Generation of Coherent UV/VUV

Radiation by Harmonic Conversion

in Gases and Plasmas

The phenomenon of Harmonic Generation (HG) has been studied since the development of powerful pulsed lasers.

The main aim is to convert visible/near infrared radiation

to shorter coherent wavelengths up to the soft-Xray

region.

Brief description of mechanism

o a bound electron is modulated by the laser field

where a is the atomic radius.

o In the weak field approximation

i.e. X_NL<< a

by series development one finds

1) The Harmonic power is proportional to I_L^q

q=harmonic order, I_L laser intensity

2) The Harmonic spectrum is constituted by ODD HARMONICS

o In the strong field regime

i.e. X_NL>»a I_L³10¹³ W/cm²

1) The Harmonic spectrum shows a plateau and the dependence on laser intensity does not follow a simple power dependence.

2) The plateau ends up at a sharp cut-off given by

where

is the so-called ponderomotive potential.

-To the HG mechanism we have to add:

What we did and what we are doing

-HG by Wave-mixing of fundamental and second harmonic

of a Nd-picosecond laser (100 mJ-20 ps)à

ODD and EVEN HARMONICS

-HG dependence on the interaction length

Jet, Uniform density, Hollow fiber

-Characterization of the source in various configurations

Jet, Uniform density, Hollow fiber

HG versus Laser intensity

HG versus Gas Density

-Correlation between harmonic generation and ionization

-Absorption coefficient of gases in VUV region

-Frequency shift of harmonics (Coll.Vrije Univ. Amsterdam)

-Development of Models for HG

Route to VUV SOURCE

Why Wave-mixing ?

Fundamental+II Harmonic

Collinear and parallel polarized

Four Harmonics (III-VI) generated

by mix of laser photons

Large enhancement of HG conversion

by Wave-mixing

-comparison of HG conversion for III h and IX h with fundamental beam

and wave mixing.

Laser Nd-YAG 20 ps EXPLA

Max energy at 1064 nm= 100 mJ

Laser intensities I(1064)»I(532)

Experimental set-up

Gas jet and uniform density modes

Uniform density means that the chamber is filled by gas.

Due to UV gas absorption only harmonics up to X order

are detectable except in Ar where spectrum is limited to IX order.

X harmonic in Ar matches a resonant line.

Typical spectra in Ar,N₂ and CO₂

comparison gas jet vs uniform density

-Uniform density (camera piena it.) enhances the conversion efficiency

by a factor of about 10

due to the increase of the interaction length

Hollow fiber mode

-in the hollow fiber laser beams propagate as a plain wave

along the fiber.

-the maximum coupling power is limited by

the gas breakdown at the fiber entrance.

-in spite of a large enhancement has been observed.

q harmonics and ions correlation in N2 gas jet (III-V)

thick line: ion signal; thin line: harmonic signal; similar results hold in Ar.

positive delay means fundamental beam anticipated as compared to 2w beam.

ion profile follows the harmonic correlation shape;

ionization is not in competition with harmonic generation:

harmonic signal grows up with ion signal within the temporal resolution.

VUV Precision Metrology Study
for Determination of
Frequency Shift in Harmonic Generation

Experimental set-up

Harmonic frequency measured by

Absorption of an atomic resonance line (Ar)

MODEL for Harmonic Generation

We are improving the simple 1 D model

Sketched above.

Since HG does not depend on the bound level structure

We are using a classical 2D-3D picture

For the motion of a bound electron

In the atomic potential

Results of the Model

Xe 100 ps

Kr 100 ps

Note the dominant role of ions

REFERENCES