Plane waves in regular arrays of dipole scatterers and effective-medium modeling

A simple analytical theory for finding eigensolutions for plane electromagnetic waves propagating along an axis in infinite regular arrays of small dipole particles is presented. The spacing between dipoles in every plane is assumed to be smaller than the wavelength; separation between the planes is arbitrary. The influence of evanescent modes is taken into account. This theory gives a model for an effective propagation constant that can be applied in a wide frequency range from the quasi-static regime to the Bragg reflection (photonic bandgap) region.     

Scattering delay time of Mie scatterers determined from steady-state and time-resolved optical spectroscopy

We have determined the scattering delay time of Mie scatterers (r = 255 nm quartz spheres in polyester resin) from a combination of steady-state (integrating-sphere) and time-resolved (frequency-domain) measurements performed in the multiple-scattering regime. The effective transport velocity of light was derived from intensity and phase measurements at four different wavelengths by using the time-integrated microscopic Beer-Lambert law. We could demonstrate a systematic underestimation of the effective transport velocity compared with the phase velocity in the medium. Assuming that this discrepancy was caused entirely by the transient nature of a single-scattering process, the data presented resulted in time delays of between 18 fs (lambda = 678 nm) and 177 fs (lambda = 1,064 nm) per scattering event. For three out of four wavelengths investigated, the measured values are in excellent agreement with values predicted by a theoretical model for the scattering delay time based on Mie theory.     

An effective-medium approach to the optical properties of heterogeneous materials with nonlinear properties

Abstract

We have derived an analytic approach, based on the hypothesis of the effective-medium theory, to evaluate the effective dielectric magnitudes, including the effective third order nonlinear optical susceptibility α(χ⁽³⁾), of a heterogeneous two-component medium in which one of the components (the host matrix or the embedded particle respectively) presents nonlinear behaviour. Our formulation allows us to solve the full nonlinear problem in the whole range of concentrations without treating the nonlinear effects as a small perturbation to the linear behaviour. Therefore, it can be considered as an upper limit of the commonly used low-field nonlinear approximations for heterogeneous materials. Under certain conditions, these composites can exhibit a bistable regime that the present theory properly describes in wide ranges of the concentration, shape, wavelength, dielectric contants and intrinsic nonlinear optical susceptibility of the nonlinear component as well as in terms of the intensity of the external electric field. The present approach has been used to calculate the nonlinear optical response of Cu—Al₂O₃ nanocomposites.     

Bidirectional reflectance distribution function of diffuse extreme ultraviolet scatterers and extreme ultraviolet baffle materials

Bidirectional reflectance distribution function (BRDF) measurements of a number of diffuse extreme ultraviolet (EUV) scatterers and EUV baffle materials have been performed with the Goddard EUV scatterometer. BRDF data are presented for white Spectralon SRS-99 at 121.6 nm; the data exhibit a non-Lambertian nature and a total hemispherical reflectance lower than 0.15. Data are also presented for an evaporated Cu black sample, a black Spectralon SRS-02 sample, and a Martin Optical Black sample at wavelengths of 58.4 and 121.6 nm and for angles of incidence of 15 degrees and 45 degrees. Overall Martin Optical Black exhibited the lowest BRDF characteristic, with a total hemispherical reflectance of the order of 0.01 and measured BRDF values as low as 2 x 10(-3) sr(-1).     

Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea.

We consider transmission through pair-correlated random distributions of lossless dielectric (globular, cylindrical, or plate-like) scatterers with length parameter a and average spacing small compared to wavelength. Each optical particle is centered in a tough adherent transparent coating whose outer surface (sphere, cylinder, or slab) has radius b smaller than or equal to a. The corresponding attenuation coefficients beta varies directly as WM involve an integral of the appropriate radial-distribution function. Using the scaled-particle equations of state and statistical-mechanics theorems, we evaluate WM explicitly as a rational function of the volume fraction W of the fluid of rigid b particles. We obtain betaM = betaO WM with betaO as the uncorrelated value; W3(W) for spheres decreases more rapidly with increasing W than W2 for cylinders, and W2 decreases faster than W1, the result for slabs. We apply the results for cylinders in terms of W2 to the problem of the transparency of the cornea (whose collagen fibers are the scatters), as posed by Maurice. The value W APPROXIMATELY 0.6 GIVES GOOD ACCORD WITH THE ESSENTIALS OF THE Data for the transparency of the normal cornea, and the opacity that results from swelling is accounted for by corresponding smaller values of W. Thus, the normal cornea is modeled as a very densely packed two-dimensional gas, with gas-particle (mechanical) radius about 60% greater than the fiber (optical) radius.     

