Classical Optical Model Research Articles

Tailoring optical constants of few-layer black phosphorus coatings: Spectroscopic ellipsometry approach supported by ab-initio simulation

2D black phosphorus (BP) has attracted extensive attention as an anisotropic platform for novel optoelectronic and polarizing optics applications. Insight into the factors that tune the optical and polarizing properties of 2D BP reveals their essential influence on BP-based photonic and optoelectronic devices. In this work, studies of the optical constants of few-layer black phosphorus coatings are studied and discussed, with particular emphasis on the complex dielectric function. Herein, the complex optical constants of multi-flake composite films in the energy range of 1.38–6.2 eV by spectroscopic ellipsometry with the use of the classical optical model have been determined. Classical optical simulations were supplied by dielectric function estimations delivered by density functional theory. Additionally, few-layer black phosphorus coatings were imaged by polarizing microscopy and investigated by Raman spectroscopy, revealing a size-tunable flake composition. The pattern analysis of the polarization images reveals a shift in polarization anisotropy originated mainly from the central region of the flake. The semi-isotropic optical properties suggest that the extinction coefficient of BP flakes defines the applications of BP in photonics, waveguides, and directional optoelectronic devices.

Tailoring Electric Field Standing Waves in Reflection–Absorption Infrared Spectroscopy to Enhance Absorbance in Buried Molecular Layers

Electric field standing waves (EFSW) that establish within thin films during their characterization by reflection–absorption infrared (RAIR) spectroscopy are shown to result in a >25-fold enhancement in the intensity of absorbance features in a molecularly thin methane (Me) layer buried within Argon (Ar) films. Using an all-optical depth profiling method and describing the interference effects responsible for these phenomena using a classical optics model, modulations in the EFSW amplitude at specific sample thicknesses are demonstrated to be responsible for these strong deviations from Beer–Lambert behavior. Tuning sample thickness is shown to enable the EFSW depth profile to be tailored, conferring greatly enhanced sensitivity and increased spatial selectivity to RAIR spectroscopy. These are highly desirable attributes for the characterization of interfacial structures and mesoscopic dynamic processes within complex buried multilayer assemblies and stratified composite films used to model and study a range of materials and life science phenomena.

Tailoring electric field standing waves in reflection–absorption infrared spectroscopy to enhance absorbance from adsorbates on ice surfaces

The spectroscopic detection of molecules adsorbed onto ice surfaces at coverages similar to those encountered under typical environmental conditions requires high surface selectivity and sensitivity that few techniques can afford. An experimental methodology allowing a significant enhancement in the absorbance from adsorbed molecules is demonstrated herein. It exploits Electric Field Standing Wave (EFSW) effects intrinsic to grazing incidence Reflection-Absorption Infrared (RAIR) spectroscopy, where film thickness dependent optical interferences occur between the multiple reflections of the IR beam at the film-vacuum and the substrate-film interfaces. In this case study, CH4 is used as a probe molecule and is deposited on a 20 ML coverage dense amorphous solid water film adsorbed onto solid Ar underlayers of various thicknesses. We observe that, at thicknesses where destructive interferences coincide with the absorption features from the CH stretching and HCH bending vibrational modes of methane, their intensity increases by a factor ranging from 10 to 25. Simulations of the RAIR spectra of the composite stratified films using a classical optics model reproduce the Ar underlayer coverage dependent enhancements of the absorbance features from CH4 adsorbed onto the ice surface. They also reveal that the enhancements occur when the square modulus of the total electric field at the film's surface reaches its minimum value. Exploiting the EFSW effect allows the limit of detection to be reduced to a coverage of (0.2 ± 0.2) ML CH4, which opens up interesting perspectives for spectroscopic studies of heterogeneous atmospheric chemistry at coverages that are more representative of those found in the natural environment.

