Assessment of FDTD Accuracy in the Compact Hemielliptic Dielectric Lens Antenna Analysis

We assess the accuracy of a standard finite-difference time-domain (FDTD) code in the analysis of the near and far-field characteristics of two-dimensional (2-D) models of small-size dielectric lens antennas made of low or high-index materials and fed by the line sources. We consider extended hemielliptic lenses and use the Muller boundary integral equations (MBIE) method as a suitable reference solution. Inaccuracies of FDTD near so-called half-bowtie resonances are detected. Denser meshing reduces the error of FDTD only to a certain level determined by the type of absorbing boundary conditions used and other fine details of the code. Out of these resonances, FDTD code is demonstrated as capable of providing sufficient accuracy in the near and far-field analysis of small-size hemielliptic lenses typical for the millimeter-wave (mm- wave) applications.

[1]  John B. Schneider,et al.  A selective survey of the finite-difference time-domain literature , 1995 .

[2]  R. Sauleau,et al.  Small Hemielliptic Dielectric Lens Antenna Analysis in 2-D: Boundary Integral Equations Versus Geometrical and Physical Optics , 2008, IEEE Transactions on Antennas and Propagation.

[3]  Gabriel M. Rebeiz,et al.  A W-band dielectric-lens-based integrated monopulse radar receiver , 1998, IMS 1998.

[4]  Alberto Toccafondi,et al.  Mutual coupling between slots printed at the back of elliptical dielectric lenses , 1999 .

[5]  Trevor M. Benson,et al.  Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a sub‐millimeter‐wave receiver , 2004 .

[6]  Kazuhiro Uehara,et al.  Lens-coupled imaging arrays for the millimeter- and submillimeter-wave regions , 1992 .

[7]  R. Sauleau,et al.  Single- and double-shell shaped lens antennas with asymmetrical radiation characteristics , 2006, 2006 First European Conference on Antennas and Propagation.

[8]  R. Sauleau,et al.  A new accurate design method for millimeter-wave homogeneous dielectric substrate lens antennas of arbitrary shape , 2005, IEEE Transactions on Antennas and Propagation.

[9]  Carlos A. Fernandes,et al.  Shaped dielectric lenses for wireless millimeter-wave communications , 1999 .

[10]  Trevor M Benson,et al.  Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  T. H. Buttgenbach An improved solution for integrated array optics in quasi-optical mm and submm receivers: the hybrid antenna , 1993 .

[12]  J. R. Mosig,et al.  Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications , 1998 .

[13]  K. Yee Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[14]  Gabriel M. Rebeiz,et al.  Wide-scan spherical-lens antennas for automotive radars , 2002 .

[15]  J. Wiersig Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities. , 2006, Physical review letters.

[16]  Claus Müller,et al.  Foundations of the mathematical theory of electromagnetic waves , 1969 .

[17]  J. Bérenger Perfectly matched layer for the FDTD solution of wave-structure interaction problems , 1996 .

[18]  George V. Eleftheriades,et al.  Design and characterization of single and multiple beam MM-wave circularly polarized substrate lens antennas for wireless communications , 1999, IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.99CH37010).

[19]  Alexander I. Nosich,et al.  The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions , 1999 .

[20]  Gabriel M. Rebeiz,et al.  Double-slot antennas on extended hemispherical dielectric lenses , 1992 .

[21]  V. Rokhlin Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[22]  A. Friedman,et al.  Modal analysis of homogeneous optical waveguides by the boundary integral formulation and the Nyström method , 1998 .

[23]  J. V. Rudd,et al.  Influence of substrate-lens design in terahertz time-domain spectroscopy , 2002 .

[24]  Gabriel M. Rebeiz,et al.  Off-axis properties of silicon and quartz dielectric lens antennas , 1997 .

[25]  Carlos A. Fernandes,et al.  Performance of lens antennas in wireless indoor millimeter wave applications , 1998, Proceedings RAWCON 98. 1998 IEEE Radio and Wireless Conference (Cat. No.98EX194).

[26]  George V. Eleftheriades,et al.  ALPSS: a millimetre-wave aperture-coupled patch antenna on a substrate lens , 1997 .

[27]  John B. Schneider,et al.  Inaccuracies in numerical calculation of scattering near natural frequencies of penetrable objects , 1993 .

[28]  R. Sauleau,et al.  Performance of reduced size substrate lens antennas for Millimeter-wave communications , 2005, IEEE Transactions on Antennas and Propagation.

[29]  Jorge Nuno Silva,et al.  Mathematical Games , 1959, Nature.

[30]  Afonso M. Barbosa,et al.  A method to overcome the limitations of G.O. in axis-symmetric dielectric lens shaping , 1996 .

[31]  S. M. Kirkup,et al.  Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods , 1995 .

[32]  S. Maci,et al.  High-frequency analysis of integrated dielectric lens antennas , 2004, IEEE Transactions on Antennas and Propagation.

[33]  J. Mosig,et al.  Three-dimensional ray-tracing to model internal reflections in off-axis lens antennas , 2006, IEEE Transactions on Antennas and Propagation.

[34]  D. Rutledge,et al.  INTEGRATED-CIRCUIT ANTENNAS. , 1983 .

[35]  C.A. Fernandes,et al.  Shaped double-shell dielectric lenses for wireless millimeter wave communications , 2000, IEEE Antennas and Propagation Society International Symposium. Transmitting Waves of Progress to the Next Millennium. 2000 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (C.