2.1.2 Ionization by Multiphoton Absorption
When the laser intensity increases very high, ionization by nonlinear photoabsorption appears to be important. This is called multiphoton ionization (MPI).
The picture of the physics is very clear as shown in Fig. 2.3, where electron at the
grand state is excited to each virtual quantum state and finally obtain enough energy
to be in the free state after pumped up like ladder-like virtual states. MPI is nonlinear
process and observed over a certain threshold of laser intensity, while the
photoionization shown in Fig. 2.3 is linear process and happens when the photon
energy is lesser than the ionization potential. It is, however, not so simple to
calculate, for example, the threshold laser intensity for MPI even for a simplest
atom hydrogen. From the first principle, we have to solve the time-dependent
Schrodinger equation (TDSE):
iħ
∂
∂t
Ψ r, t
ð Þ ¼ À
ħ
2
2m
∇
2 À
e
2
4πε 0 r
À iħA Á ∇ þ
e
2
2m
A
2
!
Ψ r, t
ð Þ
ð2:1:6Þ
Detail discussion of MPI has been given in [2] by solving (2.1.6) numerically. It is
out of the scope of the present book, and therefore let us challenge this MPI problem
based on an intuitive way as shown below. In (2.1.6), the equation to the wave
function of the virtual state is found to satisfy approximately the following relation:
Free state
Photo-ionization
Multi-photon
ionization
Bound state
Virtual state
Fig. 2.3 Schematics of multiphoton ionization process. The black lines are potential structure by
the nucleus, and the electron grand state is shown by solid red line. The vertical states are shown by
red dashed lines so that energy gap is equal to laser photon energy. In the multiphoton ionization,
the electron at the grand state climbs up like a ladder to the ionized state by absorbing multiphotons.
If the photon energy from out is larger than the ionization energy, the electron is easily ionized by
Einstein’s photoelectric effect
32
2 Laser Absorption by Coulomb Collision
When the laser intensity increases very high, ionization by nonlinear photoabsorption appears to be important. This is called multiphoton ionization (MPI).
The picture of the physics is very clear as shown in Fig. 2.3, where electron at the
grand state is excited to each virtual quantum state and finally obtain enough energy
to be in the free state after pumped up like ladder-like virtual states. MPI is nonlinear
process and observed over a certain threshold of laser intensity, while the
photoionization shown in Fig. 2.3 is linear process and happens when the photon
energy is lesser than the ionization potential. It is, however, not so simple to
calculate, for example, the threshold laser intensity for MPI even for a simplest
atom hydrogen. From the first principle, we have to solve the time-dependent
Schrodinger equation (TDSE):
iħ
∂
∂t
Ψ r, t
ð Þ ¼ À
ħ
2
2m
∇
2 À
e
2
4πε 0 r
À iħA Á ∇ þ
e
2
2m
A
2
!
Ψ r, t
ð Þ
ð2:1:6Þ
Detail discussion of MPI has been given in [2] by solving (2.1.6) numerically. It is
out of the scope of the present book, and therefore let us challenge this MPI problem
based on an intuitive way as shown below. In (2.1.6), the equation to the wave
function of the virtual state is found to satisfy approximately the following relation:
Free state
Photo-ionization
Multi-photon
ionization
Bound state
Virtual state
Fig. 2.3 Schematics of multiphoton ionization process. The black lines are potential structure by
the nucleus, and the electron grand state is shown by solid red line. The vertical states are shown by
red dashed lines so that energy gap is equal to laser photon energy. In the multiphoton ionization,
the electron at the grand state climbs up like a ladder to the ionized state by absorbing multiphotons.
If the photon energy from out is larger than the ionization energy, the electron is easily ionized by
Einstein’s photoelectric effect
32
2 Laser Absorption by Coulomb Collision