Photonic metamaterial

Photonic metamaterials are a type of electromagnetic metamaterial. These are designed to interact with optical frequencies (mid-infrared). As a type of EM metamaterial, the periodic structures are made up of single units called cells. These single units are much smaller than the wavelength of the radiated source. In the case of photonic metamaterials, the radiated source is at optical wavelengths. Furthermore, the sub-wavelength period disttnguishes the photonic metamaterial from photonic band gap structures. This is because the special optical properties do not arise from photonic bandgaps, but rather from an interaction with light which mimics atoms or ions. However, the periodic cells (meta-atoms) are fabricated on a scale, which is much larger, magnitudes larger, than the atom.

Electromagnetic metamaterials in general are designed to operate at different frequencies. For example, prior and current research is in the microwave domain with physical periodic cell structures on the scale of milimeters. Because the optical wavelengths (wavelengths of a few microns) are much shorter than microwave frequencies, photonic metamaterial cell structures are on the scale of nanometers.

In a naturally occurring, (conventional) material, the response to electric and magnetic fields, and hence to light, is determined by the atoms As a type of metamaterial, the photonic metamaterial is an artificially engineered structure. Therefore, each cell is designed with specific parameters by which it interacts with the radiated field at optical frequencies. At the same time, however, metamaterials in general and photonic metamaterials specifically, are described as homogeneous materials, or utilizing an effective medium model.

The development of photonic metamaterials

With metamaterials has come the realization of possibilities, which were once thought not possible before the late 1990s. Subwavelength imaging, super lenses, perfect lenses and EM cloaking were part of the science fiction genre. The structural units of metamaterials can be tailored in shape and size. Their composition and morphology can be artificially tuned, and inclusions can be designed and placed at desired locations to achieve new functionality. As of 2009 these possibilities are being developed in the lab, and some related metamaterial technologies are already in the commercial sector.

A fundamental beginning for understanding metamaterials in general, is understanding the propagation of light in conventional materials. Although light consists of an electric field and a magnetic field, conventional materials only react to the electric field. This results in only the most common optical effects. These common optical effects include ordinary refraction, common diffraction limitations in lenses and imaging. While researching whether or not matter interacts with the magnetic component of light, Victor Veselago discovered the possibility of a refractive index with a negative sign according to Maxwell's equations. According to Veselago, and confirmed by researchers 30 years later, a refractive index with a negative sign is the result of permittivity ε<0 and magnetic permeability μ<0.

Thirty years later μ < 0 was achieved with the first periodic split-ring resonator (SRR) structure. Specifically the SRR achieved μ < 0 at specified resonant frequencies. This was then combined with an array of metallic wires, which created the first metamterial, and the experimental demonstration of a negative index of refraction, at microwave frequencies. This was a material that was contrary to the conventional right-handed interaction of light found in conventional materials. Hence, these are dubbed left-handed materials or negative index materials, among other nomenclatures.

Within a only a few years the structures were scaled down for optical frequencies with nano-scale metamaterials. SRRs reach nanometer scales with special electron beam nanolithography techniques. A single, nanoscale, SRR cell has three very small metallic rods which are physically connected. This is configured into a U type of a shape, which then functions as a nano-inductor. The gap between the tips of the U-shape function as a nano-capacitor. Hence, it is then a nano-LC resonator, with resonance occurring at optical frequencies. These are the actual "inclusions" mentioned in the metamaterial literature, which create local electric and magnetic fields when externally excited. Most importantly, at optical frequencies, these inclusions are usually ten times smaller than the vacuum wavelength of the light C₀, at resonance frequency. The fabrication of the inclusions in this way can then be evaluated by using an effective medium approximation.

Effective medium approximations

An effective (transmission) medium approximation means that the combined overall effect of the inclusions, when reacting to an external excitation, are approximated to evaluate the metamaterial slab (the medium) as "effectively" homogenous. The slab also has effective parameters, which include effective ε, effective u. These are also approximated over the entire medium. Separate inclusions may have different values, but the overall effect results in an approximated effect for each parameter, hence, effective ε, effective u.

Typically, the metamaterials are fabricated as composite structures created by many identical resonant scattering elements with the size much smaller than the wavelength of the propagating electromagnetic waves. Such microstructured materials can be described in terms of macroscopic quantities– electric permittivity ε and magnetic permeability μ. By designing the individual unit cells of metamaterials, one may construct composites with effective properties not occurring in nature.

