In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.
Circular polarization and linear polarization can be considered to be special cases of elliptical polarization. This terminology was introduced by Augustin-Jean Fresnel in 1822, before the electromagnetic nature of light waves was known.
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (Gaussian units)
for the magnetic field, where k is the wavenumber,
is the angular frequency of the wave propagating in the +z direction, and is the speed of light.
Here is the amplitude of the field and
is the normalized Jones vector. This is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization.
At a fixed point in space (or for fixed z), the electric vector traces out an ellipse in the x-y plane. The semi-major and semi-minor axes of the ellipse have lengths A and B, respectively, that are given by
and
where with the phases and .
The orientation of the ellipse is given by the angle the semi-major axis makes with the x-axis. This angle can be calculated from
If , the wave is linearly polarized. The ellipse collapses to a straight line ) oriented at an angle . This is the case of superposition of two simple harmonic motions (in phase), one in the x direction with an amplitude , and the other in the y direction with an amplitude . When increases from zero, i.e.
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La polarisation est une propriété qu'ont les ondes vectorielles (ondes qui peuvent osciller selon plus d'une orientation) de présenter une répartition privilégiée de l'orientation des vibrations qui les composent. Les ondes électromagnétiques, telles que la lumière, ou les ondes gravitationnelles ont ainsi des propriétés de polarisation. Les ondes mécaniques transverses dans les solides peuvent aussi être polarisées. Cependant, les ondes longitudinales (telles que les ondes sonores) ne sont pas concernées.
Le formalisme de Jones est un formalisme matriciel permettant de décrire l'état de polarisation de la lumière, ou de manière générale d'une onde électromagnétique, et son évolution à travers un système optique. Ce formalisme doit son nom à son inventeur Robert C. Jones qui le définit en 1941. Dans ce formalisme, on représente la lumière polarisée par un vecteur de Jones et les éléments optiques linéaires sont représentés par des matrices de Jones.
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term linear polarization (French: polarisation rectiligne) was coined by Augustin-Jean Fresnel in 1822. See polarization and plane of polarization for more information. The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector.
We demonstrate the use of both pixelated differential phase contrast (DPC) scanning transmission electron microscopy (STEM) and off-axis electron holography (EH) for the measurement of electric fields and assess the advantages and limitations of each techn ...
A dual-shot technique based on the field basis addition of two statistically independent speckle patterns is developed to recover an input polarization through a scattering layer. It is proposed theoretically, and demonstrated both numerically and experime ...
Iop Publishing Ltd2024
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The control of movement and orientation of gas-phase molecules has become the focus of many research areas in molecular physics. Here, ND3 molecules are polarized in a segmented, curved electrostatic guide and adiabatically aligned inside a rotatable mass ...