Extended Boundary Condition Method Research Articles

Iterative extended boundary condition method for scattering by objects of high aspect ratios

The limitations of the T-matrix procedure or the extended boundary condition method (EBCM) for wave scattering problems, when used for long slender objects, are due to the shrinking volume over which the incident field is extinguished. The resulting ill-conditioning of the matrices involved makes it impossible to invert them. For nondissipative objects only, we observe that the Reinforced Modified Gram–Schmidt (RMGS) orthogonalization procedure works best of all such unitary approaches investigated, but information about the surface and the internal fields is lost in the process. An alternate approach, called the iterative EBCM (IEBCM) is more general in its scope since it provides convergent surface and internal field values and can also work for dissipative targets. This success of the IEBCM results because it extends the interior volume over which the incident field is extinguished.

Extension of the iterative EBCM to calculate scattering by low-loss or lossless elongated dielectric objects

The newly developed iterative extended boundary condition method (IEBCM) is extended to calculate the scattering by low-loss or lossless elongated dielectric objects. Specifically the iterative procedure is modified so as to utilize an initial assumption of the surface fields obtained from the Mie solution of a spherical object of the same dielectric properties. The solution for the elongated object is obtained by iteratively utilizing the regular EBCM technique to solve for objects of intermediate geometries between the substitute sphere and the object of interest. The other feature of the IEBCM which is related to subdividing the internal volume of the object into several overlapping subregions in each of which a separate field expansion is used is also utilized in the present extension. Results illustrating the adequacy of the IEBCM procedure to calculate the scattering by spheroids of an aspect ratio of more than 7:1 are presented.

Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance

The recently developed iterative extended boundary condition method (IEBCM) is used to calculate the average specific absorption rates (SAR's) in biological models of an average man and a sitting rhesus monkey at and beyond their resonance frequencies. The average SAR's for these objects are also experimentally determined in scaled saline phantoms. Close agreement thus found between the calculated and the measured SAR values validates the postresonance absorption calculations made using the novel IEBCM. Also, in order to check the adequacy of using the mixed basis functions in the IEBCM procedure, the SAR in a capped cylindrical model of an average man is calculated and the result verified experimentally. It is, therefore, concluded that to achieve an improved computational efficiency in the IEBCM, the choice of the basis functions for a particular lar subregion should be based on the geometry of that subregion.

Null field formulations for dielectric‐coated antennas

Null field formulations utilizing a generalization of the extended boundary condition method of Waterman are presented for dielectric‐coated antennas of arbitrary but smooth shapes. Spherical, prolate spheroidal and spherically capped cylindrical antennas are solved as examples. Their power radiation patterns and input conductances are plotted as functions of coating thickness. The dielectric coating effectively increases the antenna size. Furthermore, it is shown that an eccentric coating can produce a considerable shift in the power radiation patterns.

Comparison of the extended boundary condition method and perturbation method for scattering from a sinusoidal sea surface

Scattering from a lossy sinusoidal surface is examined by using two methods: extended boundary condition (EBC) and perturbation. The range of applicability of the perturbation approach is established by comparison with EBC. The range of applicability of EBC is established through numerical examples. A convergence criterion based on the sequence of partial sums of the scattered energy is suggested for the application of EBC to lossy surfaces. New analytical expressions for the perturbation solutions are given.

An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios

The recently developed iterative extended boundary condition method (IEBCM) has been used to compute the internal fields induced in homogeneous, axisymmetric, lossy dielectric objects of large aspect ratios when exposed to incident planewave radiation. Calculations were made for both the E- and k-polarization cases. The computed results for a prolate spheroidal model of an average man are found to be accurate for frequencies up to 300 MHz, while the use of the popular EBCM [1] was found to be essentially restricted to frequencies less than 70 MHz for these models and exposure conditions. The applicability of the IEBCM to composite bodies has also been examined by studying the irradiation of a capped cylindrical object. This composite object was first partitioned into several overlapping spherical subregions, and, alternatively, into two spherical subregions overlapping with a central cylindrical subregion. Spherical harmonics were used to represent the internal fields in the spherical subregions, while cylindrical expansions were utilized in the cylindrical subregions. It is shown that the second partitioning scheme is more computationally efficient and thereby suggests that the basis functions used to represent the subregional fields should be compatible with the subregional geometry. The new IEBCM, therefore, is a very valuable procedure which provides the opportunity of using the mixed basis functions in the solution.

