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Collapsing Femtosecond Laser Bullets

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. Where we are. Birmingham. Birmingham.

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Collapsing Femtosecond Laser Bullets

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  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. Where we are Birmingham

  3. Birmingham Villa Park – home of Aston Villa football club J R R Tolkien

  4. Aston University

  5. 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

  6. Principle of point-by-point laser microfabrication How to make that point Lens Laser beam Inscribedstructure Dielectric (glass)

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

  8. Shift V Depth Experimental set-up

  9. Inscription region Why femtosecond?Operational constraints H. Guo et al, J. Opt. A, (2004) self-focusing E=Pcrt

  10. Relatively low-energy femtosecond pulse may produce a lot of very localised damage • Pulse energy E=1 mJ. What temperature can be achieved if all this energy is absorbed at focal volume V=1 mm3? • E=CVrVDT • CV=0.75x103 J/kg/K • r = 2.2x103 kg/m3 • Temperature is then estimated as 1,000,000 K (!) Larger, cigar shape volume 50,000 K Transparency 5,000 K Irradiation 2,000 K

  11. Waveguides Cross section “cladding” region “core” region

  12. Low loss waveguiding Numerics Experiment

  13. Curvilinear waveguides – ultimate elements for integral optics Dubov et.al (2009)

  14. Inscription threshold Sub-wavelength inscription Intensity I Naive observation: Inscription is an irreversible change of refractive index when the light intensity exceeds certain threshold: Dn ~ I-Ith Diffraction limited beam waist = l/2 Beam profile x Careful control of pulse intensity can result in a very small structure, e.g., holes as small as ~50 nm have been created. Size of hole Experimentally determined inscription threshold for fused silica Ith = 10÷30 TW/cm2

  15. Grating with a pitch size of 250 nm Dubov et.al (2006) 10L=5.3 mm 25 mm Bragg grating is produced by means of point-by-point fs inscription.

  16. 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 ms • 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

  17. Plasma Model EM propagation

  18. Further reductions • Envelope approximation • Kerr nonlinearity • Multi-photon and avalanche ionization

  19. Simplified model Feit et al. 1977; Feng et al. 1997 Non-Linear Schrödinger Equation for envelope amplitude of electric field 800 nm K=5,6 267 nm K = 2 Plasma Absorptionand Defocusing Multi-Photon Absorption Balance equation for plasma density AvalancheIonization Multi-Photon Ionization

  20. Physical parameters (fused silica, l= 800 nm) e.g. Tzortzakis et al, PRL (2001) = 361 fs2/cm – GVD coefficient = 3.210-16 cm2/W – nonlinear refraction index = 2.7810-18 cm2 – inverse Bremsstrahlung cross-section t = 1 fs – electron relaxation time – MPA coefficient (K=5) cm2K/WK/s = 7.5 eV – ionization energy

  21. Physical parameters, cont. rat= 2.11022 cm-3 – material concentration rBD= 1.71021 cm-3 – plasma breakdown density = 2.51013 W/cm2 – naturally defined intensity threshold for MPA/MPI It is seen that ionization kicks off when intensity exceeds the threshold IMPA

  22. Multiscale spatiotemporal dynamics Germaschewski, Berge, Rasmussen, Grauer, Mezentsev,. Physica D, 2001 t y a x b z

  23. Initial condition used in numerics Pre-focused Gaussian pulse Pin – input power as= 2 mm f = 4 mm – lens focus distance tp = 80 fs Pcr=l2/2p n n2~ 2.3 MW – critical power for self-focusing Light bullet – laser pulse limited in space and time

  24. Spatio-temporal dynamics of the light bullet Mezentsev et al. SPIE Proc. 2006, 2007

  25. What is left behind the laser pulse? Intensity/IMPA Plasma concentration At infinite time light vanishes leaving behind a stationary cloud of plasma

  26. Plasma profile for subcritical power P = 0.5 Pcr

  27. Plasma profile for supercritical power P = 5 Pcr

  28. Comparison of the two regimes Sub-critical Super-critical

  29. Relation between laser spot size and pitch size of the modified refractive index X.R. Zhang, X. Xu, A.M. Rubenchik, Appl. Phys., 2004

  30. Comparison with experimentSingle shot (supercritical power P = 5 Pcr) 10 mm Distribution of plasma Numerics Microscopic image Experiment

  31. Need of full vectorial approach NLSE-based models do not describe: • Subwavelength structures • Reflection (counter-propagating waves) • Tightly focused beams ( k~kz) Yet another reason: • Finding quantitative limits for NLS-type models

  32. 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)

  33. Enormous numerical challenge • Large 3D numerical domain is needed: e.g. 5050110l3 • 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109 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

  34. kx kz 1st 3rd harmonic x z How does it look in fine detail log10(Ex2) Ex

  35. How does it look in fine detail

  36. Field asymmetry – Ex in different planes P = 0.5 Pcr P = Pcr P = 0.2 Pcr x-z plane y-z plane

  37. x z Main component of the linearly polarised pulsenear the focus ( Ex , P=5Pcr , NA=0.2)

  38. kx kz Generation of longitudinal waves: log10(|Ez(k)|) 1st 3rd harmonic

  39. Where does it matter Green box shows the scale of ll

  40. Build-up of plasma

  41. Build-up of plasma, cont.

  42. 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

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