Population inversion and pumping
threshold condition
From the equation of small signal gain one can conclude that the
population inversion required for reaching the lasing threshold:
At threshold the population inversion
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Dr. Hazem Falah Sakeek 3
Note that the lasing threshold will be readily when g(v) is
maximum at v = vo corresponding to the center of the
natural linewidth.
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Dr. Hazem Falah Sakeek 4
Pumping power required to reach
threshold condition
To find the power required for
a
4-level laser system to reach
the threshold we will use the
rate equations.
First we assume that E1>>KT
so the thermal population of
the energy level 1 is negligible.
Second we assume that the
population of the ground state
does not change during lasing
action.
R1 and R2 are the rate of
pumping then the rate
equation for the population for
the change in N2 and N1
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In steady state condition dN2/dt = dN1/dt = 0 ( we assumed that
g1=g2 and R1=0)
By solving the above two rate equations we get
and hence
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Dr. Hazem Falah Sakeek 6
For population inversion A21<A10 or T21>T10 (The upper lasing level
has a longer spontaneous emission life time than the lower level.
In most laser T21>>T10 and hence (1 - A21/A10) ? 1
At threshold
At threshold the radiation density ?v is very small and we can
assume that (?v=0)
*
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Dr. Hazem Falah Sakeek 7
From equations * & ** we get
and hence the radiation density ?v
This mean that the power output is directly proportional to the pumping
power within the laser cavity
In steady state
In steady state situation the gain becomes equal to the
losses then we can write
(N2-N1)ss = (N2-N1)th
**
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Dr. Hazem Falah Sakeek 8
At time t1 the excitation mechanism is
activated. As a result, the active
medium gain and loop gain increase.
At time t2 the active medium gain is
equal to the threshold gain, and the
round trip gain is equal to 1. Lasing
starts, and output power of the laser
start to increase.
At time t3 the input power reaches its
steady state (constant input power).
The active medium gain is a little above
threshold, and the round trip gain is a
little above “1”.
Output power from the laser continues
to rise,
At until t4 when it reaches its steady
state value. Then the active medium
gain is equal to the threshold gain, and
the gain is equal to “1”.
pumping علاقة كلا من
laser power و Gain وpower
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Physics Academy
Dr. Hazem Falah Sakeek 9
Gain saturation in
homogeneously laser
In a continuous wave laser (CW Laser) at steady state lasing, the
gain (G) is always “1”.
At this state, the gain value for each longitudinal laser mode is
dropping from the value of the small signal gain to the threshold
gain Gth, which is equal to the saturation gain.
Increasing pumping cause an increase in the output power of the
laser. The system will stabilize on higher power when the net gain
will be equal to the threshold gain.
The active medium gain depends on population inversion, and the
width of the laser line shape. This gain is influenced by the lasing
process itself, since lasing change the population inversion
conditions. Stimulated emission causes depletion of the upper
laser level, and reduces the population inversion. Thus, gain is
reduced until pumping increase the upper level population again.
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Dr. Hazem Falah Sakeek 10
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