Recently, artificially constructed metamaterials have become of considerable interest, because these materials can exhibit electromagnetic characteristics unlike those of any conventional materials. Artificial magnetism and negative refractive index are two specific types of behavior that have been demonstrated over the past few years, illustrating the new physics and new applications possible when we expand our view as to what constitutes a material. In this review, we describe recent advances in metamaterials research and discuss the potential that these materials may hold for realizing new and seemingly exotic electromagnetic phenomena.

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Metamaterials and negative refractive index.

Recent theory has predicted a superlens that is capable of producing sub–diffraction-limited images. This superlens would allow the recovery of evanescent waves in an image via the excitation of surface plasmons. Using silver as a natural optical superlens, we demonstrated sub–diffraction-limited imaging with 60-nanometer half-pitch resolution, or one-sixth of the illumination wavelength. By proper design of the working wavelength and the thickness of silver that allows access to a broad spectrum of subwavelength features, we also showed that arbitrary nanostructures can be imaged with good fidelity. The optical superlens promises exciting avenues to nanoscale optical imaging and ultrasmall optoelectronic devices.

http://science.sciencemag.org/content/sci/308/5721/534.full.pdf

Sub-Diffraction-Limited Optical Imaging with a Silver Superlens

Metamaterials are artificially engineered structures that have properties, such as a negative refractive index, not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies, but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals. Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide. Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction. Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded 'fishnet' structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices, compact resonators and highly directional sources.

Three-dimensional optical metamaterial with a negative refractive index

We show that magnetic response at terahertz frequencies can be achieved in a planar structure composed of nonmagnetic conductive resonant elements. The effect is realized over a large bandwidth and can be tuned throughout the terahertz frequency regime by scaling the dimensions of the structure. We suggest that artificial magnetic structures, or hybrid structures that combine natural and artificial magnetic materials, can play a key role in terahertz devices.

http://science.sciencemag.org/content/sci/303/5663/1494.full.pdf

Terahertz magnetic response from artificial materials.

In this paper, a new approach for the development of planar metamaterial structures is developed. For this purpose, split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) coupled to planar transmission lines are investigated. The electromagnetic behavior of these elements, as well as their coupling to the host transmission line, are studied, and analytical equivalent-circuit models are proposed for the isolated and coupled SRRs/CSRRs. From these models, the stopband/passband characteristics of the analyzed SRR/CSRR loaded transmission lines are derived. It is shown that, in the long wavelength limit, these stopbands/passbands can be interpreted as due to the presence of negative/positive values for the effective /spl epsiv/ and /spl mu/ of the line. The proposed analysis is of interest in the design of compact microwave devices based on the metamaterial concept.

Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines

We report the results of a Snell's law experiment on a negative index of refraction material in free space from 12.6 to 13.2 GHz. Numerical simulations using Maxwell's equations solvers show good agreement with the experimental results, confirming the existence of negative index of refraction materials. The index of refraction is a function of frequency. At 12.6 GHz we measure and compute the real part of the index of refraction to be $\ensuremath{-}1.05$. The measurements and simulations of the electromagnetic field profiles were performed at distances of $14\ensuremath{\lambda}$ and $28\ensuremath{\lambda}$ from the sample; the fields were also computed at $100\ensuremath{\lambda}$.

Experimental verification and simulation of negative index of refraction using Snell's law.

Negative index of refraction materials have been postulated for many years but have only recently been realized in practice. In the microwave region these materials are constructed of rings and wires deposited on a dielectric substrate to form a unit cell. We have constructed, experimentally characterized and simulated several of these structures operating in the 10 - 15 GHz range. Our simulations using Maxwell's Equations solvers have included wire arrays, ring arrays and assemblies of unit cells comprised of rings and wires. We find good agreement between the numerical simulations and experimental measurements of the scattering parameters and index of refraction. The procedure was to first model ring and wire structures on the unit cell level to obtain scattering parameters from which effective a, i and n were retrieved. Next an assembled array of unit cells forming a 12 degrees wedge was used for the Snell's Law determination of the negative index of refraction. For the structure examined the computed value of n is within 20% of the one experimentally measured in the Snell's Law experiment from 13.6 to 14.8 GHz.

Experimental determination and numerical simulation of the properties of negative index of refraction materials

We propose and implement a procedure for enhancing the sensitivity with which one can determine the phase shift experienced by a thermal light beam possessing on average fewer than four photons in passing through an interferometer. Our procedure entails subtracting exactly one (which can be generalized to m) photon from the light field exiting an interferometer containing a phase-shifting element in one of its arms. As a consequence of the process of photon subtraction, the mean photon number and signal-to-noise ratio (SNR) of the resulting light field are increased, leading to an enhancement of the SNR of the interferometric signal for that fraction of the incoming data that leads to photon subtraction.

Quantum-enhanced interferometry with weak thermal light

We propose and implement a quantum procedure for enhancing the sensitivity with which one can determine the phase shift experienced by a weak light beam possessing thermal statistics in passing through an interferometer. Our procedure entails subtracting exactly one (which can be generalized to m) photons from the light field exiting an interferometer containing a phase-shifting element in one of its arms. As a consequence of the process of photon subtraction, and somewhat surprisingly, the mean photon number and signal-to-noise ratio of the resulting light field are thereby increased, leading to enhanced interferometry. This method can be used to increase measurement sensitivity in a variety of practical applications, including that of forming the image of an object illuminated only by weak thermal light.

Interferometry with Photon-Subtracted Thermal Light

We discuss the numerical simulation of a graded refractive index (GRIN) lens with a general anisotropic medium and compare it with an equivalent nongraded positive-index-of-refraction-material (PIM) lens with an isotropic medium. To evaluate lens performance, we developed a modified eikonal equation valid for the most general form of an anisotropic or chiral medium. Our approach is more comprehensive than previous work in this area and is obtained from the dispersion relation of Maxwell's equations in the eikonal approximation. The software developed for the numerical integration of the modified eikonal equation is described. Subsequently, a full finite-difference time-dependent simulation was performed to verify the validity of the eikonal calculations. The performance of the GRIN lens is found to be improved over the equivalent PIM one. The GRIN lens is also five to ten times lighter than the equivalent PIM. A GRIN lens operating at 15 GHz is now under fabrication at Boeing, and the experimental results of this lens will be reported in a forthcoming paper.

Benjamin E. Koltenbah

Papers

Experimental verification and simulation of negative index of refraction using Snell's law.

Experimental determination and numerical simulation of the properties of negative index of refraction materials

Quantum-enhanced interferometry with weak thermal light

Interferometry with Photon-Subtracted Thermal Light

Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material