A new procedure for improving the solution stability and extending the frequency range of the EBCM

The extended boundary condition method (EBCM) has been frequently used to obtain the absorption and scattering characteristics of axisymmetric dielectric objects. For applications involving relatively high-loss dielectric objects, however, the method was usable only at frequencies below resonance. In this paper a new procedure for improving the stability and extending the frequency range of the EBCM is presented. This new procedure has two main features: 1) it is iterative, since it starts with a known solution that approximates the scattering problem, and 2) it involves separate field expansions in each of the overlapping subregions which describe the total interior volume of the object. For example, for high-loss dielectric objects, such as the biological models of humans and animals, the first step in the procedure is to replace the lossy dielectric object with a perfectly conducting one of the same shape and solving the scattering problem to determine the current density on the surface of the conductor. This surface current is then used to calculate the induced field expansions inside the dielectric object. It is shown that the numerical stability of the solution is further improved by dividing the interior region of the object into overlapping subregions, in each of which a separate field expansion is assumed. The electric and magnetic surface currents so obtained from the solution of the internal problem are then used to improve the initial estimate of the current density on the surface of the object. The iterative procedure continues until convergent values of the surface currents and the fields are obtained. Numerical results illustrating the improved stability of the iterative EBCM (IEBCM) solution at higher frequencies as well as its accuracy in calculating the absorption characteristics of a spheroidal model of man in the resonance and the postresonance frequency range are presented.

Scattering and absorption characteristics of lossy dielectric objects exposed to the near fields of aperture sources

The extended boundary condition method (EBCM) is used to obtain the absorption and scattering characteristics of lossy dielectric prolate spheroidal models of biological objects exposed to the near fields of large aperture sources. Two equivalent methods are employed to expand the incident fields, from the aperture sources, in terms of the vector spherical harmonics about the spheroidal origin. The results obtained for a spheroid located a large distance away from the aperture source agree well with those obtained from the corresponding plane-wave irradiation studies. Other near-field absorption characteristics are examined, and the applicability conditions for each of the two methods for obtaining the incident field expansions are discussed. In particular, it is emphasized that meaningful evaluation of hazardous levels of electromagnetic radiation should be made in terms of the magnitudes and the directions of the electric- and magnetic-field components, rather than the incident power density level. The calculated results also conform to the understanding previously obtained from studying irradiation of the spheroidal models of biological interest by plane waves and by near fields of various elementary radiation sources.

Scattering of light by laser fusion targets with small defects

The extended boundary condition method was used to determine the effect imperfections in small glass and metal shells have on scattered light at 10.6 microm. The results indicate that imperfections cause a shift in the locations of the minima in the differential scattering curve, a change in the extinction efficiency, and the presence of depolarized components for off-axis orientation of the object. Among these, the presence of and changes in the depolarized component are most sensitive to imperfections. We compute the depolarized scatter from shells with types I, II, and III defects and discuss the potential of light scattering as a characterization tool for laser fusion targets

Scattering by a periodic rough surface

An exact theory based on the extended boundary conditions method [S. L. Chuang and R. K. Johnson, J. Acoust. Soc. Am. 71, 1368–1376 (1982)] for acoustical scattering from a periodic rough interface between a fluid and a solid is reviewed. Good agreement between theoretical calculations and laboratory measurements is demonstrated. Theory and measurements are used to explore the effects of roughness height and shape as well as material properties on the scattering behavior. Interesting phenomena involving surface wave generation and finite aperture transducer effects are also discussed.

