Bragg Planes Research Articles

Illuminating the Bragg intersections as roots of Dirac nodal lines and high-order van Hove singularities

We theoretically reexamine nearly uniform electron models with weak crystalline potentials. In particular, we theorize the modulation of the plane-wave branches at linear regions where multiple Bragg planes intersect. Any such linear intersections involve three or more plane-wave branches diffracted by the periodic potential. Small interbranch interactions can yield various crossing and anticrossing singularities with promised breakdown of the quadratic approximation, extending alongside the intersection lines. Most of the intersections run in low-symmetric paths in the Brillouin zone and therefore we cannot completely characterize their electronic states with standard band-structure plotting methods. The present theory reveals a general mechanism in nearly uniform systems to induce the Dirac nodal lines and van Hove singularities with broken quadratic band approximation in three dimensions, which may host a variety of anomalous low-energy electronic properties. We apply the theory to a recently discovered high-temperature superconductor H3S to interpret the enigmatic density-of-state (DOS) peaking therein. The results show how and the continuous saddle points–the source of the peaked DOS–emerge, as well as reveal the companion Dirac nodal lines hidden in the conduction bands. Published by the American Physical Society 2024

Structural analysis, ferroic properties with enhanced magnetoelectric coupling in novel (1-x)BiFeO3-(x)GdFeO3 nanocomposites

Multiferroic composites exhibit substantially greater magnetoelectric interaction among order variables as compared to single-phase multiferroics, making them particularly attractive for futuristic multi-state RAM and spintronic gadgets. The multiferroic nanocomposites (1-x)BiFeO3-xGdFeO3 (x = 0.05, 0.10, 0.15, & 0.20) are synthesized by using solid-state route. The crystallographic and profile parameters are extracted from the dual-phase refinement of the rhombohedral (R3c) and orthorhombic (Pbnm) crystal structures. The optimized density, crystallite size and homogenous microstructure may be responsible for the improved dielectric and ferroic properties. TEM images reveal a reduction in the particle size (67–59 nm) upon GdFeO3 (GFO) loading. The HRTEM images unravel the interplanar spacing and associated Bragg planes, while the SAED rings validate the polycrystalline features of the samples. The high Curie temperature (Tc ̴ 643 °C) with enhanced specific heat (Cp ̴ 29.5 J/g°C) in x= 0.10 sample ensures its stable operation, efficient heat dissipation, minimal overheating, and greater thermal stability for reliable performance in demanding conditions. The surface and finite-size effects enhanced the magnetization (MS=1.04emu/g) in nanostructured ferromagnetic nanocomposite, making it a promising candidate for high-density magnetic storage devices and sensors. The high polarization (Pmax=8.39µC/cm2) and ME-coupling coefficient (αE=0.16mVcm−1Oe−1) observed in the most dense nanocomposite make it a potential candidate for magnetoelectric applications.

Material normal energy distribution for field emission analyses from monocrystalline surfaces

Electron field emission is a complicated phenomenon which is sensitive not only to the particular material under illumination but also to the specific crystalline orientation of the surface. Summarizing the ability for a crystal to emit in a particular direction would be of great use when searching for good field emitters. In this paper we propose a material normal energy distribution which describes the ability of the bound electrons to tunnel under an intense electric field. This framework breaks a computationally expensive 3-D system down to a source distribution representation applicable for more efficient 1-D models. We use the Fowler-Nordheim framework to study the yield and MTE (mean transverse energy) from sources including gold, copper, and tungsten in both monocrystalline and polycrystalline forms. We find an increase in effective work function for field emission in the (111) direction for gold and copper associated with the Bragg plane intersections of the Fermi surface.

Microstructure and energy dispersive diffraction reconstruction of 3D patterns of crystallographic texture in a shark centrum.

