1
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EE 383V
Prof. Mikhail Belkin
Lectures 9
‐
11
Difference
‐
frequency Generation and Optical Parametric Amplification
Summary of the previous lecture material
1
2
3
d
eff
Th
d
+
ti
i
li
t l
Three waves
1
,
2
, and
3
=
1
2
propagating in a nonlinear crystal.
They all interact via sum
‐
and difference
‐
frequency generation processes and can
exchange their power:
photons at
1
and
2
may combine and produce a photon at
3
alternatively, a photon at
3
may split into one photon at
1
and one at
2
These processes are all described by coupled
‐
wave equations derived earlier:
Coupled
‐
wave equations
(d
eff
is the same for all equations in
case of transparent media)

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2
Difference frequency generation (DFG)
and parametric amplification
Previously, we considered the case of sum
‐
frequency generation:
Namely, we had two input waves at
1
and
2
and we had phase matching:
k
1
+k
2
=k
3
for a process
1
+
2
=
3
. As a result,
1
and
2
interacted and produced
3
Let’s now consider the case of difference frequency generation:
Namely, we now have two input waves at
1
and
3
and we had phase matching:
k
3
‐
k
1
=k
2
for a process
3
+
1
=
2
. As a result,
1
and
2
interacted and produced
3
We have already ‘seen’ a DFG process in our calculations of SFG with pump depletion:
Remember, when we considered a case of SFG with
2
being ‘strong’
(undepletable) pump and
2
being ‘weak’ pump we got this solution for A
1
and A
3
:
Difference frequency generation
Consider this experimental situation:
We have
3
and
2
as inputs;
Are we going to generate
2
=
3
+
1
(SFG) or
2
=
3
‐
1
(DFG)?
Answer: we are going to generate both; a process that is phase
‐
matched will result in high conversion efficiency and will
dominate

3
Coupled-wave equations for DFG
Consider now that A
3
(high frequency pump) is very strong and let’s neglect its depletion:
z
(phase mismatch for DFG)
Assume:
k=0
‘Strong pump’ solution
Use initial conditions (A
2
=0) to get:
The power in strong wave A
3
goes to amplify both A
1
and A
2

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