A New Type of Expansion in Radiation Problems
TL;DR: In this article, a new type of expansion of the function of the spherical coordinates of a vector function is developed which can be used to find the vector potential due to a steady current distribution.
Abstract: A new type of expansion of $\frac{\mathrm{i}(1){{e}^{\mathrm{ikr}}}_{12}}{{r}_{12}}$ is developed. Here i is a vector function of the spherical coordinates denoted by 1 and ${r}_{12}$ is the distance between two points denoted by 1 and 2. This expansion is used in the solution of Maxwell's equations and a simple general expression is found for the energy radiated from a known current distribution. A brief application to Dirac's theory of radiation is given. An expansion for $\frac{\mathrm{i}(1)}{{r}_{12}}$ is developed which can be used to find the vector potential due to a steady current distribution.
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TL;DR: In this paper, a unified approach to solve both the elasto-dynamic and elastostatic problems of point sources in a multi-layered half-space by using the Thompson-Haskell propagator matrix technique is presented.
Abstract: SUMMARY A simple and unified approach is presented to solve both the elasto-dynamic and elastostatic problems of point sources in a multi-layered half-space by using the Thompson-Haskell propagator matrix technique. It is shown that the apparent incompatibility between the two is associated with the degeneracy of the dynamic problem when ω = 0 and both can be handled uniformly using the Jordan canonical forms of matrices. We re-derive the propagator matrices for both the dynamic and static cases. We then show that the dynamic propagator matrix and the solution converge to their static counterparts as ω → 0. Satisfactory static deformation can be obtained numerically using the dynamic solution at near-zero frequency.
579 citations
TL;DR: In this paper, the development of near-field optics theory is reviewed and the main results of the application of various practical schemes which all rely on a numerical procedure are discussed from the point of view of their ability to assess evanescent electromagnetic waves.
Abstract: The development of near-field optics theory is reviewed. We first recall that near-field optics is not limited to near-field microscopy. Broadly speaking, it concerns phenomena involving evanescent electromagnetic waves. The importance of such waves was ignored for a long time in optical and surface physics until the emergence of scanning near-field optical microscopes. Taking evanescent waves into account prevents the use of any simple approximation in the set of Maxwell's equations. The various theoretical approaches of near-field optics are discussed from the point of view of their ability to assess evanescent electromagnetic waves. We discuss the main results of the application of the various practical schemes which all rely on a numerical procedure. This review was received in February 1996.
373 citations
TL;DR: In this paper, a new and conceptually simple derivation of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge-current distribution is presented.
Abstract: A new and conceptually simple derivation is presented of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge‐current distribution. The derivation is obtained with the help of a generalized plane wave representation (known also as the angular spectrum representation) of the field. This representation contains both ordinary plane waves, and plane waves that decay exponentially in amplitude as the wave is propagated. The analysis reveals an intimate relationship between the generalized plane wave representation and the multipole expansion of the field and leads to a number of new results. In particular, new expressions are obtained for the electric and magnetic multipole moments in terms of certain components of the spatial Fourier transform of the transverse part of the current distribution. It is shown further that the electromagnetic field at all points outside a sphere that contains the charge‐current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern.
183 citations
01 Mar 1938
TL;DR: In this article, it was shown that readjustment of any existing antenna according to the ideas proposed here will increase the gain by about 1.8 in the case of an end-fire array and two antennas designed to radiate in a horizontal plane.
Abstract: It is shown that in certain types of directional antenna arrays the gain can be increased by arranging so that waves going from the array elements in the direction of maximum transmission are not strictly in phase at large distances. Three examples are given, an end-fire array and two antennas designed to radiate, as far as possible, only in a horizontal plane. In the case of the end-fire array it is shown that readjustment of any existing antenna according to the ideas proposed here will increase the gain by about 1.8. The other two examples correspond to the kind of directivity generally desired in a broadcast antenna. One of these consists of short antennas placed in concentric rings. A typical array of this type containing 22 short antennas with the radius of the outer ring equal to 1.39λ has a gain of 2.31 as compared with 1.56 for a vertical half-wave antenna. The other example of a horizontally radiating array consists of a single ring of short antennas. An example of this type is calculated which has a gain of 2.0 with a total of 23 antennas placed in a circle with a radius of 1.43λ. These figures are not given as the best that can be done, but only as examples.
182 citations
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23 Jun 2014TL;DR: In this article, a theory of frequency-domain electromagnetic scattering by a fixed finite object is presented, and the Stokes tensor tensor is measured in terms of actual optical observables.
Abstract: Preface Acknowledgements 1. Introduction 2. The macroscopic Maxwell equations and monochromatic fields 3. Fundamental homogeneous-medium solutions of the macroscopic Maxwell equations 4. Basic theory of frequency-domain electromagnetic scattering by a fixed finite object 5. Far-field scattering 6. The Foldy equations 7. The Stokes parameters 8. Poynting-Stokes tensor 9. Polychromatic electromagnetic fields 10. Polychromatic scattering by fixed and randomly changing objects 11. Measurement of electromagnetic energy flow 12. Measurement of the Stokes parameters 13. Description of far-field scattering in terms of actual optical observables 14. Electromagnetic scattering by a small random group of sparsely distributed particles 15. Statistically isotropic and mirror-symmetric random particles 16. Numerical computations and laboratory measurements of electromagnetic scattering 17. Far-field observables: qualitative and quantitative traits 18. Electromagnetic scattering by discrete random media: far field 19. Near-field scattering by a sparse discrete random medium: microphysical radiative transfer theory 20. Radiative transfer in plane-parallel particulate media 21. Weak localization 22. Epilogue Appendix A. Dyads and dyadics Appendix B. Free-space dyadic Green's function Appendix C. Euler rotation angles Appendix D. Spherical-wave expansion of a plane wave in the far zone Appendix E. Integration quadrature formulas Appendix F. Wigner d-functions Appendix G. Stationary phase evolution of a double integral Appendix H. Hints and answers to selected problems Appendix I. List of acronyms References Index.
164 citations