Elliptical polarization

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.