Purpose: Tomography using diffracted x-rays produces reconstructions mapping quantities such as crystal lattice parameter(s), crystallite size, and crystallographic texture, information quite different from that obtained with absorption or phase contrast. Diffraction tomography is used to map an entire blue shark centrum with its double cone structure (corpora calcerea) and intermedialia (four wedges). Approach: Energy dispersive diffraction (EDD) and polychromatic synchrotron x-radiation at 6-BM-B, the Advanced Photon Source, were used. Different, properly oriented Bragg planes diffract different x-ray energies; these intensities are measured by one of ten energy-sensitive detectors. A pencil beam defines the irradiated volume, and a collimator before each energy-sensitive detector selects which portion of the irradiated column is sampled at any one time. Translating the specimen along , and axes produces a 3D map. Results: We report 3D maps of the integrated intensity of several bioapatite reflections from the mineralized cartilage centrum of a blue shark. The axis reflection's integrated intensities and those of a reflection with no axis component reveal that the cone wall's bioapatite is oriented with its axes lateral, i.e., perpendicular to the backbone's axis, and that the wedges' bioapatite is oriented with its axes axial. Absorption microcomputed tomography (laboratory and synchrotron) and x-ray excited x-ray fluorescence maps provide higher resolution views. Conclusion: The bioapatite in the cone walls and wedges is oriented to resist lateral and axial deflections, respectively. Mineralized tissue samples can be mapped in 3D with EDD tomography and subsequently studied by destructive methods.

In Vivo Analgesic, Anti-Inflammatory, and Anti-Diabetic Screening of Bacopa monnieri-Synthesized Copper Oxide Nanoparticles.

In this work, an ecofriendly approach for biogenic production of copper oxide nanoparticles (CuO-NPs) was proposed by utilizing the Bacopa monnieri leaf extract as a reducing and stabilizing agent. The synthesis of CuO-NPs was instantly confirmed by a shift in the color of the copper solution from blue to dark gray. The use of UV–visible spectroscopy revealed a strong narrow peak at 535 nm, confirming the existence of monoclinic-shaped nanoparticles. The average size of CuO-NPs was 34.4 nm, according to scanning electron microscopy and transmission electron microscopy studies. The pristine crystalline nature of CuO-NPs was confirmed by X-ray diffraction. The monoclinic form of CuO-NPs with a crystallite size of 22 nm was determined by the sharp narrow peaks corresponding to 273, 541, 698, 684, and 366 Bragg’s planes at different 2θ values. The presence of different reducing metabolites on the surface of CuO was shown by Fourier transform infrared analysis. The biological efficacy of CuO-NPs was tested against Helicobacter felis, Helicobacter suis, Helicobacter salomonis. and Helicobacter bizzozeronii. H. suis was the most susceptible strain with an inhibition zone of 15.84 ± 0.89 mm at 5 mg/mL of NPs, while the most tolerant strain was H. bizzozeronii with a 13.11 ± 0.83 mm of inhibition zone. In in vivo analgesic activity, CuO-NPs showed superior efficiency compared to controls. The maximum latency time observed was 7.14 ± 0.12 s at a dose level of 400 mg/kg after 90 min, followed by 5.21 ± 0.29 s at 400 mg/kg after 60 min, demonstrating 65 and 61% of analgesia, respectively. Diclofenac sodium was used as a standard with a latency time of 8.6 ± 0.23 s. The results observed in the rat paw edema assays showed a significant inhibitory activity of the plant-mediated CuO-NPs. The percentage inhibition of edema was 74% after 48 h for the group treated with CuO-NPs compared to the control group treated with diclofenac (100 mg/kg) with 24% edema inhibition. The solution of CuO-NPs produced 82% inhibition of edema after 21 days when compared with that of the standard drug diclofenac (73%). CuO-NPs vividly lowered glucose levels in STZ-induced diabetic mice, according to our findings. Blood glucose levels were reduced by about 33.66 and 32.19% in CuO-NP and (CuO-NP + insulin) groups of mice, respectively. From the abovementioned calculations, we can easily conclude that B. monnieri-synthesized CuO-NPs will be a potential antibacterial, anti-diabetic, and anti-inflammatory agent on in vivo and in vitro basis.

