Spherical Wave Expansion Research Articles

Phase radiation characteristics of an open-ended circular waveguide

General analytical expressions are derived for the far-field amplitude and phase radiation patterns of an open-ended circular waveguide (OE-CWG) regardless of its radius or the operation frequency for the dominant and symmetric higher-order excitation modes. The derivation is based on the rigorous solution to the problem of diffraction at an open end of a waveguide proposed by Weinstein. The near-field amplitude and phase patterns of an OE-CWG are then calculated using the spherical wave expansion technique. The measurement of the radiation pattern of an OE-CWG was carried out to verify the validity of the derived expressions and a good agreement was obtained.

Integral equation analysis of scattering by a spherical microparticle coupled to a subwavelength-diameter wire waveguide

A rigorous integral equation analysis of the coupling between a fiber waveguide and an adjacent spherical particle is developed. The solution is obtained by applying the entire-domain Galerkin technique, based on Mie-type spherical wave expansion of the field in the sphere and the use of dyadic Green's function of the fiber waveguide. The conversion between cylindrical and spherical wave functions is done through classic analytical formulas. The analysis is applied to numerically investigate transmission through silica wires of subwavelength diameter in the presence of particles of comparable size. The results show the possibility of sensing microparticles through the reduction of transmitted power, which is maximum for certain critical values of the fiber diameter.

Genetic algorithm applied to determine the spherical wave expansion from amplitude-only far-field data

A method is presented for solving the spherical wave expansion (SWE) from far-field amplitude-only data. The idea is to minimize the least-squares difference between the amplitude of the measured field and that of a calculated SWE using a combination of a genetic algorithm (GA) and Newton's method. The uniqueness aspects of the problem are addressed. A measured antenna radiation pattern is analyzed with and without phase data and the results are compared. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 402–406, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21000

ON THE INFLUENCE OF INCOMPLETE RADIATION PATTERN DATA ON THE ACCURACY OF A SPHERICAL WAVE EXPANSION

The accuracy of a spherical wave expansion is examined when the expansion is calculated from incomplete data of the radiation pattern, i.e., when field data on a part of the far-field sphere is missing. The effect of antenna size and truncation index on the interpolation capacity of a SWE is examined by using an analytical expression for the radiation pattern of wire antennas of different lengths. The error of the SWE is seen to increase drastically when the smallest diameter of the dead zone surpasses the length of a period of the highest included wave function. The influence of the size and shape of the dead zone is studied by the aid of a measured pattern, of which a part of the field data is ignored. Two different ways are proposed for estimating the accuracy of the obtained SWE in a practical instance, when the field in the dead zone is unknown.

Elimination of rotation axes offset error in antenna radiation pattern measurements using spherical wave expansion

The error caused by the offset between θ - and ϕ -rotation axes is eliminated from a measured antenna radiation pattern. Proper offset is found by minimising the difference between the original data field and the field of the spherical wave expansion (SWE) calculated from the data. Errors of the original and the corrected fields are estimated as the difference from a field calculated by the IE3D simulator for the antenna. The method is verified by comparing the obtained offset with a value given by minimising the phase difference between the measured and the simulated electric fields.

Demonstration of reflection‐error reduction in antenna radiation patterns using spherical wave expansion

AbstractThis paper demonstrates how the reflection error of a radiation pattern can be reduced by means of an optimised spherical wave expansion (SWE). Disturbed and undisturbed radiation patterns are measured with and without an aluminum mast near the measured antenna. The SWEs are calculated from each measurement with the optimal truncation indices determined by a method previously introduced by this author. The differences between the disturbed and undisturbed radiation patterns are calculated for measured and corresponding SWE values. The agreement of the SWE fields is better than that of the measured ones. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 280–284, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20445

Spherical Wave Expansion of the Time-Domain Free-Space Dyadic Green's Function

The importance of expanding Green's functions, particularly free-space Green's functions in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time-domain scattering problems, similar expansions of Green's functions are expected to be useful in the time-domain. In this paper, an expression, expanded in terms of orthogonal spherical vector wave functions, for the time-domain free-space dyadic Green's function is presented and scattering by a perfectly conducting sphere is studied as an application to check numerically the validity and to demonstrate the utility of this expression.

