In electrodynamics, circular polarization (also circular polarisation) of electromagnetic radiation is a polarization such that the tip of the electric field vector, at a fixed point in space, describes a circle as time progresses. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can The electric vector, at one point in time, describes a helix along the direction of wave propagation (see the polarization article for pictures). Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations The magnitude of the electric field vector is constant as it rotates. Circular polarization is a limiting case of the more general condition of elliptical polarization. In Electrodynamics, elliptical polarization is the Polarization of Electromagnetic radiation such that the tip of the Electric field vector The other special case is the easier-to-understand linear polarization. In Electrodynamics, linear polarization or plane polarization of Electromagnetic radiation is a confinement of the Electric field vector or

Circular (and elliptical) polarization is possible because the propagating electric (and magnetic) fields can have two orthogonal components with independent amplitudes and phases (and the same frequency).

A circularly polarized wave may be resolved into two linearly polarized waves, of equal amplitude, in phase quadrature (90 degrees apart) and with their planes of polarization at right angles to each other. In Electrodynamics, linear polarization or plane polarization of Electromagnetic radiation is a confinement of the Electric field vector or Communication signals often have the form': A(t\cdot \sin ft + \phi(t    which is called envelope-and-phase form

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The term "circular polarization" is often used erroneously to describe mixed polarity signals used mostly in FM radio (87. See also Frequency modulation, FM band FM broadcasting is a broadcast Technology invented by Edwin Howard Armstrong that 5 to 108. 0 MHz), where a vertical and a horizontal component are propagated simultaneously by a single or a combined array. This has the effect of producing greater penetration into buildings and difficult reception areas than a signal with just one plane of polarization.

## Circular dichroism

Main article: Circular dichroism

Circular dichroism (CD), is the differential absorption of left- and right-handed circularly polarized light. Circular dichroism (CD is a form of Spectroscopy based on the differential absorption of left- and right-handed circularly polarized Light. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 It is a form of spectroscopy used to determine the optical isomerism and secondary structure of molecules. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ The term chiral (pronounced /ˈkaɪɹ(əl̩/ is used to describe an object that is non- superimposable on its mirror image In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials As a consequence, circular dichroism is exhibited by biological molecules, because of the dextrorotary (e. In Chemistry, an enantiomer ( from the Greek ἐνάντιος opposite and μέρος part or portion is one of two Stereoisomers that are nonsuperimposable g. some sugars) and levorotary (e. Sugar is a class of edible Crystalline substances mainly Sucrose, Lactose, and Fructose. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials g. some amino acids) molecules they contain. In Chemistry, an amino acid is a Molecule containing both Amine and Carboxyl Functional groups In Biochemistry, this Noteworthy as well is that a secondary structure will also impart a distinct CD to its respective molecules. In Biochemistry and Structural biology, secondary structure is the general three-dimensional form of local segments of Biopolymers such as Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures. A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in which In Geometry a double helix (plural helices) typically consists of two congruent helices with the same axis differing by a translation A nucleic acid is a Macromolecule composed of chains of monomeric Nucleotides In Biochemistry these Molecules carry Genetic information

## Mathematical description of circular polarization

The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is

$\mathbf{E} ( \mathbf{r} , t ) = \mid \mathbf{E} \mid \mathrm{Re} \left \{ |\psi\rangle \exp \left [ i \left ( kz-\omega t \right ) \right ] \right \}$
$\mathbf{B} ( \mathbf{r} , t ) = \hat { \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )$

for the magnetic field, where k is the wavenumber,

$\omega_{ }^{ } = c k$

is the angular frequency of the wave, and c is the speed of light. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency

Here

$\mid \mathbf{E} \mid$

is the amplitude of the field and

$|\psi\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} \psi_x \\ \psi_y \end{pmatrix} = \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right ) \\ \sin\theta \exp \left ( i \alpha_y \right ) \end{pmatrix}$

is the Jones vector in the x-y plane. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system In Optics one can describe Polarization using the Jones calculus, invented by R

If αy is rotated by π / 2 radians with respect to αx and the x amplitude equals the y amplitude the wave is circularly polarized. The Jones vector is

$|\psi\rangle = {1\over \sqrt{2}} \begin{pmatrix} 1 \\ \pm i \end{pmatrix} \exp \left ( i \alpha_x \right )$

where the plus sign indicates right circular polarization and the minus sign indicates left circular polarization. In the case of circular polarization, the electric field vector of constant magnitude rotates in the x-y plane.

If unit vectors are defined such that

$|R\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ i \end{pmatrix}$

and

$|L\rangle \ \stackrel{\mathrm{def}}{=}\ \begin{pmatrix} 1 \\ -i \end{pmatrix}$

then the polarization state can written in the "R-L basis" as

$|\psi\rangle = \left ( {\cos\theta -i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right ) |R\rangle + \left ( {\cos\theta + i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right ) |L\rangle = \psi_R |R\rangle + \psi_L |L\rangle$

where

$\psi_R \ \stackrel{\mathrm{def}}{=}\ \left ( {\cos\theta -i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right )$

and

$\psi_L \ \stackrel{\mathrm{def}}{=}\ \left ( {\cos\theta +i\sin\theta \over \sqrt{2} } \right ) \exp \left ( i \alpha_x \right )$.

## References

• Jackson, John D. (1999). Classical Electrodynamics (3rd ed. ). Wiley. ISBN 0-471-30932-X.
• Born, M. and Wolf, E. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th ed. ). Cambridge University Press. ISBN 0521642221.