This page will serve as an appendix and will be referred to frequently. I will try to keep things in alphabetical order, however as a human I am prone to mistakes, so don't be surprised if the definitions become sporadically organized.

**Colloid ** - Mechanical mixture in which one substance is homogeneously dispersed throughout another (Wikipedia)

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**Counterions ** - An ion that accompanies an ionic species in order to maintain electric neutrality (Wikipedia)

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**Cross-Section** - The concept of a cross-section is that of an effective area for collision. In most cases, this is expressed in differential form with
respect to the solid angle unit (see below). A lot of the time this describes the probability of observing a scattered particle in a given quantum state
per solid angle unit (within a given cone of observation), if the target is irradiated by a flux of one particle per surface unit:

So, to evaluate the cross section, simply take the integral of the above equation with respect to \Omega:

It is not uncommon to define the total cross sectional scattering as the total loss of electromagnetic energy from the incident wave due to both scattering and absorption:

Where the incident cross-section is , the scattering cross-section is , and the absorbed cross-section as . This loss of energy is proportional to the imaginary component of the scattering amplitude in the forward direction. This is the fundamental idea behind the Optical Theorem - a useful idea that allows us to calculate the total extinction cross section when the imaginary part of the scattering amplitude in the forward direction is known accurately. The derivation of it will be linked from here as soon as I have finished it. (Scattering of Electromagnetic Waves - Theories, applications. Pg 68)

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**Degree of Ionization ** - Proportion of neutral particles that are ionized into charged particles.

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**Electrolyte ** - Substance containing free ions that behaves as an electrically conducting medium.

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**Extinction coefficient ** - The extinction coefficient for a particular substance
is a measure of how well it scatters and absorbs light (Wikipedia). So, if light can pass through very easily, the
material has a low extinction coefficient. Alternatively, if no light can transverse a material, then it has a very high extinction
coefficient.

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**Flux** - Literally, flux is defined as the integral of a Vector quantity over a finite surface, giving a scalar quantity (Wikipedia).
For example, the magnetic flux is the integral of b over a given area.

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**Ionomeric** - Describes a polyelectrolyte that comprises copolymers containing both electrically
neutral repeating units and a fraction of ionized units (Wikipedia).

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**Metamaterials ** - Materials that gain their properties from their structure rather
than their elementary constituents. An interesting aspect of many Metamaterials is that they can be engineered to
have a negative index of refraction - an idea previously thought to be impossible. As we all know, the index of refraction
can be expressed in terms of the electric permittivity and magnetic permeability through the following relation

Metamaterials that have a negative index of refraction ("Left-handed materials") have some interesting properties - one in particular is that the Doppler shift travels in the opposite direction as with a normal medium. One possible application of a negative index of refraction material, as presented by John Pendry, is a perfect lens. Conventional lenses cannot obtain a resolution above that of the wavelength of light being used - a left-handed material has the ability to "focus all Fourier components of a 2D image, even those that do not propagate in a radiative manner" (Pendry, 2000).

Anyway, these Metamaterials are of interest because they are able to have a variable index of refraction - which may allow for the successful diversion of light around an object. In order to do this, one would need to vary the index of refraction from 0 at the inner radius to 1 at the outer radius. In a recent dem11:44 AM 6/19/2008onstration at Duke University (2006), scientists were able to successfully divert microwaves around a metal cylinder by varying the dimensions of a series of split ring resonators to yield a desired gradient of permeability. A figure that was included in the New York Times article can be found here. Additionally, I was able to model the cloaking device used at Duke in AutoCAD very accurately. However, since this exact design has already been realized, I did not push it further.

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**Optical Theorem ** - The Optical Theorem "relates the forward scattering amplitude to the total cross
section of the scatterer" (Wikipedia). The Electromagnetic Optical Theorem states (Berg):

Where and represents the scattering cross section.

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**Plasmon ** - A quasi-particle wave packet resulting from quantization of ionization energies analogous to the photon, or the phonon).

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**Polyelectrolyte ** - Polymers bearing an electrolyte group.

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**Polymer ** - A large molecule consisting of repeated patterns of covalently bonded atoms.

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**Poynting Vector** - The flux of the Poynting vector over a given area is the
rate at which electromagnetic energy flows through it. Mathematically, it is expressed in terms of W/m^2, and is defined as:

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**Solid Angle Unit **- The angle in three-dimensional space that an object subtends at a point (Wikipedia). Here is an excellent illustration
demonstrating this idea.

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**Surfactant ** - Wetting agent that lowers the surface tension of a liquid.

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