# Refractive index permittivity permeability relationship trust

### optics - Effective Refractive Index - Physics Stack Exchange

thank you but i know that the real part of dielectric constant is equal at n², for ZnO that have a small thickness. for multiple layers thin film how we calculate the. trust when I started tinkering around with all the expensive equipment. Photonic Particles from High-Index Dielectric Materials. Wave Equation. netic permeability, respectively. hey are deined as the ratios of the. This equation solves for the electric field,, at the operating (angular) frequency ( is Refractive Index is the default option for the Wave Optics Module. where we have seen that relative permittivity and permeability can be.

You can enter a homogenized conductivity for the composite material, which would be either experimentally determined or computed from a separate analysis. Within the RF Module, there are two other options for computing a homogenized conductivity: Porous Media refers to a model that has three different options for computing an effective conductivity for a mixture of up to five materials.

### DoITPoMS - TLP Library Dielectric materials - The dielectric constant and the refractive index

First, the Volume Average, Conductivity formulation is: This model is appropriate if the material conductivities are similar. If the conductivities are quite different, the Volume Average, Resistivity formulation is more appropriate: Relative Permittivity The relative permittivity quantifies how well a material is polarized in response to an applied electric field. Any material experiencing a time-varying electric field will dissipate some of the electrical energy as heat.

Known as dielectric lossthis results from the change in shape of the electron clouds around the atoms as the electric fields change. Dielectric loss is conceptually distinct from the resistive loss discussed earlier; however, from a mathematical point of view, they are actually handled identically — as a complex-valued term in the governing equation.

Keep in mind that COMSOL Multiphysics follows the convention that a negative imaginary component a positive-valued electrical conductivity will lead to loss, while a positive complex component a negative-valued electrical conductivity will lead to gain within the material.

There are seven different material models for the relative permittivity.

Relative Permittivity is the default option for the RF Module. A real- or complex-valued scalar or tensor value can be entered. The same Porous Media models described above for the electrical conductivity can be used for the relative permittivity.

Refractive Index is the default option for the Wave Optics Module. This material model assumes zero conductivity and unit relative permeability.

Be careful to note the sign: For an example of the appropriate usage of this material model, please see the Optical Scattering off of a Gold Nanosphere tutorial.

The Drude-Lorentz Dispersion model is a material model that was developed based upon the Drude free electron model and the Lorentz oscillator model. With the sum term, the combination of these two models can accurately describe a wide array of solid materials. It predicts the frequency-dependent variation of complex relative permittivity as: This approach is one way of modeling frequency-dependent conductivity.

The Debye Dispersion model is a material model that was developed by Peter Debye and is based on polarization relaxation times. The model is primarily used for polar liquids. Since this model computes a complex-valued permittivity, the conductivity is assumed to be zero.

### Refractive index - Wikipedia

This is an alternate way to model frequency-dependent conductivity. The Sellmeier Dispersion model is available in the Wave Optics Module and is typically used for optical materials. The choice between these seven models will be dictated by the way the material properties are available to you in the technical literature.

Keep in mind that, mathematically speaking, they enter the governing equation identically.

**If and µ0 represent the permittivity and permeability of vacuum,**

Relative Permeability The relative permeability quantifies how a material responds to a magnetic field. The most common magnetic material on Earth is iron, but pure iron is rarely used for RF or optical applications.

It is more typical to work with materials that are ferrimagnetic. Such materials exhibit strong magnetic properties with an anisotropy that can be controlled by an applied DC magnetic field. Opposed to iron, ferrimagnetic materials have a very low conductivity, so that high-frequency electromagnetic fields are able to penetrate into and interact with the bulk material.

A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodiumwith a wavelength of nanometersas is conventionally done. Almost all solids and liquids have refractive indices above 1. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.

## Refractive index

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. 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. 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.