REDUCTION OF ERRORS IN ANTENNA RADIATION PATTERNS USING OPTIMALLY TRUNCATED SPHERICAL WAVE EXPANSION

This paper demonstrates how the error of a measured or simulated antenna radiation pattern can be decreased by calculating a spherical wave expansion (SWE) with an optimised truncation mode index. Four radiation pattern examples are examined for which the analytical expression of the electrical field is known. Upon adding random and φ-alignment errors to the exact electric fields, the SWEs are determined and compared with the corresponding ones for the exact fields. These comparisons show that the accuracy of the calculated SWE is much better than the accuracy of the original inaccurate field. Resting on the calculated examples, a method is created which can be used to determine the optimal truncation index from the modal power distribution of a SWE without knowing the exact field. Finally, the method developed is applied to measured antenna radiation patterns.

Scattering by screw heads in reflecting surfaces and their effect on the sidelobes of reflector antennas

AbstractScrews are often used to fasten the main reflector of a reflector antenna to its support structure. The screw heads may then cause bumps in an otherwise smooth reflector surface. Thereby, they disturb the reflected fields and cause increased sidelobes. In this paper, a perturbation theory is introduced in order to calculate efficiently the increased sidelobes due to scattering from the screw heads. Screw heads are approximated as half spheres, whereby it becomes very efficient to calculate the scattering from them by using a spherical wave expansion algorithm, GIDMULT. This method has been verified by measurements in a low sidelobe antenna. We also describe some ways to reduce the scattering, such as dielectric coating of the screw heads and optimization of their locations. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 213–217, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11018

An expanded spherical wave expansion for arbitrary sound fields

Spherical wave function expansions as means of describing the acoustic field radiated by arbitrarily shaped objects are very convenient and gaining popularity. The HELS method for acoustic holography is one methodology advocating the use of spherical wave functions as a basis for the solution of the inverse acoustic problem. Such methodologies only provide an approximation to the actual sound field and as such suffer from errors, albeit understood to be bounded and manageable in a large number of cases. Based on the sound radiation model of a volume distribution of monopole sources, these approximation errors are found to be due to the presence of monopole sources outside the largest inscribed virtual sphere. Monopole sources outside that virtual sphere are not accounted for in the expansion and thus come out as errors. These errors are greatly reduced if the spherical wave function expansion is modified to account for the largest number of monopole sources in the model. This is accomplished by employing the addition theorem for spherical harmonics. This modification complicates the problem mathematically and might require a greater rate of physical sampling, however the reduction in the reconstruction errors might prove beneficial.

Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam.

We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a < or = illumination wavelength lambda). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10(-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity.

Circular scanning and equivalent magnetic currents for main plane near‐field to far‐field transformation

AbstractA method to obtain a main plane far‐field radiation pattern of an antenna under test (AUT) from the correspondent main plane near‐field pattern in a circular scanning is presented. The method is based on the reconstruction of a set of magnetic equivalent currents radiating in free space that represents the AUT. The method can be applied to the measurement of antennas with a linear distribution or with a two‐dimensional distribution under certain considerations that allow to establish integral equations relating field components and one‐dimensional current components. A Levenberg–Marquardt algorithm is used to minimize the least squares error between the fields radiated by the equivalent currents and the measured field. The far field at every aspect angle is obtained from the calculated sources. Calculations of co‐polar and cross‐polar far‐field pattern from measured near‐field data of array antennas have been carried out to compare the proposed method with a full spherical scanning followed by a spherical wave expansion method. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Analytical Solution for Characteristic Modal Power Distribution and Truncation Limit for Spherical Wave Expansion of Antenna Radiation Pattern

—In this paper the Spherical Wave Expansion (SWE) is used to represent an antenna radiation pattern. An analytical expression for the characteristic modal distribution of power radiated by an arbitrary antenna is derived from the assumption of equal average amplitude for each mode over the surface of the minimum sphere enclosing the antenna. The relative power error of a truncated expansion is obtained from the derived modal power distribution. The result offers a convenient way to determine an appropriate truncation limit of the modes in a SWE as a function of the desired accuracy and antenna size. This method is more accurate than the formulas given previously in the literature. Moreover, it allows one to choose the accuracy of the resulting field, contrary to the earlier formulas. The derived truncation limit is compared with expressions given previously in the literature and with analytically and numerically determined radiation pattern examples. The modal power distributions are also compared with the calculated examples.

