Waveguide Theory Based on Wave Optics
•
Waveguides were discussed in terms of geometric optics
or ray optics (Snell’s law total reflection etc)
or ray optics (Snell s law, total reflection etc)
•
Geometric or ray optics fails to describe certain optical
phenomena (interference, diffraction, polarization, etc)
•
More rigorous description is wave optics, or physical
optics (under what conditions is geometric optics valid?)
•
In wave optics, waveguides are dealt with by solving
Maxwell’s equations directly with appropriate boundary
conditions
EEE537 Fall 2010 C.Z. Ning, ECEE ASU
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Planar Waveguide: Polarization Constrains
General solution of the field in a 2D waveguide with
propagation direction along z
]
z)

i(
ω
[
e
)
y
x,
(
β
t
xp
E
E
−
=
]
z)

i(
ω
[
e
)
y
x,
(
β
t
xp
H
H
−
=
β
: propagation constant for propagating wave with given
free space wavelength:
π
π
λ
c
2
2
How do you determine
β
?
ω
k
0
=
=
EEE537 Fall 2010 C.Z. Ning, ECEE ASU
Part of task of waveguide theory: solve wave equation with boundary conditions!
How do you determine
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