Introduction to intense laser-matter interaction

Chul Min Kim

Advanced Photonics Research Institute (APRI),

Gwangju Institute of Science and Technology (GIST)

&

Center for Relativistic Laser Science (CoReLS),

Institute for Basic Science (IBS)

Pohang, 22 Aug. 2013

Contents

1. Preliminary Basic parameters: 𝑎0 and 𝑈𝑝 Laser intensity vs material response

2. Strong field physics (SFP) Characteristics Three-step model High harmonic generation and ultrafast spectroscopy Perspectives

3. Relativistic laser-plasma interaction (RLPI) Characteristics Single electron under a laser field Relativistic laser pulse propagation A few examples from APRI/CoReLS research activities Perspectives

𝑎0 represents the laser field

• Vector potential of a given powerLP: 𝑨 𝜏 = 𝐴 cos𝜔𝜏 𝒊

CP: 𝑨 𝜏 =𝐴

2cos𝜔𝜏 𝒊 ± sin𝜔𝜏 𝒋

where 𝜏 = 𝑡 − 𝑧/𝑐 & 𝒌 = 𝒊 × 𝒋

• Normalized vector potential 𝑎0𝑎0 =

𝐴

𝐴0where 𝐴0 =

𝑚𝑒𝑐2

𝑒

𝑎0 =𝑣𝑜𝑠

𝑐=

𝑒𝐸

𝑚𝑒𝜔0

𝑐, 𝑎 ∼ 1 ⟺ 𝑣𝑜𝑠 ∼ 𝑐

Preliminary: Basic parameters: 𝑎0 and 𝑈𝑝

𝐼 and 𝑎0

• Irradiance 𝐼

𝐼 ≡time−averaged power

area= 𝑺 =

𝑐

4𝜋𝑬 × 𝑩

• 𝐼 and 𝑎0

𝑎0 = 0.855 ⋅ 𝐼18 ⋅ 𝜆𝜇𝑚2

where 𝐼18: irradiance in 1018 W/cm2

Ex.) 𝑎0 = 1 & 𝜆 = 800 nm 𝐼 = 2.14 × 1018W/cm2

Preliminary: Basic parameters: 𝑎0 and 𝑈𝑝

Preliminary: Basic parameters: 𝑎0 and 𝑈𝑝

𝑈𝑝 represents the influence of the laser field on the electron

• Ponderomotive potential 𝑈𝑝

Def.) Kinetic Energy of an electron under an EM field

Contributed by1. Transverse oscillation ∝ 𝑎02. Longitudinal oscillation (LP only) ∝ 𝑎0

2

3. Longitudinal drift ∝ 𝑎02

1 only (non-relativistic): 𝑈𝑝 = 𝑚𝑒𝑐2 ⋅

𝑎02

4

1 only (mildly relativistic): 𝑈𝑝 = 𝑚𝑒𝑐2 ⋅ 1 +

𝑎02

2− 1

1+2+3 (strongly relativistic): 𝑈𝑝 = 𝑚𝑒𝑐2 ⋅

𝑎02

4𝑚𝑒𝑐

2 = 0.511 MeV

Preliminary: Laser intensity vs material response

Material response depends on laser intensity

Po

nd

ero

mo

tive

po

ten

tia

l (𝝀~𝝁𝒎

)

APRI/CoReLSNonR bound/free e- non-perturbative nonlinear optics: HHG

/ ATI / …

R e, NonR p- HHG, self-focusing, transparency,

self-steepening, laser wakefields,

indirect p drive

R p, UltraR e, nucleons- Direct p drive, radiation reactions,

photonuclear processes

Quantum vacuum

- pair creation, dielectric vacuum

Material response levels & phenomena

Modified from Tajima et al., Optik &

Photonik, 2010

SFP: Characteristics

Non-perturbative nonlinearity due to free-electron states

𝑈𝑝 ∼ 𝐼𝑝 (eV) where 𝐼𝑝 ionization potential

Laser field ~ atomic field

involvement of free-electron states, leading to insensitive dependence on nonlinear orders

sub-cycle response (structural change, ionization)

For 𝜆~𝜇𝑚

1. 𝐼 ≲ 1010 W/cm2 : perturbative nonlinear optics

2. 𝐼 ∼ 1013W/cm2 : non-perturbative nonlinear optics

3. 𝐼 ∼ 1016W/cm2 : plasma optics

To observe SFP phenomena, an ultrashort pulse duration (∼𝑂(𝜆)) is required not to be overshadowed by low-intensity phenomena. femtosecond lasers