Furthermore, although these materials are artificially constructed they are behaving as "real" materials, because real materials also have a periodic structure; but - at atomic scales. Real materials have a refractive index, just like these artificial materials. However, these artificial materials are able to create the overall effect of negative refractive index. So there is no qualitative difference between a metamterial and a natural dielectric material. There is only a quantitative difference - the unit sizes interacting with light (EM radiation) are magnitudes larger with left-handed metamaterials.

The mechanics of optical frequency metamaterials

Stacking layers is important to achieve the desired results at optical frequencies. However, the surface configuration (non-planar, bulk) of the SRR metamaterial layers normally prevents stacking. Although a single-layer SRR structure can easily be constructed on a dielectric surface, it is relatively difficult to stack these bulk structures due to the tight alignment tolerance requirements. However, a layer by layer stacking technique for SRRs was published in 2007. It uses dielectric spacers to apply a planarization procedure to flatten the SRR layer.. As a result it appears that any number of layers can be made this way, including any chosen number of unit cells as well as intentional designing of the spatial arrangements of subsequent layers..

Photonic metamaterials: coupling magnetism at optical frequencies

The magnetic component of a radiated electromagnetic field has virtually no effect on natural occurring materials at optical frequencies. Therefore, for natural occurring materials magentic permeabiltiy, μ = 1 at optical frequencies. With the emegence of metamaterials, a new domain of optical materials has been created, and magnetic permeability µ no longer equals unity for materials at optical frequencies. For metamaterials µ ≠ 1, and much research and experimentation has been accomplished for permeability less than 0 (negative values); μ < 0.

Reviewing the characteristics of predetermined, engineered, periodic structures such as SRRs leads to an understanding of the physics of a periodic metamaterial. Meta-atoms are used to create conditions where a normally weak magnetic effect on materials is now strengthend in the new artificial materials. A meta-atom could be an SRR cell, the arrayed wire component of a YIG tuner, or any other artificial material designed to be periodic. This periodicity is one of the defining features of a photonic metamaterial, and which helps to distinguish it from a photonic crystal.

In such a design, the meta-atom becomes a larger scale, milimeter sized, magnetic dipole, when compared to the picometer sized atom. A meta-atom creates a magnetic dipole moment analgalous to the magnetic dipole moment of natural atoms. For meta-atom constructed from the precious metal, gold the condition of μ < 0 can be achieved at telecommunication frequencies but, still not across the range of the visible frequencies. The visible frequency has been elusive because the plasma frequency of any metal is the ultimate limiting condition.

Researchers are earnestly engaged in combining negative "magnetic" permeability μ < 0 with negative "electric" permeability ε < 0, which can occur in each meta-atom when engineered to do so.

In 2006 researchers from various research facillities agreed to state the following: "Possibly, the real potential of the photonic metamaterials lies in other unexplored areas, for example, in chiral metamaterials or in nonlinear metamaterials. In any case, given today’s possibilities regarding the nanofabrication of tailored “atoms,” only our own imagination and creativity set the limits."

Three-dimensional photonic metamaterials at optical frequencies

As has been already established, metamaterials are artificial media, and the unit cells of metamaterials is much smaller than the wavelength of light. As of December 2007, the physical characteristics of metamaterials, which include negative permeability and negative refraction, had been limited to demonstrations in two-dimensions. However, a group of researchers at the Physikalisches Institut - Universität Stuttgart perceived that the practical applications of these physical characteristics require three-dimensional bulk like structures. Up to this time, fabrication techniques were most compatible in the GHz range for microwave applications.

By simply stacking printed circuit boards applications were available at GHz frequencies in the microwave range. This fabrication technique of metal–dielectric stacks is successful in this frequency range. However, a stacking technique in the optical (infrared) domain encountered technical problems which limited the number of stacked layers. So, an alternative to the unsuccessful stacking attempt was presented. The selected alternative is the split-ring resonator (SRR) structure. The SRR structure is widely used, and has induced negative values for permeability, for certain frequency ranges. SRR have been used in metamaterials since the 2001 demonstration.

