Polarization of a Plane Wave | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


1
Page 2


1
Polarization
The polarization of a plane wave refers to the direction of the 
electric field vector in the time domain.
We assume here that the wave is traveling in the positive z direction.
2
( ,) zt E
( )
, zt S
x
y
z
Page 3


1
Polarization
The polarization of a plane wave refers to the direction of the 
electric field vector in the time domain.
We assume here that the wave is traveling in the positive z direction.
2
( ,) zt E
( )
, zt S
x
y
z
Consider a plane wave with both x and y components
ˆˆ () ( )
jkz
xy
E z xE yE e
-
= +
( =  )
yx
EE ß - In general, phase of phase of
Assume:
x
j
y
Ea
E be
ß
= =
=
real number
Polarization (cont.) 
Phasor domain:
3
x
y
x
E
y
E
Page 4


1
Polarization
The polarization of a plane wave refers to the direction of the 
electric field vector in the time domain.
We assume here that the wave is traveling in the positive z direction.
2
( ,) zt E
( )
, zt S
x
y
z
Consider a plane wave with both x and y components
ˆˆ () ( )
jkz
xy
E z xE yE e
-
= +
( =  )
yx
EE ß - In general, phase of phase of
Assume:
x
j
y
Ea
E be
ß
= =
=
real number
Polarization (cont.) 
Phasor domain:
3
x
y
x
E
y
E
Time Domain:
( )
( )
( )
( )
Re cos
Re cos
j t
x
j j t
y
ae a t
be e b t
?
ß ?
?
?ß
= =
= = +
E
E
Depending on b/a and ß, three different cases arise:
4
? Linear polarization
? Circular polarization
? Elliptical polarization
Polarization (cont.) 
x
y
() t E
0 z =
Page 5


1
Polarization
The polarization of a plane wave refers to the direction of the 
electric field vector in the time domain.
We assume here that the wave is traveling in the positive z direction.
2
( ,) zt E
( )
, zt S
x
y
z
Consider a plane wave with both x and y components
ˆˆ () ( )
jkz
xy
E z xE yE e
-
= +
( =  )
yx
EE ß - In general, phase of phase of
Assume:
x
j
y
Ea
E be
ß
= =
=
real number
Polarization (cont.) 
Phasor domain:
3
x
y
x
E
y
E
Time Domain:
( )
( )
( )
( )
Re cos
Re cos
j t
x
j j t
y
ae a t
be e b t
?
ß ?
?
?ß
= =
= = +
E
E
Depending on b/a and ß, three different cases arise:
4
? Linear polarization
? Circular polarization
? Elliptical polarization
Polarization (cont.) 
x
y
() t E
0 z =
Power Density:
*
1
2
S EH = ×
( )
*
1
ˆˆ ˆ ˆ
2
y
x
xy
E
E
S xE yE x y
??
??
?? ??
= + ×- +
??
?? ??
?? ??
??
,
y
x
yx
E
E
HH
??
= = -
( )
2
2 1
ˆ
2
xy
S zE E
?
= +
Assume lossless medium (? is real):
5
2 1
ˆ
2
S zE
?
=
or
From Faraday’s law:
Polarization (cont.) 
Hence