Far-field measurements for mobile phones with smallnumber of measurement locations

A simple method for the characterisation of radiated fields is presented that is based on the application of the spherical wave expansion. The spherical wave coefficients are solved in a new manner by using an iterative matrix (IM) method. The method can be used to decrease the number of field samples required to characterise the radiated field compared to the conventional matrix method. The performance of the IM method is illustrated with simulated field measurements for mobile phones.

Influence of phantom head on measurementsof radiated fields of mobile phones

The influence of the phantom head on the required number of far-field measurement locations for the determination of radiation characteristics of mobile phones is examined at 1.8 GHz using the spherical wave expansion technique. Results show that e.g. the total radiated power of mobile phones can be determined with about 50 measurement locations with an uncertainty of less than 0.1 dB.

A new procedure for specifying nonradiating current distributions and the fields they produce

This paper reports a new procedure for specifying monochromatic nonradiating (NR) current distributions (NR sources) and the electric and magnetic fields they produce (NR fields). Vector spherical harmonics and a Fourier–Bessel series are used to derive a new vector spherical-wave expansion for continuous NR fields confined within a spherical volume. The analysis yields complete orthogonal sets in terms of which all such NR fields can be expanded. By making use of a Maxwell operator representation for NR current distributions, we obtain a new series expansion for NR current distributions confined within a spherical volume. The analysis also yields complete sets for such NR current distributions. The developed theory is illustrated with special cases.

T-matrix determination of effective permittivity for three-dimensional dense random media

In this paper, we present a full wave method for determining the effective permittivity for random media in three dimensions. The type of media addressed is composed of spherical dielectric particles in a homogeneous dielectric background. The particle volume fraction ranges from 0 to 40% and dielectric contrast may be significantly different from the background medium. The method described relies on the T-matrix approach for solving Maxwell's equations using a spherical wave expansion in conjunction with a Monte-Carlo simulation for calculating the mean scattered field confined within a prescribed fictitious boundary. To find the effective permittivity, the mean scattered field is compared with that of a homogeneous scatterer whose shape is defined by the fictitious boundary and its dielectric constant is varied until the scattered fields are matched. A complete description of the T-matrix approach is given along with an explanation of why the recursive form of this technique (RATMA) cannot be used for addressing this problem. After the method development is completed, the results of our numerical technique are compared against the theoretical methods of the quasi crystalline approximation and the effective field approximation to demonstrate the region of validity of the theoretical methods. The examples contained within the paper use between 30 and 120 included spheres (with radii ranging from from ka=0.6 to 0.8) within a larger, fictitious sphere of diameter kD=8.4.

Time-domain near-field analysis of short-pulse antennas .I. Spherical wave (multipole) expansion

The radiation from a time-dependent source distribution in free-space is analyzed using time-domain (TD) spherical wave (multipole) expansion. The multipole moment functions are calculated from the time-dependent source distribution. The series convergence rate in the near and far zone and the bounds on the near-zone reactive field are determined as functions of the source support and of the pulse length. The formulation involves a spherical transmission line representation that can be extended to more general spherical configurations. This formulation also describes the field and energy transmission mechanisms in a physically transparent fashion that will be used in a companion paper to define and explore fundamental concepts such as TD reactive energy and Q and to derive bounds on the antenna properties. Finally, the concepts discussed above are demonstrated numerically for pulsed radiation by a circular current disk.

Introduction to spherical field theory

Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional systems. The coupled one-dimensional systems are then converted to partial differential equations and solved numerically. We demonstrate the methods of spherical field theory by analyzing Euclidean φ 4 theory in two dimensions.

Electronic Structures and Optical Properties of GeTe and Ge 2Sb 2Te 5

The optical properties of GeTe and Ge2Sb2Te5 have been studied by means of the density functional theory (DFT) in the local density approximation (LDA). The electronic band structures were obtained by two methods, the plane wave (PW) and spherical wave (SW) expansions of the wave functions. GeTe was calculated to be semiconductive, and Ge2Sb2Te5 to be semimetallic. The frequency dependent optical constants such as refractive index and extinction coefficient were calculated and compared with those obtained experimentally. The origin of the peaks in the extinction coefficient spectra was assigned in terms of the transitions between Ge, Sb and Te p states. Dynamical calculations with respect to Ge2Sb2Te5 have also been performed in order to obtain an understanding of its structural features. The displacements of the Te atoms were found to be larger than those of the Ge and Sb atoms.