here - Faculty of Science - University of Waterloo

Modal Analysis
• Modal Decomposition
E( x,
y,
z)
= ∑ a
m
m
E
m
( x,
y,
z)
with
⎡ ∂
⎢
⎣∂x
2
2
+
∂
2
∂y
2
+
k
2
0
n
2
( x,
⎤
y,
z)
⎥ E
⎦
m
( x,
y,
z)
=
β ( x,
2
m
y,
z) E
m
( x,
y,
z)
• Approximate Forward Solution
E(
∑
−iβ
m ( x,
y,
z ) ∆z
x,
y,
z + ∆z)
= e E
m
( x,
y,
z)
m
Faculty of Science - Department of
Physics 5/3/2009
D. Yevick - Evolution Operators and
Boundary Conditions
7