Metamaterials for Aerospace Applications

Metamaterials for Aerospace Applications

Defense Intelligence Reference Document, Acquisition Threat Support. DIA-08-1004-006, 6 April 2010 (ICOD: 1 December 2009).

Prepared by the Defense Intelligence Agency. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency Advanced Aerospace Weapon System Applications (AAWSA) Program.

Definition of Metamaterials

A metamaterial is defined as an artificial medium whose properties (mechanical, optical, magnetic, or other) cannot be found in naturally-occurring materials. The emphasis of this study will be on electromagnetic and optical metamaterials. Such metamaterials can exhibit rather extreme properties, such as negative refractive index, which implies that both electric permittivity and magnetic permeability must be negative, that is, ε and µ both less than zero (Reference 1). Such metamaterials used to be called "left-handed" because of the unusual phase relationship between the electric and magnetic fields. Specifically, in most positive index media, including vacuum, one uses the right-hand rule to define the relationship between electric field (E), magnetic field (H), and the propagation wavenumber (k). The physical basis of the right-hand rule is that the direction of energy propagation defined by the Poynting vector S = cE × H/4π and the direction of the phase velocity (defined by the wavenumber k) must coincide. That does not hold true for negative index metamaterials, where the two directions are opposite; therefore, the left-handed relationship must hold for the three vectors. Nevertheless, the "left-handed" designation did not withstand the test of time because it was causing confusion and creating irrelevant allusions to helical (a.k.a. chiral) structures. Although chiral structures can indeed exhibit negative index behavior (Reference 2), chirality is not necessary.

A typical metamaterial consists of resonant elements such as Split Ring Resonators (SRR). An example of an SRR is shown in Figure 1. The main function of the SRR is to enable strong magnetic response of the structure. A simple empirical formula exists for the magnetic permeability of a metamaterial comprised of the SRRs:

(Equation 1, the resonant formula for the magnetic permeability, is too damaged in the released scan to reproduce.)

where ωM is the resonant frequency of the SRR, and F is proportional to the volume filling factor of SRRs. It is noteworthy that SRRs are designed in such a way that it has a large capacitance. As the result, the resonant frequency of an SRR is small (that is, the SRR-containing cell is very sub-wavelength). In the example shown in Figure 1 (taken from Reference 6), the unit cell operated at ω/2π = 10 GHz is λ/10. In fact, the sub-wavelength size of the metamaterial is what distinguishes them from their close cousins: photonic crystals. By properly designing magnetic SRRs, it is possible to achieve any value of µ for any given frequency. Special challenges exist for optical structures, though, as will be explained below.

Figure 1. Example of a Metamaterial Component: the Magnetic Split Ring Resonator (SRR) Design. In-plane lattice parameters are a1 = a2 = 10/3 mm. The ring is square, with edge length l = 3 mm and tracewidth w = 0.2 mm. The substrate is 381 µm-thick Duroid 5870 (ε = 2.33, td = 0.0012 at 10 GHz, where td is the loss tangent). The Cu film, from which the SRRs are patterned, is 17 µm thick. The parameters r and s are given in the table together with the associated value of µr (Reference 6).

| cyl | r | s | µr | |---|---|---|---| | 1 | 0.260 | 1.654 | 0.003 | | 2 | 0.254 | 1.677 | 0.023 | | 3 | 0.245 | 1.718 | 0.052 | | 4 | 0.230 | 1.771 | 0.085 | | 5 | 0.208 | 1.825 | 0.120 | | 6 | 0.190 | 1.886 | 0.154 | | 7 | 0.173 | 1.951 | 0.188 | | 8 | 0.148 | 2.027 | 0.220 | | 9 | 0.129 | 2.110 | 0.250 | | 10 | 0.116 | 2.199 | 0.279 |

Electric properties of metamaterials can be similarly controlled. An example of a planar electrically-active metamaterial is shown in Figure 2.

Figure 2. Example of Another Metamaterial Component: Electric Ring Resonator (ERR). This component provides tunable resonant electric response to the incident electromagnetic field, and can be utilized for engineering the frequency-dependent dielectric permittivity ε(ω). Possible application: THz and microwave absorbers. (Reference 7)

The electric response of such (or similar) metamaterial is given by

(Equation 2, the resonant formula for the dielectric permittivity, is too damaged in the released scan to reproduce.)

where ω0 is the resonant frequency and Γ is the loss coefficient.

Negative index metamaterials are by no means the only potentially useful metamedia. Several new concepts such as Indefinite Permittivity Metamaterials (IPM) (References 3, 4) and Epsilon-Near-Zero (ENZ) metamaterials (Reference 5) have recently emerged and found some exciting applications that will be reviewed below. IPMs can be used as ultra-compact spatial filters (both high-pass and low-pass), whereas ENZ metamaterials can be used for making sub-wavelength waveguides capable of coupling close to 100 percent of the incident radiation (Reference 8), as well as directing it around tight bends with negligible bending losses. Yet another class of planar metamaterials, complementary metamaterials (CMMs), has recently emerged (Reference 7). Instead of using metallic structures deposited on a substrate (left panel of Figure 3), CMMs consist of slits in the continuous metal screen (right panel of Figure 3). The shape of the slits coincides with that of the materials themselves. Such complementary metamaterials have been recently used for making epsilon-near-zero waveguides (Reference 8).

Figure 3. Geometry of Original Planar Metamaterial Unit Cells (OE1-OE6) and Their Complements (CE1-CE6). The polarization of normally incident electromagnetic radiation is configured as shown in OE1 and CE1 for the original and complementary metamaterials, respectively. (Reference 9)

In general, metamaterials offer a new way of designing electromagnetic structures with arbitrary values of permittivity/permeability tensors, as well as other parameters (such as bi-anisotropy coefficient). In many instances, metamaterials enable us to considerably minimize sizes of resonators, transmission lines, and so forth. Such miniaturization is possible due to the resonant nature of the individual unit cells. Specifically, the structures shown in Figure 3 have high capacitance; therefore, their individual sizes are very sub-wavelength. That enables arrangement within sub-wavelength units that can be densely packed and result in strongly miniaturized components. It is this miniaturization that makes metamaterials interesting for aerospace application where small weight and size are essential.

