Near and far field

About: Near and far field is a research topic. Over the lifetime, 15922 publications have been published within this topic receiving 220571 citations.

Antenna theory and design

Abstract: Foreword to the Revised Edition. Preface to the Revised Edition. Preface. I SOURCE-FIELD RELATIONS SINGLE ANTENNA ELEMENTS. 1 The Far-Field Integrals, Reciprocity, Directivity. 1.1 Introduction. 1.2 Electrostatics and Magnetostatics in Free Space. 1.3 The Introduction of Dielectric, Magnetic, and Conductive Materials. 1.4 Time-Varying Fields. 1.5 The Retarded Potential Functions. 1.6 Poynting's Theorem. 1.7 The Stratton-Chu Solution. 1.8 Conditions at Infinity. 1.9 Field Values in the Excluded Regions. 1.10 The Retarded Potential Functions: Reprise. 1.11 The Far Field: Type I Antennas. 1.12 The Schelkunoff Equivalence Principle. 1.13 The Far Field: Type IL Antennas. 1.14 The Reciprocity Theorem. 1.15 Equivalence of the Transmitting and Receiving Patterns of an Antenna. 1.16 Directivity and Gain. 1.17 Receiving Cross Section. 1.18 Polarization of the Electric Field. 2 Radiation Patterns of Dipoles, Loops, and Helices. 2.1 Introduction. 2.2 The Center-Fed Dipole. 2.3 Images in a Ground Plane. 2.4 A Monopole Above a Ground Plane. 2.5 A Dipole in Front of a Ground Plane. 2.6 The Small Current Loop. 2.7 Traveling Wave Current on a Loop. 2.8 The End-Fire Helix. 3 Radiation Patterns of Horns, Slots and Patch Antennas. 3.1 Introduction. 3.2 The Open-Ended Waveguide. 3.3 Radiation from Horns. 3.4 Center-Fed Slot in Large Ground Plane. 3.5 Waveguide-Fed Slots. 3.6 Theory of Waveguide-Fed Slot Radiators. 3.7 Patch Antennas. II ARRAY ANALYSIS AND SYNTHESIS. 4 Linear Arrays: Analysis. 4.1 Introduction. 4.2 Pattern Formulas for Arrays with Arbitrary Element Positions. 4.3 Linear Arrays: Preliminaries. 4.4 Schelkunoff's Unit Circle Representation. 5 Linear Arrays: Synthesis. 5.1 Introduction. 5.2 Sum and Difference Patterns. 5.3 Dolph-Chebyshev Synthesis of Sum Patterns. 5.4 Sum Pattern Beamwidth of Linear Arrays. 5.5 Peak Directivity of the Sum Pattern of a Linear Array. 5.6 A Relation Between Beamwidth and Peak Directivity for Linear Arrays. 5.7 Taylor Synthesis of Sum Patterns. 5.8 Modified Taylor Patterns. 5.9 Sum Patterns with Arbitrary Side Lobe Topography. 5.10 Discretization of a Continuous Line Source Distribution. 5.11 Bayliss Synthesis of Difference Patterns. 5.12 Difference Patterns with Arbitrary Side Lobe Topography. 5.13 Discretization Applied to Difference Patterns. 5.14 Design of Linear Arrays to Produce Null-Free Patterns. 6 Planar Arrays: Analysis and Synthesis. 6.1 Introduction. 6.2 Rectangular Grid Arrays: Rectangular Boundary and Separable Distribution. 6.3 Circular Taylor Patterns. 6.4 Modified Circular Taylor Patterns: Ring Side Lobes of Individually Arbitrary Heights. 6.5 Modified Circular Taylor Patterns: Undulating Ring Side Lobes. 6.6 Sampling Generalized Taylor Distributions: Rectangular Grid Arrays. 6.7 Sampling Generalized Taylor Distributions: Circular Grid Arrays. 6.8 An Improved Discretizing Technique for Circular Grid Arrays. 6.9 Rectangular Grid Arrays with Rectangular Boundaries: Nonseparable Tseng-Cheng Distributions. 6.10 A Discretizing Technique for Rectangular Grid Arrays. 6.11 Circular Bayliss Patterns. 6.12 Modified Circular Bayliss Patterns. 6.13 The Discretizing Technique Applied to Planar Arrays Excited to Give a Difference Pattern. 6.14 Comparative Performance of Separable and Nonseparable Excitations for Planar Apertures. 6.15 Fourier Integral Representation of the Far Field. III SELF-IMPEDANCE AND MUTUAL IMPEDANCE, FEEDING STRUCTURES. 7 Self-Impedance and Mutual Impedance of Antenna Elements. 7.1 Introduction. 7.2 The Current Distribution on an Antenna: General Formulation. 7.3 The Cylindrical Dipole: Arbitrary Cross Section. 7.4 The Cylindrical Dipole: Circular Cross Section, Hallen's Formulation. 