SFP: Three-step model

The basic concepts of SFP are given by the Corkum’s three-step model

Recombination and high

harmonic generation

Tunneling ionization

Above-threshold ionization

(rescattering)

Double ionization

Corkum, Phys. Rev. Lett. 71, 1993

Acceleration

ℏ𝜔𝑋 = 𝐼𝑝 + 𝐾. 𝐸. (≤ 3.17𝑈𝑝)

Odd harmonics only (𝑑 𝑡 = −𝑑(𝑡 +𝑇

2))

Time-frequency distribution

HHG can produce attosecond EUV pulses

SFP: HHG and ultrafast spectroscopy

Phys. Rev. A 72, 033817 (2005)J. Phys. B 39, 3199 (2006)

HHG spectrum shows typical features of non-perturbative nonlinear optics

• Perturbative HHGΓ𝑛 ∝ 𝜎𝑛𝐼

𝑛 where 𝜎𝑛 drops exponentially with 𝑛: sensitive dependence on the nonlinear order

∵ Ψ(bound) is localized?

• Non-perturbative HHGPlateau: insensitive dependence

∵ Ψ(free) is non-localized?

SFP: HHG and ultrafast spectroscopy

Li, Phys. Rev. A 39, 5751 (1989)

Strong HHG with a two-color field

SFP: HHG and attophysics

Phys. Rev. A 72, 033817 (2005)

• 0.6 𝜇J @

21 nm

• Even and

odd

harmonics

Selection and enhancement of short-

path contribution leading to strong

HHGPhys. Rev. Lett. 94, 243901 (2005)

HH + IR

Holography with de Broglie waves

𝑃1s3p(𝑡) (---) & 𝑁2𝜔(𝑡) (─)reconstructed

HHG pulses can probe ultrafast ionization dynamics

SFP: HHG and attophysics

Phys. Rev. Lett. 108, 093001 (2012)

SFP: Perspectives

The basic elements of SFP are understood well, but applications of SFP are still challenging

• Investigation/control of molecular electron dynamics

• Stronger, shorter, shorter-wavelength EUV pulses 𝜆~nm

𝜏 = 80 as @ ~100 eV 𝐸 = 50 nJ @ 13 nm, 𝐸 = 50 nJ @ 13 nm

• From HH-IR pump-probe to HH-HH pump-probe

• More details http://www.attoworld.de/ Krausz, Rev. Mod. Phys. 81, 163 (2009) Winterfeldt, Rev. Mod. Phys. 80, 117 (2008) Gaarde, J. Phys. B 41, 132001 (2008)

RLPI: Characteristics

Relativistic, collective, laser-plasma interaction

1. 𝑈𝑝 ≫ 𝐼𝑝 (eV) instantaneous plasma generation

where 𝐼𝑝 ionization potential

2. 𝑈𝑝 ≫ 𝑘𝑇𝑒 (keV) collective plasma

3. 𝑈𝑝 > 𝑚𝑒𝑐2 (MeV) relativistic interaction

“Relativity in action” in many-body systems (plasma) dominated by collective behavior

Macchi, A Superintense Laser-Plasma Interaction Theory Primer, 2013

𝑎0 = 0.01 (𝐼 = 2.1 × 1014 W/cm2), LP𝑧 ≪ 𝑥 ≪ 𝜆

𝑎0 = 1 (𝐼 = 2.1 × 1018 W/cm2), LP𝜆 ≪ 𝑥 ≲ 𝑧

In relativistic regime, longitudinal motion, non-locality, and inertia increase are introduced

RLPI: Single electron under a laser field

RLPI: Relativistic laser pulse propagation

Relativistic mass increase modifies the refractive index

• (mildly) relativistic refractive index

𝜂 = 1 −𝜔𝑝2

𝜔2𝛾0= 1 −

4𝜋𝑒2𝑛𝑒

𝑚𝑒𝛾0

where 𝜔𝑝2 =

4𝜋𝑒2𝑛𝑒

𝑚𝑒, 𝛾0 = 1 +

𝑎02

2

• 𝑣𝑝 =𝑐

𝜂and 𝑣𝑔 = 𝑐 ⋅ 𝜂

• At the beam center Higher intensity: 𝛾0 ↑, 𝜂 ↑, 𝑣𝑝 ↓, 𝑣𝑔 ↑ More ionization: 𝑛𝑒 ↑, 𝜂 ↓, 𝑣𝑝 ↑, 𝑣𝑔 ↓ Ponderomotive channeling: 𝑛𝑒 ↓, 𝜂 ↑, 𝑣𝑝 ↓, 𝑣𝑔 ↑

