ECE 414, Spring 2011
Homework #5
Out: 03/10/2011
Due: 03/22/2011
(1)
In the diagram shown below, the pump P
2
(i.e., electrons, flash lamp,
another laser, etc.) excites atoms from state 0 to state 2, nothing to state
1. To make the problem simple and tractable, assume state 0 is not
depleted to any significant extent for any time (i.e., dN
0
/dt=0); use the
simple decay route indicated; neglect stimulated emission; assume
1
= 2
μs and
2
= 1 μs; and let P
2
=10
20
cm
3
s
1
. Use symbols for (a) and (b) and
find numerical values for (c) and (d).
(a) What are the rate equations for states 2 and 1?
(b) Give an expression for the densities N
2,1
as a function of time.
(c) Over what time interval
t is the population difference N
2
N
1
> 0?
(d) What are the steadystate populations in 2 and 1?
(2)
Consider the atomic system shown below being irradiated by an external
wave tuned to the center of the 2
1 transition with 1 being the ground
state. The wave pumps the atoms from 1 to 2 and also stimulates the
atoms back to 1 from 2. In addition, the atoms in state 2 decay back to 1
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 Spring '11
 Alenxendra
 Atom, Photon, Light, Fundamental physics concepts, Stimulated emission, Excited state

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