Negative Refraction

Negative Refraction? Invisibility?

How does it work!

MARTEN POUTSMA

Student ID: 37588018

Words; 2093

"First, a disclaimer: Invisibility cloaks like Harry Potter's are nowhere near becoming reality. Nor has anyone unearthed proof that the infamous Philadelphia experiment--in which U.S. Navy scientists in 1943 supposedly made a destroyer and its crew vanish--really took place. Stygian crystals, said to confer invisibility in Star Wars films and books, remain figments of writers' imaginations. And not one invisibility shield yet exists, not even a mouse-size one"

Knowing this and keeping it in the back of our mind the reality is like this: Scientists have been doing a lot of thinking about how light and matter interact. And recent advances resurrected the notion of negatively refracting materials.

In most materials, the electromagnetic properties arise directly from the characteristics of constituent atoms and molecules. Because these constituents have a limited range of characteristics, the millions of materials that we know of display only a limited palette of electromagnetic properties. But in the mid-1990s John B. Pendry, in collaboration with scientists at Marconi Materials Technology in England, realized that a "material" does not have to be a slab of one substance. Rather it could gain its electromagnetic properties from tiny structures, which collectively create effects that are otherwise impossible . This led to the discovery of a combination of metamaterials that provided the elusive property of negative refraction. "Metamaterials" refers to materials that are a composite of two or more optical materials combined into a structure which has new properties quite different from its basic materials. To understand how negative refraction works one must first understand the concept of refraction and waves itself.

Refraction

One of the most fundamental concepts of optical effects is refraction, or the bending of light as it passes the interface between two materials. This particular phenomenon of refraction is well-known to most of us although

we might not think of it as such: for example, an object under water viewed by an observer above the water appears in a different position than it actually is. Fisherman who hunt with spears, know this and they have learned to adjust their aiming. Refraction is also the basic principle behind lenses and other optical elements that focus, steer, guide or otherwise manipulate light.

The underlying principle of refraction can be easily understood and applies to all electromagnetic waves--not just visible light. Every material, including air, has an index-of-refraction (or refractive index). When an electromagnetic wave travels through the interface of a material with refractive index n1 to another material with refractive index n2, the change in its trajectory can be determined from the ratio of refractive indices n2/n1 by the use of Snell's Law .

Waves

Fig 1: Maxwell's equations in a material.

The Electromagnetic waves are governed by Maxwell's equations. These equations show that the waves contain electric and magnetic fields. When an electromagnetic wave enters a material, the fields of the wave interact with the electrons and other charges of the atoms and molecules that compose the material, causing them to move about. This interaction alters the motion of the wave and chngs the speed or in other words the, wavelength. The appropriate Maxwell's equations that describe wave propagation within a material, are shown in the figure to the right. From these equations it is observed that there are two fields--one electric (E) and the other magnetic (H). And there are also two other parameters, called the electric permittivity (e) and the magnetic permeability (m).

Fig 2: Anatomy of an Electromagnetic Wave: Electromagnetic waves consist of in-phase, oscillating electric and magnetic fields. Plane waves, as shown here, have electric and magnetic fields that are polarized at right angles to each other. The field directions in a plane wave also form right angles with respect to their direction of travel (the propagation direction).

Negative refraction

All transparent or translucent materials that we know of possess a positive refractive index--a refractive index that is greater than zero. The basic question whether there is a fundamental reason why a material with a negative refractive index cannot excists, was asked by Victor Veselago, a Russian physicist. In 1968, Veselago published a theoretical analysis of the electromagnetic properties of materials with negative permittivity and negative permeability. The electric permittivity and the magnetic permeability are commonly used material parameters that describe how materials polarize in the presence of electric and magnetic fields. Maxwell's equations relate the permittivity and the permeability to the refractive index as follows:

The sign of the index is usually taken as positive. However, Veselago showed that if a medium has both negative permittivity and negative permeability, this convention must be reversed: we must choose the negative sign of the square root! Though after years of searching, Veselago failed to find anything having the electromagnetic properties he had been searching for, and his conjecture faded into obscurity.

Fig 3:

Then why are there no materials with negative ε and μ? One first needs to understand what it means to have a negative ε or μ and how negative values occur in materials. It is known that the permittivity and permeability are the only relevant material parameters for electromagnetic waves. If this is known it is possible to imagine a 'material parameter space' into which all materials can be placed. On the X-axis we plot values of the permittivity, and on the Y-axis the values that correspond with the permeability. The results can be seen in the graph below, the axes intersect at the origin (where both permeability and permittivity are equal to zero). In this simplistic but very logically representation, it can be imagined that all materials--as