While the most spectacular progress in the field of electromagnetic metamaterials has so far occurred in the microwave range, it is the optical (visible, infrared, mid-infrared) spectral regions that hold most promise for revolutionary applications. Electromagnetic metamaterials have a tremendous potential for revolutionizing propagation, storage, and conversion of electromagnetic waves across the entire Electromagnetic Spectrum. In our opinion, the most exciting applications that are relevant for aerospace applications include energy harvesting, developing novel optical devices with unusual yet practically important capabilities (for example, non-reciprocal devices), enhancing the efficiency of nonlinear optical devices, developing novel imaging modalities capable of breaking the diffraction limit (for example, super-lenses, hyper-lenses, far field super-lenses), and developing novel lithographic techniques.

Optical metamaterials are still a very new area. Just a handful of experimental demonstrations of multi-layer (truly bulk) optical metamaterials exist at the moment. Among the most recent ones are (a) demonstration of the negative index optical metamaterial at the telecommunications wavelength (Reference 10) that used the so-called fishnet structure shaped as a prism for demonstrating Snell's Law, and (b) demonstration of the Indefinite Permittivity Material (IPM) and negative refraction (which, in the context of anisotropic metamaterials, is not the same as negative refractive index) in the mid-infrared part of the spectrum (Reference 11). These structures have the distinction of being multi-layer (or bulk). Most previous examples of optical metamaterials have dealt with single or double-layer substances which cannot be, strictly speaking, characterized as metamaterials. The difficulty in obtaining strong magnetic activity in optical metamaterials has been explained in several recent reviews (References 12, 13). In a nutshell, the issue is that the magnetic moment of most structures, including atomic systems, is very small, much smaller than the electric moment. Therefore, it is difficult to observe any optical effects that can be clearly assigned to magnetic activity. This is especially true for the structures that are much smaller than one wavelength. Exceptions, such as artificially constructed split rings, are possible. However, such structures cannot be operated at very high frequency because of the excitation of electrostatic resonances (Reference 12). In other words, when the resonant frequency is too high (or the dielectric permittivity of a metal is not sufficiently large), electrostatic resonances disrupt magnetic activity. More specifically, the energy inside and in the vicinity of a metamaterial element (for example, Split Ring Resonator) becomes predominantly electrostatic, that is, in the form of the kinetic energy of oscillating electrons. The recently described multi-layer fishnet (Reference 10) is not an exception: its unit cell (that is, the lateral period) is only one-half of the operating wavelength.

Figure 4. Recent Optical Metamaterials for Telecommunication Wavelength λ = 1.5 µm (left and middle) and Mid-Infrared IPM. The multi-layer fishnet is made of silver films separated by a dielectric spacer. A focused ion beam was used to produce the prism-shaped fishnet. The IPM was obtained by depositing interleaved 80 nm layers of In0.53Ga0.47As and Al0.48In0.52As. The layers, approximately 8.1 µm thick, grown by molecular beam epitaxy on lattice-matched InP substrates. The InGaAs layers were uniformly doped to create different values of permittivity in alternating layers. (References 10 and 11)

That is not to say that there is not ongoing theoretical and experimental work on designing optical metamaterials for practical applications. The author's research group at UT-Austin has designed the first Plasmonic Negative Index Metamaterials (P-NIM) super-lens (Reference 14), developed novel techniques for analyzing optical properties of plasmonic nanostructures, including band-structure calculations of periodic nanostructures (Reference 15), and quasi-static calculations of plasmonic resonances (Reference 16). The UT-Austin group has also designed a number of unique sub-wavelength P-NIMs in the optical part of the spectrum (References 14, 17, 18), and has recently published a review of optical P-NIMs (Reference 12). The group has also contributed to developing and experimentally implementing the concept of the "perfect lens" (Reference 19) based on plasmonic/polaritonic materials. A perfect lens enables imaging of sub-wavelength objects in the infrared part of the spectrum, including objects buried under the surface. Also developed is a Wide-Angle "Perfect" Absorber of Mid-Infrared Radiation (WAPAMIR) (Reference 20) based on the negative index metamaterial whose impedance is perfectly matched to vacuum.

Below is a concise summary of various topics/applications that are especially suitable for the aerospace industry. This study concentrates on the facility of metamaterials to miniaturize various optical and microwave components. Metamaterials can also be used for imaging very small (sub-wavelength) objects without resorting to costly and space-consuming near-field scanning optical microscopy. Also described are the ongoing efforts in the field to make extremely compact metamaterials-based lasers. Smaller lasers mean smaller weight and more room for other diagnostic devices and useful payload within the confines of a space vehicle. Applications of metamaterials to photon harvesting is especially fitting for advanced aerospace platforms because of the necessity to collect electromagnetic energy for battery recharging, diagnostic spectroscopy, and other vital functions of a space vehicle.

