here - Faculty of Science - University of Waterloo

Scalar Wave Equation
• Scalar, Monochromatic Electric Field
⎛ ∂
⎜
⎝ ∂z
Defining
Y
0
2
⎛ ∂
⎜
⎝ ∂z
2
2
=
2
+
k
+
0
∂
2
∂x
k
2
n
1 ∂
2 2
n ∂y
2
0
0
0
n
∂
+
∂y
= n
2
0
2
2
( X
2
0
2
+
k
reference
, X
and N =
+ Y
0
2
0
n
2
⎞
( r )
⎟ Ε( x,
y,
z)
= 0
⎠
0
2
1 ∂
= ,
2 2 2
k0
n ∂x
0
2
n ( r )
−1,
we have
2
n
0
⎞
+ N)
⎟ E( x,
y,
z)
= 0
⎠
Faculty of Science - Department of
Physics 5/3/2009
D. Yevick - Evolution Operators and
Boundary Conditions
5