Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry.

In this work, we discuss the precision of the effective medium approximation (EMA) model in the data analysis of spectroscopic ellipsometry (SE) for solid materials with micro-rough surfaces by drawing the regime map. The SE parameters ψ (amplitude ratio) and Δ (phase difference) of the EMA model were solved by rigorous coupled-wave analysis. The electromagnetic response of the actual surfaces with micro roughness was simulated by the finite-difference time-domain method, which was validated by the experimental results. The regime maps associated with the SE parameters and optical constants n (refractive index) and k (extinction coefficient) of the EMA model were drawn by a comparison of the actual values with the model values. We find that using EMA to model micro-rough surfaces with high absorption can result in a higher precision of the amplitude ratio and extinction coefficient. The precisions of ψ, Δ, n and k increase as the relative roughness σ/λ (σ: the root mean square roughness, λ: the incident wavelength) decreases. The precision of ψ has an influence on the precision of k and the precision of Δ affects the precision of n. Changing σ alone has little effect on the regime maps of the relative errors of SE parameters and optical constants. A superior advantage of drawing the regime map is that it enables the clear determination as to whether EMA is able to model the rough surfaces or not.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media.

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

Measurement of the Optical Constants of Sand Samples Using Ellipsometry on Sand-Adhesive Composites.

In order to model the propagation of light through a sand cloud, it is critical to have accurate data for the optical constants of the sand particles that comprise it. The same holds true for modeling propagation through particles of any type suspended in a medium. Few methods exist, however, to measure these quantities with high accuracy. In this paper, a characterization method based on spectroscopic ellipsometry (SE) that can be applied to a particulate material is presented. In this method, a polished disc of an adhesive compound is prepared, and its optical constants are measured. Next, a mixture of the adhesive and a sand sample is prepared and processed into a polished disc, and SE is performed. By treating the mixture as a Bruggeman effective medium, the optical constants of the particulate material are extracted. For verification of the proposed method, it is first applied to pure silica powder, demonstrating good agreement between measured optical constants and literature values. It is then applied to Arizona road dust, a standard reference material, as well as real desert sand samples. The resulting optical constant data is input into a rigorous scattering model to predict extinction coefficients for various types of sand. Modeling results are compared to spectroscopic measurements on static sand samples, demonstrating good agreement between predicted and measured spectral properties including the presence of a Christiansen feature near a wavelength of 8 µm.

Printable Nanocomposite Metalens for High-Contrast Near-Infrared Imaging.

Printable metalenses composed of a silicon nanocomposite are developed to overcome the manufacturing limitations of conventional metalenses. The nanocomposite is synthesized by dispersing silicon nanoparticles in a thermally printable resin, which not only achieves a high refractive index for high-efficiency metalenses but also printing compatibility for inexpensive manufacturing of metalenses. The synthesized nanocomposite exhibits high refractive index >2.2 in the near-infrared regime, and only 10% uniform volume shrinkage after thermal annealing, so the nanocomposite is appropriate for elaborate nanofabrication compared to commercial high-index printable materials. A 4 mm-diameter metalens operating at the wavelength of 940 nm is fabricated using the nanocomposite and one-step printing without any secondary operations. The fabricated metalens verifies a high focusing efficiency of 47%, which can be further increased by optimizing the composition of the nanocomposite. The printing mold is reusable, so the large-scale metalenses can be printed rapidly and repeatedly. A compact near-infrared camera combined with the nanocomposite metalens is also demonstrated, and an image of the veins underneath human skin is captured to confirm the applicability of the nanocomposite metalens for biomedical imaging.

Improved Infrared Optical Constants from Pressed Pellets: II. Ellipsometric n and k Values for Ammonium Sulfate with Variability Analysis.

