Numerical calibration in FDTD to compute complex reflectioncoefficient of periodic structures

The use of a reference load (here, a short circuit) in a finite difference time-domain method combined with Floquet boundary conditions in order to compute the complex reflection coefficient of infinite periodic structures is described. The short circuit imposes the position of a reference plane, essential for the calculation of the phase. This approach is called `numerical calibration', by analogy with the experimental calibration of network analysers     

Finite-difference time-domain simulations of the effects of air gaps in double-shell extended hemispherical lenses

The effects of parasitic air gaps on the input impedance and radiation characteristics of dense double-shell integrated lens antennas are studied numerically at millimetre waves using the finite-difference time-domain method. The lens core is made up of Macor or silicon, and is coated with a quarter wavelength matching layer. Two kinds of gaps are compared: they are located either (i) between both shells of the lens, or (ii) between the lens base and the feed substrate. We show that their impact is much more critical in the second case, and that it becomes dramatic for silicon lenses, even with very thin gaps (smaller than ? ₀/100); the three major observed effects are the following: (i) strong shift of the resonant frequency, (ii) beam broadening and directivity loss, (iii) increase of the side lobe level.     

Beam focusing using 60 GHz Fabry-Perot resonators with uniform and non-uniform metal grids

A new structure of millimetre-wave focusing antennas is presented. It consists of a plane-parallel Fabry-Perot resonator comprising two uniform and non-uniform inductive metal meshes excited by a horn antenna. The beam focusing is performed with the non-uniform mirror, the geometry of which is chosen so that it behaves as a spherical equiphase surface with a desired radius of curvature. The resulting radiation patterns are Gaussian; their directivity is controlled by the curvature of the synthesised wavefront. This concept is successfully validated in the 60 GHz band.     

Compact Ka-Band Lens Antennas for LEO Satellites

Two new compact lens antenna configurations are presented and compared for data link communications with LEO satellites at 26 GHz. These lenses match a secant type radiation pattern template in the elevation plane while having a mechanically scanned sector beam in azimuth to enhance gain as much as possible. No rotary joints or multiple feeds are required and emphasis is put also on the compactness of the proposed solutions (< 6lambda₀). Two alternative lens configurations are evaluated numerically and experimentally: one is based on modified axial-symmetric dome lens geometry, and the other one consists of a full 3-D double-shell lens antenna. In contrast to current nearly omnidirectional antennas, the directivity of our lens prototypes is above 15.4 dBi. Up to 4.2 dB loss obtained in the prototypes can be significantly reduced by using lower loss dielectrics and matching layers, without affecting the conclusions. The numerical and experimental results are in good agreement with the radiation specifications given the compact size of the antennas.     

Ultra-Wideband Wave Reactances of Capacitive Grids

The accuracy of transmission line models of two-dimensional freestanding capacitive grids is studied on a very wide frequency band. The grids are of infinite extent in the transverse directions and are illuminated by a linearly polarized normally incident plane wave. Comparison with reference results deduced from Finite-Difference Time-Domain (FDTD) simulations allows determining the range of validity of commonly used equivalent circuits It is shown that their accuracy strongly depends on the dimensions of the grids and the operating wavelength. Although very convenient, their implementation for calculating the frequency response of multi-layer systems could lead to unreliable results. Two closed-form new models are thus proposed. The first one results from an optimized expression of the well-known Marcuvitz's impedance, and the second one involves a series resonant LC circuit shunted by an additional capacitance. Both formulations are very accurate for a wide range of grid geometries and over the whole visible region (wavelength > grid constant).     

A new concept of focusing antennas using plane-parallel Fabry-Perot cavities with nonuniform mirrors

An original configuration of low-profile directive antennas is presented in V-band. The focusing effect is performed by a plane-parallel Fabry-Perot (FP) resonator illuminated by a printed antenna. Both reflecting mirrors are made of metal strip gratings. The dimensions of the strips and slots of the nonperiodic output mirror are much smaller than the working wavelength; they are computed locally so that this mirror behaves as a spherical equiphase surface. Theoretical and experimental results show that the radiation patterns are symmetric and have low sidelobes. The antenna directivity is controlled by the value of the synthesized radius of curvature, that is to say by the nonperiodic distribution of the metal strips. It typically varies between 15 and 23.5 dB at 60 GHz. This new radiating structure is much more compact than substrate lenses and is compatible with low-cost multilayer technologies at millimeter wave frequencies. This is a possible candidate for user mobile-stations of indoor broadband communication systems.     

A complete procedure for the design and optimization of arbitrarily shaped integrated lens antennas

This paper proposes a new design methodology of arbitrarily shaped integrated lens antennas (ILAs). First, we describe the design principles and numerical techniques of the optimization iterative loop. The starting lens shape, deduced from a general synthesis method based on geometrical optics principles, is optimized so that the radiation pattern of the ILA complies with an arbitrary amplitude-shaped template. The optimization procedure is local and is based on a multidimensional conjugate gradient method. Then, the capabilities and potentialities of this approach are demonstrated numerically using two examples. In the first one, an ILA radiating a secant-squared beam in one principal plane and a flat-top beam in the orthogonal plane is designed for indoor communications in V-band. In the second example (Gaussian/flat-top beam), we show for the first time that the joint optimization of the feed together with the lens shape is a very promising design methodology. Finally, our design tools are validated experimentally in Q-band through the synthesis and optimization of a peculiar small shaped ILA (28 mm/spl times/28 mm/spl times/15 mm) fed by an aperture-coupled microstrip patch antenna.     

Small Hemielliptic Dielectric Lens Antenna Analysis in 2-D: Boundary Integral Equations Versus Geometrical and Physical Optics

We assess the accuracy and relevance of the numerical algorithms based on the principles of geometrical optics (GO) and physical optics (PO) in the analysis of reduced-size homogeneous dielectric lenses prone to behave as open resonators. As a benchmark solution, we use the Muller boundary integral equations (MBIEs) discretized with trigonometric Galerkin scheme that has guaranteed and fast convergence as well as controllable accuracy. The lens cross-section is chosen typical for practical applications, namely an extended hemiellipse whose eccentricity satisfies the GO focusing condition. The analysis concerns homogeneous lenses made of rexolite, fused quartz, and silicon with the size varying between 3 and 20 wavelengths in free space. We consider the 2D case with both - and -polarized plane waves under normal and oblique incidence, and compare characteristics of the near fields.     

A new accurate design method for millimeter-wave homogeneous dielectric substrate lens antennas of arbitrary shape

The synthesis and the optimization of three-dimensional (3-D) lens antennas, consisting of homogeneous dielectric lenses of arbitrary shape and fed by printed sources, are studied theoretically and experimentally at millimeter(mm)-wave frequencies. The aim of the synthesis procedure is to find a lens profile that transforms the radiation pattern of the primary feed into a desired amplitude shaped output pattern. This synthesis problem has been previously applied for dielectric lenses and reflectors. As far as we know, we propose, for the first time, to adapt and implement it for the design of substrate lens antennas. The inverse scattering problem is solved in two steps. In the first one, the geometry of the 3-D lens is rigorously derived using geometrical optics (GO) principles. The resulting second-order partial-differential equation is strongly nonlinear and is of the Monge-Ampe/spl grave/re (M.A) type. The iterative algorithm implemented to solve it is described in detail. Then, a surface optimization of the lens profile combined with an analysis kernel based on physical optics (PO) is performed in order to comply with the prescribed pattern. Our algorithms are successfully validated with the design of a lens antenna radiating an asymmetric Gaussian pattern at 58.5 GHz whose half-power beamwidth equals 10/spl deg/ in H plane and 30/spl deg/ in E plane. The lens is illuminated by a microstrip 2/spl times/2 patch antenna array. Two lens prototypes have been manufactured in Teflon. Before optimization, the measured radiation patterns are in very good agreement with the predicted ones; nevertheless, the -12 dB side lobes and oscillations appearing in the main lobe evidence a strong difference between the desired and measured patterns. This discrepancy is significantly reduced using the optimized lens.     

Performance of reduced size substrate lens antennas for Millimeter-wave communications

This paper presents the theoretical performance (input impedance, -10 dB return-loss bandwidth, radiation patterns and surface efficiencies) of reduced size substrate lenses fed by aperture-coupled microstrip patch antennas. The diameter of the extended hemispherical homogeneous dielectric (/spl epsiv//sub r,lens/) lenses varies between one and five wavelengths in free-space, in order to obtain radiating structures whose directivity is comprised between 10 and 25 dB. A lot of configurations of lenses are investigated using the finite-difference time-domain methods technique and compared in the 47-50 GHz band as a function of their diameter, extension length and dielectric constant. In particular, the analysis of internal reflections-in time and frequency domains-shows that the latter have potentially a strong influence on the input impedance of small lens antennas, even for low values of /spl epsiv//sub r,lens/(2.2), whereas the usual limit (beyond which anti-reflection coatings are required) is /spl epsiv//sub r,lens/=4. We also demonstrate that the diffraction limit of reduced size lenses is reached for extension lengths varying between 50% and 175% of the extension of synthesized ellipses, depending on the lens material and diameter. Finally, we show that superdirective structures with surface efficiencies reaching 250% can be obtained with small lens diameters, justifying the interest in reduced size lens antennas.