Alignment dependence of HHG from N2, O2 and CO2

Dept. of Physics, KSU

Oct. 19, 2005

A.T. Le, X.M. Tong, and C.D. Lin

Outlines

• Introduction

• MO-ADK: a simplified picture

• HHG in N2 and O2: a comparison

• Minima in HHG: interference effect

• Case of CO2

• Summary and outlook

Ionization

23rd HHG

N2

O2

CO2

N2 and O2: HHG and ionization are in phase

CO2 is different!!!

N2 and O2: HHG and ionization are in phase

CO2 is different!!!

Kanai et al, Nature, 435, 470 (2005)

Laser parameters: 50fs, 800nm, 2x1014W/cm2

Temperature ~ 80K

Vozzi et al, PRL 2005Vozzi et al, PRL 2005

800nm, 30fs

250 J

Inversion found at harmonic 33

Inversion found at harmonic 33

Two-Point Emitter model

MO-ADK ionization rates of O2 and N2

• Strong dependence on alignment;

• For N2 good agreement with Litvinyuk et al, PRL 2003;

• Agrees well with recent experiments at KSU;

• Strong dependence on alignment;

• For N2 good agreement with Litvinyuk et al, PRL 2003;

• Agrees well with recent experiments at KSU;

Our initial goals

• Analytic form for angular dependence (both ionization and HHG)?

• Why CO2 is different?

Pn(-x)=(-1)n Pn(x)

For homonuclear diatomic molecules:

HHG: Three-Step model

1. Tunneling ionization: depends on orientation

2. Propagation in laser field

3. Recombination: depends on orientation

Question:

Is the alignment dependence of ionization is more important?

Question:

Is the alignment dependence of ionization is more important?

Ionization: MO-ADK theory

Main contribution from m’=0 Main contribution from m’=0

Tong et al, PRA 2002

0.25 0.5 0.75 1 1.25 1.5

1

2

3

4

5

6

7

)(cos78.02

02.2)0'( 22

5 PmB

N2

Numerical results from Zhao et al, PRA 2003

N2 case

0.25 0.5 0.75 1 1.25 1.5

0.1

0.2

0.3

0.4

0.5

0.25 0.5 0.75 1 1.25 1.5

2.5

5

7.5

10

12.5

15

17.5

O2

CO2

0max 40

0max 30

Numerical resultsZhao et al, PRA 2003

Numerical resultsZhao et al, PRA 2003

Analytical result with only m’=0

Molecular Orbital from GAMESS

Molecular Orbital from GAMESS

HHG: Lewenstein model

)coscos()2/.cos(

)cossin()2/.sin(

21

21

pRRp

pRRp

)(cos)()coscos(

)(cos)()cossin(

22

1212

ll

ll

PaBa

PaAa

)(cos)()coscos(

)(cos)()cossin(

22

1212

ll

ll

PaBa

PaAa

0.5 1 1.5 2 2.5 3

-0.75

-0.5

-0.25

0.25

0.5

0.75

0.5 1 1.5 2 2.5 3

0.2

0.4

0.6

0.8

1sin(1*cos(θ)),

with 1 term

cos(1.5*cos(θ)),

with 2 terms

Present results Zhou et al (PRA 2005)

Discrepancies foundDiscrepancies found

Numerical results

Comparison for different intensities

Need to include depletion for high intensity

cutoff ~ 47

N2

• 800nm;

• 30fs, Gaussian envelope;

• 3x1014 W/cm2

N2

• 800nm;

• 30fs, Gaussian envelope;

• 3x1014 W/cm2

Typical result of HHG

Note the even orders

Note the even orders

Evidence of interference effect

Now odd orders!

Symmetry

Now odd orders!

Symmetry

Go one step further: ionization OR recombination at one center.

What are the results?

Go one step further: ionization OR recombination at one center.

What are the results?

Note the even orders

Note the even orders

More evidence

N2

800nm; 30fs

3x1014 W/cm2

cutoff ~ 47

Dependence on the alignment angle

N2

800nm, 30fs

5x1014 W/cm2

cutoff ~ 71

Positions of the minima not changed

Positions of the minima not changed

High intensity

N2

1064nm, 30fs

3x1014 W/cm2

Minima scale with wavelength

Minima scale with wavelength

Long wavelength

N2

800nm; 30fs

3x1014 W/cm2

N2

800nm; 30fs

3x1014 W/cm2

Position of the minima moved towards higher order, as orientation angle increases

Minima moving away

Lein et al, PRL 2002Lein et al, PRL 2002

Solved numerically 2D Schrodinger equation for H2

+

Lein et al, PRA 2002Lein et al, PRA 2002

Positions of the Max & Min are given by:

Two-point emitter model

Numerical data from 2D H2+ and H2

NOTE:

• Min & Max are interchanged for different symmetries

• Controversy about

NOTE:

• Min & Max are interchanged for different symmetries

• Controversy about

Blue: without atomic potential

Red: with atomic potential

N2

Blue: without atomic potential

Red: with atomic potential

O2

Problem with large angles?

Problem with large angles?

Zimmermann et al, PRA 2005Zimmermann et al, PRA 2005

Weak-field approx. for recombination

0

1

2

0 2 4

Minima: x

Maxima: +

N2

Very complicatedVery complicated

CO2 O2

R=0.232nm R=0.121nm

Quantum chemistry GAMESS code & MOLEKEL plotQuantum chemistry GAMESS code & MOLEKEL plot

CO2

Almost no contribution from C-center (small polarization term)

Almost no contribution from C-center (small polarization term)

cutoff ~ 31

Preliminary results

No significant differences between these molecules!??

No significant differences between these molecules!??

Summary & Outlook

1. HHG is max at 0o for N2 and 45o for O2

2. Minima in HHG due to interference effect

• Resolve the discrepancies

• Case of CO2

• Finish analytical approach

Next:

N2 HOMO in momentum spaceN2 HOMO

N2 HOMO in momentum space

s-wave contribution

N2 HOMO: s-wave contribution

N2 HOMO in momentum space

p-wave contributionN2 HOMO: p-wave contribution

dy dz

Higher intensity:

N2

800nm, 30fs

5x1014 W/cm2

Higher intensity:

N2

800nm, 30fs

5x1014 W/cm2