Editing Polarization (waves) (section)

=== Polarization ellipse ===
{{Main|Polarization ellipse}}
[[File:Polarisation ellipse2.svg|class=skin-invert-image|left|200px]]
For a purely polarized monochromatic wave the electric field vector over one cycle of oscillation traces out an ellipse.
A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the '''orientation angle''' {{mvar|ψ}}, defined as the angle between the major axis of the ellipse and the {{mvar|x}}-axis<ref name=Stetten>{{cite book | last1=Sletten | first1=Mark A. | last2=Mc Laughlin | first2=David J. | title=Encyclopedia of RF and Microwave Engineering | chapter=Radar Polarimetry | publisher=John Wiley & Sons, Inc. |editor-last=Chang|editor-first=Kai | date=2005-04-15 | isbn=978-0-471-65450-6 | doi=10.1002/0471654507.eme343 }}</ref> along with the '''ellipticity''' {{math|1=''ε'' = ''a/b''}}, the ratio of the ellipse's major to minor axis.<ref>{{cite book | chapter=6 Reflector Antennas | chapter-url=http://ww.helitavia.com/skolnik/Skolnik_chapter_6.pdf | editor-first=Merrill Ivan | editor-last=Skolnik | first1=Helmut E. | first2=Gary E. | first3=Daniel | last1=Schrank | url=http://www.geo.uzh.ch/microsite/rsl-documents/research/SARlab/GMTILiterature/PDF/Skolnik90.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.geo.uzh.ch/microsite/rsl-documents/research/SARlab/GMTILiterature/PDF/Skolnik90.pdf |archive-date=2022-10-09 |url-status=live | title=Radar Handbook | publisher=McGraw-Hill | last2=Evans | last3=Davis | year=1990 | pages=6.30, Fig 6.25 | isbn=978-0-07-057913-2}}</ref><ref>{{cite book|editor-last=Ishii|editor-first=T. Koryu|title=Handbook of Microwave Technology|url=https://books.google.com/books?id=c3fNCgAAQBAJ&pg=PA177|volume=2: Applications|year=1995|publisher=Elsevier|isbn=978-0-08-053410-7|page=177}}</ref><ref>{{cite book|last=Volakis|first=John|title=Antenna Engineering Handbook, Fourth Edition|url=https://books.google.com/books?id=bmdFAAAAYAAJ|year=2007|publisher=McGraw-Hill|isbn=9780071475747|at=Sec. 26.1 | postscript=: ''Note'': in contrast with other authors, this source initially defines ellipticity reciprocally, as the minor-to-major-axis ratio, but then goes on to say that "Although [it] is less than unity, when expressing ellipticity in decibels, the minus sign is frequently omitted for convenience", which essentially reverts to the definition adopted by other authors.}}</ref> (also known as the [[axial ratio]]). The ellipticity parameter is an alternative parameterization of an ellipse's [[Eccentricity (mathematics)#Ellipses|eccentricity]] <math display=inline>e=\sqrt{1 - b^2/a^2},</math> or the '''ellipticity angle''', <math display=inline>\chi=\arctan b/a</math> <math display=inline>=\arctan 1/\varepsilon</math> as is shown in the figure.<ref name=Stetten /> The angle {{mvar|χ}} is also significant in that the latitude (angle from the equator) of the polarization state as represented on the Poincaré sphere (see below) is equal to {{math|±2''χ''}}. The special cases of linear and circular polarization correspond to an ellipticity {{mvar|ε}} of infinity and unity (or {{mvar|χ}} of zero and 45°) respectively.