Spectroscopic Study of HNO3Dissociation on Ice

A detailed spectroscopic study of HNO(3):H(2)O binary amorphous mixtures, and of the adsorption of HNO(3) onto ice, is reported. Using a classical optics model, the extent of intermixing and of ionic dissociation of adsorbed HNO(3), which forms a strong acid with liquid water, is determined as a function of HNO(3) coverage and temperature. Even at temperatures as low as 45 K, where intermixing is limited to at most a few molecular layers at the interface, ionic dissociation of adsorbed HNO(3) is observed to be extensive. While some amount of molecularly adsorbed HNO(3) is observed at the surface of ice at 45 K, its ionic dissociation occurs irreversibly upon heating the ice substrate to 120 K. The molecularly adsorbed state of HNO(3) is not restored upon cooling, suggesting HNO(3) is a metastable entity at the surface of ice. Therefore, despite ionic dissociation of HNO(3) being thermodynamically favored, it appears to be kinetically inhibited at the surface of amorphous solid water at temperatures below 120 K.

Manipulating the Microcavity Structure for Highly Efficient Inverted Top-Emitting Organic Light-Emitting Diodes: Simulation and Experiment

A comprehensive theoretical and experimental study on inverted top-emitting organic light-emitting diodes (ITOLEDs) with a microcavity structure is demonstrated. In the ITOLEDs, tris-(8-hydroxyquinoline) aluminum (Alq3) is used as the emitting material and the outcoupling capping layer, and the 2, 9-dimethyl-4, 7-diphenyl-1, 10-phenanthroline is used as the hole/exciton-blocking layer to confine most emitting dipoles exactly at the desired resonant position. A classical optical model is adopted to simulate the electroluminescence intensity and the spectral characteristics as a function of a viewing angle. The factors that influence optical interference effects and light outcoupling are discussed systematically. The optimized ITOLED shows an enhanced outcoupling efficiency and highly saturated colors compared with that of the corresponding conventional bottom-emitting light-emitting diode while the angular dependence of the emission wavelength is minimized.

Dissociative adsorption of hydrogen fluoride onto amorphous solid water

Adsorption of hydrogen fluoride (HF) onto amorphous solid water films at 50 K is reported to yield a strong absorbance continuum in their reflection-absorption infrared spectra (RAIRS). This and other complex features observed in the RAIRS spectra of stratified binary composite HF:H(2)O nanoscopic films deposited onto Pt(111) are interpreted quantitatively using a classical optics model. Comparison with experimental data allows us to determine that the absorbance continuum is due to absorption within the film (as opposed to trivial optical effects) and that the extent of intermixing and uptake is mostly limited to the first few molecular layers. Furthermore, extensive isotope scrambling is demonstrated by the observation of similar Zundel continua upon codeposition of neat HF, or DF, and H(2)O vapors onto Pt(111) at 50 K. These observations are consistent with those expected from extensive ionic dissociation of HF upon dissolution within, and adsorption onto, ASW at 50 K.

Infrared Spectroscopy and Optical Constants of Porous Amorphous Solid Water

Reflection-absorption infrared spectra (RAIRS) of amorphous solid water (ASW) films grown at 20 K on a Pt(111) substrate at various angles (theta(Beam) = 0-85 degrees ) using a molecular beam are reported. They display complex features arising from the interplay between refraction, absorption within the sample, and interference effects between the multiple reflections at the film-substrate and film-vacuum interfaces. Using a simple classical optics model based on Fresnel equations, we obtain optical constants [i.e., n(omega) and k(omega)] for porous ASW in the 1000-4000 cm(-1) (10-2.5 microm) range. The behavior of the optical properties of ASW in the intramolecular OH stretching region with increasing theta(Beam) is shown to be strongly correlated with its decreasing density and increasing surface area. A direct comparison between the RAIRS and calculated vibrational spectra shows a large difference ( approximately 200 cm(-1)) in the position of the coupled H-bonded intramolecular OH stretching vibrations spectral feature. Moreover, this band shifts in opposite directions with increasing theta(Beam) in RAIRS and vibrational spectra demonstrating RAIRS spectra cannot be interpreted straightforwardly as vibrational spectra due to severe optical distortions from refraction and interference effects.