Heating Effects in the Structure of Non-metamict Allanite-(La) from Palawan, Philippines

Allanite is one of the most common sources of rare-earth elements (REEs) and contains significant amounts of thorium (Th) and uranium (U). The presence of radioactive Th and U nuclides in the mineral exposes it to long-term radiation. Like other natural minerals containing Th and U, allanite can be used as a natural analog to understand the long-term radiation effects in high-level nuclear waste (HLW) matrices. Allanite group mineral is generally found in the amorphous phase due to structural damage induced by self-irradiation. In this work, crystalline allanite-(La) samples collected in San Vicente, Palawan, Philippines – having a low absorbed -dose of ~ 1014 α-decays/ mg – were heated at 450, 650, and 850 °C to study the response of non-metamict allanite to heating at elevated temperatures, particularly at the early stages of exposure to alpha-particle radiation. An increase in structural order was observed upon heating to 450 and 650 °C, which is exhibited by a decrease in the unit cell volume by 1.6% and a decrease of the full width at half maximum (FWHM) of selected Bragg planes. It was evident that certain Bragg planes respond differently to the annealing temperatures with preferential reorientation. After annealing at 850 °C, however, the loss of OH bonds was observed in the infrared (IR) spectra, and the broadening of Bragg peaks was seen in the x-ray diffraction (XRD) patterns, suggesting an onset of structural degradation. Surface cracks are also seen in the scanning electron microscope (SEM) images. The study shows that the non-metamict allanite-(La) mineral structure responds to heating similarly to that of metamict ones reported in the literature. This study will provide data on the properties of allanite as part of the ongoing studies on radiation damage in silicate matrices.

Fractal energy gaps and topological invariants in hBN/graphene/hBN double moiré systems

We calculate the electronic structure in quasiperiodic double-moir\'e systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can be characterized by a set of integers, which are associated with an area in the momentum space. The corresponding area is geometrically interpreted as a quasi Brillouin zone, which is a polygon enclosed by multiple Bragg planes of the composite periods and can be uniquely specified by the plain wave projection in the weak potential limit.

Direct thermal decomposition of FeCl3.6H2O in oleic acid forms hematite cube and nano octahedron structure with quasicrystalline and supercell symmetries for enhanced photoelectrochemical functionality

The direct formation of hematite nanostructures by the thermal decomposition of precursor salt in the oleic acid is discussed here. The obtained nanostructures show interesting structural properties with the unique presence of quasicrystalline and supercell symmetries. The quasicrystalline symmetry obtained is of 2- fold and 3-fold icosahedral symmetries. HRTEM study of the single nano octahedron each faces reveals different axis of symmetry along with the presence of 2-fold icosahedral quasicrystal. The synthesis route results well distributed hematite nano octahedron, where urea plays a role in controlling its distribution as confirmed by FESEM studies. Next, a mechanism is proposed for how 24 h aged Hematite nano octahedron decays with increased acidity of the reaction medium in the presence of urea? It is found that the Urea deprotonated first and keep the nano octahedron morphology stable depending on the salt to urea molar ratio. Finally, the photoelectrochemical properties of the hematite nano octahedron film is studied, and a photocurrent density of 200 μA/cm2 is obtained for non -Urea mediated one (24 O. A.). From the XRD comparison of both films (24 h and 24 O.A.), it is found that (110) Bragg plane diffracted intensity increases without Urea, which helps in the enhancement of the photocurrent density due to a well-established electronic conductivity of Hematite along (001) Basal plane.

Engineering novel gold nanoparticles using Sageretia thea leaf extract and evaluation of their biological activities

An eco-friendly method for biogenic synthesis of gold nanoparticles (AuNPs) was developed using leaf extract of Sageretia thea as a reducing, stabilizing, and capping agent. AuNPs synthesis was immediately confirmed from a color change in the gold solution from yellow to ruby red. UV–visible spectroscopy technique showed a sharp narrow peak at 535 nm that confirmed the presence of spherical and cubic-shaped nanoparticles. SEM and TEM analyses revealed that the average size of AuNPs was 36 and 13 nm, respectively. XRD revealed the pure crystalline nature of AuNPs. The sharp narrow peaks corresponding to (111), (200), (220), and (311) Bragg's planes at 2θ position denoted the cubic shape of AuNPs with a crystallite size of 18 nm. FTIR analysis showed the existence of various reducing metabolites, which capped over the surface of Au. The biological efficacy of AuNPs was tested against Klebsiella pneumonia, Staphylococcus aureus, and Bacillus subtilis. K. pneumonia was the most susceptible strain with an inhibition zone of 12 ± 0.2 mm (200 µg/mL dose), while the most tolerant strain was B. subtilis with a 6 ± 0.4 inhibition zone. The antioxidant potential was detected with DPPH scavenging activity, where the maximum scavenging activity was recorded at100 µg/mL. In analgesic activity, AuNPs showed superior efficiency as compared to leaf extract. The maximum latency time observed was 77.15 ± 0.39 s at a dose level of 300 mg/kg followed by 6.77 ± 0.30 s at 200 mg/kg, demonstrating 80.16% and 75.90% of analgesia, respectively. While diclofenac sodium was used as a standard with a latency time of 8.92 ± 0.32 s. The maximum metabolic activity of promastigote was seen at 150 µg/mL, which shows 91.21% lethality at 150 µg/mL with LD50 28.15, LD70 98.72, LD90 605.70, and 2.106 Chi-square values. In conclusion, the present findings demonstrate that AuNPs synthesized by plant extract might be applied as an alternative to synthetic drugs for different pathogenic diseases.