• Complementary Metamaterials for Energy Harvesting. Development of ultra-thin photovoltaic and thermo-photovoltaic cells is hampered by weak photon absorption in semiconductors. Metamaterials can modify absorption making it wavelength-selective (tunable), highly efficient, and, if desired, wide-angle. Recently a way has been found for creating quarter-wavelength resonators backed by leaky mirrors made out of CMMs.
• Far Field Super-Lens Based on the Interferometry of Sub-Diffraction Waves. Sub-diffraction imaging has long been considered to be possible only using near-field microscopes. Those are fairly complex, slow-scanning, and large devices that are not appropriate for advanced aerospace platforms. Metamaterials enable new imaging modalities: super-lenses, hyper-lenses, and far-field super-lenses. In addition to a survey of the existing scientific literature, novel ideas on developing a new interferometric Far-field Super-Lens (FSL) based on the multi-beam multi-detector technique utilizing materials with Indefinite Permittivity Tensor are presented. Fabrication of such Indefinite Permittivity Materials (IPMs) for the mid-infrared part of the spectrum is achieved and demonstrates the capabilities of transmitting electromagnetic waves with the spatial period much smaller than the vacuum wavelength of light. Interference between sub-diffraction waves enables disentangling multiple diffractive orders and extracting their amplitudes.
• Nonlinear Non-Reciprocal Chiral Metamaterials: Developing Novel Optical Isolators and "One-Way" Microwave Mirrors. These developments are motivated by the need to construct one-way "light diodes" for compact optical isolators. Presently there are two approaches to optical isolation: the most common using magnetic fields, and the less developed based on using nonlinearities. A different approach relies on the phenomenon of adiabatic mode conversion in nonlinear chiral metamaterials. Preliminary theoretical results for a simple chiral fiber with a variable twist period (pitch) that enables full transmission of a tightly confined core mode in the forward direction and full mode-conversion of the core mode into a cladding mode for the backwards propagation is obtained.
• Slowing Down Light and Miniaturizing Optical Components Using the Phenomenon of Electromagnetically Induced Transparency in Metamaterials. The speed of light places a natural limit on the size of optical/microwave components. Metamaterials offer an exciting opportunity to slow down light. This has two major implications: (a) light can be stored/manipulated in smaller volumes, and (b) nonlinear effects are strongly enhanced by the resulting energy compression.

Applications to Sub-Diffraction Imaging: Super-Lens and Hyper-Lens

The super-lens is one of the earliest applications of metamaterials (Reference 21), and its principle is shown in Figure 5. Without the super-lens, all information about sub-diffraction (or sub-wavelength, which is equivalent) features of the periodic object would have been lost. The reason for the information loss is evanescent decay of the large spatial wavenumbers. The only method of accessing/measuring these features would be to scan the object using a near field scanning optical microscope. By inserting a super-lens between the object and the imaging plane, evanescent waves may be amplified and the image transferred forward. Unfortunately, this approach by itself does not remove the need for a near-field scanning device: the image that is recreated in the imaging plane is still sub-wavelength, and needs to be read out.

Figure 5. Schematic of the Super-Lens with n = −1 Refractive Index Corresponding to (ε = −1, µ = −1) Surrounded By Vacuum. The super-lens' presence enables imaging sub-diffraction objects such as the periodic grating shown here.

There are, however, interesting circumstances when it is very important to transport the image towards the scanning device. One such special circumstance is spatially-resolved spectroscopy of small (for example, cellular) structures. One can envision space expeditions to other planets that could, potentially, result in finding some evidence of primitive cellular-level life. It would then be highly desirable to examine the structure of the living cell in its natural environment. In all likelihood, that environment would be liquid. Therefore, it would be very desirable to examine the cell without actually touching it with a tip of a near-field optical microscope. Thus, the sub-surface imaging of a small object which is buried underneath a liquid layer would be necessary. No such experiments have so far been conducted. However, several years ago there was an experiment demonstrating imaging of sub-diffraction objects buried under the layer of silicon dioxide.

The schematic and experimental results from the experiment (Reference 19) are shown in Figure 6. In this experiment the sub-wavelength objects were simple holes that were milled in the metal using an FIB. They were buried underneath the super-lens consisting of SiC (negative epsilon material for mid-infrared frequencies) and silicon dioxide (positive epsilon material). Note that this configuration (a material with positive permittivity and a material with negative permittivity joined together: sandwiched or positioned next to each other) is typical for a near-field super-lens. The difference between the near-field super-lens shown in Figure 6 and the "ideal" super-lens shown in Figure 5 is that the ideal also requires a material with a negative value of magnetic permeability.

Figure 6. Schematic of the SiC-Based Super-Lens Which is Imaging Sub-Wavelength Holes Buried Under the SiO2 Layer. The imaged objects are λ/20 holes milled in gold using FIB. The scattered signal is picked up by the tip of an NSOM and directed towards the IR detector. Depending on the imaging wavelength, either amplitude (e) or the phase (f, g) of the signal are prominent.

As the laser beam scatters off the sub-wavelength holes, its electric field is picked up by the tip of a Near-Field Scattering Optical Microscope (NSOM) and re-scattered into the far-field. There it is interfered with the reference pulse and picked up by an infrared detector. Note that this interferometric technique enables one to extract both the phase and amplitude of the field, as shown in Figure 6. This significantly broadens the spectral range over which the super-lens yields meaningful information. For example, the amplitude contrast is highest at λ = 10.85 µm shown in panel (e) while the phase contrasts are the highest at λ = 11.03 µm and λ = 10.65 µm.

Despite the convenience of the near-field super-lens (that is, its ability to transport the image), it still requires an NSOM to read out the image. Within the confines of an advanced aerospace platform such device (with its necessary auxiliaries) may not fit. Therefore, one has to consider alternative metamaterials-based ideas for sub-diffraction imaging. One such idea, the hyper-lens, has been proposed recently by two groups (References 22–24), and already experimentally tested by another group (Reference 25). The principle of the hyper-lens is very simple: to use an indefinite permittivity medium (sometimes referred to as the hyperbolic medium because the relationship between the propagation wavenumbers and the frequency, also known as the constant frequency contour, has a hyperbolic nature) in a tapered format. Several conceptual implementations such as the spoke-like structure and the cylindrical multi-layer structure (see Figure 7, left panel) have been suggested. The hyper-lens works on two principles: (a) indefinite permittivity materials (of which the super-lens is one example) are capable of propagating sub-diffraction waves, and (b) the expanding nature of the hyper-lens can magnify images to the λ/2 size, at which point they become observable in a conventional microscope. One recent experimental implementation of the hyper-lens in UV is shown in the right panel of Figure 7. The hyper-lens is made of 16 layers of Ag/Al2O3. This specific hyper-lens was used for imaging a line pair object with line width of 35 nm and spacing of 150 nm and was operated at λ = 400 nm. The magnified image (350 nm spacing) can be clearly resolved with an optical microscope, numerical aperture (NA) = 1.4, thus demonstrating magnification and projection of a sub-diffraction-limited image into the far field.

