Radiation properties of a uniaxial chiral quadratic inhomogeneous slab under oblique incidence

In this paper, the focussing of the transmitted electromagnetic field through a quadric inhomogeneous slab of lossless uniaxial chiral medium is derived using transmission coefficient under oblique incidence. The inhomogeneity in the uniaxial chiral slab has been incorporated through permittivity parameter. Asymptotic ray theory provides valid field everywhere except at focal point where it gives infinite value. Singularity of the field at focal point is addressed using Maslov's method. The derived analytical field expressions at caustic or focal point of uniaxial quadratic inhomogeneous slab have been solved numerically using MATHEMATICA. The effects of chirality parameter, axial permittivity, transvers permittivity, angle of incidence on the refracted field are discussed and the effects of Brewster angle on the focussed field are also discussed. The results obtained using Maslov's method are compared with Huygens–Kirchhoff's integral which are in good agreement.     

Ambartsumian's principle of invariance and the reflection of radio waves from plane inhomogeneous slabs

Using Ambartsumian's principle of invariance we investigate for radio waves the reflection coefficient of a plane inhomogeneous slab. We find that the reflection coefficient, as a function of slab thickness, satisfies the Riccati equation. From this equation we deduce a geometric theorem on the upper and lower bounds of the reflection coefficient. We illustrate the theorem by applying it to several special cases.     

Instability of dipole magnetoexcitons in quantum wells' and graphene superlattices

We propose the Bose-Einstein condensation and superfluidity of quasi-two-dimensional spatially indirect magnetobiexcitons in a slab of superlattice with alternating electron and hole layers consisting from the semiconducting quantum wells (QWs) and graphene superlattice in high magnetic field. For this system the instability of the ground state of interacting two-dimensional indirect magnetoexcitons in a slab of superlattice with alternating electron and hole layers in high magnetic field is found. The density of superfluid component ns(T) and the temperature of the Kosterlitz-Thouless phase transition to the superfluid state in the system of two-dimensional indirect magnetobiexcitons, interacting as electrical quadrupoles, are obtained for both QW and graphene realizations.     

Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D_f=2.5 and 3; and overall fractal radii R in the range 4?R?10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.     

The effect of a strain induced field on the dielectric property of a ferroelectric bilayer system

The Transverse Ising Model (TIM) based on the effective-field theory has been developed to study the physical properties of the ferroelectric bilayer system BaTiO₃/SrTiO₃ (BTO/STO), based on the differential operator technique. The effect of strain on the interfacial layers between two different slabs (A and B) can be described by the effective built-in field E₂. The ferroelectric behavior of a bilayer system is strongly influenced by strain and associated with slab thickness. The phase transition temperature shifts toward a higher value on increasing the slab thickness. The susceptibility strongly depends on both the strength of strain and the slab thickness. The height of the peak from the plot of susceptibility against temperature decreases on increasing the slab thickness. The pyroelectric coefficient changes into a round peak at the transition temperature that is different from the sharp peak in the absence of external and strain-induced fields.     

Collective modes in a slab of interacting nuclear matter

We consider a slab of nuclear matter and investigate the collective excitations, which develop in the response function of the system. We introduce a finiterange realistic interaction among the nucleons, which reproduces the full G-matrix by a linear combination of gaussian potentials in the various spin-isospin channels. We then analyze the collective modes of the slab in theS=T=1 channel: for moderate momenta hard and soft zero-sound modes are found, which exhaust most of the excitation strength. At variance with the results obtained with a zero range force, new “massive” excitations are found for the vector-isovector channel.     

Distribution of the amplitude of the magnetic potential of diffractive beams generated in a ferrite slab by a surface spin wave incident on a slit in an opaque screen

The total magnetic potential generated in the far field of a ferrite slab as a result of a plane noncollinear surface spin wave incident on a slit in an opaque screen is investigated. The dependence of the potential amplitude from the polar angle in the plane of a ferrite slab is calculated for different orientations of the screen with relative to an external magnetic field magnetizing the slab. It is found that two diffractive beams are generated in the slab as a result of spin diffraction on the slit. The angular width of each beam depends largely on the slit’s orientation and can be greater or smaller than value λ _n /D (where D is the slit’s width and λ _n is the length of the spin wave corresponding to each beam).     

Revisiting the Balazs thought experiment in the presence of loss: electromagnetic-pulse-induced displacement of a positive-index slab having arbitrary complex permittivity and permeability

Over a half-century ago, Balazs proposed a thought experiment to deduce the form of electromagnetic momentum in a lossless and non-dispersive slab by imposing conservation of global momentum and system center-of-mass velocity after a pulse has traveled through the slab. Here, we revisit the Balazs thought experiment by explicit calculations of momentum transfer and center-of-mass displacement of a non-dispersive, positive-index slab of arbitrary complex permittivity and permeability using a set of postulates consisting only of Maxwell’s equations, a generalized Lorentz force law, the Abraham form of the electromagnetic momentum density, and conservation of both pulse and slab mass. In the case where the slab is lossless, we show that a pulse of arbitrary shape incident onto the slab conserves both global momentum and system center-of-mass velocity, consistent with the starting postulates of the Balazs thought experiment. In the case where the slab is lossy, we show, within the context of the above postulates, that global momentum is always conserved and that system center-of-mass velocity is conserved only when mass transfer from the pulse to the slab is described by an incremental pulse-mass-transfer model, proposed here, in which the pulse deposits mass in the slab with a distribution corresponding to the instantaneous mass density profile of the pulse.     

Multi-Harmonic homodyne approach for optical property measurement of turbid medium in transmission geometry

The accurate determination of both absorption and scattering properties in homogeneous diffuse medium is critical in many applications of diffuse optical imaging, especially in clinical applications such as breast cancer diagnosis. In this paper, we report a frequency-domain method to simultaneously measure both absorption and reduced scattering coefficients (μ_a and μ_s′) in transmission geometry, based on a parallel homodyne approach using a RF-modulated laser source and a gain-modulated image intensifier. This method enables fast multi-pixel phase-sensitive measurement, which leads to an efficient way to obtain μ_a and μ_s′ values via the well-known analytical Green's function solution in slab geometry. We developed an approximate formula of the analytical solution that is especially suitable for multi-pixel data analysis. In addition, we present a comprehensive multi-harmonic data analysis that includes DC data, which offers multi-frequency information from a single-frequency dataset, hence leading to improved accuracy and stability in measurement.     

WHEN DOES A MEASUREMENT OR EVENT OCCUR?

Within quantum mechanics, a complete set of commutting observables can be found which describe the attributes of a system at a given time. However, the correct way to describe attributes of a system in time is still an open question. We discuss the difficulties in extending the standard approach of quantum mechanics to describe attributes of a system in time. We find that measuring when an event occurred and measuring that it occurred, are complimentary in Bohr's sense. To exemplify the differences between measurements at a given time and in time, we will compare Rovelli's recent proposal (quant-ph/9802020), to determine “at what time does a measurement occurred” with another model of a continuous measurement in time. Rovelli's scheme answers the question “has the measurement already occurred at a certain time?”, but does not answer to the more difficult question: “when did the measurement occur?” We also discuss the use of the probability current to measure the time at which a particle arrives to a certain location.     

On the resolvent of Milne's integral equation for a spherical,isotropically-scattering medium

Recently, determination of the resolvent kernel of Milne's integral equation for a spherical, isotropically-scattering medium with internal sources has been made by several authors (cf. Heaslet and Warming;⁽¹⁾Nagirner;⁽²⁾Wilson and Sen⁽³⁾). In this paper, it is shown how to compute the resolvent kernel of the above Milne's equation in terms of the modified Sobolev's Φ-function, which is reduced to the angular integration of the source function in the diffuse radiation field by a finite slab. In other words, once the X- and Y-functions of a slab with twice the optical radius of the sphere have been computed and a Cauchy system for the source function has been solved, the resolvent kernel under consideration can be determined by integration of the modified Sobolev Φ-function.     

Dynamical Green's function theory to study the optical phenomena related to metamaterials

We combine a space–time Lorentz transformation with a dyadic Green's function technique to establish a general and rigorous dynamical theory, which can be employed to study the optical phenomena occurring in a moving environment. As the applications of this method, we studied the Doppler effects of a source moving near a metamaterial slab and the super imaging effect achieved by a moving metamaterial lens. Many interesting anomalous phenomena were discovered, induced typically by the interplays between the source and the surface waves of the metamaterial slab.     

Regulating economic systems in a multi-trait model of self-organized criticality

We study the effect of size-based regulation on an economic system. A multiple-trait model of self-organized criticality is used to simulate the economic system. The major difference of this work from previous studies is that firm's fitness is not characterized by a single number but by M traits. Each trait represents one aspect of the competitiveness of the firm, and firm's size is one of these traits. Major finding drawn from the present study is that the effectiveness of regulations decreases with increasing M, i.e., size-based regulations are less effective when the overall fitness of a firm is determined by more factors.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Theoretical analysis about 2π ambiguity of the piston error in sparse optical synthetic aperture imaging system

In recent years, sparse-optical-synthetic-aperture telescope has emerged as an important developing trend for large-scale telescope, where the correction of piston error among different sub-apertures plays an important role for achieving high resolution. The 2π ambiguity effect is the most important aspect of piston error's influences upon system's far-field intensity, which was theoretically analyzed at first. Then the bi-sub-aperture system was taken as an example to test the correctness of the theoretical model through distributions of the system's far-field intensity. In addition, a theoretical proof was made to get some important properties of piston errors within such kind of system. From the results, it is shown that the 2π ambiguity comes along with any piston error in the system, and this effect stands independent for different piston errors between different pair of sub-apertures. The derivation also provides effective theoretical model for related concerns within such kind of system.     

Wetting of Heterogeneous Surfaces at the Mesoscopic Scale

We consider the problem of wetting on a heterogeneous wall with mesoscopic defects: i.e., defects of order L ^ε , 0<ε<1, where L is some typical length-scale of the system. In this framework, we extend several former rigorous results which were shown for walls with microscopic defects.^{(10, 11)} Namely, using statistical techniques applied to a suitably defined semi-infinite Ising-model, we derive a generalization of Young's law for rough and heterogeneous surfaces, which is known as the generalized Cassie–Wenzel's equation. In the homogeneous case, we also show that for a particular geometry of the wall, the model can exhibit a surface phase transition between two regimes which are either governed by Wenzel's or by Cassie's law.     

Modification of the total reflection modes in a dielectric film by one metal boundary

The optical modes in a dielectric slab are considerably changed by replacing the dielectric medium on one side of the slab by a metal. In particular, the TH mode m = 0 shows the behavior of a surface plasma wave. The modes were excited in a reflection experiment by the use of prism film coupling in an Al-LiF-air system, the results are in satisfactory agreement with theory.     

Solitonen in Wellenleitern mit nichtlinearer optischer Beschichtung

Solitons in a Waveguide with a Thin Nonlinear Optical Slab Starting from Maxwell's equations the influence of a thin nonlinear optical slab embed in a waveguide on the propagation of a monomode (TE) pulse is investigated. The amplitude of the pulse is described by a nonlinear Schrödinger equation (NLS) containing parameters of the waveguide with the nonlinear slab and leading to solitons in the nonlinear modified waveguide.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.