Optical implementations, oracle equivalence, and the Bernstein-Vazirani algorithm

We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical optical model capable of implementing any algorithm (on $n$ qubits) that does not involve entanglement. The Bernstein-Vazirani algorithm (with a suitably modified oracle), wherein a hidden $n$ bit vector is discovered by one oracle query as against $n$ oracle queries required classically, belongs to this category. In our scheme, the modified oracle is also capable of computing $f(x)$ for a given $x$, which is not possible with earlier versions used in recent NMR and optics implementations of the algorithm.

A New Way of Looking at Nuclear Resonant Scattering

A new model for nuclear-resonant scattering of gamma radiation from resonant matter has been developed and is summarized here. This “coherent-path” model has lead to closed-form, finite-sum solutions for radiation scattered in the forward direction. The solution provides a unified microscopic picture of nuclear-resonant scattering processes. The resonant absorber or scatterer is modeled as a one-dimensional chain of “effective” nuclei or “effective” planes. The solution is interpreted as showing that the resonant radiation undergoes sequential scattering from one absorber “nucleus” or “plane” to another before reaching the detector. For recoil-free processes the various “paths” to the detector contribute coherently. The solution for this case gives calculated results that are indistinguishable from those using the classical optical model approach, although the forms of the solutions are completely different. The coherent-path model shows that the “speed-up” and “dynamical beating” effects are primarily a consequence of the fact that the single “effective” nuclear scattering processes are 180° out of phase with the incident radiation while the double nuclear scattering processes are in phase with the incident radiation. All multiple scattering paths are, and must be, included. The model can also treat the incoherent processes, i.e., processes involving gamma emission with recoil or conversion-electron emission. The source of the resonant gamma radiation can be from a radioactive source or from synchrotron radiation: both cases are treated. The model is used to explain and understand the results when each of the following experimental procedures is applied: time-differential Mossbauer spectroscopy, time-differential synchrotron radiation spectroscopy, enhanced-resolution resonant-detector Mossbauer spectroscopy, and the “gamma echo”.

Quantum mechanical model for nuclear-resonant scattering of gamma radiation

A one-dimensional quantum mechanical model for nuclear-resonant scattering of gamma radiation from matter is developed assuming the source radiation is gamma decay. A closed-form, finite-sum solution for the radiated intensity is obtained by restricting the calculation to coherent forward scattering. The solution provides a unified microscopic picture of nuclear-resonant scattering processes in which the radiation undergoes sequential scattering from one nucleus to another before reaching the detector. For recoil-free processes the various `paths' to the detector contribute coherently. The solution for this case gives results identical to the classical optical model. The one-dimensional model shows that the `speed-up' and `dynamical beating' effects are primarily a consequence of the fact that the single-nuclear scattering processes are out of phase with the incident radiation while the double-nuclear-scattering processes are in phase with the incident radiation. All multiple-scattering paths are, and must be, included. The model can treat the incoherent processes, i.e. processes involving gamma emission with recoil or conversion-electron emission. The results show that a correction may be needed when analysing time-differential Mössbauer spectroscopic data due to incoherent processes that occur in the absorber.

The inelastic channel in time-domain Mössbauerspectroscopy

Time-domain Mossbauer spectroscopy has been interpreted by Hamermesh using a classical optical model. One of the most interesting aspects of the experiments is the observation of a “speed-up” effect. This speed-up effect can be observed by measuring the gamma radiation coming from the source after transmission through a nuclear-resonant “filter”, i.e., the elastic channel, using the delayed-coincidence time-to-amplitude conversion method. This time-domain speed-up effect occurs in the coherent forward scattering of the nuclear-resonant gamma radiation. Time-domain nuclear-resonant forward scattering results observing the inelastic channel, i.e., the X-ray following internal conversion, using a radioactive source have not been obtained previously. Such results are presented for the radioactive-source case using both 57Fe and 73Ge. These two isotopes were chosen because of the differences in the values of the internal conversion coefficients α, i.e., α is 8 and 1310, respectively, for the two cases. In each case experimental data, using both the elastic channel and the inelastic channel, are given. Commercial sources and absorbers of iron-in-rhodium foils were used for the 57Fe experiments. For the 73Ge experiments, we prepared our own sources by electroplating 73As onto Ge single crystals. The Ge absorber was the enriched 73Ge single crystal originally prepared by Pfeiffer. Fits to the experimental elastic-channel data are given using the classical optical model. Our preliminary experimental results using the inelastic channel are inconclusive.