Coherent optical reflectance from a monolayer of large particles adsorbed on a glass surface

We develop a coherent-scattering model for the reflection of light from a monolayer of large particles and low surface coverage. The model takes into account multiple scattering between particles of the monolayer and with the substrate, and it can be used around the critical angle in an internal reflection configuration. We compare the results of the model with our own reflectivity data taken with latex particles adsorbed on a glass-water interface and with a simpler effective-medium model.     

Mie scattering interferometer and its application to the study of Raman scattering from molecules at a mercury interface

Interference fringes are observed produced by Mie scattering of laser light from a single microstructure or from a random array of microstructures supported above a reflecting surface. These fringes are the basis of a simple interferometer which can be used to measure distances from thousands of angstroms to centimeters. The interferometer is used to measure the height of liquid above a mercury surface. Raman scattering (RS) from the liquid is measured, and an upper limit of 10(3) is placed on the enhancement of RS from molecules at the interface. Enhancement of RS in a wedge between mercury and solid is examined theoretically.     

Effective Mie scattering of a spherical fractal aggregate and its application in turbid media

An effective Mie-scattering model is developed to deal with the scattering property of a spherical fractal aggregate consisting of scattering particles. In this model the scattered field of a scattering particle is given by the classical Mie-scattering theory. On the basis of the Monte Carlo simulation method, we determine the physical parameters of a scattering aggregate, the scattering efficiency Q, and the anisotropy value g, as well as their dependence on the size and the effective mean-free-path length of a scattering aggregate. Accordingly, photon migration through a microscope objective focused into a turbid medium including scattering aggregates is simulated to understand the effect of complex tissue on image quality.     

In vivo 783-channel diffuse reflectance imaging system and its application

A fiber-based reflectance imaging system was constructed to produce in vivo absorption spectroscopic images of biological tissues with diffuse light in the cw domain. The principal part of this system is the 783-channel fiber probe, composed of 253 illumination fibers and 530 detection fibers distributed in a 20x20 mm square region. During illumination with the 253 illumination fibers, diffuse reflected lights are collected by the 530 detection fibers and recorded simultaneously as an image with an electron multiplying CCD camera for fast data acquisition. After signal acquisition, a diffuse reflectance image was reconstructed by applying the spectral normalization method we devised. To test the applicability of the spectral normalization, we conducted two phantom experiments with chicken breast tissue and white Delrin resin by using animal blood as an optical inhomogeneity. In the Delrin phantom experiment, we present images produced by two methods, spectral normalization and reference signal normalization, along with a comparison of the two. To show the feasibility of our system for biomedical applications, we took images of a human vein in vivo with the spectral normalization method.     

Electrical resistivity of In-Sb liquid system and its relation to thermodynamic behaviour

The electrical resistivity of liquid alloys in the system In-Sb has been determined using a.d.c. four probe method. The resistivities range from 40 to 120 cm and show a positive temperature dependence. A maximum in electrical resistivity is observed at compositions close to that of the inter-metallic compound InSb. Such a compound behaves as a semiconductor in the solid state and as a metal in the liquid state. Maxima are found in the reduced resistivity and in the excess thermodynamic stability at about 50 at % Sb.     

Coherent control of spontaneous emission in a four-level system

Abstract

In this article we study the potential for coherently control spontaneous emission in a four-level scheme. Our control parameter is the relative phase of two laser fields having the same angular frequency. We investigate in detail the trapping conditions, the population dynamics and the behaviour of the (long time) spontaneous emission spectrum, which are now phase dependent. Inhibition of spontaneous emission and extreme spectral narrowing are shown as the relative phase is varied. Our results are interpreted using a dressed state analysis of the dynamics.     