Figure 7. Theoretical Concepts (left panel) and Experimental Implementation (right panel) of an Optical Hyper-lens Capable of Magnifying Sub-Diffraction Objects to Observable (larger than λ/2) Size. Panels credited to Jacob, Alekseyev and Narimanov, Opt. Exp. 2006; Salandrino and Engheta, PRB 2006; Govyadinov and Podolsky, PRB 2006; Liu et al., Science 2007.

Note that the hyper-lens concept does not require employing a bulky near-field scanning optical microscope. However, the practical implementation of the hyper-lens is by no means simple. The original implementation required depositing the sample on the curved surface of the hyper-lens. A more practical implementation of the super-lens has been theoretically proposed by another group (Reference 26). The concept is shown in Figure 8. The hyper-lens involves an array of thin metallic wires converging towards the tip. As is demonstrated, a dense array of metal wires separated by much less than the wavelength constitutes a metamaterial with the indefinite permittivity tensor. Specifically, the tensor component along the wires is given by:

(Equation 3, the permittivity tensor component along the wires, is too damaged in the released scan to reproduce.)

where the z component is along the wires and perpendicular direction is normal to the wires. Because the only propagating waves are the TEM waves satisfying the ω = kzc dispersion relation, this meta-medium is strongly anisotropic and supports sub-wavelength waves which perform imaging. The spatial resolution is given by the spacing between wires. Figure 8 (right panel) shows the magnified image of a small (λ/25) object placed at the tip of the hyper-lens. The magnification factor is 5x.

Figure 8. Hyper-Lens Based on a Converging Array of Metal Wires. A small object can be placed at the tip, illuminated from the top, and magnified by the expanding array of wires. Left panel: schematic. Right panel: λ/25 object magnified by a factor 5x by the expanding hyper-lens. This hyper-lens can operate at mid-IR frequencies. (Reference 26)

Another concept for sub-wavelength imaging employing metamaterials is the so-called Far-Field Super-Lens (FSL). The concept is pioneered in Reference 27. The idea is described in Figure 9. A sub-wavelength object (for example, two slits) is located at the bottom of a multi-layer super-lens. Another sub-wavelength grating is deposited on top of the super-lens. Because the super-lens (and for that matter, any indefinite permittivity material) is capable of propagating sub-diffraction waves, the electromagnetic perturbations created by the object are propagated through the super-lens upwards, until they encounter the sub-wavelength grating. At that point these sub-wavelength perturbations are diffracted on the image-releasing grating and converted into the far-field electromagnetic waves. Those far-field waves are collected by the objective of a microscope and observed through the eyepiece. The schematic is shown in Figure 9(a). Note that, again, there is no need for NSOM. The actual implementation of the FSL used the following object: a nanowire pair with 50 nm wide slit and 70 nm gap inscribed by focused ion beam on a 40 nm thick Cr film on the quartz substrate. Diffraction-limited image from a conventional optical microscope cannot resolve the two nanowires (NA = 1.4, λ0 = 377 nm) as can be seen in Figure 9(c), but the FSL-equipped microscope can as shown in Figure 9(d).

Figure 9. Far-Field Super-Lens Based on an Indefinite Permittivity Metamaterial Placed Between the Object and the Image-Releasing Grating. The grating releases into the far field sub-diffraction waves produced by light scattering off the object. The role of the metamaterial is to propagate sub-diffraction waves from object to grating. (Reference 27)

Despite the success of this demonstration, there are serious issues involved in imaging sub-wavelength objects. Specifically it is pointed out in Reference 27 that multiple diffractive orders can become entangled, that is, launched in the same direction into the far field. Disentangling these diffraction orders is very important. The payoff would be imaging of fully 2-D (flat) objects with a resolution smaller than the period of the image-releasing grating. More precisely, this ambiguity is illustrated by the right panel in Figure 10. If the sub-wavelength object is represented by the continuous spectrum (blue line), then the spectrum can be sampled within the discrete set of "zones" which are defined by the diffractive orders of the image-releasing grating. The width of each zone is 2π/D, and they are labeled as 1st order, 2nd order, and so forth. Wave numbers belonging to the different zones can be diffracted onto the same far-field detector as explained in Figure 10. In order to disentangle the 1st and the 2nd zones, a single detector cannot provide sufficient information. It turns out that using two detectors (A and B) and two laser beams (Beam A and Beam B) provides additional information that is sufficient to disentangle the two zones. This additional information is obtained by comparing the intensity on the two detectors A and B. Another advantage of this imaging technique is that it is interferometric in nature. Therefore, even if the contribution of some of these spectral zones' orders is very weak, it can still be detected because of the high sensitivity of the interferometric techniques. What makes this interference special is that it involves sub-diffractive waves propagating through the indefinite permittivity metamaterial. Below some of the experiments conducted in the laboratory that demonstrate such interference are discussed.

