 Chernogolovka, 3 August 2009 4 Birmingham J R R Tolkien Villa Park – home of Aston Villa football club

5. ZAKHAROV-70 Chernogolovka, 3 August 2009 5 Aston University

6. ZAKHAROV-70 Chernogolovka, 3 August 2009 6 Outline  What’s the buzz? A.L. Webber, 1970 Who cares?  [Some] experimental illustrations  Tell me what’s happening! – numerical insight in what’s happening  Outlook/Conclusions

7. ZAKHAROV-70 Chernogolovka, 3 August 2009 7 Principle of point-by-point laser microfabrication Laser beam Lens Dielectric (glass) Inscribed structure How to make that point

8. ZAKHAROV-70 Chernogolovka, 3 August 2009 8 Femtosecond micro-fabrication/machining. Micromachining. Mazur et al 2001 Microfabrication of 3D couplers. Kowalevitz et al 2005 3D microfabrication of Planar Lightwave Circuits. Nasu et al 2005 Laser beam Lens Aston 2003-2009 <100 nm

9. ZAKHAROV-70 Chernogolovka, 3 August 2009 9 Experimental set-up V Shift Depth

10. ZAKHAROV-70 Chernogolovka, 3 August 2009 10 Why femtosecond? Operational constraints Inscription region H. Guo et al, J. Opt. A, (2004) E=P cr  self-focusing

11. ZAKHAROV-70 Chernogolovka, 3 August 2009 11 Relatively low-energy femtosecond pulse may produce a lot of very localised damage  Pulse energy E= 1  J. What temperature can be achieved if all this energy is absorbed at focal volume V= 1  m 3 ?  E=C V  V  T  C V = 0.75x10 3 J/kg/K   = 2.2x10 3 kg/m 3  Temperature is then estimated as 1,000,000 K (!) Larger, cigar shape volume 50,000 K Transparency 5,000 K Irradiation 2,000 K

12. ZAKHAROV-70 Chernogolovka, 3 August 2009 12 “core” region “cladding” region Cross sectionWaveguides

13. ZAKHAROV-70 Chernogolovka, 3 August 2009 13 Low loss waveguiding Numerics Experiment

14. ZAKHAROV-70 Chernogolovka, 3 August 2009 14 Curvilinear waveguides – ultimate elements for integral optics Dubov et.al (2009)

15. ZAKHAROV-70 Chernogolovka, 3 August 2009 15 Sub-wavelength inscription Size of hole Careful control of pulse intensity can result in a very small structure, e.g., holes as small as ~50 nm have been created. x Diffraction limited beam waist =  2 Beam profile Intensity I Experimentally determined inscription threshold for fused silica I th = 10÷30 TW/cm 2 Naive observation: Inscription is an irreversible change of refractive index when the light intensity exceeds certain threshold:  n ~ I-I th Inscription threshold

16. ZAKHAROV-70 Chernogolovka, 3 August 2009 16 Grating with a pitch size of 250 nm 10  =5.3  m 25 mm Bragg grating is produced by means of point-by-point fs inscription. Dubov et.al (2006)

17. ZAKHAROV-70 Chernogolovka, 3 August 2009 17 Fs inscription scenario  In fs region, there is a remarkable separation of timescales of different processes which makes possible a separate consideration of  Electron collision time< 10 fs  Propagation+ionisation ~ 100 fs  Recombination of plasma~ 1 ps  Thermoplasticity/densification~ 1  s  Separation of the timescales allows to treat electromagnetic propagation in the presence of plasma separately from other [very complex] phenomena  Plasma density translates to the material temperature as the energy gets absorbed instantly compared to the thermoelastic timescale

18. ZAKHAROV-70 Chernogolovka, 3 August 2009 18 Model EM propagation Plasma

19. ZAKHAROV-70 Chernogolovka, 3 August 2009 19 Further reductions  Envelope approximation  Kerr nonlinearity  Multi-photon and avalanche ionization

20. ZAKHAROV-70 Chernogolovka, 3 August 2009 20 Simplified model Multi-Photon Absorption Avalanche Ionization Plasma Absorption and Defocusing Feit et al. 1977; Feng et al. 1997 Balance equation for plasma density Multi-Photon Ionization Non-Linear Schrödinger Equation for envelope amplitude of electric field  nm K=5,6  nm K = 2

21. ZAKHAROV-70 Chernogolovka, 3 August 2009 21 Physical parameters (fused silica, = 800 nm) = 361 fs 2 /cm – GVD coefficient = 3.2  10 -16 cm 2 /W – nonlinear refraction index = 2.78  10 -18 cm 2 – inverse Bremsstrahlung cross-section  = 1 fs – electron relaxation time – MPA coefficient ( K=5 ) cm 2K /W K /s  eV – ionization energy e.g. Tzortzakis et al, PRL (2001)