7.5 The Method of Moments. 7.6 Solution of Hallen's Integral Equation: Pulse Functions. 7.7 Solution of Halle'n's Integral Equation: Sinusoidal Basis Functions. 7.8 Self-Impedance of Center-Fed Cylindrical Dipoles: Induced EMF Method. 7.9 Self-Impedance of Center-Fed Cylindrical Dipoles: Storer's Variational Solution. 7.10 Self-Impedance of Center-Fed Cylindrical Dipoles: Zeroth and First Order Solutions to Hallen's Integral Equation. 7.11 Self-Impedance of Center-Fed Cylindrical Dipoles: King-Middleton Second-Order Solution. 7.12 Self-Impedance of Center-Fed Strip Dipoles. 7.13 The Derivation of a Formula for the Mutual Impedance Between Slender Dipoles. 7.14 The Exact Field of a Dipole: Sinusoidal Current Distribution. 7.15 Computation of the Mutual Impedance Between Slender Dipoles. 7.16 The Self-Admittance of Center-Fed Slots in a Large Ground Plane: Booker's Relation. 7.17 Arrays of Center-Fed Slots in a Large Ground Plane: Self-Admittance and Mutual Admittance. 7.18 The Self-Impedance of a Patch Antenna. 8 The Design of Feeding Structures for Antenna Elements and Arrays. 8.1 Introduction. 8.2 Design of a Coaxially Fed Monopole with Large Ground Plane. 8.3 Design of a Balun-Fed Dipole Above a Large Ground Plane. 8.4 Two-Wire-Fed Slots: Open and Cavity-Backed. 8.5 Coaxially Fed Helix Plus Ground Plane. 8.6 The Design of an Endfire Dipole Array. 8.7 Yagi-Uda Type Dipole Arrays: Two Elements. 8.8 Yagi-Uda Type Dipole Arrays: Three or More Elements. 8.9 Frequency-Independent Antennas: Log-Periodic Arrays. 8.10 Ground Plane Backed Linear Dipole Arrays. 8.11 Ground Plane Backed Planar Dipole Arrays. 8.12 The Design of a Scanning Array. 8.13 The Design of Waveguide-Fed Slot Arrays: The Concept of Active Slot Admittance (Impedance). 8.14 Arrays of Longitudinal Shunt Slots in a Broad Wall of Rectangular Waveguides: The Basic Design Equations. 8.15 The Design of Linear Waveguide-Fed Slot Arrays. 8.16 The Design of Planar Waveguide-Fed Slot Arrays. 8.17 Sum and Difference Patterns for Waveguide-Fed Slot Arrays Mutual Coupling Included. IV CONTINUOUS APERTURE ANTENNAS. 9 Traveling Wave Antennas. 9.1 Introduction. 9.2 The Long Wire Antenna. 9.3 Rhombic and Vee-Antennas. 9.4 Dielectric-Clad Planar Conductors. 9.5 Corrugated Planar Conductors. 9.6 Surface Wave Excitation. 9.7 Surface Wave Antennas. 9.8 Fast Wave Antennas. 9.9 Trough Waveguide Antennas. 9.10 Traveling Wave Arrays of Quasi-Resonant Discretely Spaced Slots [Main Beam at theta0= arccos(beta/k)]. 9.11 Traveling Wave Arrays of Quasi-Resonant Discretely Spaced Slots (Main Beam Near Broadside). 9.12 Frequency Scanned Arrays. 10 Reflectors and Lenses. 10.1 Introduction. 10.2 Geometrical Optics: The Eikonal Equation. 10.3 Simple Reflectors. 10.4 Aperture Blockage. 10.5 The Design of a Shaped Cylindrical Reflector. 10.6 The Design of a Doubly Curved Reflector. 10.7 Radiation Patterns of Reflector Antennas: The Aperture Field Method. 10.8 Radiation Patterns of Reflector Antennas: The Current Distribution Method. 10.9 Dual Shaped Reflector Systems. 10.10 Single Surface Dielectric Lenses. 10.11 Stepped Lenses. 10.12 Surface Mismatch, Frequency Sensitivity, and Dielectric Loss for Lens Antennas. 10.13 The Far Field of a Dielectric Lens Antenna. 10.14 The Design of a Shaped Cylindrical Lens. 10.15 Artificial Dielectrics: Discs and Strips. 10.16 Artificial Dielectrics: Metal Plate (Constrained) Lenses. 10.17 The Luneburg Lens. APPENDICES. A. Reduction of the Vector Green's Formula for E. B. The Wave Equations for A and D. C. Derivation of the Chebyshev Polynomials. D. A General Expansion of cosm v. E. Approximation to the Magnetic Vector Potential Function for Slender Dipoles. F. Diffraction by Plane Conducting Screens: Babinet's Principle. G. The Far-Field in Cylindrical Coordinates. H. The Utility of a Csc2 theta Pattern. Index.

