ABSTRACT
The polarization vector describes the polarization state of plane waves in 3D while the Jones vector describes monochromatic plane waves propagating along the z-axis. The Poynting vector S describes the instantaneous flow of energy of an electromagnetic wave. Optical detectors measure a time averaged flow of energy, called the flux or irradiance. Monochromatic light is periodic with a single frequency. Due to this periodicity, its electric field vector traces a simple figure, the polarization ellipse, the most iconic representation of polarized light. The electric field vector associated with linearly polarized light oscillates in a single direction. Circularly polarized light has a constant electric field amplitude whose orientation uniformly rotates in the transverse plane. For each state, a time helix E(x,y,t) and a space helix E(x,y,z) can be drawn as a three-dimensional space curve. Note that the space helix and the time helix have opposite helicity, due to the minus sign in (k z – ω t). Polarization states are orthogonal when their major axes are 90° apart, their helicities are opposite, and the ellipticities have equal magnitude. The Jones vector is most commonly expressed in terms of its x and y components, but other orthogonal polarization bases are also used. The combination of two plane waves of the same frequency traveling in the same direction is simulated by the addition of their Jones vectors. Electromagnetic waves are commonly written with one of two different sign conventions. Either the phase decreases with time and increases in space, (k z – ω t), or the phase increases with time and decreases in space, (ω t -k z). Depending on the choice, various plus and minus signs must be adjusted in the mathematical descriptions for circularly and elliptically polarized light. Both conventions, decreasing phase and increasing phase, are in widespread use.