The completed SRR metamaterial layers cannot be stacked, as it is not a flat (or planar) surface. This design pevents stacking. So, the SRR layers were flattened with dielectric spacers.

Dyakonov surface waves in photonic metamaterials

Suitable photonic metamaterial structures can support lossless surface waves of the form envisaged by Dyakonov. Surface waves are a special type of waves that are confined at the very boundary between two different media. By their very nature, surface waves are unique tools to explore the properties of material interfaces. This includes not only intrinsic properties but also extrinsic effects, thus making surface waves ideal tools for sensing physical, chemical, and biological agents. They feature genuine physical phenomena as well as prospects for far-reaching applications.

A unique type of surface waves was discovered theoretically by Dyakonov more than a decade ago. Like plasmons polaritons, they exist at the surface of two different materials, and should feature similar excitation and detection properties. However, in contrast to plasmons, Dyakonov surface waves exist in transparent media; thus they are lossless.

Negative-index photonic metamaterial at 780 nm wavelength

Photonic metamaterials are tailored artificial optical materials composed of sub-wavelength metallic building blocks that can be viewed as nano-scale electronic circuits. These building blocks or “photonic atoms” are densely packed into an effective material such that the operation wavelength (gamma) is ideally much larger than the lattice constant a for the polarization configuration shown in the metamaterial can be viewed as composed of two sets of sub-circuits or “atoms”: A coil with inductance L in series with two capacitors with net capacitance C as an LC circuit, providing a magnetic resonance at the LC resonance frequency. Long metallic wires, acting like a diluted metal below the effective plasma frequency of the arrangement. Negative magnetic permeability and the negative electric permittivity are created, which leads to lead to a negative index of refraction. Silver was used as constituent material because it is known to introduce significantly lower losses than gold and other noble metals at visible frequencies.

Optical negative-index metamaterials

Describing the recent progress (in 2006) made in creating nanostructured metamaterials with a negative index at optical wavelengths, and discusses some of the devices that could result from these new materials.

Experimental demonstration of near-infrared NIMs

Received 7 March 2005 and published in September of that year was the first fabrication and experimental verification of a transversely structured metal-dielectric-metal multilayer exhibiting a negative refractive index around 2 μm. Both the amplitude and the phase of the transmission and reflection were measured experimentally, and are in good agreement with a rigorous coupled wave analysis.

Three-dimensional optical metamaterial

Here is a 3D optical metamaterial having negative refractive index with a very high figure of merit ref# of 3.5. 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. Constructed as a 21-layer fishnet structure with a unit cell parameters of a = 5.860 µm, b = 5.565 µm and c = 5.265 µm.

Negative refraction at 813 nm and 772 nm

Wavelengths of 813 nm and 772 nm approach the red end of the visible spectrum. A double negative refraction occurs at 813 nm and single negative refraction occurs at 772 nm.

Phase-engineered Metamaterial Structures and Devices

Electromagnetic metamaterials are inherently dispersive: their constitutive pa- rameters (permittivity and permeability) are functions of frequency or, equivalently, their dispersion relation is a nonlinear function of frequency.

Since the invention of the superheterodyne receiver by Edwin Armstrong in 1918 and, later, the development of e±cient harmonic signal generators, most radio communication systems have been narrow-band in nature. However, the explosion of needs for high data-rate wireless links is currently producing a paradigmatic shift of radio toward broadband and ultra-wideband spec- trum operation. In this context, the unprecedented and tailorable dispersive properties of metamaterials may provide solutions to several new challenges. While the past decades have fo- cused on magnitude engineering and filter design we predict that the forthcoming decades will experience major interest in phase engineering (where the term "phase engineering" is intended to represent both "dispersion and nonlinearity" engineerings) along with phase-engineered devices. In this case metamaterials are expected to play an important role.

See also

• Acoustic metamaterials
• Metamaterial
• Negative index metamaterials
• Metamaterial antennas
• Perfect lens
• Photonic crystal
• Seismic metamaterials
• Split-ring resonator
• Terahertz metamaterials
• Tunable metamaterials

Electromagnetic interactions

• Bloch wave
• Casimir effect
• Dielectric
• EM radiation
• Electron mobility
• Permeability (electromagnetism)*
• Permittivity*
• Wavenumber
• Photo-dember
• Impedance