Interaction of laser pulses with atoms and molecules and spectroscopic applications

Raman scattering

1 12 3

Vibrational levels

Pump StokesPump

anti-Stokes

Raman frequencies in spectrum due to modulation of scattered light by molecular vibrations

P q E dIc

d P dt n

dI I N d

d q d

( ) , [( / ) ]1

4 32 2 2

0

2

( ' ) ( ' )

( ' ) ' 4

P ' 0 Inelastic scattering

Electronic-resonance Raman scattering

n transitioelectronic of

frequency resonance is where iiL ,

i iLisI

221

t coefficien absorption sI

Characteristic Raman shifts for different bonds

A. Fadini and F.-M.Schnepel, Vibrational spectroscopy (Wiley, New York, 1989).

Impulsive excitation of low-frequency modes and pump-probe study of oscillations of molecules and n-particles

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0 =72cm-1=28cm

-1

=20fs

=50fs=100fs

Spe

ctra

l com

pone

nt (

norm

aliz

ed)

Frequency (cm-1)

Schematic of femtosecond spectroscopy in a pump –probe configuration

Delay

Pump

Probe

DetectorSample

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Am

plitu

de,

a.u

.

Delay time, picosec

0 250 500 750 10000.00

0.05

0.10

0.15

0.20

0.25

Frequency, GHz

Am

plit

ud

e, a

.u.

Temporal response Spectrum

Femtosecond pump-probe spectroscopy of n-particles (d~15 nm)

N-particle breathing mode oscillations

The same principle is applicable for n-particles and molecules

Schematic of the energy levels and optical transitions in CARS

1 12 3

1 2, waves are all sent

Example: wave interaction in CARS,Phase matching conditions

Requirement of phase matching condition k3=k1+k1’-k2; three waves create polarization wave (w3,k3)

Coherent anti-Stokes Raman spectroscopy (CARS)

Plane waves signal

2 2

2 2 1

2

2 /

) 2 / sin( ~

kL

kL L I I I CARS CARS

where

CARS i d d

2 1

1 ~

2 1 2 k k k

For gaussian beams

2

~ 2 a

L confocal parameter

2

2 2 1

2 2

d d

P P P CARS

But the CARS signal is limited by limitations on the intensity!!!The object can be destroyed.

- nonlinear susceptibility tensor

- wave vector mismatch

Physical values and processes for strong-field laser physics

atomic field strength (Hydrogen atom)

Intensity required for ionization (Ar)

Example: bandwidth requirement for an attosecond pulse:

Typical atomic time-scale: Bohr orbit time

Typical displacement of an ionized electron in the laser field

𝐸𝐻=6.1×109 𝑉𝑐𝑚

𝐼 ≈ 1014 𝑊𝑐𝑚2

Corresponding field strength

𝐸=1.9×108 𝑉𝑐𝑚

𝜏=2𝜋𝑎𝑐

=152𝑎𝑡𝑡𝑜𝑠𝑒𝑐𝑜𝑛𝑑𝑠

𝑥0=𝑒𝐸𝑚𝜔2=2.7𝑛𝑚

𝜏 [𝐹𝑊𝐻𝑀 ]=50𝑎𝑠𝜏×𝛥 𝑓 ≥ 0.44

𝛥 𝑓 =0.44 /50𝑎𝑠=−>𝜆≈ 30𝑛𝑚

h𝜈 [800𝑛𝑚 ]=1.55𝑒𝑉

New phenomena: ionization, high harmonic generation (HHG), fragmentation of molecules.

Ionization: Multiphoton and tunnel MECHANISMS

Leonid Keldysh, 1964: adiabaticity parameter

multiphoton ionization,

probability

tunnel ionization, probability

𝛾=√ 𝐼𝑝2𝑈𝑝

𝛾 2≫1 ,

¿𝛾 2≪ 1 , 𝑃 ∝exp [− 2 (2𝐸𝑖 )

2/3

3𝐹 ]Atomic system of units𝑐=𝑚𝑒=ℏ=1

L V Keldysh, Soviet. Physics – JETP, 20(5), 1307 (1964) [Cited 3341 times!]