Infrared reflectance analysis is facilitated via the comparison of spectra recorded in situ to a databank of actual or synthetic infrared reflectance spectra. It has recently been shown that reference spectra corresponding to the many different morphological forms of the same chemical can be generated synthetically using the imaginary, k, and real, n, components of the complex refractive index, n∼ = n + ik. One method to obtain the n and k vectors is infrared ellipsometry, which measures the changes in amplitude, tan Ψ, and phase, Δ, of polarized light reflected from the sample both as a function of wavenumber and angle of incidence. The method requires specularly reflected light, so best results are usually obtained with polished planar samples of large surface area. Due to the difficulties of obtaining such samples, however, we investigate the possibility of pressing powders of neat materials and obtaining the corresponding optical constants from the pellets. In this paper, variability in the sample pellet and preparation method is investigated, as is variability in the fitting procedure for the derived optical constants. The n/k vectors are derived from the measured ellipsometric parameters, tan ψ and Δ, as they are fit by an oscillator model which yield n(ν∼) and k(ν∼) vectors as a function of wavenumber, ν∼. Construction of the oscillator model is not automatic and depends on significant input from the analyst as well as the sample's physical characteristics. For pellet pressing, the experimental variability was found to be minimized for size-selected powdered samples as gauged by the minimal variance in ψ and Δ for three different pellets; similarly, the analytical precision for multiple measurements of the same pellet was also quite good, suggesting that a pressed pellet is a viable sample preparation method. Experimental variabilities were comparatively small; the greatest variability came in the analytic fitting procedure with differences in the k-peak values up to 10% for only the sharpest bands arising from four different fits to the same data set. The final ellipsometric n/k data are compared to literature values obtained from crystalline ammonium sulfate ((NH4)2SO4) samples as well as single-angle reflectance measurements that also used pressed pellets. Comparison with the previous literature values shows generally good agreement, although larger k-values are observed for the independent sets of data derived from pressed pellets. These data are suggested as an improved set of optical constants for (NH4)2SO4.

Tunable Nanoporous Anodic Alumina Photonic Crystals by Gaussian Pulse Anodization.

This study presents a Gaussian pulse anodization approach to generate nanoporous photonic crystals with highly tunable and controllable optical properties across the visible-NIR spectrum. Nanoporous anodic alumina Gaussian photonic crystals (NAA-GPCs) are fabricated in oxalic acid electrolyte by Gaussian pulse anodization, a novel form of pulse-like anodization. The effect of the Gaussian pulse width in the anodization profile on the optical properties of these photonic crystals is assessed by systematically varying this fabrication parameter from 5 to 60 s. The optical features of the characteristic photonic stopband (PSB) of NAA-GPCs-the position of the central wavelength, full width at half-maximum, and intensity-are found to be highly dependent on the Gaussian pulse width, the angle of incidence of incoming photons, and the nanopore diameter of NAA-GPCs. The effective medium of NAA-GPCs is assessed by monitoring spectral shifts in their characteristic PSB upon infiltration of their nanoporous structure with analytical solutions of d-glucose of varying concentration (0.0125-1 M). Experimental results are validated and mechanistically described by theoretical simulations, using the Looyenga-Landau-Lifshitz effective medium approximation model. Our findings demonstrate that Gaussian pulse anodization is an effective nanofabrication approach to producing highly sensitive NAA-based PC structures with versatile and tunable PSBs across the spectral regions. The findings provide new exiting opportunities to integrate these unique PC structures into photonic sensors and other platform materials for light-based technologies.

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds.

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.

Block Copolymer Patterning for Creating Porous Silicon Thin Films with Tunable Refractive Indices.

We investigated the use of block copolymer (BCP) self-assembly for tuning the optical properties of silicon. We fabricated porous silicon by etching a hexagonally ordered pore pattern onto the surface of silicon wafers using poly(styrene-2-vinylpyridine) to prepare the etch mask. Contrary to typical BCP lithography, we did not need to use a range of different polymers to vary the pore size. We used the dry etching time as a way to increase the pore diameter and thus the porosity. The optical properties of the fabricated porous thin films were characterized by two effective medium approximations. Both the volume-averaging theory and the 2D Maxwell-Garnett theory gave similar effective refractive index values, although the latter was more accurate in predicting the film porosity. The refractive indices of the produced thin films could be varied by controlling the porosity. A maximum decrease of 30% in the refractive index was observed at 34% porosity compared to bulk silicon. We also demonstrated over a 60% decrease in the reflectance of silicon at 500 nm wavelength. The presented BCP method can be used to tailor semiconductor and dielectric layers for photonic applications without the size limitations of conventional lithography or the unpredictability of other pore-forming fabrication methods.

