ZAKHAROV-70 Chernogolovka, 3 August 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

ZAKHAROV-70 Chernogolovka, 3 August

3 Where we are Birmingham

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

ZAKHAROV-70 Chernogolovka, 3 August Aston University

ZAKHAROV-70 Chernogolovka, 3 August 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

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

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

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

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

ZAKHAROV-70 Chernogolovka, 3 August 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

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

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

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

ZAKHAROV-70 Chernogolovka, 3 August 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

ZAKHAROV-70 Chernogolovka, 3 August 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)

ZAKHAROV-70 Chernogolovka, 3 August 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

ZAKHAROV-70 Chernogolovka, 3 August Model EM propagation Plasma

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

ZAKHAROV-70 Chernogolovka, 3 August Simplified model Multi-Photon Absorption Avalanche Ionization Plasma Absorption and Defocusing Feit et al. 1977; Feng et al 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

ZAKHAROV-70 Chernogolovka, 3 August Physical parameters (fused silica, = 800 nm) = 361 fs 2 /cm – GVD coefficient = 3.2  cm 2 /W – nonlinear refraction index = 2.78  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)

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

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

ZAKHAROV-70 Chernogolovka, 3 August 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

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

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

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

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

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

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

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

ZAKHAROV-70 Chernogolovka, 3 August 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

ZAKHAROV-70 Chernogolovka, 3 August 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)

ZAKHAROV-70 Chernogolovka, 3 August Enormous numerical challenge  Large 3D numerical domain is needed: e.g. 50  50   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

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

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

ZAKHAROV-70 Chernogolovka, 3 August 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

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

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

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

ZAKHAROV-70 Chernogolovka, 3 August Build-up of plasma

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

ZAKHAROV-70 Chernogolovka, 3 August 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