Multiphoton Ionization

𝑛ℏ𝜔+𝐴→𝑒−+𝐴+¿ ¿ photons ionize an atom: Kinetic energy of the electron:

𝐾𝐸=𝑛ℏ𝜔−𝑉 𝐼𝐸

𝑃 ( 𝐼 )∝𝐼𝑛Ionization probability from perturbation theory:𝛾≫1Multiphoton condition

(from Keldysh theory):

Photoelectric effect

(C)

Multiphoton Ionization Above Threshold Ionization (ATI)

Courtesy of Nathan Hart and Gamze Kaya

Ionization of Argon by femtosecond pulses

Ionization of Ar, 200 fs pulses from a Ti:sapphire laser (800 nm). The theoretical ion yields are, from left to right, calculatedfrom Szoke’s model (Perry et al 1988), Perelomov, Popov, Terent’ev, 1966 (PPT) model, Ammosov, Delone Kraynov, 1986 (ADK) theory and strong-field approximation (SFA, Reiss, 1980).

𝐴𝑟 +¿ ¿𝐴𝑟 +¿ ¿

𝐴𝑟 2+¿¿

𝐴𝑟 3+¿¿𝐴𝐷𝐾

𝑃𝑃𝑇

S F J Larochelle, A Talebpoury and S L Chin,J. Phys. B: At. Mol. Opt. Phys. 31, 1215 (1998)

Multiple ionization of Ar at higher peak intensities of 200 fs pulses from a Ti:sapphire laser (800 nm).

S Larochelle, A Talebpoury and S L Chin, J. Phys. B: At. Mol. Opt. Phys. 31 1201 (1998)

Ar

Dynamics of Ar ionization by femtosecond pulses

Calculated ionization levels in argon for a 19 fs laser pulse at a peak laser intensity of , using ADK rates: laser pulse envelope (black); Ar(blue); (green); (red); (pink); (brown). The right axis shows the predicted HHG cutoff energy for the chosen laser intensity, calculated from the cutoff rule (Ecutoff=Ip+ 3:2Up).

Arpin et al. PRL 103, 143901 (2009)

Electron trajectories after ionization

Cut off for high harmonic generation (HHG)

Cut off energy for HHG

𝑈𝑝 [𝑒𝑉 ]=𝑚2 (𝑒𝐸𝜔 )

2

=9.33 ×10− 14 𝐼 [ 𝑊𝑐𝑚2 ] (𝜆 [𝜇𝑚 ] )2

h𝜈 [800𝑛𝑚 ]=1.55𝑒𝑉

𝐸𝑐𝑢𝑡 𝑜𝑓𝑓=𝐼𝑝+3.17𝑈𝑝

𝑁𝐻𝐻𝑐𝑢𝑡 𝑜𝑓𝑓 [ 𝐴𝑟 , 1014𝑊 /𝑐𝑚2]=¿𝑁𝐻𝐻𝑐𝑢𝑡 𝑜𝑓𝑓 [ 𝐴𝑟 , 1015𝑊 /𝑐𝑚2]=¿

Energy of electron returning parent atom

HHG in Argon (15.6 eV)

• Cutoff energy is at 23rd harmonic, eV (34.8 nm)• The laser power at 800 nm is 930 mW and a pulse duration 50 fs.

4 0 5 0 6 0 7 0 8 00

2 0

4 0

6 0

8 0

W a v e l e n g t h n m Inte

nsi

tyarb.un

it11th

13th

15th 17th 19th 21th

(b)

19th21st 17th 15th

13th 11th23d cutoff

Three step model

Step 1 Step 2 Step 3

Recombination Electron acceleration in laser field

Tunnel ionization

XUV

P. B. Corkum “Plasma perspective on strong field multi-photon ionization”P. B. Corkum, F. Krausz, “Attosecond Science”S. Haessler et. al., “Attosecond imaging of molecular electronic wavepackets”

Courtesy Muhammed Sayrac

Experiments on H2+ in intense laser fields

(simplest molecule)• Photodissociation: H2

+ + nhν H+ + H

• Coulomb explosion: H2+ + nhν H+ + H+ + e-

(Pavicic, 2005)At intensities (>1012 W/cm2) the coupling between 1sσg and 2pσu becomes very strong