Polarization of electromagnetic radiation

Circular polarization of electromagnetic radiation is a polarization such that the tip of E, at a fixed point in space, describes a circle as time progresses. E, at one point in time, describes a helix along the direction of wave propagation k. The magnitude of the electric field vector is constant as it rotates. Circular polarization is a limiting case of elliptical polarization. The other special case is the easier-to-understand linear polarization. Circular (and elliptical) polarization is possible because the propagating E and El fields... 

Faraday effect The rotation of the plane of polarization of electromagnetic radiation... 

In the previous section we defined several characteristic properties of electromagnetic radiation, including its energy, velocity, amplitude, frequency, phase angle, polarization, and direction of propagation. Spectroscopy is possible only if the photon s interaction with the sample leads to a change in one or more of these characteristic properties. 

The plane of polarization is conventionally taken to be the plane containing the direction of E and that of propagation in Figure 2.1 this is the xy plane. The reason for this choice is that interaction of electromagnetic radiation with matter is more commonly through the electric component. 

So far we have only considered scalar interference, however, the vector nature of electromagnetic radiation can give rise to polarization interference... 

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

These speculations about the ionic, polar, or electronic nature of chemical bonding, which arose largely from solution theory, resulted mostly in static models of the chemical bond or atom structure. In contrast is another tradition, which is more closely identified with ether theory and electrodynamics. This tradition, too, may be associated with Helmholtz, especially by way of his contributions to nineteenth-century theories of a "vortex atom" that would explain chemical affinities as well as the origin of electromagnetism, radiation, and spectral lines. 

The oscillating dipole is a source of electromagnetic radiation of the same frequency, polarized in the direction of the oscillations. At large distances, the wave is spherical. According to the electromagnetic theory, the resulting electric vector at a point in the equatorial plane of the dipole is a>2/ r c2 times the moment of the dipole at time t — r /c. The amplitude of the spherically scattered wave at unit distance in the equatorial plane is therefore... 

Collision-induced absorption is a well developed science. It is also ubiquitous, a common spectroscopy of neutral, dense matter. It is of a supermolecular nature. Near the low-density limit, molecular pairs determine the processes that lead to the collision-induced interactions of electromagnetic radiation with matter. Collision-induced absorption by non-polar fluids is particularly striking, but induced absorption is to be expected universally, regardless of the nature of the interacting atoms or molecules. With increasing density, ternary absorption components exist which are important especially at the higher temperatures. Emission and stimulated emission by binary and higher complexes have also... 

A further important property of synchrotron radiation concerns its polarization characteristics. The radiation is completely polarized, and the kind of polarization depends on the direction of the circulating electron beam as well as on the direction of photon emission. In order to understand these polarization properties, it is useful to recall the result for the emission of electromagnetic radiation from an electron moving with non-relativistic velocity in a circle the electric field vector follows the same shape and orientation as the projection of the electron s path onto a plane perpendicular to the observation direction. 

We have not failed to recognize that appropriately designed (6,0) carbon and C/B/N nanotubes may display considerably enhanced nonlinear optical activity. This term refers to the response of the dipole moment of a molecule (or the polarization of bulk material) to the oscillating electric field of electromagnetic radiation.82 85 The component of the dipole moment along an axis i in the presence of an electric field e can be represented by a Taylor series ... 

The intensities of electromagnetic radiation emitted at the frequency >3 from these oscillating polarizations are... 

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