interaction of laser pulses with atoms and molecules and spectroscopic applications
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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
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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