Lecture 10
Manley –Rowe Relations
For lossessmedia
(1)
(2)
*
*
0
2
i
i
i
i
i
i
dI
dA
dA
n
c
A
A
dz
dz
dz
ε
=
+
1
ϖ
2
ϖ
3
ϖ
*
0
2
i
i
i
i
I
n
cA A
ε
=
*
*
*
*
1
0
eff
1
3
1
2
0
eff
1
3
1
2
4
exp(
k )
. .
8
Im
exp(
k )
dI
d
iA A A
i
z
c c
d
A A A
i
z
dz
ε
ϖ
ε
ϖ
=
⋅
- ∆
+
= -
⋅
- ∆
*
*
2
8
Im
exp(
k )
dI
d
A A A
i
z
ε
ϖ
= -
⋅
- ∆
1
(3)
Manley-Rowe (1959)
0
eff
2
3
1
2
dz
*
*
*
3
0
eff
3
3
1
2
0
eff
3
3
1
2
8
Im
exp(
k )
8
Im
exp(
k )
dI
d
A A A
i
z
d
A A A
i
z
dz
ε
ϖ
ε
ϖ
= -
⋅
∆
=
⋅
- ∆
1
2
3
I
I
I
I
=
+
+
(
29
*
*
3
1
2
0
eff
1
2
3
3
1
2
0
8
Im
exp(
k )
dI
dI
dI
dI
d
A A A
i
z
dz
dz
dz
dz
ε
ϖ
ϖ
ϖ
=
=
+
+
= -
+
-
⋅
- ∆
0
3
1
2
1
2
3
I
I
I
d
d
d
dz
dz
dz
ϖ
ϖ
ϖ
=
= -
i
i
I
ϖ
Intensity of wave in
photons per unit area per unit time
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Beams exchange photons, but total number is constant.
Alternate representation of M-R relations:
(a)
(b)
Three conserved quantities
Rate of photon creation at
equals rate of

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- Fall '10
- Shalaev
- Constant of integration, Zagreb, Field Island, D2, DA postcode area
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