Relativistic self-focusing

• Power threshold to overcome diffraction

𝑃𝑐 ≅ 17.5 ⋅𝜔

𝜔𝑝

2

GW

Ex.) 𝑛𝑒 = 1017 − 1019 cm−3, 𝑃𝑐 = 2 − 10 TW

Plasma focuses relativistic pulses

RLPI: Relativistic laser pulse propagation

http://www.mpq.mpg.de/lpg/research/RelLasPlas/Rel-

Las-Plas.html

X

phase front

Relativistic self-transparency

• 𝜂 ≤ 0 reflection

• Cut-off frequency

𝜔𝑐 =𝜔𝑝

𝛾0

• Cut-off frequency lowering

• Pulse cleaning

Plasma can be more transparent to relativistic pulses

RLPI: Relativistic laser pulse propagation

http://www.mpq.mpg.de/lpg/research/RelLasPlas/Rel-

Las-Plas.html

Relativistic self-steepening

• Stronger parts have higher 𝑣𝑔s.

• Formation of an optical shock

Plasma steepens relativistic pulses

RLPI: Relativistic laser pulse propagation

http://www.mpq.mpg.de/lpg/research/RelLasPlas/Rel-

Las-Plas.html

Laser pulses excite plasma oscillations, i.e. laser wakefield

• Optimum excitation condition

pulsewidth ∼1

𝜔𝑝

Relativistic laser pulse propagation

Gibbon, Short Pulse Laser

Interactions with Matter, 2005

Laser wakefield can accelerate electrons up to GeV

• Electrons are accelerated

where 𝐸𝑥 < 0 (width =𝜆𝑝

2)

• 𝐸𝑥 ∼𝑚𝑒𝑐𝜔𝑝

𝑒2 𝛾max − 1 ≥

GV/cm

Cf). RF accelerator, 𝐸𝑥 ∼ MV/cm

• The fundamental speed limit bring coherence and stability: relativistic coherence (Tajima)

RLPI: Relativistic laser pulse propagation

Gibbon, Short Pulse Laser

Interactions with Matter, 2005

ALPS

(APRI Laser Plasma Simulator )

• Particle-in-cell

• Maxwell-Vlasov equations

• 1D3V, 2D3V, and 3D3V

• Written in C

• Lorentz boost implemented

• Under continuous development

CompNet

(Snow White & Dwarfs)

A Large-scale simulation is a must

RLPI: A few examples from APRI/CoReLS research activities

RLPI: A few examples from APRI/CoReLS research activities

Multiple self-injection produces multiple spectral groups

Nature Photonics 2, 571, 2008

RLPI: A few examples from APRI/CoReLS research activities

Seeded acceleration can produce more energetic electrons

arXiv:1307.4159, accepted by Phys. Rev. Lett.

RLPI: A few examples from APRI/CoReLS research activities

The plasma with L/𝜆 ≫ 1 can generate stronger, higher harmonics

Nature Comm. 3, 1231, 2012

Self-induced Oscillating Flying Mirror

RLPI: A few examples from APRI/CoReLS research activities

Intense laser pulse can accelerate protons collectively.

arXiv:1304.0333

Acceleration of protons

by collective electrons

• Relativistic nonlinear physicsRelativistic coherenceExtreme conditionsNon-localityCf.) atomic nonlinear physics

Inherent coherence, limited field strength, mostly local

• Ultrarelativistic laser-matter interaction

Radiation reactionDirect proton drivePhoto-nuclear processes

• Relativistic engineeringParticle/radiation sourcesPlasma as optical components

• Laboratory astrophysicsScaled-downed experiments of astrophysical/early-universe processes

Extreme conditions achievable with lasers

With

conventional

means

With lasers

E (quasistatic) 106 V/cm

(accelerator)

1012 V/cm

B (quasistatic) 106 gauss

(superconducti

ng magnet)

1010 gauss

Temperature 109 K (Tokamak) 1012 K

Pressure 105 bar

(diamond anvil)

1011 bar

RLPI is rich!

RLPI: Perspectives

• PW Ti:Sapphire Laser

(1) Beam line I: 30 fs, 1.0 PW @ 0.1 Hz

(2) Beam line II: 30 fs, 1.5 PW @ 0.1 Hz

• 100-TW Laser: Dt = 30 fs, E = 3 J @ 10 Hz

IBS Center for Relativistic Laser Science

PW Ti:Sapphire Laser