Editing Polarization (waves) (section)

==== Non-transverse waves ====
In addition to transverse waves, there are many wave motions where the oscillation is not limited to directions perpendicular to the direction of propagation. These cases are far beyond the scope of the current article which concentrates on transverse waves (such as most electromagnetic waves in bulk media), but one should be aware of cases where the polarization of a coherent wave cannot be described simply using a Jones vector, as we have just done.

Just considering electromagnetic waves, we note that the preceding discussion strictly applies to plane waves in a homogeneous isotropic non-attenuating medium, whereas in an [[anisotropic]] medium (such as birefringent crystals as discussed below) the electric or magnetic field may have longitudinal as well as transverse components. In those cases the [[electric displacement]] {{math|'''D'''}} and [[magnetic flux density]] {{math|'''B'''}}{{clarify|reason=But B doesn't appear above.|date=May 2015}} still obey the above geometry but due to anisotropy in the [[electric susceptibility]] (or in the [[magnetic permeability]]), now given by a [[tensor]], the direction of {{math|'''E'''}} (or {{math|'''H'''}}) may differ from that of {{math|'''D'''}} (or {{math|'''B'''}}). Even in isotropic media, so-called [[inhomogeneous wave]]s can be launched into a medium whose refractive index has a significant imaginary part (or "[[Complex index of refraction#Complex index of refraction and absorption|extinction coefficient]]") such as metals;{{clarify|reason=Is this the same as having a complex value of the wave impedance η that was employed in the previous section? The discussion should be made consistent and the assumptions on the reality of η (or not) should be made explicit.|date=May 2015}} these fields are also not strictly transverse.<ref name=Griffiths1998>{{cite book|author=Griffiths, David J.|title=Introduction to Electrodynamics|edition=3rd|publisher=Prentice Hall|date=1998|isbn=0-13-805326-X|url=https://archive.org/details/introductiontoel00grif_0}}</ref>{{rp|179–184}}<ref name="New2011">{{cite book|author=Geoffrey New|title=Introduction to Nonlinear Optics|date=7 April 2011|publisher=Cambridge University Press|isbn=978-1-139-50076-0}}</ref>{{rp|51–52}} [[Surface wave]]s or waves propagating in a [[waveguide]] (such as an [[optical fiber]]) are generally {{em|not}} transverse waves, but might be described as an electric or magnetic [[transverse mode]], or a hybrid mode.

Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down. An extreme example is [[radial polarisation|radially]] or tangentially polarized light, at the focus of which the electric or magnetic field respectively is {{em|entirely}} longitudinal (along the direction of propagation).<ref>{{cite journal |doi=10.1103/PhysRevLett.91.233901 |author=Dorn, R. |author2=Quabis, S. |author3=Leuchs, G. |name-list-style=amp |title=Sharper Focus for a Radially Polarized Light Beam |journal=Physical Review Letters |date=Dec 2003 |volume=91 |issue=23 | pages=233901 |bibcode=2003PhRvL..91w3901D |pmid=14683185}}</ref>

For [[longitudinal wave]]s such as [[sound wave]]s in [[fluid]]s, the direction of oscillation is by definition along the direction of travel, so the issue of polarization is normally not even mentioned. On the other hand, sound waves in a bulk [[solid]] can be transverse as well as longitudinal, for a total of three polarization components. In this case, the transverse polarization is associated with the direction of the [[shear stress]] and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of the solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in [[seismology]].