Perfect Dielectric

In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field (for example, if the field is moving parallel to the positive ''x'' axis, the negative charges will shift in the negative ''x'' direction). This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarised, but also reorient so that their symmetry axes align to the field.

The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important for explaining various phenomena in electronics, optics, solid-state physics and cell biophysics.

Terminology

Although the term '' insulator'' implies low electrical conduction, ''dielectric'' typically means materials with a high polarisability. The latter is expressed by a number called the relative permittivity. The term insulator is generally used to indicate electrical obstruction while the term dielectric is used to indicate the energy storing capacity of the material (by means of polarisation). A common example of a dielectric is the electrically insulating material between the metallic plates of a capacitor. The polarisation of the dielectric by the applied electric field increases the capacitor's surface charge for the given electric field strength.

The term '' dielectric'' was coined by William Whewell (from '' dia'' + ''electric'') in response to a request from Michael Faraday. A ''perfect dielectric'' is a material with zero electrical conductivity ( cf. perfect conductor infinite electrical conductivity), thus exhibiting only a displacement current; therefore it stores and returns electrical energy as if it were an ideal capacitor.

Electric susceptibility

The electric susceptibility ''χ_e'' of a dielectric material is a measure of how easily it polarises in response to an electric field. This, in turn, determines the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

It is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarisation density P such that

$\mathbf = \varepsilon_0 \chi_e \mathbf,$

where ''ε''₀ is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity ''ε_r'' by

$\chi_e\ = \varepsilon_r - 1.$

So in the case of a vacuum,

$\chi_e\ = 0.$

The electric displacement D is related to the polarisation density P by

$\mathbf \ = \ \varepsilon_0 \mathbf + \mathbf \ = \ \varepsilon_0 \left(1 + \chi_e\right) \mathbf \ = \ \varepsilon_0 \varepsilon_r \mathbf.$

Dispersion and causality

In general, a material cannot polarise instantaneously in response to an applied field. The more general formulation as a function of time is

$\mathbf(t) = \varepsilon_0 \int_^t \chi_e\left(t - t'\right) \mathbf(t')\, dt'.$

That is, the polarisation is a convolution of the electric field at previous times with time-dependent susceptibility given by ''χ_e''(Δ''t''). The upper limit of this integral can be extended to infinity as well if one defines for . An instantaneous response corresponds to Dirac delta function susceptibility .

It is more convenient in a linear system to take the Fourier transform and write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product,
$\mathbf(\omega) = \varepsilon_0 \chi_e(\omega) \mathbf(\omega).$

The susceptibility (or equivalently the permittivity) is frequency dependent. The change of susceptibility with respect to frequency characterises the dispersion properties of the material.

Moreover, the fact that the polarisation can only depend on the electric field at previous times (i.e., for ), a consequence of causality, imposes Kramers–Kronig constraints on the real and imaginary parts of the susceptibility ''χ_e''(''ω'').

Dielectric polarisation

Basic atomic model

In the classical approach to the dielectric, the material is made up of atoms. Each atom consists of a cloud of negative charge (electrons) bound to and surrounding a positive point charge at its center. In the presence of an electric field, the charge cloud is distorted, as shown in the top right of the figure.

This can be reduced to a simple dipole using the superposition principle. A dipole is characterised by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled ''M''. It is the relationship between the electric field and the dipole moment that gives rise to the behaviour of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure. This isn't always the case, and is a major simplification, but is true for many materials.)

When the electric field is removed the atom returns to its original state. The time required to do so is the so-called relaxation time; an exponential decay.

This is the essence of the model in physics. The behaviour of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behaviour. Important questions are:
*Is the electric field constant or does it vary with time? At what rate?
*Does the response depend on the direction of the applied field ( isotropy of the material)?
*Is the response the same everywhere ( homogeneity of the material)?
*Do any boundaries or interfaces have to be taken into account?
*Is the response linear with respect to the field, or are there nonlinearities?

The relationship between the electric field E and the dipole moment M gives rise to the behaviour of the dielectric, which, for a given material, can be characterised by the function F defined by the equation:
$\mathbf = \mathbf(\mathbf).$

When both the type of electric field and the type of material have been defined, one then chooses the simplest function ''F'' that correctly predicts the phenomena of interest. Examples of phenomena that can be so modelled include:

* Refractive index
*Group velocity dispersion
*Birefringence
* Self-focusing
* Harmonic generation

Dipolar polarisation

Dipolar polarisation is a polarisation that is either inherent to polar molecules (orientation polarisation), or can be induced in any molecule in which the asymmetric distortion of the nuclei is possible (distortion polarisation). Orientation polarisation results from a permanent dipole, e.g., that arising from the 104.45° angle between the asymmetric bonds between oxygen and hydrogen atoms in the water molecule, which retains polarisation in the absence of an external electric field. The assembly of these dipoles forms a macroscopic polarisation.

When an external electric field is applied, the distance between charges within each permanent dipole, which is related to chemical bonding, remains constant in orientation polarisation; however, the direction of polarisation itself rotates. This rotation occurs on a timescale that depends on the torque and surrounding local viscosity of the molecules. Because the rotation is not instantaneous, dipolar polarisations lose the response to electric fields at the highest frequencies. A molecule rotates about 1 radian per picosecond in a fluid, thus this loss occurs at about 10¹¹ Hz (in the microwave region). The delay of the response to the change of the electric field causes friction an