Ever since Merlin's invention (Reference 28) of the sub-diffraction near-field plate, it has become clear that the interference between sub-diffraction electromagnetic fields can result in the formation of a deeply sub-wavelength image. The near-field plate, however, is not an imaging device; its purpose is to create a well-defined image using an elaborate pre-fabricated sub-wavelength structure on the plate's surface. The goal for this study is to observe an a priori unknown sub-wavelength image using a near-field structure. In the past, successes (Reference 19) in retrieving images of sub-wavelength objects (such as λ/20 holes) using an NSOM for radiation detection are achieved. An NSOM is a near-field instrument; therefore, a much more desirable detection method would involve far-field detection. To advance this goal, and to develop a tool sometimes referred to as the FSL, we have initiated research on multi-beam multi-detector sub-wavelength holography illustrated in Figure 10.

Figure 10. Tomographic Multi-Beam Multi-Detector Holography of Sub-Wavelength Objects Using Indefinite Permittivity Medium (IPM). Incident beams scatter off the sub-wavelength object, propagate through the IPM, and then get re-scattered into the far field by the grating with the period D. The purpose of the multi-detector arrangement is to disentangle the k1 and k2 spatial wave numbers in the object's spectrum (shown in the left panel). Beams A and B are phase-shifted with respect to each other.

Our implementation of the FSL utilizes an IPM whose dielectric permittivity tensor is anisotropic and contains positive and negative components: the component perpendicular to the IPM/object interface is positive while the parallel component is negative. We have already fabricated such IPMs using SiO2-SiC-SiO2 multi-layers, and are investigating other approaches involving selectively-doped semiconductor multi-layers similar to the ones used by Gmachl's group at Princeton. SiO2-SiC-SiO2 multi-layers are produced in-house (with SiC films shipped by Professor Ferro from University of Lyons, France). The main function of the IPM is to propagate sub-diffraction waves, whose parallel wavenumber exceeds ω/c, with as little decay as possible. That happens because these sub-diffraction waves are no longer evanescent. It is demonstrated experimentally that there exists a frequency range for which sub-diffraction waves propagate through the IPM with less attenuation than the radiation-zone waves, whose parallel wavenumber is smaller than ω/c; see Figure 11.

Figure 11. First Experimental Demonstration of Propagating Sub-Diffraction Waves in the IPM. (Left): experimental setup demonstrating how sub-diffraction waves are launched into the IPM using FIB-fabricated sub-wavelength grating. Because the periods of the bottom ("launching") and top ("transforming") gratings are different, far-field observation of different harmonics of the bottom grating is enabled. (Right): experimental results — the first sub-diffraction harmonic of the grating (green line) becomes stronger than the zeroth radiation-zone harmonic of the grating (blue line) in the region where the perpendicular permittivity is positive and the parallel permittivity is negative.

Once sub-diffraction waves propagate through the IPM, they can diffract on the image-releasing grating (see Figure 10) and be radiated out into the far field. A detector array can be used to collect the signal and reconstruct the image. Unfortunately, different wave numbers of the object are directed into the same detector and produce an ambiguity in extracting their respective amplitudes. This ambiguity is illustrated by Figure 10: wave numbers k1 = Δk + 2π/D and k2 = Δk + 4π/D are directed to the same far-field detector. Simply put, a single number (intensity of light with the wave number Δk smaller than ω/c incident on the detector) is insufficient for determining two scattering amplitudes A(k1) and A(k2). Therefore, a new concept has to be developed, and the multi-detector technique is such a concept.

The concept requires two detectors and two coherent laser beams. The two beams are formed using a beam-splitter and a variable delay line imparting a phase shift to the two beams (see the actual experimental photograph in Figure 13 where the beam-splitter BS and the Delay Line are shown). We have theoretically demonstrated that the intensity dependences of the two detector intensities I1(ψ) and I2(ψ) as a function of the phase delay ψ provides enough information to recover both A(k1) and A(k2).

Figure 12. (Left): Schematic for 2-Beams/2-Detectors Interferometric Measurement. (Right): Numerical Simulation — intensity on the two detectors as a function of the phase delay between beams A and B produced by the interference between the zeroth and first diffractive orders of the bottom diffractive grating. The second detector provides the necessary second data point which is necessary for separating the contributions of different diffractive orders.

Two sets of experiments demonstrating the feasibility of the concept are conducted. None of these experiments constitutes imaging per se. However, without demonstrating the two key milestones described below, proper imaging experiments cannot be attempted.

The first milestone involves demonstrating that IPM indeed supports propagating (non-evanescent) sub-diffraction waves. Figure 11 shows the experimental schematic (left panel) and experimental results. The bottom grating "imprints" its Fourier components (zeroth, first, second, third, and so forth) onto the incident laser pulse, thereby generating electromagnetic waves that are launched into the SiC-based IPM. The zeroth harmonic is inside the radiation zone (that is, it is not sub-diffraction), while the first, second, and so forth are sub-diffraction. These EM waves scatter off the top grating having a slightly different period and are released into the far field. Because the direction in which waves are released depends on the Fourier harmonic's number, we can experimentally separate and measure them. Clearly, the relative magnitudes of these diffractive orders dramatically vary as a function of the laser wavelength. For example, the zeroth diffraction order clearly dominates in the frequency range where the perpendicular permittivity is negative and the parallel permittivity is positive. However, in the frequency range where the perpendicular permittivity is positive and the parallel permittivity is negative, the first diffractive order becomes larger than the zeroth one. This confirms the recently predicted effect that for IPMs one can indeed observe a very counterintuitive effect: sub-diffraction waves can indeed propagate with less loss than the diffraction-limited ones.

The second milestone involves demonstrating the possibility of observing the interference of sub-diffraction electromagnetic waves inside the IPM using the two-beam/two-detector technique. Figure 10 demonstrates this interference pattern which reveals the phase advance of the sub-diffraction waves inside the IPM. While we have so far demonstrated the interference between the first Fourier component of the grating (sub-diffraction) and the zeroth Fourier component, we see the possibility of interfering even more sub-diffraction waves (2nd and 3rd).

