Matrix method to predict the spectral reflectance of stratified surfaces including thick layers and thin films

The most convenient way to assess the color rendering of a coated, painted, or printed surface in various illumination and observation configurations is predict its spectral, angular reflectance using an optical model. Most of the time, such a surface is a stack of layers having different scattering properties and different refractive indices. A general model applicable to the widest range of stratified surfaces is therefore appreciable. This is what we propose in this paper by introducing a method based on light transfer matrices: the transfer matrix representing the stratified surface is the product of the transfer matrices representing the different layers and interfaces composing it, each transfer matrix being expressed in terms of light transfers (e.g. diffuse reflectances and transmittances in the case of diffusing layers). This general model, inspired of models used in the domain of thin films, can be used with stacks of diffusing or nonscattering layers for any illumination-observation geometry. It can be seen, in the case of diffusing layers, as an extension of the Saunderson-corrected Kubelka-Munk model and Kubelka's layering model. We illustrate the through an experimental example including a thin coating, a thick glass plate and a diffusing background. 2. Introduction For a long time, the variation of the spectral properties of surfaces and objects by application of coatings has been a wide subject of investigation for physicians who proposed several models based on specific mathematical formalisms according to the type of physical components and the application domain. In the domain of paints, papers, and other diffusing media, a classical approach is to use the Kubelka-Munk system of two coupled differential equations to describe the propagation of diffuse fluxes in the medium [1,2]. The extension of this model by Kubelka to stacks of paint layers is based on geometrical series describing the multiple reflections and transmissions of these diffuse fluxes between the different layers [3,4]. Geometrical series were also used by Saunderson [5] when deriving his correction of the Kubelka-Munk model in order to account for the internal reflections of light between the paint layer and the paint-air interface, by Clapper and Yule [6] in their reflectance mode

Two-flux and multiflux matrix models for colored surfaces

International audienceThis paper presents various extensions of the so-called two-flux models for prediction of reflectance and transmittance of diffusing media, i.e. the ubelka-Munk model, and the extension of Kubelka-Munk for stacks of diffusing layers. A first matrix formulation of the Kubelka-Munk differential equations leads to a matrix framework based on transfer matrices, which can be extended to stacks of diffusing layers, stacks of nonscattering films, and stacks of scattering and non-scatterings films as a generalization of the Williams-Clapper model for prediction of the reflectance of paper photographs, each of these configurations being illustrated through various examples. This paper also exposes the limitsof the two flux approach and shows that the matrix formalism extends in a straightforward manner to multiflux models, where the size of the matrices is increased

Plasmonic Waveguide Lithography for Patterning Nanostructures with High Aspect-Ratio and Large-Area Uniformity

The rapid development of the semiconductor industry in the past decades has driven advances in nano-manufacturing technologies towards higher resolution, higher throughput, better large-area uniformity, and lower manufacturing cost. Along with these advancements, as the size of the devices approaches tens of nanometers, challenges in patterning technology due to limitations in physics, equipment and cost have quickly arisen. To solve these problems, unconventional lithography systems have attracted considerable interest as promising candidates to overcome the diffraction limit. One recently evolved technology, plasmonic lithography, can generate subwavelength features utilizing surface plasmon polaritons (SPPs). Evanescent waves generated by the subwavelength features can be transmitted to the photoresist (PR) using plasmonic materials. Another approach of plasmonic lithography involves the use of hyperbolic metamaterial (HMM) structures, which have been studied intensively because of their unique electromagnetic properties. Specifically, epsilon near zero (ENZ) HMMs offer the potential to produce extremely small features due to their high optical anisotropy. Despite the advancements in plasmonic lithography, several key issues impede progress towards more practical application, which includes shallow pattern depth (due to the evanescent nature of SPPs), non-uniformity over a large area (due to the interference of multiple diffraction orders) and high sensitivity of the roughness on the films and defects on the mask. The light intensity in the PR is very weak which results in an extremely long exposure time. To this end, this dissertation is dedicated to plasmonic lithography systems based on SPP waveguides and ENZ HMMs for patterning nanostructures with high aspect-ratio and large-area uniformity. New schemes are exploited in this thesis to address these challenges. Lithography systems based on a specially designed waveguide and an ENZ HMM are demonstrated. By employing the spatial filtering properties of the waveguide and the ENZ HMM, the period, linewidth and height of the patterns can be well controlled according to various design purposes. Periodic structures were achieved in both systems with a half-pitch of approximately 50 ~ 60 nm, which is 1/6 of the exposure wavelength of 405 nm. The thickness of the PR layer is around 100 ~ 250 nm, which gives an aspect-ratio higher than 2:1. The subwavelength patterns are uniform in cm2 areas. In addition to the design principle, various numerical simulations, fabrication conditions and corresponding results are discussed. The design principle can be generalized to other materials, structures and wavelengths. The real-world performance of the lithography system considering non-idealities such as line edge roughness and single point defect is analyzed. Comparisons between the plasmonic systems based on different design rules are also carried out, and the advantages of the spatial frequency selection principle is verified. The plasmonic waveguide lithography systems developed in this dissertation provide a technique to make deep subwavelength features with high aspect-ratio, large-area uniformity, high light intensity distribution, and low line-edge-roughness for practical applications. Compared with the previously reported results, the performance of plasmonic lithography is drastically improved. A plasmonic roller system combining the photo-roller system and plasmonic lithography is also developed. This plasmonic roller system can support a continuous patterning with a high throughput for cost sensitive applications. Several potential applications of the plasmonic materials including near field spin Hall effects and a particle based Lidar design are explored. Other advances towards plasmonic functional devices including silicon (Si) nanowire (NW) arrays, light-thermal converters and plasmonic lasers are also reported.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144126/1/sxichen_1.pd

