November 10, 2009 / Vol. 7, No. 11 / CHINESE OPTICS LETTERS 971
Theoretical analysis on the eff iciency of optical-optical
double-color double-r esonance multiphoton i onization
Guiyin Zhang (
ÜÜÜ
BBB
ÕÕÕ
)
∗
and Yidong Jin (
ÀÀÀ
)
School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
∗
E-mail: gyzhang65@yahoo.com.cn
Received February 23, 2009
Analytic formula of the efficiency of optical-optical double-color double-resonance multi-photon ionization
(OODR-MPI) is derived from the dynamic rate equation about the interaction of photon and material.
Based on this formula, the influence of characteristic of the pump and probe laser on the ionization
efficiency of (1+2+1) OODR-MPI process is simulated theoretically. It is shown that the pump laser will
affect the ionization efficiency by the number control of the molecules excited to the first resonance state.
The ionization efficiency is decided by the probe laser directly. Both of the excited molecules and ionization
efficiency increase with the intensity and pulse duration of the laser until saturation. It is also found th at
the longer the delay time of the probe laser to the pump one is, t he lower the ionization efficiency would
be. The delay time ought to be smaller than the lifetime of the excited molecule in the practical use of the
OODR-MPI technique.
OCIS codes: 020.4180, 260.5210.
doi: 10.3788/COL20090711.0971.
The technique of multi-photon ionization (MPI) is an
effective method for detecting trace elements and ob-
serving the hig h energy electronic states of atoms and
molecules
[1−5]
. It provides information about not only
the molecular states and molecular structures, but also
the reac tion dynamics of the correlating energy levels. In-
vestigations show that when this technique is used to ob-
serve the high energy levels of the molecule, the molecule
is ionized usually via multi-resonance states due to the
dense rovibronic energy levels. This makes the o bta ined
sp e ctrum very complex. Sometimes it is difficult to a s-
sign the spectral lines. To overco me this defect, the tech-
nique of optical-optical double-resonance MPI (OODR-
MPI) is coming into use. In this method, the pump laser
excites the molecules to the first resonance electronic
state, and the probe laser makes the excited molecules
be ionized via the second resonance state. The char-
acteristic of the second resonance state is observed by
scanning the probe laser. The step for the spectral tran-
sition turns into the first resonance state by the effect of
the pump laser. So the structure of the spectrum is sim-
plified. This is suitable fo r the investigation of the higher
energy levels
[6−11]
. Because the technique of OODR-MPI
is based on the detection of the ions, so how to increase
the ionization efficiency is a main topic for its practical
use. In view of that the dynamic rate equation about the
intera c tion of photon and material is simple, the co nce pt
is clear. T he analytic formula of the ionization efficiency
in the process of OODR-MPI is derived from the rate
equation. Use this formula, the influence of characteris-
tic of the pump and probe laser together with the delay
time of the probe laser to the pump one on the ionization
efficiency is numerically simulated.
In the process of OODR-MPI, the molecule is ionized
by absorbing pump and probe photons and via two inter-
mediate resonance states. This process can be s hown as
a model of four energy levels of Fig. 1. Usually, there is a
time delay of the probe laser to the pump one during the
OODR-MPI experiment. The delay time is longer than
the pulse duration of the pump laser, but shorter than
the relaxation time o f the excited molecules in the first
resonance state. So this double-re sonance process can be
thought as composed of two steps. The first one is the
molecules excited to the first resonance state 2> by ab-
sorbing pump photons. The second is that the excited
molecules ionized by absorbing probe photons and v ia
the second resonance state 3>. The molecules excited
to the first resonance state can de-excited by the pro-
cess of spontaneous radiation, stimulated radiation, and
collision relaxation process. When observing the charac-
teristic of the high electronic states with the technique of
double-resonance, the second resonance state is Rydberg
one usually. Radiation from the molecules of the Ryd-
berg state can be neglected due to the small tra nsition
probability. The laser pulse duration is 35 ps
[5−7]
. It is
much s maller than the pe riod of the collision relaxation
process. So the collision process can also b e neglected in
the excitation process.
The rate equation of the variation of molecule number
density during the first step can be described as
dn
1
dt
= −σ
1
I
m
1
n
1
+ σ
1
I
m
1
n
2
+ k
F
n
2
, (1)
Fig. 1. Dynamic model of the double-resonance multiphoton
ionization.
1671-7694/2009/110971-04
c
2009 Chinese Optics Letters