X-ray birefringence and dichroism in lithium niobate, LiNbO3

Accurate synchrotron-radiation X-ray transmission measurements have been carried out on hexagonal LiNbO3 in the vicinity of the Nb K-absorption edge (E = 18.986 keV). The experiments were performed on the two-axis diffractometer at HASYLAB in dedicated mode of DORIS II (3.7 GeV). Single-crystal wafers cut perpendicular to [10.0] were rotated around the monochromatized beam using an experimental set up analogous to the optical polarizing- microscope. Both the horizontally and vertically polarized components of the transmitted radiation were recorded at the same time and analysed in terms of a classical optical model derived from the Jones calculus. Fits to the observations yielded agreement indices between 0.013 and 0.052 supporting the applicability of the model to X-ray energies. X-ray dichroism and birefringence are proved to occur at resonance energies, and all findings show the possibility of simultaneous assessment of anisotropies of the real and imaginary parts of the refractive index in a uniaxial crystal. They also indicate that the polarization of the transmitted radiation (of suitable energy) can be varied considerably in dependence of crystal thickness and orientation with respect to the polarization direction of the incident radiation. For special structures like LiNbO3, where the tensorial scattering factor of the edge atom (Nb) is invariant against the symmetry operations of the space group, the method yields also the energy-dependent anisotropy of the anomalous-dispersion corrections, f′ and f′′, in the same experiment.

Classical and semiclassical theory of symmetric exchange collisions: An inversion procedure for low-energy He* (2 1S, 2 3S)+He differential scattering

A straightforward derivation based on an intuitive classical optical model description of collisions of the A*+A type leads to a simple semiclassical theory of direct/exchange scattering. The theory is shown to give an accurate description of low-energy He*–He collisions by comparison with exact quantum mechanical calculations, and is used as the basis for an analytical inversion procedure which yields both of the potential curves from a single angular distribution measurement. The inversion method is applied to our crossed beam measurements of He* (2 1S, 2 3S)+He differential scattering at 0.94 kcal/mole nominal collision energy to derive the relevant potential curves at large internuclear distance. The success of the method depends strongly on the accurate inclusion of apparatus resolution effects in the analysis.

Reflection Model and High-Energyπ−pBackward Peaks

We propose a classical optical model for high-energy elastic scattering. The model predicts that the logarithmic slopes for forward differential cross sections should be either the same or twice as large as the backward ones. The backward peak is due to the contribution from the discontinuity in the boundary of the optical medium. The model has the property that the mechanisms responsible for the forward and backward scatterings are not independent of each other. This is contrasted with conventional models which view the forward and backward scatterings as arising from independent mechanisms. For example, in absorptive and Regge-pole models the main contribution to the forward scattering comes from $t$-channel exchange, while backward scattering arises from $u$-channel exchange. A fit is made to the high-energy ${\ensuremath{\pi}}^{\ensuremath{-}}p$ data in both forward and backward directions, and good results are obtained.

Simplistic Analysis of Reactive Scattering II. Initial and Final Distortions

AbstractThe angular distribution of reactively scattered molecules is discussed in terms of a classical optical model. The deflection in a reactive scattering is considered, for direct reactions, as the sum of an initial and final deflection. The formal validation of this approach is discussed with a distorted wave approach and within a more general, reaction matrix formulation.

Opacity analysis of inelastic molecular collisons: III. the conservation of the total cross section

Abstract The classical optical model is used to prove that the magnitude of the total cross section is independent of the extent of inelastic processes. Refinements are necessary to obtain quantitative estimates and account for very long range inelastic collisions.