Concurrent deep UV diffractions enabled by the Bragg condition and crystal symmetry in silica inverse opals

Understanding the unexplored deep ultraviolet (UV) diffraction from photonic crystals will pave the way forward for developing diffractive optical elements in the deep UV wavelength range (190–250 nm). Herein we optically characterized the deep UV diffraction from our highly ordered 3D silica inverse opals fabricated by a co-assembly method and calculated their photonic band structures. Presence of a photonic stopband along their ΓL crystallographic direction is observed from the band structure. Presence of cracks and defects in these inverse opals impacts their deep UV photonic stopbands. Angle dependent diffraction measurements quantify the spacing of the (111) planes in the face-centered cubic inverse opal. Laser diffraction in the deep UV range yields a hexagonally symmetric six-spot pattern surrounding a central bright spot associated with Bragg diffraction in these inverse opals. Unlike earlier work, this feature has been observed with light at multiple wavelengths well within the stopband. Analysis of the deep UV diffraction pattern leads to the possibility of concurrent Bragg diffraction and (111) plane symmetry derived diffraction from our inverse opal PhC that are wavelength dependent.

Closer look at transmissive polarization volume holograms: geometry, physics, and experimental validation.

In this work, we took a closer look at transmissive polarization volume holograms (T-PVH) to provide clarifications on their geometry, physics, and optical responses by finite-difference time-domain (FDTD) simulation and experimental validation. First, we introduced the four possible geometries of T-PVH and simulated their optical responses in terms of diffraction efficiency, polarization selectivity, and polarization output. It is shown that the configuration we called "Slanted T-PVH (B-θ/D-θ+90)," where the director is perpendicular to the Bragg planes, has the advantageous property of maintaining circular output polarization states. For this configuration, a detailed simulation of spectral, angular, and polarization responses was completed. Finally, we validated the FDTD simulation results of the Slanted T-PVH (B-θ/D-θ+90) structures with experiments.

Thermal Properties of Bayfol® HX200 Photopolymer.

Bayfol® HX200 photopolymer is a holographic recording material used in a variety of applications such as a holographic combiner for a heads-up display and augmented reality, dispersive grating for spectrometers, and notch filters for Raman spectroscopy. For these systems, the thermal properties of the holographic material are extremely important to consider since temperature can affect the diffraction efficiency of the hologram as well as its spectral bandwidth and diffraction angle. These thermal variations are a consequence of the distance and geometry change of the diffraction Bragg planes recorded inside the material. Because temperatures can vary by a large margin in industrial applications (e.g., automotive industry standards require withstanding temperature up to C), it is also essential to know at which temperature the material starts to be affected by permanent damage if the temperature is raised too high. Using thermogravimetric analysis, as well as spectral measurement on samples with and without hologram, we measured that the Bayfol® HX200 material does not suffer from any permanent thermal degradation below C. From that point, a further increase in temperature induces a decrease in transmission throughout the entire visible region of the spectrum, leading to a reduced transmission for an original 82% down to 27% (including Fresnel reflection). We measured the refractive index change over the temperature range from C to C. Linear interpolation give a slope for unexposed film, with the extrapolated refractive index at C equal to . This refractive index change decreases to when the material is fully cured with UV light, with a C refractive index equal to . Spectral properties of a reflection hologram recorded at 532 nm was measured from C to C. A consistent 10 nm spectral shift increase was observed for the diffraction peak wavelength when the temperature reaches C. From these spectral measurements, we calculated a coefficient of thermal expansion (CTE) of by using the coupled wave theory in order to determine the increase of the Bragg plane spacing with temperature.

