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Polarization is the orientation of waves toward a particular direction: it is not the direction the waves are traveling, but a direction perpendicular to that. For example, a taut string's wave-motion traveling down the string consists of some constantly-moving displacement, which often is in a particular direction, such as alternating vertically. Its displacement could also be horizontal, or along some diagonal: any such attitude is possible. A measure specifying this direction specifies the wave's polarization. Sound waves in a fluid do not have such polarization: their oscillation is of the pressure at each point rather than of a displacement of something in some specific direction within space.
Electromagnetic waves (EMR) include such a direction (in the manner of the string's wave) but typically a beam of EMR is a mix of waves with displacements in all directions, having no direction in particular and the EMR is termed unpolarized, reserving the term polarized for any tendency towards particular directions. Thus EMR can be partially polarized, just a little, or a lot. Types of astronomically-produced EMR with such polarization include maser radiation, synchrotron radiation, radiation from active galaxies, pulsars, the cosmic microwave background, and light scattered by dust. Magnetic fields affect the polarization of EMR generated within or passing through and polarimetric observation often aims at learning about such magnetic fields. Polarization of EMR from dust suggests non-spherical grains that are aligned, e.g., by a magnetic field. The polarization may be detected in starlight, in which case, a number of stars within a region of the celestial sphere showing identical polarization suggests it was caused by an interstellar cloud in the foreground rather than from the stars themselves.
Alternately to such polarization toward a particular direction (which is termed linear), polarization can be circular, in which the wave's oscillation such that the direction of displacement is oscillating in a circle. Regarding waves on a string, this would be a traveling spiral. Such rotation is either rightward or leftward (according to the right hand rule), termed right-hand circular polarization (or RHCP) or left-hand circular polarization (or LHCP). Pure circular polarization is equivalent to two simultaneous linear polarizations that are out of phase by a quarter wavelength: it can be thought of as having two components, each a linear polarization. Such simultaneous linear polarizations can also be out of phase by other fractions of a wavelength, which produce additional types of polarization.