Coherent state path integral approach to multi-time correlation functions and photon emission in a semiconductor microcavity

In this paper by using the coherent state path integral field theory approach, we calculate the grand canonical partition function of an interacting combined system in the presence of the relevant source terms. It allows us to calculate multi-time correlation functions of interacting systems without using the quantum regression theorem. Then, we investigate the power spectrum and the second-order correlation function of the emitted photons from a microcavity in the presence of excitations of a semiconductor quantum well. By using the Hubbard–Stratonovich transformation, we investigate the effects of reservoir, detuning, the Coulomb interaction and the phase space filling on the power spectrum and the second-order correlation function of the emitted photons.     

Reliability approach to the random imperfection sensitivity of columns

Acta Mechanica - Buckling of stochastically imperfect finite columns on a mixed quadratic-cubic elastic foundation is studied. The imperfection function is assumed to be a normally distributed...     

Regression and correlation analyses of a linear relation between random intervals

In this paper we develop regression and corrclation analyses of a certain general linear relation between two random elements whose values are non-empty compact intervals. To this purpose, we firstly extend the least-squares method to deal with the involved random elements on the basis of a generalized metric defined on the space of the considered intervals. As a complementary study, a coefficient quantifying the strength of the linear relation between the two random elements is also presented, and a discussion of the extreme values for this measure is presented. A real-life example illustrates these studies. Research partially supported by DGESIC/MEC Grants No. DGE-99-PB98-1534 and No. DGE-98-PB97-1282.     

Measuring the overshoot of a moving servo element in relation to its velocity

Measurement Techniques -     

Fiberwalk: a random walk approach to fiber representative volume element creation

Attaining accurate representative geometry for a finite element analysis at various scales can be a challenging research task. Added complications arise when the geometry is representing a manufactured or biological composite. In this study, a representative geometry of linear fibrous composites was created at the microscale and is employed to reproduce crystalline microfibril stacking of Kevlar to form a single fibril joined by a non-ordered crystal structure. The structure can have ellipsoidal or rectangular microfibrils stacked in ellipsoidal or rectangular fibrils and may have any desired packing ratio within the 1–100% range. In order to build a fibrous structure along a path, a Random Walk methodology was used. Since the directionality of the fibers is random, but always stepping from one side of the path toward the other, the fibers can wind around each other and tangle or terminate if needed. Another key concept of this method is the addition of a rotation matrix operation for the path of the fibers. This allows the path around the three local coordinates to be in a linear or sinusoidal direction. The resultant geometry produced can represent the tortuous path nanofibrils undergo. Moreover, rotation about the path axis allows for the twisted geometry of ring spun yarn, and metal cable to be reproduced. Inclusion of spherical objects to the path of the fibers has been accommodated to reproduce fiber projection around, or end at, an obstruction in their path. This approach allows representing impurities at the fibril, fiber, or yarn level of composite fabric manufacturing.     

Characterization of the human iris spectral reflectance with a multispectral imaging system

We present a multispectral system developed and optimized for measurement of the spectral reflectance and the color of the human iris. We tested several sets of filters as acquisition channels, analyzed different reconstruction algorithms, and used different samples as training sets. The results obtained show that a conventional three-channel color camera (RGB) was enough to reconstruct the analyzed reflectances with high accuracy, obtaining averaged color differences of around 2-3 CIEDE2000 units and root mean square errors of around 0.01. The device developed was used to characterize 100 real irises corresponding to 50 subjects, 68 prostheses used in clinical practice, and 17 cosmetic colored contact lenses.     

A new approach to series of independent random variables

The aim of this paper is to provide an alternative approach to the classical theory ofsums of independent random variables. It shows that the Kolmogorov inequalities may be avoided in the proof of thethree series theorem, and theequivalence lemma follows from a very simple argument. The main idea is to relate the a. s. convergence of a series to the fact that their paths remain bounded.