Rendering transparent materials with a complex refractive index: semi-conductor and conductor thin layers

The scope of the present work was to evaluate the role of the complex refractive index in optical diffusion studies for imaging purposes. In particular, phosphor materials and their corresponding optical transmission characteristics play significant role in x-ray detectors, cathode ray tubes, microscopy techniques, white LED applications and have an impact on other scientific fields including chemical, energy, optoelectronic and space industries. The complex refractive index is associated with the optical attenuation capabilities of phosphor materials, either scattering or absorption, which in turn influences their imaging characteristics. In order to examine the complex refractive index effects, a simulation model was developed by taking into account the following: (i) phosphors of different layer thickness, 100 μm (thin layer) and 200 μm (thick layer), (ii) packing density 50%, (iii) three values of light wavelengths 400, 550, and 700 nm, and (iv) particle diameter in the range 10–10 mm. The complex refractive index was considered to vary: (a) from 1.5 up to 2.0 the real part and (b) from 10−6 up to 10−4 the imaginary part. The role of the complex refractive index on the optical parameters was examined within the framework of Mie scattering theory. Optical diffusion was assessed through Monte Carlo simulation techniques and the most important conclusion of the results was the achievement of improved phosphor spatial resolution by increasing the real part of the refractive index and not the imaginary one.

We recently developed an approach to the estimation of the complex permittivity (ϵ) and thickness (d) of very thin layers using measurements of their transmittance, front-side reflectance and back-side reflectance. The approach is based on a limited expansion of the Abelès characteristic matrix elements and is especially designed for characterization of very thin layers. In this paper we investigate the uncertainties of the estimated real part of ϵ (ϵ1), the imaginary part of ϵ (ϵ2) and d of semiconductor thin layers that are due to the methodological error and the experimental uncertainties in the optical quantities measured. It is shown that the effect of the uncertainties in the measurable quantities is significantly stronger than that of the methodical error and increases considerably with the decrease of the ratio d/λ (λ being the wavelength). An efficient two-step procedure is proposed to reduce this effect. First, we supply a criterion for determination of d with the lowest uncertainty from the ensemble of estimations constructed on a wavelength by wavelength basis. This is crucial for the next step: the estimation of ϵ1 and ϵ2. The approach proposed ensures estimation of ϵ1, ϵ2 and d with the highest accuracy, limited only by the methodological error.

In this paper, we consider a plane electromagnetic wave incident onto a dielectric plate, which has one surface covered with a thin layer of metal. An oblique incident angle was considered for the TE (s polarization in optic) and TM (p polarization) plane waves. The thin metal layer is treated as an infinitesimal thickness. It was characterized by a surface conductivity and accounted for by a tangential magnetic field component step induced by the current flow in the metal layer. Compact expressions, which describe the reflection, transmission and absorption in a dielectric plate covered with a thin layer of metal, have been obtained. It was shown that by choosing the appropriate surface conductivity, the Fabry-Perot transmission resonances can be shifted to the position where the maximum reflection is observed in the case of an uncovered dielectric. On the other hand, the elimination of the Fabry-Perot resonances can be also achieved by choosing a proper metal surface conductivity. Measurements of the reflection from the glass covered with a thin layer of metal have been performed in a wide microwave frequency range (2–12 GHz) revealing a large difference in the measured reflection coefficient from the dielectric and metalized surfaces. The measured results fit well with those calculated by employing analytical expressions obtained in this paper.

Higher power circuits in steadily decreasing structures are changing failure mechanisms that were previously uncritical for the semiconductor industry into critical ones. Such a failure mechanism is, for example, the material fatigue of thin metal layers induced by cyclic loading, leading to disruption the failure mode of the metal layer. If a corrosive medium penetrates in addition, due to a crack in the device housing, the degradation of the metal can be accelerated. In this study corrosion sensitivity of thin aluminium and copper layers to iodine was verified in a feasibility study. A test vehicle is available for characterising disrupted, thin metal layers. It is a micro cantilever beam with a meander-shaped thin metal layer on top. After an optimisation and calibration phase, 1 µm thick aluminium layers were disrupted by alternating mechanical loading ((70 - 180). 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> cycles) in a newly developed, low-cost, tabletop vibration tester in a thermally stable environment. The test vehicles are then corroded in an iodine vapour corrosion tester at an accelerated rate. Preliminary tests on the corrosion of thin aluminium and copper layers were performed within a feasibility study and the iodine vapour corrosion tester was thus confirmed. A dependence of the corrosion sensitivity on the disruption could be proven. These results need to be verified within further investigations.