Theory of Nanometric Optical Tweezers

Abstract: We propose a scheme for optical trapping and alignment of dielectric particles in aqueous environments at the nanometer scale. The scheme is based on the highly enhanced electric field close to a laser-illuminated metal tip and the strong mechanical forces and torque associated with these fields. We obtain a rigorous solution of Maxwell’s equations for the electromagnetic fields near the tip and calculate the trapping potentials for a dielectric particle beyond the Rayleigh approximation. The results indicate the feasibility of the scheme. [S0031-9007(97)03687-9] Optical trapping by highly focused laser beams has been extensively used for the manipulation of submicronsize particles and biological structures [1]. Conventional optical tweezers rely on the field gradients near the focus of a laser beam which give rise to a trapping force towards the focus. The trapping volume of these tweezers is diffraction limited. Near-field optical microscopy enables the optical measurements at dimensions beyond the diffraction limit and makes it possible to optically monitor dynamics of single biomolecules [2]. The potential application of optical near fields to manipulate atoms or nanoparticles has been discussed in Ref. [3]. In this Letter, we present a new methodology for calculating rigorously and self-consistently the trapping forces acting on a nanometric particle in the optical near field and propose a novel high-resolution trapping scheme. The proposed nanometric optical tweezers rely on the strongly enhanced electric field at a sharply pointed metal tip under laser illumination. The near field close to the tip mainly consists of evanescent components which decay rapidly with distance from the tip. The utilization of the metal tip for optical trapping offers the following advantages: (1) The highly confined evanescent fields significantly reduce the trapping volume; (2) the large field gradients result in a larger trapping force; and (3) the field enhancement allows the reduction of illumination power and radiation damages to the sample. High resolution surface modification based on the field enhancement at laser-illuminated metal tips has been recently demonstrated [4]. It is essential to perform a rigorous electromagnetic analysis to understand the underlying mechanism for the field enhancement. Our analysis is therefore relevant not only to optical tweezers, but also to other applications, such as surface modification, nonlinear spectroscopy and near-field optical imaging. To solve Maxwell’s equations in the specific geometry of the tip and its environment, we employ the multiple multipole method (MMP) which recently has been applied to various near-field optical problems [5]. In MMP, electromagnetic fields are represented by a series expansion of known analytical solutions of Maxwell’s equations. To determine the unknown coefficients in the series expansion, boundary conditions are imposed at discrete points on the interfaces between adjacent homogeneous domains. Once the resulting system of equations is solved and the coefficients are determined, the solution is represented by a self-consistent analytical expression. Figure 1 shows our three dimensional MMP simulation of the foremost part of a gold tip (5 nm tip radius) in water for two different monochromatic plane-wave excitations. The wavelength of the illuminating light is l › 810 nm (Ti:sapphire laser), which does not match the surface plasmon resonance. The dielectric constants of tip and water were taken to be « › 224.9 1 1.57i and « › 1.77, respectively [6]. In Fig. 1(a), a plane wave is incident from the bottom with the polarization perpendicular to the tip axis, whereas in Fig. 1( b) the tip is illuminated from the side with the polarization parallel to the tip axis. A striking difference is seen for the two different polarizations: in Fig. 1( b), the intensity

Spherical near-field antenna measurements

Abstract: * Chapter 1: Introduction * Chapter 2: Scattering matrix description of an antenna * Chapter 3: Scattering matrix description of antenna coupling * Chapter 4: Data reduction in spherical near-field measurements * Chapter 5: Measurements * Chapter 6: Error analysis of spherical near-field measurements * Chapter 7: Plane-wave synthesis * Appendix 1: Spherical wave functions, notation and properties * Appendix 2: Rotation of spherical waves * Appendix 3: Translation of spherical waves * Appendix 4: Data processing in antenna measurements * Appendix 5: List of principal symbols and uses

An overview of near-field antenna measurements

Abstract: After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified.