Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound

A model of scattering is used to relate average differential scattering cross section and power spectra of scattering medium variations. The model expresses the average differential scattering cross section as a sum of the power spectrum of medium compressibility variations, the power spectrum of density variations weighted by the square of the cosine of the scattering angle, and the cross-power spectrum of compressibility and density variations weighted by twice the cosine of the scattering angle. Known values of the average differential scattering cross section at a minimum of three different scattering angles and temporal frequencies corresponding to the same spatial frequency are used to calculate each of the three power spectra. Since noise and statistical fluctuations are present in actual measurements of average differential scattering cross section, the calculations of power spectra are obtained from an overdetermined set of equations to which a solution is found by using a singular value decomposition. Data derived from a model for scattering from a cloud of correlated particles are employed to show the influence of additive noise. Calculations are also made from measurements of scattering from three suspensions of particles that have a different average radius in each suspension but are similarly modeled by scattering from a cloud. Additionally, the calculations are applied to measurements of average differential scattering cross section of calf liver. The results show that determination of the power spectra of scattering medium variations can be made under practical conditions, and also imply that density variations contribute significantly to scattering by calf liver.     

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.     

Tamm interface states in ZnSe/BeTe periodic heterostructures

The spectral response of the lateral optical anisotropy of periodic undoped type-II ZnSe/BeTe heterostructures with nonequivalent interfaces was studied by ellipsometry. The spectra revealed two types of features corresponding to optical transitions with energies lying in the bandgap. The position of features of the first type does not depend on the heterostructure period. Features of the second type shift toward lower energies with decreasing period of the heterostructure. This behavior is explained in terms of a model taking into account the existence of electronic and hole interface states and of a mixed-type interface state.     

Differential magnetoreflection spectroscopy of doped and undoped II–VI semiconductor quantum wells

A method has been developed for recording and analyzing the differential magnetoreflection (magnetotransmission) spectra of semiconductor structures with quantum wells. The method was used to determine the exciton g-factor in semimagnetic CdTe/(Cd, Mn)Te heterostructures with quantum wells. In nonmagnetic structures with quantum wells containing a two-dimensional electron gas, the excitonic damping depends on the spin state of the exciton. This effect is explained by the exchange contribution to exciton-electron scattering. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 44–49 (10 January 1997)     

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.     

Effect of the external electric field on the kinetics of recombination of photoexcited carriers in a ZnSe/BeTe type II heterostructure

The kinetics of the radiative recombination of photoexcited electrons and holes for a spatially direct transition in a ZnSe/BeTe type II heterostructure in an external electric field has been analyzed. A strong decrease (more than two orders of magnitude) in the photoluminescence intensity, as well as a decrease in the duration of the relaxation of the direct transition, is observed when the electric field is applied. The energy levels and wavefunctions of electrons and holes in the ZnSe/BeTe heterostructure subjected to the electric field have been numerically calculated. It has been shown that the observed decrease in the photoluminescence intensity and duration of the relaxation of the direct transition is due to both an increase in the radiative recombination time and an increase in the rate of escape of photoexcited holes from the above-barrier level in the ZnSe layer to the BeTe layer.     

Basic Requirements of Spin-Flip Raman Scattering on Excitonic Resonances and Its Modulation through Additional High-Energy Illumination in Semiconductor Heterostructures

We describe the major requirements to experimentally perform and observe resonant spin-flip Raman scattering on excitonic resonances in low-dimensional semiconductors. We characterize in detail the properties of this resonant light scattering technique and evaluate the criteria, which must be fulfilled by the experimental setup and the semiconductor sample studied to be able to observe a spin-flip scattering process. We also demonstrate the influence of additional unpolarized laser illumination with energies, which exceed considerably the band gap energy of the semiconductor nanostructure under study, on the resonantly excited electron spin-flip scattering in InAs-based quantum dot ensembles as well as on the paramagnetic Mn-ion spin-flip in (Zn,Mn)Se/(Zn,Be)Se quantum wells.     

Normalization of ultrasonic scattering measurements to obtain average differential scattering cross sections for tissues

An integral expression is derived for the normalization of ultrasonic scattering data to obtain an average differential scattering cross section per unit volume for tissue which is modeled as a random, fluidlike medium. The expression assumes narrowband signals and involves the incident beam, receiver beam pattern, and time gates. The beams and gates combine to form a window which limits the scattering volume. The derivation of the expression requires that the dimensions of the window be large compared to the correlation length of the scattering medium. Numerical values of the normalizing integral are given for cylindrical and beamlimited scattering volumes as a function of incident frequency and scattering angle under the assumptions of Gaussian beams and rectangular time gates. A set of curves is presented to relate the percent difference between the result for backscatter from a cylindrical scattering volume and from a beamlimited scattering volume which does not include the truncation effect of the cylinder boundary. Although similar in form to normalizations used by others, the integral in this paper is obtained from a derivation which treats physical parameters rigorously and provides a precise statement of conditions which are sufficient to obtain system-independent scattering data.