Figure 13. (Left): Experimental Setup for 2-Beams/2-Detectors Interferometric Measurement in Our Lab. (Right): Preliminary Experimental Results — infrared intensity on two detectors (red and black lines) are (i) different from each other; (ii) have a sinusoidal dependence on the delay line position (in microns), which is equivalent to the phase delay between the two beams; (iii) are shifted in phase by the amount equal to twice the phase difference between the 1st order (sub-diffraction) and 0th order (radiation zone) Fourier components of the bottom grating. Measurements taken at λ = 10.8 µm and λ = 11.3 µm.

With these two milestones established, it is now possible to conduct true sub-wavelength imaging experiments using two (or more) far-field detectors and jointly processing their inputs.

Applications to Circuits and Waveguide Miniaturization: Slowing Down and Manipulating Electromagnetic Pulses (EMP) Using Advanced Metamaterials

Given the space constraints of an advanced aerospace platform and the amount of the useful payload that has to be carried, it is very important that every optical and microwave component be as small as possible. Because of the very large speed of light, there is a natural limit to how small such components can be made. Any structure capable of processing EMPs (be those optical, THz, or microwave) of temporal duration τ must be at least L = cτ long. For example, a 1 ns microwave pulse can be manipulated inside a device that is at least 1 ft long. Pulse manipulation can be understood very broadly by pulse compression, frequency shifting, harmonics generation, or other. For aerospace communications systems, it may be very desirable to have the ability to manipulate the format of EMPs, that is, to change their frequency, duration, and repetition rate. Slowing down or even stopping the EMP can circumvent the length requirement if the group velocity is reduced to a value much smaller than c, and thus the required length is L = vgτ.

Figure 14. Schematic of Pulse Compression in Magnetized Plasma. A radiation pulse with initial frequency ω0 and duration τ slows down in the plasma to a group velocity vg0 much smaller than c. Adiabatic spatially uniform variation of the magnetic field changes the radiation frequency to ω1 and increases the group velocity to vg1, much larger than vg0. The emerging pulse is compressed to τ1 = τ vg0/vg1. (Reference 29)

An example of the pulse slowing down and subsequent manipulation is first discussed in Reference 29 in the somewhat esoteric context of magnetized plasma. Pulse duration, frequency, and (for multiple pulses) repetition rate can be controlled by storing (or slowing down) electromagnetic waves and subsequently changing the system's parameters. The essence of the compact pulse manipulator is shown in Figure 14. The pulse is slowed down inside the compact plasma device and manipulated by changing the magnitude of the magnetic field. The advantage of slowing the pulses down is three-fold. First, the device can be made smaller, resulting in size savings. Second, the temporal scale on which the system has to be manipulated is lengthened because the pulse is moving slowly. Finally, the potentially large ratio between vg1 and vg0 results in the more dramatic dynamic range of possible pulse compression ratios. Plasma-based devices may not be appropriate in the aerospace context because of their large size, power requirements, large magnetic coils, and so forth.

Fortunately, metamaterials offer some exciting opportunities for slowing down electromagnetic waves as has been recently recognized (Reference 30). Specifically, the authors have theoretically demonstrated that an axially varying heterostructure with a metamaterial core of negative refractive index can be used to efficiently and coherently bring light to a complete standstill. One of the most remarkable aspects of the approach is that it works for relatively broadband pulses. The broadband capability is achieved through "tapering" (or axial variation) of a metamaterial's parameters such as the effective ε and µ. Due to tapering, each frequency component of the wave packet is stopped at a different guide thickness, leading to the spatial separation of its spectrum and the formation of a "trapped rainbow." In Reference 30, the authors have actually opted for a physical tapering of the waveguide (that is, reducing the thickness of the NIM waveguide along the length of the waveguide), although other approaches such as varying ε and µ will also work.

Figure 15. Trapped Rainbow: a Waveguide with Negative Index Core Can Stop Light. A guided wave packet is efficiently injected from the ordinary waveguide to the left-handed heterostructure LHH, inside which it propagates smoothly owing to the slow (adiabatic) reduction in the thickness of the core. The smallest (red) frequency components of the wave are stopped at the smallest core thicknesses of the LHH, while the largest (blue) components stop at correspondingly larger core thicknesses. (Reference 30)

The schematic of the light-stopping structure based on the waveguide with a negative index core (dubbed left-handed heterostructures or LHHs in Reference 30) is shown in Figure 14. Although light stopping is possible in other guided configurations that do not necessarily require µ to be negative (for example, a metal-dielectric-metal waveguide would suffice), the key here is that perfect impedance matching can be achieved for the metamaterials-based waveguides with the negative index core. That is very important for maximizing the coupling efficiency from the regular waveguide to the LHH. Although Reference 30 does not present any specific ideas as to what could be done with the slowed down and/or stopped light, the schematic shown in Figure 13 provides some key ideas. Moreover, the prospect of producing a low-loss negative index material in the optical domain still remains somewhat distant. Therefore, it may be worthwhile to examine other approaches to slowing down light that have emerged in the past few years.

Stopping and/or slowing down light is an old idea originating from the atomic concept of Electromagnetically Induced Transparency (EIT). The phenomenon has been considered to be purely quantum mechanical until several groups have demonstrated that it has some classical analogies (Reference 31). Remarkably, at least one group has demonstrated in the past year that EIT can be achieved using plasmonic metamaterials (Reference 32). The idea is to create a plasmonic "molecule" consisting of a radiative element coupled with a subradiant (dark) element. The plasmonic molecule showed electromagnetic response that closely resembles the electromagnetically induced transparency in an atomic system. Because of its subwavelength dimension, this electromagnetically induced transparency-like molecule was shown to be suitable as a building block to construct a "slow light" plasmonic metamaterial. The specific design of the plasmonic molecule is shown in Figure 15.