Small Bragg-plane slope errors revealed in synthetic diamond crystals.

Wavefront-preserving X-ray diamond crystal optics are essential for numerous applications in X-ray science. Perfect crystals with flat Bragg planes are a prerequisite for wavefront preservation in Bragg diffraction. However, this condition is difficult to realize in practice because of inevitable crystal imperfections. Here, X-ray rocking curve imaging is used to study the smallest achievable Bragg-plane slope errors in the best presently available synthetic diamond crystals and how they compare with those of perfect silicon crystals. It is shown that the smallest specific slope errors in the best diamond crystals are about 0.08 (3) µrad mm-2. These errors are only 50% larger than the 0.05 (2) µrad mm-2 specific slope errors measured in perfect silicon crystals. High-temperature annealing at 1450°C of almost flawless diamond crystals reduces the slope errors very close to those of silicon. Further investigations are in progress to establish the wavefront-preservation properties of these crystals.

Femtosecond photoemission electron microscopy of surface plasmon polariton beam steering via nanohole arrays

Directional control over surface plasmon polariton (SPP) waves is a prerequisite for the development of miniaturized optical circuitry. Here, the efficacy of single and dual component SPP steering elements is explored through photoemission electron microscopy. Our imaging scheme relies on two-color photoemission and counter-propagating SPP generation, which collectively allow SPPs to be visualized in real space. Wave-vector difference mixing between the two-dimensional nanohole array and photon momenta enables SPP steering with directionality governed by the array lattice constant and input photon direction. In our dual component configuration, separate SPP generation and Bragg diffraction based steering optics are employed. We find that array Bragg planes principally influence the SPP angles through the array band structure, which allows us to visualize both positive and negative refractory waves.

Effect of Deposition Voltage on Layer Thickness, Microstructure, Cu/Ni Sheet Resistivity of Deposition Results by Magnetic Field Electroplating Assisted Technique

The purpose of this research is to make the Cu/Ni thin layer as an alternative to basic RTD materials through electroplating methods assisted by magnetic fields. Electroplating was carried out with variation in deposition voltage ranging from 1 to 5 V. The results of this study indicate that the deposition voltage applied to the coating affects the thickness, sheet resistivity, and microstructure of the coating. Thickness increases with increasing deposition voltage. The diffraction intensity and crystal size tend to increase with increasing deposition voltage. The distance between Bragg planes after the coating is almost equal for all samples. The highest sheet resistivity was obtained in the coating sample with a 4-volt deposition voltage.

Structural, thermal, dielectric and multiferroic investigations on LaFeO3 composite systems

The present study focuses on developing multiferroic properties in the perovskite orthoferrite LaFeO3 (LFO) at room temperature. The effect of perovskite ferroelectric and spinel magnetic interface has been investigated on the ferroelectric and magnetic properties of LFO. The composite systems are prepared by solid-state reaction route, using BaTiO3 (BTO) as the perovskite ferroelectric phase and CoFe2O4 (CFO) as the magnetic phase. The phase purity of the samples is confirmed through X-ray diffraction and the Fourier transform infrared spectroscopy. The physical interaction of BTO and CFO with LFO is perceived from the peak broadening and shifting. Rietveld refinement confirms the single-phase orthorhombic formation of LaFeO3–CoFe2O4–BaTiO3 composites. The energy dispersive X-ray analysis reveals that the samples are without any impurity and the relative concentrations of constituent phases are close to the expected values. High-resolution transmission electron microscopy is utilized to determine the interplanar spacing and hence Bragg planes. Selected area electron diffraction (SAED) patterns reveal the polycrystalline nature of samples with a small local ordering. Specific heat variation against temperature depicts an anomaly at lower temperature around 130 °C that represents the transition of BaTiO3 from tetragonal ferroelectric to cubic paraelectric phase. The variation of dielectric constant with frequency is consistent with Maxwell–Wagner interfacial polarization model. The dielectric behavior of the composite systems reveals the frequency independent anomaly at the Curie temperature of BaTiO3, consistent with specific heat measurements. The simultaneous presence of ferroelectric and magnetic hysteresis loops confirms the multiferroism in the samples. The exchange bias effect is observed in all the samples and coercivity decreases with the increase in BaTiO3 concentration.