Electromagnetic Modeling of Oil Shale Retorts for Remote Sensing Purposes

We report here some work on the modeling of oil shale retort for remote sensing purposes. The aim is to obtain useful information about the contents of the retort (e.g., rubble size, void ratio, etc.) by means of electromagnetic probes. In this paper, the retort is modeled by a spheroid with an average dielectric constant which depends on the void ratio. The near field due to a radiating dipole source in the vicinity of a spheroidal retort is computed using the Extended Boundary Condition Method. Numerical results are given at 4 MHz for a retort with major axis 45.7 m (150 ft), minor axis 25.1 m (82.5 ft), bulk dielectric constant 8.8 + 3.7j, and various void ratios. The results indicate that estimates of the void ratio by remote electromagnetic measurements may be feasible under favorable conditions, but many technical problems remain to be overcome before quantitative determinations are possible.

Irradiation of prolate spheroidal models of humans and animals in the near field of a small loop antenna

Analysis of the near‐field irradiation of prolate spheroidal models of humans and animals by a small coaxial loop antenna is described. The near fields of the antenna are known exactly and hence are used to identify the suitable field parameters involved in the near‐field absorption in the spheroidal model. An integral equation is formulated in terms of the transverse dyadic Green's function, and the fields radiated by the current loop are expanded in terms of the vector spherical harmonics. The extended boundary condition method is then employed to solve the integral equation. The power distribution and the average specific absorption rate (SAR) are calculated and plotted, for different human and animal models, as a function of the separation distance from the loop. It is shown that for distances less than 5λ the average SAR values oscillate about the far‐field value. In particular, for d/λ < 0.4 an increase in the average SAR values was generally observed. It is also shown that in spite of the complicated nature of the near fields the absorption characteristics can still be explained in terms of the incident radiation. Furthermore, from the calculated SAR distributions at different frequencies it is shown that at all frequencies, excessive heating occurs at the surface of the spheroid while a limited absorption occurs in the central region around the major axis. This result is of particular importance in hyperthermia, where extensive efforts are being directed toward achieving deep‐tissue heating by a coaxial coil carrying RF power at about 27 MHz.

Absorption characteristics of prolate spheroidal models exposed to the near fields of electrically small apertures.

Irradiation of prolate spheroidal models of biological models by the near fields of electrically small apertures is analyzed. The solution procedure involves the replacement of the aperture source by an equivalent configuration of electric and magnetic dipoles. The specific absorption rate (SAR) induced in the irradiated object is then calculated using the extended boundary condition method (EBCM). Numerical results are presented for the exposure case where the incident electric field at the spheroid location is parallel to the major axis of the model. This polarization is associated with the maximum low-frequency absorption in biological models and, hence, is the most important polarization case in microwave dosimetry.

Acoustic wave scattering from a fluid/solid periodic rough surface

A rigorous theory based on the extended boundary condition method is proposed to solve the problem of elastic wave scattering from a periodic fluid/solid interface. The diffraction efficiencies of the reflected compressional wave in the fluid and the transmitted shear and compressional waves are calculated. The energy conservation criterion is used to check the accuracy of the numerical results. The effect of loss (viscoelasticity) in the solid is also included. The wave diffraction from a water and acrylic rough surface is measured. Good agreement between the theory and the experiment is obtained.

Wave scattering from a periodic dielectric surface for a general angle of incidence

The scattering of electromagnetic waves from a periodic dielectric interface is studied for a general angle of incidence. It is called conical diffraction in grating theory for the general case where the incident wave vector is not perpendicular to the ruling direction of the gratings. We adopt the electric and magnetic field components along the row direction as the two unknown scalar functions and reduce the vector nature of the problem to solving simple matrix equations to obtain the scattered fields. The extended boundary condition method is applied with the Fourier series expansion for the surface fields. For the special case of incidence angle perpendicular to the row direction, the results are reduced to those developed before. Numerical results are obtained to show that energy conservation and reciprocity are obeyed for scattering by sinusoidal surfaces for the general case. This serves to check the consistency of the formalism.

