Robert E. Collin

Evaluation of antenna Q

A method is presented for evaluating the Q of an antenna, where the Q is defined as in conventional network theory. The method consists of subtracting the energy density associated with the power flow from the total energy density, thus enabling the magnetic and electric reactive energy to be computed. Specific application of the method is made to the evaluation of the Q of spherical and cylindrical modes. It is verified that the Q becomes very large when the order of the mode exceeds k_{0}a where a is the radius of the sphere or cylinder on which the sources are located.

The signal-to-noise ratio of nuclear magnetic resonance surface coils and application to a lossy dielectric cylinder model. I. Theory

Surface coils are used in magnetic resonance imaging (MRI) for their high signal-to-noise ratio (S/N) when placed near the-region to be imaged. However, their optimization for high field MRI systems is hampered by the lack of understanding of the electromagnetic effects taking place at high frequencies when a coil is placed near the human body. The aim of this work was to calculate the S/N of surface coils using complete solutions to Maxwells equations and also to study the high frequency effects and parameters determining the S/N. Here the authors present a general approach to the computation of the S/N of surface coils using the reciprocity principal and the complex Poynting vector for arbitrary coil and body geometries. This approach is then applied to the case of the human body modeled as an infinitely long homogeneous dielectric cylinder exhibiting both conductive and dielectric losses. The S/N of a coil of unspecified geometry facing the cylinder is derived using a dyadic Greens function. Complete solutions for the fields of a dipolar source arbitrarily located in the cylinder are first derived, and applying the reciprocity principle, the authors deduce the fields created at the dipole position by a coil excited with a unit radiofrequency current. These yield the expressions for the power dissipated in the cylinder, for its reciprocal the noise picked up by the coil, and also for the signal received. Any coil geometry and any coil or source position can be evaluated with this infinite cylinder model. It is valid at all frequencies and for any tissue parameter. The general approach to the computation of the S/N of MRI coils can be applied to other body geometries as well. >

Electromagnetic scattering from perfectly conducting rough surfaces (a new full wave method)

A method that does not make use of the telegraphists equations and takes into account the two-dimensional roughness of the surface from the start is developed. It is shown that the scattering coefficients obtained agree with those given in earlier work by E. Bahar (1973, 1987). The method is based on reducing the three-dimensional scattering problem to a two-dimensional problem by expanding each rectangular component of Maxwells equations in terms of local basis functions along the perpendicular direction to the mean surface. The transformed two-dimensional field equations are solved using Fourier transforms. The full wave solutions are also compared with the first-order perturbation solutions, the Kirchhoff-type solutions, and integral equation results. >

Some observations about the near zone electric field of a Hertzian dipole above a lossy earth

In some recent publications, King (1990, 1992) and King and Sandler (1994) have provided formulas for the electromagnetic field radiated by an infinitesimal vertical Hertzian dipole above a lossy homogeneous half space (earth) and above a lossy half space coated by a thin dielectric layer. Several authors have questioned the accuracy of the King-Sandler formulas, particularly for field points close to the dipole (Yokoyama (1995), Wait (1996), Mahmoud (1999)). The authors have responded to these critiques by asserting that their formulas are accurate subject only to the restriction that the magnitude of the relative permittivity of the lossy half space is greater than 9. The principal results they obtain are that the near zone fields are independent of the electrical parameters of either the coating or the homogeneous half space. In this communication we provide some results obtained from a numerical evaluation of the exact integral for the near zone axial electric field along with numerical results obtained from an evaluation of the approximate integral used by King and Sandler. The King-Sandler formulas show that there is no contribution to the near zone axial electric field from a term they called the surface wave field. Our numerical evaluations show that this is not the case, in actual fact the surface wave term makes a significant contribution to the near zone axial electric field. We also present a quasistatic analysis that provides an alternative formula for calculating the near zone field. Our analysis supports the conclusions reached by Wait and Mahmoud.

Scattering of an incident Gaussian beam by a perfectly conducting rough surface

The modifications of the regular full wave theory for rough surface scattering by an incident Gaussian beam instead of a plane wave are developed. The Gaussian beam is produced by a large circular aperture that has a Gaussian illumination. It is shown that provided the incident Gaussian beam has a plane phase front over the extent of the rough surface patch and the linear dimensions of the rough patch are large compared with the surface height correlation length, the normalized scattering cross-section is the same as for an incident plane wave. >

Aperture efficiency for paraboloidal reflectors

The definition and formulas for cross polarization, phase error, and illumination efficiency given by Ludwig and Thomas are shown to not always account for the correct cross polarization and phase error loss. New definitions and formulas are proposed that give a better separation of the losses associated with cross-polarized radiation, phase errors, and nonuniform aperture illumination.

Frequency Dispersion Limits Resolution in Veselago Lens

The properties of a lossless Veselago lens is examined when the material parameters epsilon and mu are frequency dispersive. A complete solution is presented that is based on the use of Fourier transforms in the frequency domain and is obtained in terms of the residues at the poles and branch cut integrals. It is shown that for an incident fleld with a flnite frequency spectrum the excited evanescent fleld consists of resonant even and odd surface wave modes that do not grow exponentially within the slab. For a lossless slab and a sinusoidal signal of flnite duration, at a single frequency corresponding to that where the relative values of epsilon and mu equal i1, Pendrys solution is obtained along with excited surface wave modes and other interfering waves that makes it impossible to obtain a coherent reconstruction of the spatial spectrum of the object fleld at the image plane. If the slab material is lossy the excited interfering surface wave modes will decay away in a relatively short time interval, but as shown by other investigators the resolution of the lens will be reduced in a very substantial way if the losses are moderate to large.

Scattering of a Gaussian laser beam by a large perfectly conducting cylinder: physical optics and exact solutions

Two particularly accurate solutions representing the scatter of a Gaussian laser beam from a perfectly conducting cylinder, one a physical optics solution using a series Greens function and the other an exact solution, are developed. A comparison of their resulting numerical data follows in order to validate the two solutions. The practicality of these solutions is then demonstrated by using the exact solution to plot the power distribution of the scattered beam on a sensor, and to confirm that the strategic placement of a cylinder in the path of a laser beam enables amplification of the laser beam deflection angle.

An accurate closed-form approximate representation for the Hankel function of the second kind

A second-order asymptotic evaluation of the Hankel function is presented and its numerical evaluation for the case of large orders and large arguments is compared with the numerical results obtained using forward recursion. It is shown that the second-order results are very accurate as long as the argument is a few percent larger than the order of the function.

Spherical shell of ENG metamaterial surrounding a dipole antenna

We present an exact analytical solution for the radiation impedance of an infinitesimal dipole surrounded by a thin spherical shell of epsilon negative material (ENG). The negative epsilon leads to a non-Foster reactance in the equivalent circuit and a much broader impedance bandwidth than would be expected from the Q of the antenna. When dispersion is considered, the non-Foster reactance disappears and the Q reverts back to the value based on the ratio of stored energy to radiated power. The analysis shows that a thin shell of ENG material provides no significant improvement in the performance of the dipole antenna.