Figure 16. "Plasmonic Molecule" Exhibiting EIT. Left: radiative element (metal strip) by itself gets strongly polarized by the incident EM wave, resulting in weak transmission and strong reflection. Right: radiative element coupled to the "dark" element (two strips). The dark element possesses a non-radiative quadrupole resonance which is excited by the radiative element and de-polarizes the radiative element. The result: vanishing reflection, high transmission. Color bar: field normalized to the incident laser field at λ = 700 nm. (Reference 32)

This specific plasmonic molecule consists of the "dark state" (two parallel plasmonic antennas oriented perpendicular to the incident vertical electric field) and the "radiative state" (single plasmonic antenna oriented parallel to the electric field). The quality factor of the "dark antenna" state is an order of magnitude higher than that of the "radiative" antenna. When the "radiative" antenna is spatially separated from the "dark" antenna (or when the dark antennas are not present at all), all or most of the incident radiation is reflected from an array of "radiative" antennas whenever the resonance frequency of the antenna coincides with that of the laser. In this example, the long antenna is 128 nm long, and the resonance wavelength is at λ = 700 nm. The key effect here is that the resonance of the "dark" antenna should be at the same wavelength.

Because the exploited resonance has a quadrupole nature, it is slightly red-shifted. For that reason, the length of the "dark" antenna is 100 nm. When the two antennas are brought together, the radiative antenna polarizes the dark antenna, which, in turn, depolarizes the radiative antenna. As a result, the dipole moment of the coupled system is drastically reduced, the reflection drops and transmission increases to almost 100 percent (limited only by losses). Most of the energy is now stored inside the non-radiative (dark) antenna.

If multiple layers of dark/bright antennas are employed as shown in Figure 16, then one can achieve one of the most important manifestations of EIT: "slow" light. Slow light can have many interesting technological applications because (a) slow light is easy to manipulate by changing the structure's parameters (as described in the section on tunable metamaterials), and (b) slow light has a high field intensity (enhanced by the ratio of the free-space propagation speed to the slow propagation speed); therefore, all nonlinear processes are enhanced for slow light. Such nonlinear processes may include harmonics generation, optical diode action (see the section on non-reciprocal optical elements), and many others.

Figure 17. True Multi-Layer Metamaterial With a Unit Cell Shown in Figure 15: radiative antenna (single metal strip) coupled to a dark antenna (two perpendicular metal bars). Such metamaterial exhibits "slow" light propagation along the incidence direction, slowed down by a factor 30 or more. (Reference 32)

It is important to realize that the geometry suggested in Reference 32 is not unique. For example, the dark and radiative antennas need not reside in the same plane. Nor is the effect of EIT (and the related phenomenon of slow light) limited to the optical domain. Both infrared and microwave-range designs have started emerging. These frequency domains are likely to be of greater use for advanced aerospace platforms than the visible range targeted by most studies.

Metamaterials for Energy Harvesting

One of the most important applications of metamaterials is related to developing "perfect absorbers" of infrared electromagnetic radiation, be it in the mid-to-long infrared part of the spectrum (making it relevant for night vision, harvesting of the Earth glow mid-infrared radiation, and so forth) or in the near-to-mid-IR spectrum (making it relevant for day-time infrared photography of the earth terrain). For example, day-time infrared photography relies on the different sunlight reflectivities of surfaces (for example, snow, brick walls, concrete walls, grass, and so forth), and can easily distinguish between those surfaces. This reflectivity differential tends to be the greatest between 2 and 3 microns, and rapidly decays toward longer wavelengths. Open sky contains very little infrared radiation, which explains why infrared imaging/photography is very important for aerial and satellite surveys. Because light scattering in the atmosphere scales as λ⁻⁴, imaging through the atmosphere in the visible range is impossible, and infrared imaging becomes important. This is especially true for the range between 1 and 4 µm. For longer wavelengths (beyond 10 µm) this brightness differential is largely gone because the emission spectrum is dominated by thermal emission. In fact, the Earth glow maximum is beyond 10 µm, with most of the energy contained in the range between 3 µm and 14 µm. This longer wavelength (mid-to-far IR) spectral range is also very important. It can be used for night-time energy scavenging by high-altitude satellites and other aerospace platforms.

There has been a surge of activity in this area, first in the microwave/THz part of the electromagnetic spectrum (References 33, 34), and subsequently in mid-to-far infrared (Reference 20). The concept of narrow-band metamaterials-based absorbers introduced in Reference 33 has the potential for developing highly efficient bolometer arrays. When applied to the infrared part of the spectrum, it can be used for space navigation, especially when weak infrared signals from specific stellar objects need to be picked up and discriminated from other radiation sources. For such applications, the narrow-band "perfect" absorption is highly suitable. An array of such bolometers would reject (reflect) all undesirable frequencies and focus on the single wavelength characteristic of the source of interest. Moreover, if an array of different (for example, tuned to different frequencies) narrow band detectors can be deployed, then the hyper-spectral imaging capability could bring additional benefits. For example, absolute temperatures of a radiation source (that is, stellar bodies) could be accurately determined, and could improve the accuracy of space navigation further.

Figure 18. "Perfect" Narrow-Band Microwave Absorber. (a-c): unit cell design. Right panel: simulated absorption, transmission and reflection. (Reference 33)

One possible design for the microwave frequency band is shown in Figure 17. High absorption is accomplished by reducing reflections to zero. This is accomplished by choosing metamaterials parameters such that the effective permittivity equals the effective permeability at the resonant frequency ωr. Note that both the real and imaginary parts of the permittivity and permeability must be equal to each other, and that the imaginary parts do not necessarily need to be small for absorber applications. In fact, it is desirable that they are not too small, thereby enabling 100 percent absorption within a single layer of metamaterial. The above design can be scaled down to the THz range, as was later demonstrated in Reference 34. It is difficult to find strongly absorbing materials at THz frequencies that are compatible with standard photolithography. Thus, a potential application of these metamaterial structures is as absorbing elements in thermal detectors. A strong absorption coefficient is also necessary to have a small thermal mass. This is important for optimizing the temporal response of thermal detectors. The metamaterial presented here has a 6 micron thick film (that is, λ/50 thickness for THz radiation) and 70 percent absorptivity, which yields an absorption coefficient of 2,000 cm⁻¹.

