Negative Index of Refraction
In Left Hand Material

Composite MetaMaterials Have Unnatural Electromagnetic Properties

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http://www-physics.ucsd.edu/lhmedia/how.html

How Do MetaMaterials Work?

 

MetaMaterials exhibit electromagnetic properties not observed in nature. An example MetaMaterial is composed of conducting split ring resonators (SRRs) and wires on thin fiberglass circuit board material, arranged in a regular array of cells. For X-band the SRRs and wires are arranged into a two-dimensional structure with a 5mm lattice parameter. The figure (a) below is a diagram of an SRR. Figure (b) shows one unitcell.

 

 

 

 

To start with, the index of refraction (n) is given by:

where ε is the permittivity, µ is the permeability, ε_o and µ_o are the free-space permittivity and permeability, respectively. Near the resonant frequency of the split ring resonators (SRRs) the magnetic field drives the permeability below zero on the high frequency side of the resonance and the resonant response of the wires in the electric fields. The general expressions for ε and µ are as follows:

Where ω_ep is the electric plasma frequency, ω_eo is the electric resonance frequency, ω_mp is the "magnetic plasma frequency", ω_mo is the magnetic resonance frequency. The following parameters were plugged into the previous equations to generate the plot below.

Notice that both µ and ε are negative from about 10.4 GHz to 11 GHz. In this frequency band the MetaMaterial is "left-handed", that is, the familiar right hand rule ExH=S becomes reversed. In this regime, the phase velocity and group velocity point in opposite directions. Energy is transmitted in the opposite direction of propagation.

 

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http://www.eetimes.com/at/news/showArticle.jhtml?articleID=18400308

PORTLAND, Ore.

Metamaterial experts bridged the terahertz gap recently by demonstrating a magnetic sensor based on split-ring resonators. By downsizing a microwave SRR from 5 millimeters to 50 microns, the researchers demonstrated a magnetic response that bridges the terahertz gap, thereby opening the door to solid-state sensors that can see through solid objects.

In the terahertz gap-roughly between the wavelengths of 1 micron and 300 microns (or in the 100-GHz and 30-THz frequency range) is too fast for silicon, which peaks out above 100 gigahertz (300-micron wavelength), but too slow for optical, which bottoms out at less than 30 terahertz (1-micron wavelength). As a result, the search is on for materials that can bridge the terahertz gap between 100 GHz and 30 THz.

,According to doctoral candidate Willie Padill and physics professor Dimitri Baso at the University of California at San Diego (UCSD), the terahertz range is important for automated inspection, zero-visibility navigation, biomedical imaging and security applications.

In 1968, Russian theorist Victor Veselago predicted that metamaterials with these properties would interact with their environment in a manner precisely the opposite of the way natural materials react. MetaMaterials use repeated composite structures like SRRs with properties specifically engineered to enable permeability and permitivity to take on both positive and negative values. Those two properties determine how a material will interact with electromagnetic radiation, from high-frequency light down to terahertz waves, microwaves and radio waves. All natural materials have both positive permeability and permitivity, but metamaterials can have negative permeability and permitivity, which is unheard-of in nature.

To downsize from microwave to terahertz frequencies, the UCSD researchers had a conductive pattern lithographically imprinted in the shape of copper split-ring resonators arranged into a 2-D structure with a repeated 50-micron lattice. The SRRs were arranged in groups of two resonators each, a smaller ring inside a larger one. Next, the UCSD researchers want to demonstrate that micron-sized SRRs can also detect absorption patterns in the terahertz range, enabling chip-sized SRRs to "see through" clothing and baggage to identify weapons and explosives, or to guide an airplane on a foggy night.

The work was supported by the Multidisciplinary University Research Initiative sponsored by the Defense Advanced Research Projects Agency through the Office of Naval Research and the U.S. Army Research Office, as well as the National Science Foundation.

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http://www.ee.duke.edu/Academics/Undergraduate/IndStudy03/ScottC2003.html

Towards Negative Index Material: Magnetic Response

Colin Scott, Senior Pratt Engineering Undergraduate Research Fellow, Electrical Engineering
Dr. Steven Cummer, Assistant Professor, Department of Electrical and Computer Engineering

Introduction

A material that simultaneously possesses negative permeability and negative permittivity would cause electromagnetic waves traveling through this medium to exhibit certain unnatural characteristics. One of these properties is a reversal in the right-handed rule which the electric and magnetic fields follow with respect to the propagation vector of the wave. In these materials there would be a left-handed relationship between these vector quantities, hence the name left-handed materials (LHM). Another very interesting property is a negative refractive index for the material, hence the alternate name negative index material (NIM). Materials that have such properties would be very useful in elecromagnetics. They could be used in novel antennas, filters and waveguides for electromagnetic communications. They could also improve semiconductor lithography techniques and near-field imaging techniques.

Materials with simultaneously negative permeability and permittivity can be realized with carefully designed lattices of conducting materials, which separately result in either negative permeability or permittivity, can be interlaced to simultaneously obtain negative properties of permittivity and permeability.

Results

A building block of this artificial magnetic media, which was a split-ring resonator (SRR). A lattice of SRRs act as a homogenous, artificial magnetic medium that would have a negative permeability over a certain frequency range. I experimentally verified that it performed as a material with the functional form of permeability as follows:

This is the functional form which would provide the appropriate magnetic response necessary for the production of NIM.

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The full final report is available here in Adobe Acrobat Reader (pdf) format.

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http://www.fen.bilkent.edu.tr/~ozbay/Papers/60-02apl-LHMbayndir.pdf

In recent years, Composite MetaMaterials "CMMs" have inspired great interest due to their unique physical properties and novel applications of these materials. [1,2] Two important parameters, electrical permittivity ε and magnetic permeability µ, determine the response of the material to the electromagnetic radiation. Generally, ε and µ are both positive in ordinary materials. While ε could be negative in ordinary materials (for instance in metals), no natural materials with negative mare known. However, for certain structures which are called left-handed materials (LHM), both the effective permittivity ε_eff and permeability µ_eff possess negative values. In such materials the index of refraction is less than zero, and therefore, phase and group velocity of an electromagnetic (EM) wave can propagate in opposite directions. This behavior leads to a number of interesting properties. [3] The phenomena of negative index of refraction was first theoretically proposed by Veselago in 1968. [4] Veselago also investigated various interesting optical properties of the negative index structures.

http://www.fen.bilkent.edu.tr/~ozbay/Papers/70-03-ieee-ozbay_tap_2003.pdf http://www.photonics.com/spectra/tech/XQ/ASP/techid.848/QX/read.htm http://ceta-p5.mit.edu/metamaterials/papers/external/2004/Krowne_prl_2004.pdf http://ceta-p5.mit.edu/metamaterials/papers/external/2000/smith.K_prl_2000.pdf http://www.fen.bilkent.edu.tr/~ozbay/Papers/70-03-ieee-ozbay_tap_2003.pdf

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