Local structure investigation of cobalt ferrite-based nanoparticles by synchrotron X-ray diffraction and absorption spectroscopy

In this work, the local structure of ferrite nanoparticles (CoFe2O4) composed of a cobalt ferrite core surrounded by a thin layer of maghemite (CoFe2O4@γ-Fe2O3) was investigated by crossing analyses of X-ray powder Diffraction (XRD), X-ray Absorption Spectroscopy (XANES/EXAFS) and Diffraction Anomalous Fine Structure (DAFS). The proportion of the core and the shell phases was carefully checked by chemical analysis. The whole of these multiple complementary techniques confirmed the non-equilibrium site occupancy in the cobalt ferrite core. The cation distribution was precisely determined showing that about 15% of cobalt ions are located at tetrahedral sites. The results of EXAFS spectra indicated interatomic distances very close to bulk values. The mean coordination number of both metallic cations was found to be lower than expected for bare nanoparticles and reflected the core-shell structure in CoFe2O4@γ-Fe2O3 ones. Finally, DAFS analyses were applied to enlighten the local structure around iron atoms in specific Bragg planes.

The Mirror: Mother of All Symmetries in Crystals

Mirror symmetry is found to be the only fundamental symmetry in crystalline solids because all other symmetries, such as rotation, inversion, rotoreflection, rotoinversion and translational periodicity can be easily derived from suitable combinations of mirrors. Similarly, the point group symmetries can also be derived from the same. The mirror combination scheme is found to work in accordance with the principle of Wigner-Seitz cells and Brillouin Zones (and not with the conventional unit cells as proposed by Bravais), where the zone boundaries of a Brillouin zone represent different sets of Bragg planes obtained from diffraction pattern of the given crystal, while the diffraction of given crystal takes place in terms of decreasing interplanar spacing in reciprocal space. Because the Wigner Seitz cells, the Brillouin zones and the diffraction patterns possess defined origin and exhibit spherical symmetry, they cannot have translational symmetry of any kind (microscopic or macroscopic). Results obtained on the basis of this concept help us to remove the existing ambiguities in crystallography and make the crystal structure determination simple. Further, prima facie the diffraction patterns are found to take care of the proposed 'systematic absences' arising due to the so called lattice centering, glide planes and screw axes without actually taking them into consideration. This newly and first discovered concept is expected to explain all other complicated or less understood issues related to crystallography.

PbS and PbS/CdS quantum dots: Synthesized by photochemical approach, structural, linear and nonlinear response properties, and optical limiting

Abstract

Dynamic plasma/metal/dielectric photonic crystals in the mm-wave region: Electromagnetically-active artificial material for wireless communications and sensors

Inexorable demand for increasing bandwidth is driving future wireless communications systems into the 100 GHz–1 THz region, thereby fueling demand for new sources and modulators but also complementary devices such as resonators, phase shifters, and filters. Few such devices exist at present, and the electromagnetic properties of those available at millimeter-wavelengths are generally fixed and characterized by broad (i.e., low Q) resonances. We introduce a class of 3D plasma/metal/dielectric photonic crystals (PPCs), operating in the 120–170 GHz spectral range, that are dynamic (tunable and reconfigurable at electronic speeds) and possess attenuation and transmission resonances with bandwidths below 50 MHz. Interference between sublattices of the crystal, which controls the resonance line shapes, is manipulated through the crystal structure. Incorporating Bragg arrays of low-temperature plasma microcolumns into a dielectric/metal scaffold that is itself a static crystal forms two interwoven and electromagnetically coupled crystals. Plasma-scaffold lattices produce multiple, narrowband attenuation resonances that shift monotonically to higher frequencies by as much as 1.6 GHz with increasing plasma electron density. Controlling the longitudinal geometry of the PPC through electronic activation of successive Bragg planes of plasma columns reveals an unexpected double-crystal symmetry interaction at 138.4 GHz and resonance Q values above 5100. The introduction of point or line defects into plasma column/polymer/metal crystals increases transparency at resonances of the scaffold (Borrmann effect) and yields Fano line shapes characteristic of coupled resonators. The experimental results suggest the suitability of PPC-based metamaterials for applications including multichannel communications, millimeter-wave spectroscopy, and fundamental studies of multiple, coupled resonators.