Collapsing Femtosecond Laser Bullets

transcript

ZAKHAROV-70 Chernogolovka, 3 August 20091

Collapsing Femtosecond Laser BulletsCollapsing Femtosecond Laser Bullets

Vladimir Mezentsev, Holger SchmitzMykhaylo Dubov, and Tom Allsop

Photonics Research GroupAston UniversityBirmingham, United Kingdom

The Fifth International Conference SOLITONS COLLAPSES AND TURBULENCE

Where we are

BirminghamBirmingham

Birmingham

J R R TolkienVilla Park –

home of Aston Villa football club

Aston University

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

Principle of point-by-point laser microfabrication

Laser beamLens

Dielectric (glass)

Inscribedstructure

How to make that point

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

Aston 2003-2009

<100 nm

Experimental set-up

Why femtosecond?Operational constraints

Inscriptionregion

H. Guo et al, J. Opt. A, (2004)

E=Pcr self-focusing

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 m3?

E=CVVT

CV=0.75x103 J/kg/K

= 2.2x103 kg/m3

Temperature is then estimated as 1,000,000 K (!)Larger, cigar shape volume 50,000 K

Transparency 5,000 KIrradiation 2,000 K

370mW 66 um 50 mm per second

0 5 10 15 20 25 30 35

Distanse, um

ase, ra

“core” region

“cladding” region

Cross sectionWaveguides

Low loss waveguiding

Numerics

Experiment

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

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.

Diffraction limitedbeam waist = 2

Beam profile

Intensity I

Experimentally determined inscription threshold for fused silica Ith = 10÷30 TW/cm2

Naive observation:Inscription is an irreversible change of refractive index when the light intensity exceeds certain threshold: n ~ I-Ith

Inscription threshold

Grating with a pitch size of 250 nm

25 mm Bragg grating is produced by means of point-by-point fs inscription.

Dubov et.al (2006)

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

EM propagation Plasma

Further reductions

Envelope approximation

Kerr nonlinearity

Multi-photon and avalanche ionization

Simplified model

Multi-Photon Absorption

AvalancheIonization

Plasma Absorptionand Defocusing

Feit et al. 1977; Feng et al. 1997

Balance equation for plasma density

Multi-PhotonIonization

Non-Linear Schrödinger Equation for envelope amplitude of electric field

nmK=5,6

nmK = 2

Physical parameters (fused silica, = 800 nm)

k = 361 fs2/cm – GVD coefficient

= 3.210-16 cm2/W – nonlinear refraction index

= 2.7810-18 cm2

– inverse Bremsstrahlung cross-section = 1 fs – electron relaxation time

– MPA coefficient (K=5)

cm2K/WK/s eV – ionization energy

e.g. Tzortzakis et al, PRL (2001)

Physical parameters, cont.

at = 2.11022 cm-3 – material concentration

BD= 1.71021 cm-3 – plasma breakdown density

It is seen that ionization kicks off when intensity exceeds the threshold IMPA

= 2.51013 W/cm2 – naturally defined intensity threshold for MPA/MPI

Multiscale spatiotemporal dynamics

Germaschewski, Berge, Rasmussen, Grauer, Mezentsev,. Physica D, 2001

Initial condition used in numerics

Pre-focused Gaussian pulse

Pin – input poweras = 2 mmf = 4 mm – lens focus distancetp = 80 fs

Pcr=2/2 n n2 ~ 2.3 MW – critical power for self-focusing

Light bullet – laser pulse limited in space and time

Spatio-temporal dynamics of the light bulletMezentsev et al. SPIE Proc. 2006, 2007

What is left behind the laser pulse?

Intensity/IMPA Plasma concentration

At infinite time light vanishes leaving behind a stationary cloud of plasma

Plasma profile for subcritical power P = 0.5 Pcr

Plasma profile for supercritical power P = 5 Pcr

Comparison of the two regimes

Sub-critical Super-critical

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

Microscopic imageExperiment

Distribution of plasmaNumerics

Comparison with experimentSingle shot (supercritical power P = 5 Pcr)

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

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)

Enormous numerical challenge

Large 3D numerical domain is needed:e.g. 5050110 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~2109 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

How does it look in fine detail

log10(Ex2)

1st 3rd harmonic

How does it look in fine detail

Field asymmetry – Ex in different planes

x-z plane

y-z plane

P = 0.2 Pcr P = 0.5 Pcr P = Pcr

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

Generation of longitudinal waves: log10(|Ez(k)|)

1st 3rd harmonic

Where does it matter

Green box shows the scale of ll

Build-up of plasma

Build-up of plasma, cont.

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

Collapsing Femtosecond Laser Bullets

Documents