A comprehensive sensitivity study has been made using Mie theory to determine the effect of realistic variations in values of real and imaginary parts of the complex index of refraction on volume extinction and absorption coefficients for a wide range of log normal particle size distributions (defined by geometric mean radius r(g) and geometric standard deviation sigma(g)). Wavelengths lambda from the visible (0.55 microm) through the middle ir (10.6 microm) were considered. Extinction is independent of the complex index to within 20% for the majority of realistic particle size distributions, providing lambda < 2 microm. However, changes in extinction by up to an order of magnitude are caused by realistic variations in refractive indexes for 2 microm </= lambda </= 10.6 microm, with the real index being more important in affecting extinction than the imaginary index. Similar changes are caused by variations in particle size distribution for values of refractive indexes typical of atmospheric constituents. For bimodal size distributions representative of desert aerosols, values of the complex refractive index that result in minimum and maximum extinction coefficients are given. Absorption is generally less dependent on size distribution than is extinction and is not, in general, linear with the imaginary index, especially for broad particle distributions.

We present the results of a comparison study in which a simple, automated, and unsupervised algorithm, which we call the arrange and average algorithm, was used to infer microphysical parameters (complex refractive index (CRI), effective radius, total number, surface area, and volume concentrations) of atmospheric aerosol particles. The algorithm normally uses backscatter coefficients ( β ) at 355, 532, and 1064 nm and extinction coefficients ( α ) at 355 and 532 nm as input information. We compared the performance of the algorithm for the existing “3 β +α” and potential “3 β +3α” configurations of a multiwavelength aerosol Raman lidar or highspectral-resolution lidar (HSRL). The “3 β +3α” configuration uses an extra extinction coefficient at 1064 nm. Testing of the algorithm is based on synthetic optical data that are computed from prescribed CRIs and monomodal logarithmically normal particle size distributions that represent spherical, primarily fine mode aerosols. We investigated the degree to which the microphysical results retrieved by this algorithm benefits from the increased number of input extinction coefficients.

Refractive indices and extinction coefficients of lithium fluoride in thin film coated at room temperature are deduced from reflectance curves from 100 to 120 nm. These refractive indices are smaller but approximately follow the same dispersion law as crystalline LiF indices. The extinction coefficients are of the order of 0.1, i.e., 105 times higher than those of crystalline LiF. The absorption by the low-energy tail of an exciton band has been represented by the Urbach rule. These complex refractive indices have been used to optimize the first-order efficiency of LiF-coated Al gratings of the NASA FUSE (Far Ultraviolet Spectroscopic Explorer) space mission.

This paper presents the application of a theoretically developed method that provides plasma parameter solution space information from measured RF attenuation that occurs during reentry. The purpose is to provide reentry plasma parameter information from the communication signal attenuation. The theoretical development centers around the attenuation and the complex index of refraction. The methodology uses an imaginary index of the refraction matching algorithm with a tolerance to find suitable solutions that satisfy the theory. The imaginary matching terms are then used to determine the real index of refraction resulting in the complex index of refraction. Then a filter is used to reject nonphysical solutions. Signal attenuation-based plasma parameter properties investigated include the complex index of refraction, plasma frequency, electron density, collision frequency, propagation constant, attenuation constant, phase constant, complex plasma conductivity, and electron mobility. RF plasma thickness attenuation is investigated and compared to the literature. Similar plasma thickness for a specific signal attenuation can have different plasma properties.

