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In electrodynamics, polarization is a property of waves, such as light and other electromagnetic radiation. Unlike more familiar wave phenomena such as waves on water or sound waves, electromagnetic waves are three-dimensional, and it is their vector nature that gives rise to the phenomenon of polarization.
The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves. A plane wave is one where the direction of the magnetic and electric fields are confined to a plane perpendicular to the propagation direction. Simply because the plane is two-dimensional, the electric vector in the plane at a point in space can be decomposed into two orthogonal components. Call these the x and y components (following the conventions of analytic geometry). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time in the fixed plane we are talking about. By considering the shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure), we obtain a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue) with time, along with its x and y components (red/left and green/right) and the path made by the vector in the plane (purple):
Consider first the special case (left) where the two orthogonal components are in phase. In this case the strength of the two components are always equal or related by a constant ratio, so the direction of the electric vector (the vector sum of these two components) will always fall on a single line in the plane. We call this special case linear polarization. The direction of this line will depend on the relative amplitude of the two components. This direction can be in any angle in the plane, but the direction never varies.
Now consider another special case (center), where the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. Notice that there are two possible phase relationships that satisfy this requirement. The x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector in the plane formed by summing the two components will rotate in a circle. We call this special case circular polarization. The direction of rotation will depend on which of the two phase relationships exists. We call these cases right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates.
All the other cases, that is where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase (e.g. right) are called elliptical polarization because the sum electric vector in the plane will trace out an ellipseThe Ellipse is also an elliptical street immediately in front of the White House. In mathematics, an ellipse is a figure corresponding to a circle which has been stretched in one direction. This is an example of a conic section and can be defined as the l (the "polarization ellipse").
In nature, electromagnetic radiation is often produced by a large ensemble of individual radiators, producing waves independently of each other. This type of light is termed incoherentCoherence is a property of waves that measures the ability of the waves to interfere with each other. Two waves that are coherent can be combined to produce an unmoving distribution of constructive and destructive interference (a visible interference patt. In general there is no single frequency but rather a spectrum of different frequencies present, and even if filtered to an arbitrarily narrow frequency range, there may not be a consistent state of polarization. However, this does not mean that polarization is only a feature of coherent radiation. Incoherent radiation may show statisticalStatistics is the science and practice of developing human knowledge through the use of empirical data. It is based on statistical theory which is a branch of applied mathematics. Within statistical theory, randomness and uncertainty are modelled by proba correlationIn probability theory and statistics, the correlation also called correlation coefficient between two random variables is found by dividing their covariance by the product of their standard deviations. It is defined only if these standard deviations are f between the components of the electric field, which can be interpreted as partial polarization. In general it is possible to describe an observed wave field as the sum of a completely incoherent part (no correlations) and a completely polarized part. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.
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