Monomer Derived Poly(Furfuryl)/BaTiO3 0-3 Nanocomposite Capacitors: Maximization of the Effective Permittivity Through Control at the Interface.

Frequency stable, high permittivity nanocomposite capacitors produced under mild processing conditions offer an attractive replacement to MLCCs derived from conventional ceramic firing. Here, 0-3 nanocomposites were prepared using gel-collection derived barium titanate nanocrystals, suspended in a poly(furfuryl alcohol) matrix, resulting in a stable, high effective permittivity, low loss dielectric. The nanocrystals are produced at 60 °C, emerging as fully crystallized cubic BTO, 8 nm, paraelectric with a highly functional surface that enables both suspension and chemical reaction in organic solvents. The nanocrystals were suspended in furfuryl alcohol inside a uniquely prepared mold, in which volume fraction of nanocrystal filler (νf) could be varied. Polymerization of the matrix in situ at 70-90 °C resulted in a nanocomposite with a higher than anticipated effective permittivity (up to 50, with νf only 0.41, 0.5-2000 kHz), exceptional stability as a function of frequency, and very favorable dissipation factors (tan δ < 0.01, νf < 0.41; tan δ < 0.05, νf < 0.5). The increased permittivity is attributed to the covalent attachment of the poly(furfuryl alcohol) matrix to the surface of the nanocrystals, homogenizing the particle-matrix interface, limiting undercoordinated surface sites and reducing void space. XPS and FTIR confirmed strong interfacial interaction between matrix and nanocrystal surface. Effective medium approximations were used to compare this with similar nanocomposite systems. It was found that the high effective permittivity could not be attributed to the combination of two components alone, rather the creation of a hybrid nanocomposite possessing its own dielectric behavior. A nondispersive medium was selected to focus on the frequency dependent permittivity of the 8 nm barium titanate nanocrystals. Experimental corroboration with known theory is evident until a specific volume fraction (νf ≈ 0.3) where, due to a sharp increase in the effective permittivity, approximations fail to adequately describe the nanocomposite medium.

Charge density dependent two-channel conduction in organic electric double layer transistors (EDLTs).

A transport model based on hole-density-dependent trapping is proposed to explain the two unusual conductivity peaks at surface hole densities above 10(13) cm(-2) in rubrene electric double layer transistors (EDLTs). Hole transport in rubrene is described to occur via multiple percolation pathways, where conduction is dominated by transport in the free-site channel at low hole density, and in the trap-site channel at larger hole density.

Engineering optical properties of gold-coated nanoporous anodic alumina for biosensing.

The effect in the Fabry-Pérot optical interferences of nanoporous anodic alumina films coated with gold is studied as a function of the porosity and of the gold thickness by means of reflectance spectroscopy. Samples with porosities between 14 and 70% and gold thicknesses (10 and 20 nm) were considered. The sputtering of gold on the nanoporous anodic alumina (NAA) films results in an increase of the fringe intensity of the oscillations in the spectra resulting from Fabry-Pérot interferences in the porous layer, with a reduction in the maximum reflectance in the UV-visible region. For the thicker gold layer, sharp valleys appear in the near-infrared (IR) range that can be useful for accurate spectral shift measurements in optical biosensing. A theoretical model for the optical behavior has also been proposed. The model shows a very good agreement with the experimental measurements, what makes it useful for design and optimization of devices based on this material. This material capability is enormous for using it as an accurate and sensitive optical sensor, since gold owns a well-known surface chemistry with certain molecules, most of them biomolecules.