This article represents an analytical formulation for optical properties of absorbing metallic nanoparticles in visible region of electromagnetic spectrum based on Mie theory, in order to find a clear relationship between fundamental characteristics of nanoparticles with their spectral behavior and color coordinate in CIELAB color space. Calculations were performed on nanoparticles with various diameters (d = 50, 100, and 200 nm), as well as complex refractive index with different real (n = 1.5, 2.0, 2.5, and 3.0) and imaginary (k = 0.001 and 0.1) parts. Obtained results reveal that scattering phenomena in nanoparticles are strongly linked to the particle size parameter and complex index of refraction. The results indicate that the reflectance and lightness (L*) of nanoparticles increases as a result of increase in their size and real part of complex refractive index and decrease with increasing the imaginary part of complex refractive index. The CIELAB colorimetric system was used for analysis the color of nanoparticles. According to obtained results, all nanoparticles have greenish‐blue color, and undergo color change as a result of varying in their size and the complex refractive index. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 477–483, 2016

This paper proposes a new type of a porous silicon-based optical microcavity biosensor using a thin metal layer. The detection system was composed of a bottom distributed Bragg reflector (DBR) of porous silicon as an overlayer. After changing the refractive index of the defect layer through interactions of biomaterial, a thin metal layer was deposited onto the defect layer as a top mirror to form a complete microcavity. The optical sensitivity of the new microcavity biosensor with a single DBR and metal mirror can still be high only with the level f modification of a single porous layer, which is comparable to that of the conventional microcavity biosensor with two DBRs, where the modification of multiple porous layers is required. The results of the numerical simulation for the cavity quality and sensitivity of the proposed microcavity biosensor were provided.

Aerosol Robotic Network (AERONET) Sun photometer observations were carried out at Ouarzazate, Morocco, during the Saharan Mineral Dust Experiment (SAMUM) 2006. Data from one measurement day, 19 May 2006, are used to derive particle optical and microphysical parameters with AERONET's latest version of light‐scattering model for non‐spherical particle geometry. In our analysis we also make use of a novel measurement channel at 1638 nm wavelength. We compare the results to data products obtained by airborne high‐spectral‐resolution lidar, several ground‐based Raman lidar, and airborne and ground‐based in situ measurement platforms. We chose that specific measurement day because the dust plume was vertically well mixed. Extinction coefficients from AERONET Sun photometer and lidar observations and in situ measurements agree well. Ångström exponents from Sun photometer and lidar are in close agreement, too. Airborne in situ measurements of dust particle size distributions show larger effective radii than inferred from the AERONET data. Complex refractive indices that are derived with the AERONET algorithm differ from the values obtained with different independent techniques employed in our study. The single‐scattering albedo was derived from the airborne observations of particle size distributions and complex refractive indices. Single‐scattering albedo differs to the value inferred from the AERONET data. The differences may be attributed to the different effective radii that we obtained from the various techniques. The differences between the data products from the various measurement platforms, however, cannot be generalized, as we could only test data for one measurement day. An analysis of additional measurements is under way.

