ECE615_Lecture_10 - Lecture 10 Manley Rowe Relations For...

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

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