
32 Microwave Engineering
E r E e E e
j j x y z
( )
( )
= =
− ⋅ − + +
0 0
β β
n r
ˇ
cos A cos B cos C
(2.25a)
In time varying form with the assumption of E
0
being complex ( E
0
= E
r
+ jE
i
)
the above expression becomes
E r t E e E n r t E n r
j n r t
r i
( , ) [ ] ( ) (
( )
= = ⋅ − + ⋅ −
− ⋅ −
Re cos sin
0
β ω
β βω
ˇ
ˇ ˇ
ωωt)
(2.25b)
Since the wave propagation in general is a three-dimensional phenome-
non, components of phase velocity have to be different along different space
coordinates. Figure 2.9b illustrates oblique incidence of a ray on a surface
along the y-axis. As can be seen, the wavelength (
λ
y
) and phase velocity (
υ
y
)
along this surface (or along perp