22. ZAKHAROV-70 Chernogolovka, 3 August 2009 22 Physical parameters, cont.  at = 2.1  10 22 cm -3 – material concentration  BD = 1.7  10 21 cm -3 – plasma breakdown density It is seen that ionization kicks off when intensity exceeds the threshold I MPA = 2.5  10 13 W/cm 2 – naturally defined intensity threshold for MPA/MPI

23. ZAKHAROV-70 Chernogolovka, 3 August 2009 23 Multiscale spatiotemporal dynamics a b Germaschewski, Berge, Rasmussen, Grauer, Mezentsev,. Physica D, 2001 t y x z

24. ZAKHAROV-70 Chernogolovka, 3 August 2009 24 Initial condition used in numerics Pre-focused Gaussian pulse P in – input power a s = 2 mm f = 4 mm – lens focus distance t p = 80 fs P cr = 2 /2  n n 2 ~ 2.3 MW – critical power for self-focusing Light bullet – laser pulse limited in space and time

25. ZAKHAROV-70 Chernogolovka, 3 August 2009 25 Spatio-temporal dynamics of the light bullet Mezentsev et al. SPIE Proc. 2006, 2007

26. ZAKHAROV-70 Chernogolovka, 3 August 2009 26 What is left behind the laser pulse? Intensity/I MPA Plasma concentration At infinite time light vanishes leaving behind a stationary cloud of plasma

27. ZAKHAROV-70 Chernogolovka, 3 August 2009 27 Plasma profile for subcritical power P = 0.5 P cr

28. ZAKHAROV-70 Chernogolovka, 3 August 2009 28 Plasma profile for supercritical power P = 5 P cr

29. ZAKHAROV-70 Chernogolovka, 3 August 2009 29 Comparison of the two regimes Sub-criticalSuper-critical

30. ZAKHAROV-70 Chernogolovka, 3 August 2009 30 Relation between laser spot size and pitch size of the modified refractive index X.R. Zhang, X. Xu, A.M. Rubenchik, Appl. Phys., 2004

31. ZAKHAROV-70 Chernogolovka, 3 August 2009 31 Microscopic image Experiment Distribution of plasma Numerics Comparison with experiment Single shot (supercritical power P = 5 P cr ) 10  m

32. ZAKHAROV-70 Chernogolovka, 3 August 2009 32 Need of full vectorial approach NLSE-based models do not describe:  Subwavelength structures  Reflection (counter-propagating waves)  Tightly focused beams ( k  ~k z ) Yet another reason:  Finding quantitative limits for NLS-type models

33. ZAKHAROV-70 Chernogolovka, 3 August 2009 33 Implementation principles  Finite Difference Time Domain (FDTD)  Kerr effect  Drude model for plasma  Dispersion  Elaborate implementation of initial conditions and absorbing boundary conditions  Efficient parallel distribution of numerical load (MPI)

34. ZAKHAROV-70 Chernogolovka, 3 August 2009 34 Enormous numerical challenge  Large 3D numerical domain is needed: e.g. 50  50  110 3  High resolution is required to resolve sub-wavelength structures, higher harmonics, transient reflection and scattering: e.g. 20 meshpoints per wavelength and even greater resolution for wave temporal period ~ 2  10 9 meshpoints containing full-vectorial data of EM fields, polarisation and currents  Takes 2+ man-years of software development  A single run to simulate 0.25 ps of pulse propagation takes a day for 128 processors

35. ZAKHAROV-70 Chernogolovka, 3 August 2009 35 How does it look in fine detail z x kzkz kxkx ExEx log 10 (E x 2 ) 1 st 3 rd harmonic

36. ZAKHAROV-70 Chernogolovka, 3 August 2009 36 How does it look in fine detail

37. ZAKHAROV-70 Chernogolovka, 3 August 2009 37 Field asymmetry – E x in different planes x-z plane y-z plane P = 0.2 P cr P = 0.5 P cr P = P cr

38. ZAKHAROV-70 Chernogolovka, 3 August 2009 38 Main component of the linearly polarised pulse near the focus ( E x, P=5P cr, NA=0.2 ) z x

39. ZAKHAROV-70 Chernogolovka, 3 August 2009 39 Generation of longitudinal waves: log 10 (|E z (k)|) kzkz kxkx 1 st 3 rd harmonic

40. ZAKHAROV-70 Chernogolovka, 3 August 2009 40 Where does it matter Green box shows the scale of l  l

41. ZAKHAROV-70 Chernogolovka, 3 August 2009 41 Build-up of plasma

42. ZAKHAROV-70 Chernogolovka, 3 August 2009 42 Build-up of plasma, cont.

43. ZAKHAROV-70 Chernogolovka, 3 August 2009 43 Conclusions+Road Map  Modelling of fs laser pulses used for micromodification is a difficult challenge due to stiff multiscale dynamics  Adaptive modelling can is developed as a versatile approach which makes detailed 3D modelling feasible  Realistic fully vectorial models are required to account for  subwavelength dynamics  reflected/scattered waves  polarisation/vectorial effects  adequate description of plasma  Quantitative limits of NLS-based models are to be established