ΔE Á Δt !
ħ
2
ð2:1:7Þ
This is the uncertain principle, and it takes time Δt for the electron at the ground
state to excite to the virtual state with its energy ΔE above the ground state.
The size of the electron cloud in a hydrogen atom is approximately 1 Å (¼
10
À8 cm). The ionization energy of the ground state electron is 13.6 eV. Consider the
interaction with laser photons whose wavelength 1.06 μm of glass laser. Then, each
photon energy is about 1 eV. A simplest image of the MPI is that if an electron can
simultaneously absorb 14 or more photons, the electron in the ground state becomes
a free electron.
Let us evaluate coarsely using only uncertainty principle, how much laser
intensity can be expected from multiphoton absorption. Calculate for case of laser
intensity I ¼ 10
15 W/cm
2 . The number of photons that pass through the crosssectional area of hydrogen atoms is:
10
15
1:6 Â 10
À19
 10
À8
À
Á 2 ¼ 6:3 Â 10
17
1=s
½
ð2:1:8Þ
If many photons interact with the wave function of hydrogen atom, as can be seen
from the uncertainty principle, there is a possibility of absorbing laser photons before
virtual energy levels disappear.
Assuming ΔE ¼ 1eV in (2.1.7) as a virtual state that absorbs 1 eV photon, then
the life time of the virtual state is:
Δt ¼
1:05 Â 10
À34
2 Â 1:6 Â 10
À19
¼ 3:3 Â 10
À16
s
½
ð2:1:9Þ
The time required for the electron to climb up the all virtual levels as shown in
Fig. 4.12 is the time τ ion that about 14 photons are absorbed by the electron until it is
ionized:
τ ion ¼ 14 Â 3:3 Â 10
À16
% 5 Â 10
À15
s
½
ð2:1:10Þ
Therefore, if 14 or more photons collide with the wave function of an electron bound
to atom in a time shorter than 5 fs, the bound electron can absorb the energy of the
laser photons from the ground state by the multiphoton absorption. The phenomenon
of absorbing energy of laser via jumping of electron through such virtual levels is
called multiphoton absorption.
The above intuitive evaluation shows that when the laser intensity is 10
15 W/cm
2 ,
in the life time of the virtual levels, the following number of photons interact with
each electron:
2.1 Plasma Generation by Lasers
33
ħ
2
ð2:1:7Þ
This is the uncertain principle, and it takes time Δt for the electron at the ground
state to excite to the virtual state with its energy ΔE above the ground state.
The size of the electron cloud in a hydrogen atom is approximately 1 Å (¼
10
À8 cm). The ionization energy of the ground state electron is 13.6 eV. Consider the
interaction with laser photons whose wavelength 1.06 μm of glass laser. Then, each
photon energy is about 1 eV. A simplest image of the MPI is that if an electron can
simultaneously absorb 14 or more photons, the electron in the ground state becomes
a free electron.
Let us evaluate coarsely using only uncertainty principle, how much laser
intensity can be expected from multiphoton absorption. Calculate for case of laser
intensity I ¼ 10
15 W/cm
2 . The number of photons that pass through the crosssectional area of hydrogen atoms is:
10
15
1:6 Â 10
À19
 10
À8
À
Á 2 ¼ 6:3 Â 10
17
1=s
½
ð2:1:8Þ
If many photons interact with the wave function of hydrogen atom, as can be seen
from the uncertainty principle, there is a possibility of absorbing laser photons before
virtual energy levels disappear.
Assuming ΔE ¼ 1eV in (2.1.7) as a virtual state that absorbs 1 eV photon, then
the life time of the virtual state is:
Δt ¼
1:05 Â 10
À34
2 Â 1:6 Â 10
À19
¼ 3:3 Â 10
À16
s
½
ð2:1:9Þ
The time required for the electron to climb up the all virtual levels as shown in
Fig. 4.12 is the time τ ion that about 14 photons are absorbed by the electron until it is
ionized:
τ ion ¼ 14 Â 3:3 Â 10
À16
% 5 Â 10
À15
s
½
ð2:1:10Þ
Therefore, if 14 or more photons collide with the wave function of an electron bound
to atom in a time shorter than 5 fs, the bound electron can absorb the energy of the
laser photons from the ground state by the multiphoton absorption. The phenomenon
of absorbing energy of laser via jumping of electron through such virtual levels is
called multiphoton absorption.
The above intuitive evaluation shows that when the laser intensity is 10
15 W/cm
2 ,
in the life time of the virtual levels, the following number of photons interact with
each electron:
2.1 Plasma Generation by Lasers
33