Abstract. Modeling the interaction of dust with long-wave (LW) radiation is still a challenge because of the scarcity of information on the complex refractive index of dust from different source regions. In particular, little is known about the variability of the refractive index as a function of the dust mineralogical composition, which depends on the specific emission source, and its size distribution, which is modified during transport. As a consequence, to date, climate models and remote sensing retrievals generally use a spatially invariant and time-constant value for the dust LW refractive index. In this paper, the variability of the mineral dust LW refractive index as a function of its mineralogical composition and size distribution is explored by in situ measurements in a large smog chamber. Mineral dust aerosols were generated from 19 natural soils from 8 regions: northern Africa, the Sahel, eastern Africa and the Middle East, eastern Asia, North and South America, southern Africa, and Australia. Soil samples were selected from a total of 137 available samples in order to represent the diversity of sources from arid and semi-arid areas worldwide and to account for the heterogeneity of the soil composition at the global scale. Aerosol samples generated from soils were re-suspended in the chamber, where their LW extinction spectra (3–15 µm), size distribution, and mineralogical composition were measured. The generated aerosol exhibits a realistic size distribution and mineralogy, including both the sub- and super-micron fractions, and represents in typical atmospheric proportions the main LW-active minerals, such as clays, quartz, and calcite. The complex refractive index of the aerosol is obtained by an optical inversion based upon the measured extinction spectrum and size distribution. Results from the present study show that the imaginary LW refractive index (k) of dust varies greatly both in magnitude and spectral shape from sample to sample, reflecting the differences in particle composition. In the 3–15 µm spectral range, k is between ∼ 0.001 and 0.92. The strength of the dust absorption at ∼ 7 and 11.4 µm depends on the amount of calcite within the samples, while the absorption between 8 and 14 µm is determined by the relative abundance of quartz and clays. The imaginary part (k) is observed to vary both from region to region and for varying sources within the same region. Conversely, for the real part (n), which is in the range 0.84–1.94, values are observed to agree for all dust samples across most of the spectrum within the error bars. This implies that while a constant n can be probably assumed for dust from different sources, a varying k should be used both at the global and the regional scale. A linear relationship between the magnitude of the imaginary refractive index at 7.0, 9.2, and 11.4 µm and the mass concentration of calcite and quartz absorbing at these wavelengths was found. We suggest that this may lead to predictive rules to estimate the LW refractive index of dust in specific bands based on an assumed or predicted mineralogical composition, or conversely, to estimate the dust composition from measurements of the LW extinction at specific wavebands. Based on the results of the present study, we recommend that climate models and remote sensing instruments operating at infrared wavelengths, such as IASI (infrared atmospheric sounder interferometer), use regionally dependent refractive indices rather than generic values. Our observations also suggest that the refractive index of dust in the LW does not change as a result of the loss of coarse particles by gravitational settling, so that constant values of n and k could be assumed close to sources and following transport. The whole dataset of the dust complex refractive indices presented in this paper is made available to the scientific community in the Supplement.

The temperature-induced complex refractive index (CRI) effect of graphene is demonstrated theoretically and experimentally based on a graphene coated in-fiber MZI (Mach–Zehnder interferometer). The relationships between real and imaginary parts of the graphene CRI and temperature are obtained through investigating the dip wavelength and intensity of the MZI interference spectrum changing with temperature, respectively. The temperature effect of CRI of the graphene is also analyzed theoretically. Both experimental and theoretical studies show that the real part and imaginary part of the CRI nonlinearly decrease and increase with temperature increasing, respectively. This graphene-coated in-fiber MZI structure also possesses the advantages of easy fabrication, miniaturization, low cost and robustness. It has potential applications in nanomaterial-based optic devices for communication and sensing.

As is well known, the mask in projection printing is a thin (about 1,am thick) object, composed of numerous variable domains. The various domains contain different complex refractive indices. These refractive indices form a discontinuous "mask function" ,appearing as a coefficient in the Maxwell-Material (MM) equation1 that describes the transmission of the electric field through the 3D mask domain. The right-hand side of this equation involves the gradient of the dot-product of the electric field with the gradient of the log of the refractive index. Within each feature, the refractive index is a constant. Therefore its gradient vanishes, and the resulting local MM equation is the wave equation. However, at a feature boundary (chrome-quartz, phase-i— phase-2, etc.) the complex refractive index is discontinuous, resulting in a highly singular delta-function-like coefficient. The trailing components of the field display the standard Maxwell discontinuity conditions, resulting in two very singular terms, i.e. a derivative of a delta function and a product of two delta functions. Such a source term, with such a remarkable oscillation, will be the origin of extreme instability in the numerical solution of the equations, no matter which direct solution algorithm is employed. Accordingly, the derivation of a preconditioner, namely a function which contains most of the unpleasantness of the equation times a function to be found, is absolutely essential to obtain accurate solutions in a reasonable time. Through an elaborate uniformly asymptotic scheme and scale analysis, we have derived such a preconditioner. The solution of the direct MM equation was compared with the solution using the preconditioner, and it gave us the confidence that we were on the right track. It actually means that one wishes to find the mask's Green function which, when convolved with the electric field incident on the mask, yields the exiting field which then enters the imaging optical system. It is the purpose of this paper to demonstrate the results obtained thus far, as well as to illustrate its implications on defocus linewidth control.

Investigation on an evanescent wave fiber-optic absorption sensor based on fiber loop cavity ring-down spectroscopy