Polarization of Electric Field
Editors : 粘紘 、 黃楚翔 、 鄭伊佐
Advisor : Professor Jean-Fu
Kiang
By definition , polarization is the
characteristic that describes how the direction of time varying field
oscillating at a point in space changes with time . Here we discuss about electric
field in EM-wave . To simplify the discussion , we decompose the electric field
into two direction , 
and 
, as two components
, and let it propagate in the 
direction . For a
uniform plane wave propagating in an arbitrary direction , that is :
, where 
is the direction of propagation
, or the wave number vector ,
where 
is the position vector , such as 
in Cartesian coordinate .
We
consider that if the wave propagating in 
direction , then
with =
Here
we use the phasor notation
and
be two decomposition in the and direction .
Then
the total electric field can be represented :
Letandhave
a phase difference of φ ,
and amplitude ratio of direction to the direction is A , namely
, and 
,
thus ,
we have : 
Analyze the
polarization at a fixed point , that is , fixed z=0 .We will demonstrate
several situation in A (amplitude) andφ(phase angle) . Note that 
and amplitude of is 
, and
we demonstrate the electric field’s
oscillating direction and amplitude as a vector.
Case (1) : φ=0 ( Linear Polarization )
Since the electric
field oscillates along a line , it is called linear polarization .
Case (2)
: φ=
, A =1 ( Circular Polarization )
The electric field’s
oscillating direction and amplitude vector will rotate on a circle , hence it
is called circular polarization .
Case (3)
: A≠1 , φ=
( Elliptical
Polarization )
The electric field’s
oscillating direction and amplitude vector will rotate on an ellipse , hence it
is called elliptical polarization .
l
Left-hand
and Right-hand Polarization ( LH. and RH. ) :
If the vector
rotates in the clockwise sense , we call it right-hand polarization , i.e. as t
increases , the phasor angel of electric field will decrease. On the other hand
, it will rotate in the counterclockwise sense and is called left-hand polarization
.
For example , case
(2) is left-hand polarization . If φ=
, we have a right-hand
polarization : 
(1) Linear polarization
Aerial view and x-y cross-sectional view
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(2) Right-hand circular polarization ( RHCP )
Aerial view and x-y cross-sectional view
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Perspective view on z - axis
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(3) Left-hand
elliptical polarization ( LHEP ) : A = 0.5
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Aerial view and x-y cross-sectional view
Perspective view on z- axis
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(4) Left-hand
elliptical polarization ( LHEP ) : A = 2
Aerial view and x-y cross-sectional view
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Perspective view on z- axis |