Intelligent Multi-channel Meta-imagers for Accelerating Machine Vision

Rapid developments in machine vision have led to advances in a variety of industries, from medical image analysis to autonomous systems. These achievements, however, typically necessitate digital neural networks with heavy computational requirements, which are limited by high energy consumption and further hinder real-time decision-making when computation resources are not accessible. Here, we demonstrate an intelligent meta-imager that is designed to work in concert with a digital back-end to off-load computationally expensive convolution operations into high-speed and low-power optics. In this architecture, metasurfaces enable both angle and polarization multiplexing to create multiple information channels that perform positive and negatively valued convolution operations in a single shot. The meta-imager is employed for object classification, experimentally achieving 98.6% accurate classification of handwritten digits and 88.8% accuracy in classifying fashion images. With compactness, high speed, and low power consumption, this approach could find a wide range of applications in artificial intelligence and machine vision applications.Comment: 15 pages, 5 figure

Light Trapping in Plasmonic Solar Cells

Subwavelength nanostructures enable the manipulation and molding of light in nanoscale dimensions. By controlling and designing the complex dielectric function and nanoscale geometry we can affect the coupling of light into specific active materials and tune macroscale properties such as reflection, transmission, and absorption. Most solar cell systems face a trade-off with decreasing semiconductor thickness: reducing the semiconductor volume increases open circuit voltages, but also decreases the absorp- tion and thus the photocurrent. Light trapping is particularly critical for thin-film amorphous Si (a-Si:H) solar cells, which must be made less than optically thick to enable complete carrier collection. By enhancing absorption in a given semiconductor volume, we can achieve high efficiency devices with less than 100 nm of active region. In this thesis we explore the use of designed plasmonic nanostructures to couple incident sunlight into localized resonant modes and propagating waveguide modes of an ultrathin semiconductor for enhanced solar-to-electricity conversion. We begin by developing computational tools to analyze incoupling from sunlight to guided modes across the solar spectrum and a range of incident angles. We then show the potential of this method to result in absorption enhancements beyond the limits for thick film solar cells. The second part of this thesis describes the integration of plasmonic nanos- tructures with a-Si:H solar cells, showing that designed nanostructures can lead to enhanced photocurrent over randomly textured light trapping surfaces, and develops a computational model to accurately simulate the absorption in these structures. The final chapter discusses the fabrication of a high-efficiency (9.5%) solar cell with a less than 100 nm absorber layer and broadband, angle isotropic photocurrent enhance- ment. Moreover, we discuss general design rules where light trapping nanopatterns are defined by their spatial coherence spectral density.</p

Single Photon Counting UV Solar-Blind Detectors Using Silicon and III-Nitride Materials

