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Polarizer is an idealized nonphysical model of a polarizing filter. When unpolarized light is incident on Polarizer, the transmitted light is polarized in the sense that it is tagged with a specified polarization state number. If polarized (tagged) light is incident on a Polarizer, and the polarization state of the light matches the state of the filter, then the light passes through unchanged; if the state number of the light is different than that of the filter, the light is blocked.
The unphysical parts of Polarizer properties are that:
(a) Any number of polarization states are allowed, represented by the number 1, 2, 3, etc., with 0 representing "unpolarized" light.
(b) When unpolarized light is put through a Polarizer the intensity is not affected, it is simply tagged with a state number.
The unphysical properties of the Polarizer can actually be rather useful for wave-optics modeling: they provide a simple formal mechanism for separating and combining different beams in a system without inserting a larger number of components that have no effect on the wave properties of the beams.