One drawback of the original design was the narrow angular range of the absorber. The absorption dropped dramatically when the incidence angle was as small as 20 degrees. The reason for that is a relatively large unit cell of the metamaterial. In fact, when the unit cell size is larger or comparable to λ/2n, where n is the refractive index of the substrate, it is inappropriate to call such structure a "metamaterial." A true impedance-matched metamaterial would, in fact, always have a very broad angular response.

Figure 19. Wide-Angle Plasmonic Absorber Based on Negative Index Metamaterial. Right panel: schematic of an absorption-measuring experiment. A generic metamaterial with εxx = µzz = −1 + i and µxx = 1 is assumed. Left panel: angular dependence of the absorption for a generic and specific (shown in the inset) metamaterial. Both exhibit wide-angle absorptivity. (Reference 20)

This fact can be expressed by a simple formula for the absorption coefficient A (Reference 20):

(Equation 4, the angular formula for the absorption coefficient, is too damaged in the released scan to reproduce.)

where we have assumed that, for normal incidence, this metamaterial is impedance-matched: εxx = µzz = −1 + i. Equation 4 can be simplified under the assumption that the permittivity magnitude is large and µxx = 1, implying that A is about 0.97 even for an incidence angle of π/6. The challenge, of course, is to design a true impedance-matched optical metamaterial. Success has been achieved in designing such a metamaterial (Reference 20).

The recently published design is shown in Figure 19. The unit cell consists of two layers of plasmonic antennas: the cut-wire antenna that imparts magnetic (as well as some electric) response to this metamaterial, and the continuous-wire antennas that impart a purely electric response. It is found that the wide-angle capability could be very important for several applications. Wide-angle power absorption efficiency is desirable for miniaturizing photodetectors or microbolometers down to the wavelength size.

Figure 20. Specific Design of a Wide-Angle Plasmonic Absorber Based on Negative Index Metamaterial Operating at λ = 1550 nm. Left panel: schematic of the silver-based plasmonic structure, 20 nm and 80 nm layers. Right panel: extracted permittivity and permeability for the normal incidence demonstrate impedance matching, εxx = µzz = −1 + i. (Reference 20)

For example, to focus light on a wavelength-sized photodetector or micro-bolometer requires high-NA optics (a NA = 0.5 or higher). Therefore, a photodetector should be able to absorb light incident at 30 degree angle. For advanced aerospace platforms it is easy to envision a scenario where an airborne platform is powered by a high-power infrared laser source located on Earth. If the wavelength falls inside the transparency window of the atmosphere (between 3 and 4 µm, and also around 10 µm), then such a prospect is not too farfetched because scattering in mid-infrared by atmospheric gases is essentially zero. For such a remote powering scenario to be feasible, one would need a highly efficient absorber at the specific wavelength corresponding to that of the source. Moreover, as the space platform is moving, it is desirable that the absorption remain high even for non-normal incidence angles.

The second application is for thermophotovoltaics (TPV) (Reference 35). Some type of thermophotovoltaic converter will almost undoubtedly be installed on the advanced aerospace platforms of the future. Presently even advanced (experimental) electric cars are using TPV cells to convert the heat from their engines into electricity. Such converters have already been shown to be capable of increasing the range of electric vehicles by a factor of 3. We believe that metamaterials could play an important role in developing highly efficient TPV cells. By virtue of Kirchhoff's law, emissivity of a thermal emitter approaches the blackbody limit only if the absorptivity approaches unity. Moreover, wavelength-selective radiators can dramatically improve the efficiency of current generation in a TPV cell if their emission spectrum is matched to the bandgap of the TPV converter. For example, a typical TPV converter, GaSb, has the bandgap of EG = 0.7 eV that would be ideally suited to a wavelength-selective radiator operating in near infrared around λ = 1.7 µm.

Figure 21. (Left): Experimental Result, Reflectivity Versus Wavelength, that Inspired the Proposed Effort — a Modestly Absorbing Material (SiC) Turns Into a "Perfect Mid-IR Absorber" When a Quarter-Wavelength-Thick SiC Film Is Backed by a Metal Mirror. (Right): Theoretical Plot — Constant Reflectivity Contours Plotted in the real and imaginary refractive index space. High material absorptivity is required to achieve perfect absorption. Posed question: can a metamaterials-based semi-transparent mirror enhance absorption and result in an almost-perfect ultra-thin absorber?

The perfect absorbers shown in Figures 17 to 19 may be too complex for practical applications. Metamaterials tend to be lossy because of the large field concentration in the metal. Therefore, work has recently started on a new type of metamaterial (the so-called CMMs mentioned in the Introduction) that could potentially make weakly-absorbing semiconductors (that is, Si in the visible) absorb much stronger. The goal here is to make a thin (although not necessarily a very sub-wavelength) absorber backed up by a sheet of CMMs which would prevent reflections and result in a very high absorption. Applications that are considered are essentially the same as for the "perfect" absorbers described above. For example, satellites can use the Earth glow for nighttime battery recharging. The collected power is quite high; 1 m² of black surface at

(The released copy ends here, mid-sentence, at the foot of printed page 23. Printed pages 24 to 31 are absent from the FOIA release: the remainder of Metamaterials for Energy Harvesting, and the sections Nonlinear Non-Reciprocal Chiral Metamaterials (p. 27), Tunable Switchable Metamaterials (p. 30), Summary and Conclusions (p. 31) and References (p. 31), all of which are listed on the report's own contents page. The chiral-metamaterial and slow-light programmes are described in the author's four-bullet overview above.)