Collapsing Femtosecond Laser Bullets
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Transcript of Collapsing Femtosecond Laser Bullets
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
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Where we are
BirminghamBirmingham
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Birmingham
J R R TolkienVilla Park –
home of Aston Villa football club
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Aston University
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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
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Principle of point-by-point laser microfabrication
Laser beamLens
Dielectric (glass)
Inscribedstructure
How to make that point
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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
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Experimental set-up
V
Shift
Depth
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Why femtosecond?Operational constraints
Inscriptionregion
H. Guo et al, J. Opt. A, (2004)
E=Pcr self-focusing
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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
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370mW 66 um 50 mm per second
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
0 5 10 15 20 25 30 35
Distanse, um
Ph
ase, ra
d
“core” region
“cladding” region
Cross sectionWaveguides
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Low loss waveguiding
Numerics
Experiment
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Curvilinear waveguides – ultimate elements for integral optics Dubov et.al (2009)
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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 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
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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)
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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
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Model
EM propagation Plasma
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Further reductions
Envelope approximation
Kerr nonlinearity
Multi-photon and avalanche ionization
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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
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Physical parameters (fused silica, = 800 nm)
2n
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
g
K
atKK
E
55
)(
103.1
– MPA coefficient (K=5)
cm2K/WK/s eV – ionization energy
e.g. Tzortzakis et al, PRL (2001)
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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
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Multiscale spatiotemporal dynamics
a
b
Germaschewski, Berge, Rasmussen, Grauer, Mezentsev,. Physica D, 2001
t
yx
z
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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
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Spatio-temporal dynamics of the light bulletMezentsev et al. SPIE Proc. 2006, 2007
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What is left behind the laser pulse?
Intensity/IMPA Plasma concentration
At infinite time light vanishes leaving behind a stationary cloud of plasma
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Plasma profile for subcritical power P = 0.5 Pcr
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Plasma profile for supercritical power P = 5 Pcr
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Comparison of the two regimes
Sub-critical Super-critical
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Relation between laser spot size and pitch size of the modified refractive indexX.R. Zhang, X. Xu, A.M. Rubenchik, Appl. Phys., 2004
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Microscopic imageExperiment
Distribution of plasmaNumerics
Comparison with experimentSingle shot (supercritical power P = 5 Pcr)
10 m
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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
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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)
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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
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How does it look in fine detail
z
x
kz
kx
Ex
log10(Ex2)
1st 3rd harmonic
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How does it look in fine detail
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Field asymmetry – Ex in different planes
x-z plane
y-z plane
P = 0.2 Pcr P = 0.5 Pcr P = Pcr
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Main component of the linearly polarised pulsenear the focus ( Ex , P=5Pcr , NA=0.2 )
z
x
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Generation of longitudinal waves: log10(|Ez(k)|)
kz
kx
1st 3rd harmonic
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Where does it matter
Green box shows the scale of ll
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Build-up of plasma
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Build-up of plasma, cont.
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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