Resonant scattering for characterization of axisymmetric dielectric objects

Resonances in the electromagnetic scattering by dielectric objects are investigated both numerically and experimentally with particular emphasis on their direct application to object characterization. Low ka calculations for spheres and an infinite circular cylinder illustrate the modal nature of the resonances and the dependence of the resonance spectra on refractive index and size. Experiments show that the specific wavelengths at which resonances occur in the scattering intensity from a glass fiber can be used to determine its diameter to a high accuracy. The extended boundary condition method is used to calculate the low ka resonances of a prolate spheroid and a finite circulate cylinder with the anticipation that the scattering resonances may be particularly suitable for characterizing randomly oriented nonspherical objects.

A new iterative procedure to solve for scattering and absorption by dielectric objects

We have devised a new iterative technique to improve the Extended Boundary Condition Method (EBCM) frequently used to solve for the scattering and absorption by lossy dielectric objects. This technique has two main features: 1) it requires an initial assumption of the external surface fields, and 2) it partitions the interior of the object into a number of overlapping subregions, thus assuring a more efficient numerical convergence. Preliminary results indicating the enhanced stability of the new iterative EBCM technique are presented.

Postresonance electromagnetic absorption by man and animals

A surface integral equation (SIE) method is used to calculate the specific absorption rate (SAR) in spherically capped cylindrical models irradiated by an axially incident electromagnetic plane wave (K polarization) in a frequency range for which calculations previously have not been available (80-400 MHz for man models). In the SIE method, the electromagnetic (EM) field relations are formulated in terms of electric and magnetic currents on the surface of the model. The average SAR is calculated from the far scattered EM fields by means of the forward scattering theorem. SAR data calculated by the SIE method agree with data calculated by the extended boundary condition method (EBCM) for frequencies up to 80 MHz (the upper frequency limit of the EBCM) for man models. For rat models exposed to 1-3 GHz radiation, reasonable agreement was also obtained with the limited experimental data available.

A Method Extending the Boundary Condition for Analyzing Guided Modes of Dielectric Waveguides of Arbitrary Cross-Sectional Shape

A method based on the extended boundary condition method is presented for analyzing guided modes of dielectric waveguides of arbitrary cross-sectional shape. Numerical integration needed in this method is only over the boundary periphery line of the waveguide. Nevertheless, it is applicable to the waveguides with any refractive index difference between core and cladding ranging from negligibly small to considerably large difference, as well as to certain types of waveguide with inhomogeneous core. Approximate formulas for the case of weakly guiding are also derivable from the general basic set of equations presented. Numerical examples are given to verify the usefulness and accuracy of this method.

Scattering from a periodic rough surface between a fluid and a solid

A rigorous theory based on the extended boundary condition method is proposed to solve the problem of diffraction from a fluid/solid interface which has periodic roughness. The extended boundary condition is derived by applying Green's theorem to the total fields and the Green's functions for the periodic surface in the fluid region and the solid region separately. A complete set of basis functions (Fourier series) is then chosen for the expansions of the unknown displacements and the tractions on the surface. The set of integral equations is reduced to simple matrix equations which are solved for the coefficients of the basis functions of the surface fields. The diffraction efficiencies of the incident plane wave from the fluid to the reflected compressional waves and the transmitted compressional and shear waves of different Floquet modes are calculated. Energy conservation is used to check the accuracy of the numerical results. The case of a lossy (viscoelastic) solid is included in the study. For experimental verification, an acrylic block was machined to have a symmetric sawtooth surface profile with a height 0.49 mm and a period 5.08 mm. The scattering from this block immersed in water is measured at 500 kHz. The diffraction efficiencies of different Floquet modes in the water are measured versus angle of incidence. Very good agreement is achieved between the theory and the experiment.