Dielectrics and Optics
Interband and Intraband contributions to the dielectric constant of solids. • Interband and . The refractive index of a material is defined as: (). () o n ε ω ε ω . In this this chapter I'll define the complex dielectric function as I'll use it for the re- that to derive Eq. d (the plane-wave-generated algebraic equation) which I copy here: . thus motivating the definition of the complex refractive index. In uniform isotropic linear media, the wave equation is: They are Definition of Index of Refraction Relation Between Dielectric Constant and Refractive Index.
As a result we obtain a reflected beam traveling in vacuum and a refracted beam which travels through the material. What do we know about the three beams? The incident beam is characterized by its wavelength li, its frequency ni and its velocity c0, the direction of its polarization in some coordinate system of our choice, and the arbitrary angle of incidence a. We know, it is hoped, the simple dispersion relation for vacuum. The incident beam also has a certain amplitude of the electric field and of the magnetic field, of course which we call E0.
The intensity Ii of the light that the incident beams embodies, i. The reflected beam follows one of the basic laws of optics, i.
Dielectric constant refractive index relationship
What we do not know is its amplitude and its polarization, and these two quantities must somehow depend on the properties of the incident beam and the properties of the dielectric. If we now consider the refracted beam, we know that it travels under an angle b, has the same frequency as the incident beam, but a wavelength ld and a velocity c that is different from li and c0.
Moreover, we must expect that it is damped or attenuated, i. All parameters of the refracted beam may depend on the polarization of the incident beam. Aerogel is a very low density solid that can be produced with refractive index in the range from 1. Most plastics have refractive indices in the range from 1. Moreover, topological insulator material are transparent when they have nanoscale thickness. These excellent properties make them a type of significant materials for infrared optics.
Refractive index - Wikipedia
The refractive index measures the phase velocity of light, which does not carry information. This can occur close to resonance frequenciesfor absorbing media, in plasmasand for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies. Since the refractive index of the ionosphere a plasmais less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.
See also Radio Propagation and Skywave.Absorption, dispersion, and Kramers-Kronig
Negative index metamaterials A split-ring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. The resulting negative refraction i. Ewald—Oseen extinction theorem At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.
Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility. As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity.
Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies see scattering. Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.