Ultraviolet (UV) studies in astronomy, cosmology, planetary studies, biological and medical applications often require precision detection of faint objects and in many cases require photon-counting detection. We present an overview of two approaches for achieving photon counting in the UV. The first approach involves UV enhancement of photon-counting silicon detectors, including electron multiplying charge-coupled devices and avalanche photodiodes. The approach used here employs molecular beam epitaxy for delta doping and superlattice doping for surface passivation and high UV quantum efficiency. Additional UV enhancements include antireflection (AR) and solar-blind UV bandpass coatings prepared by atomic layer deposition. Quantum efficiency (QE) measurements show QE > 50% in the 100–300 nm range for detectors with simple AR coatings, and QE ≅ 80% at ~206 nm has been shown when more complex AR coatings are used. The second approach is based on avalanche photodiodes in III-nitride materials with high QE and intrinsic solar blindness

Heterojunction Structures for Photon Detector Applications

The work presented here report findings in (1) infrared detectors based on p-GaAs/AlGaAs heterojunctions, (2) J and H aggregate sensitized heterojunctions for solar cell and photon detection applications, (3) heterojunctions sensitized with quantum dots as low cost solar energy conversion devices and near infrared photodetectors. (1)A GaAs/AlGaAs based structure with a graded AlGaAs barrier is found to demonstrate a photovoltaic responsivity of ~ 30mA/W (~ 450mV/W) at the wavelength of 1.8 mm at 300K. Additionally the graded barrier has enhanced the photoconductive response at 78 K, showing a responsivity of ~ 80mA/W with a D*=1.4×108 Jones under 1V bias at 2.7 mm wavelength. This is an approximately 25 times improvement compared to the flat barrier detector structure, probably due to the improved carrier transport, and low recapture rate in the graded barrier structure. However, these graded barrier devices did not indicate a photoresponse with photoconductive mode at 300K due to high shot noise. Additionally, two generation-recombination noise components and a 1/f noise component were identified. A series of GaAs/AlGaAs multilayer hetero-junction structures were tested as thermal detectors. A superlattice structure containing 57% Al fraction in the barrier and 3 × 1018 cm-3 p-doped GaAs emitter showed the highest responsivity as a thermal detector with a TCR of ~ 4% K-1, at 300K. (2)The photovoltaic properties of heterojunctions with J-/ H- aggregated dye films sandwiched between n– and p-type semiconductors were investigated for potential application as solar cells and IR detectors. Films of cationic dye Rhodamine-B-thiocyanate adsorbed on Cu2O substrate are found to form organized dye layers by self-assembled J- aggregation, resulting in large red-shifts in the photo -response. Additionally, cells sensitized with a pentamethine cyanine dye exhibited a broad spectral response originating from J- and H-aggregates. The photocurrent is produced by exciton transport over relatively long distances with significant hole-mobility as well as direct sensitized injection at the first interface. (3) A ZnO/PbS-QD/Dye heterostructure had enhanced efficiency compared to ZnO/Dye heterostructure as a solar cell. Furthermore, a ZnO/PbS-QD structure has demonstrated UV and NIR responses with 4×105V/W (390 nm) and 5.5×105 V/W (750 nm) under 1V bias at 300K

Study of propagation and detection methods of terahertz radiation for spectroscopy and imaging

The applications of terahertz (THz, 1 THz is 1012 cycles per second or 300 pm in wavelength) radiation are rapidly expanding. In particular, THz imaging is emerging as a powerful technique to spatially map a wide variety of objects with spectral features which are present for many materials in THz region. Objects buried within dielectric structures can also be imaged due to the transparency of most dielectrics in this regime. Unfortunately, the image quality in such applications is inherently influenced by the scattering introduced by the sample inhomogeneities and by the presence of barriers that reduces both the transmitted power and the spatial resolution in particular frequency components. For continued development in THz radiation imaging, a comprehensive understanding of the role of these factors on THz radiation propagation and detection is vital. This dissertation focuses on the various aspects like scattering, attenuation, frequency filtering and waveguide propagation of THz radiation and its subsequent application to a stand-off THz interferometric imager under development. Using THz Time Domain spectroscopic set-up, the effect of scattering, guided THz propagation with loss and dispersion profile of hollow-core waveguides and various filtering structures are investigated. Interferometric detection scheme and subsequent agent identification is studied in detail using extensive simulation and modeling of various imaging system parameters

Multispectral photography for earth resources

A guide for producing accurate multispectral results for earth resource applications is presented along with theoretical and analytical concepts of color and multispectral photography. Topics discussed include: capabilities and limitations of color and color infrared films; image color measurements; methods of relating ground phenomena to film density and color measurement; sensitometry; considerations in the selection of multispectral cameras and components; and mission planning