Light can be imagined as electromagnetic waves, and can be
expressed using its electrical field by following equations:
or
where u_{1} and u_{2} are two unit
vectors to indicated the direction of two orthogonal components,
w is the angular frequency of the wave; k is the
wave number whose absolute value is 2p/l
(l is the wavelength of light in medium),
and the directional part indicate the propagating direction of
the light; s is the directional distance for study the
amplitude of electrical field; A_{1} and A_{2}
are amplitude and d_{1}
and d_{2}
are phases.
The trace of the end of electrical field is normally used
to describe the polarization state. As we can see from
following graph, ellipse is the general case of polarization.
To specify polarized wave, q
(azimuth angle, the direction of long axis of the ellipse), e (ellipticity
 the ratio the short to the long axis), A (amplitude, the half
of the diagonal of the most tighten rectangle box), directional
wave number k, handness and the exact phase.
Normally, A, wave number and the exact phase are not concerned
in the study. The parameters under interest can be
converted to amplitude ratio and phase difference between the
two components, and vice versa.
When the two components of the electrical field are exactly in
phase to each other, the ellipticity will be 0 and the light is
linearlly polarized. Another special case is circular
polarization, where the ellipticity is 1 and the phase
difference is 90 or 270 degree.
The equations above supposed a single wavelength, which
indicates a strict monochromatic light. Commonly, light
is superposition of many waves, each of which can be expressed
by the equation in the part of their lifetime. They
might differ in the frequency (color), and amplitudes and
phases (polarization). Polarization is an indication of
how the light spirally propagates in the space. If all the
waves followed the same rule of polarization (same ratio of
amplitude and phase difference), the light is said to be
polarized. Sunlight, which is composed of light wave
with different wavelength and polarization style, can be
polarized after reflected from surface of water.
Photographer normally need an analyzer to get rid of the
strong reflection from the surface and catch the fishes in the
water.
