of Physics, Stanford University
Stanford Linear Accelerator Center
What is High Harmonic Generation?
High harmonic generation describes the
conversion of laser radiation from one fixed frequency to high
harmonics of that frequency. This happens in a atomic or molecular jet
(white cloud coming out of the orange nozzle in the movie).
We need high laser fields to drive the process and therefore we focus
intense red fs-pulses onto the gas jet. After the pulse (travelling from
right to left) passes the jet, it has blue colored components. The
radiation in this pulse extends into the ultraviolet and vacuum
The details of the laser matter interaction in the gas jet:
laser pulse has a strong electromagnetic field, where the electric
field is much larger than the magnetic field. The electric field of the
laser can get as strong as the field between electron and proton.
The ionization-recollision happens on each half cycle of the laser
pulse. The spectra generated on each half cycle are added coherently,
which leads to a structuring of the emitted spectrum into odd
harmonics. Therefore, the process is called high harmonic generation.
With strong laser pulses light up to the 51st harmonic and beyond is
visible, reaching up to the soft Xray range.
on the left side summarizes the details of the high harmonic generation
process. The upper row (a-c) represents a classical point of view, the
bottom row depicts the same steps with the quantum wave function (d-f).
The electron sits unperturbed in the Coulomb
potential (black line) of an atom. The laser field is very strong (~1010V/m)
and adds the red potential. In the superposition, the potential is bend
down and the electron can tunnel through the barrier. The ionization is
the highest at the field maxima (a+d).
The electron is now
accelerated in the laser field to energies of several eV. For distinct
ionization times, the electron returns and recollides with the atom
from which it was born (b+e).
Upon recollision, the
electron kinetic energy is transferred into photons. The maximal
kinetic energy of the electron is 3.2 times the ponderomotive potential
Up=e2E2/(4mew2laser), where E is the electric field of the laser, e is the electron charge, me its mass and wlaser the laser angular frequency. The recollsion leads to the emission of a single, very broad light spectrum (c+f).
What do we find out?
quantum mechanics, the recolliding electron is represented as a de
Broglie wave. This wave shifts over the molecular or atomic orbital,
from which it was originally ionized. During this shifts, interferences
occur, that modulate the amplitude and phase of the harmonic radiation.
graph exemplifies the interference on the highest molecular orbital
(HOMO) of the CO2 molecule (the two lobes in the middle). The
recolliding wave is shown at two different times. It interferes with
the HOMO and thereby creates a dipole that radiates the harmonics. We
are tracing the interferences from the harmonic spectra, measuring both
their amplitude an phase.
The molecular features shape the emitted high harmonic light, opening the perspective to shape attosecond pulses.
Furthermore, the harmonic generation process can be used itself by observing short time electronic dynamics in the molecule.
How do we use High Harmonic Generation?
In our lab, we study high harmonic
generation on molecules, that means we have molecules in the gas jet
instead of atoms. Molecules have more degrees of freedom than atoms
(the vibrations and rotations), and we can use them to shape the high
harmonic spectrum. To determine the electronic structure of the
molecule, we need to fix their axes in space by molecular alignment.
Molecular Alignment and High Harmonic Generation
Usually, the internuclear axis of molecules randomly oriented at any
given time. By the interaction with a strong infrared, nonresonant
laser pulse (shown red), all internuclear axes in an ensemble can be
align in one direction. The laser induces a dipole in the molecules,
that is strongest parallel to the internuclear axis. This dipole aligns
with the linear polarization of the laser field, and thereby forces the
molecules into alignment.
Classically, the molecules will align best shortly after the laser pulse has passed.
||Due to theier small size, the
molecules do not follow the laws of classical physics. A quantum
mechanical description describes their behaviour. In the quantum world,
the alignment of the wave packet occurs not only one time, but
repeatetly in so called revivals. The graph on the left side shows the
alignment as a function of time. The alignment
parameter <cos2θ> is 1/3
for an isotropic
ensemble. It reaches maximal and minimal values at the so called half and full revival denoted by Trev/2 and Trev.
The revivals are typical for a coherent superposition of anharmonic
quantum states and are very similar in anharmonic vibrational
|We perform the experiment in a pump-probe fashion: a first pump-pulse
aligns the molecules and a second, stronger pulse creates high
harmonics on the molecules.
The spectra are saved as a function of pump-probe delay, and we see a
modulation in time of the harmonic intensity with the alignment. We use
the modulation as a function of wavelength to calculate the
interference structures in the harmonic generation.