Electromagnet refraction

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

In the second broad class of spectroscopy, the electromagnetic radiation undergoes a change in amplitude, phase angle, polarization, or direction of propagation as a result of its refraction, reflection, scattering, diffraction, or dispersion by the sample. Several representative spectroscopic techniques are listed in Table 10.2. 

The connection between the molar polarization Pm and the molar refraction Rm is through Maxwell s theory of electromagnetism, according to which e = (at low-frequency fields). This is the basis for considering the molar refraction a measure of polarizability. 

Specular reflection of electromagnetic radiation at the (electrochemical) interface is generally described by Fresnel equations. Supposing the most simple case that both the electrolyte and electrode are transparent and differ only in their refractive indexes, nx and n2, the reflectivity for normal incidence of the radiation equals ... 

If measurements are made in thin oxide films (of thickness less than 5 nm), at highly polished Al, within a small acceptance angle (a < 5°), well-defined additional maxima and minima in excitation (PL) and emission (PL and EL) spectra appear.322 This structure has been explained as a result of interference between monochromatic electromagnetic waves passing directly through the oxide film and EM waves reflected from the Al surface. In a series of papers,318-320 this effect has been explored as a means for precise determination of anodic oxide film thickness (or growth rate), refractive index, porosity, mean range of electron avalanches, transport numbers, etc. 

The velocity of electromagnetic waves through any material other than the vacuum is (e ) 2 = v and the ratio n = c/v is called the index of refraction of that material. It follows that n = y /x/eoMo and, since the ratio n/fio 1, except for ferromagnetic materials, the index of refraction is commonly defined as the square root of the dielectric constant, e/e0- Since the frequency of the field is not affected by the medium, refraction can be described equally well as a change of the wavelength of light passing between different transparent media. 

Since the absorption process is 7r/2 out of phase with the electromagnetic field its effect on the index of refraction will also lag in the same way behind the simple dielectric effect. The total index of refraction is therefore formulated as 77 = n + ik, where k is the absorptive contribution. 

Electromagnetic radiation has its origins in atomic and molecular processes. Experiments demonstrating reflection, refraction, diffraction and interference phenomena show that the radiation has wave-like characteristics, while its emission and absorption are better explained in terms of a particulate or quantum nature. Although its properties and behaviour can be expressed mathematically, the exact nature of the radiation remains unknown. 

We consider a radially symmetric structure as illustrated in Fig. 12.2. The guiding defect, consisting of a material of refractive index ndefect, is surrounded by distributed Bragg reflectors on both sides, where the reflectors layers are of refractive indices ni and n2. All the electromagnetic field components can be expressed in terms of the z-component of the electric and magnetic fields14. These components satisfy the scalar Helmholtz equation, which in cylindrical coordinates is given by ... 

More detailed analysis shows that the application of the low refractive index substrates not only increases the penetration depth into the cover media, but also since the mode profile is reversed places a larger portion of the electromagnetic power flowing in the waveguide structure into the cover media, thus increasing the sensor sensitivity for refractive index variations in the cover solution9 15. 

Theory The initial understanding of the refraction of light dates back to Maxwell s study of electromagnetic radiation. Ernst Abbe invented the first commercial refractometer in 1889 and many refractometers still use essentially the same design. 

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

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