Theory of super-directive linear arrays

Abstract

Using data pertaining to the elementary radiator feeding and geometrical arrangement, expediently selected characteristics of ah aerial system are defined, viz. : geometrical gain, geometrical quality and tolerance sensitivity. The geometrical gain gives the gala of an array of isotropic radiators ; the geometrical quality shows how many times less is the band width of the array than that of the elementary radiator ; the tolerance sensitivity is the numerical expression of the extent to which the system is sensitive to current distribution variations. These characteristic properties ate arrived at by making such simplifications in the strict physical definitions as result, on the one hand, in the separation of the properties relevant to the constructional details of the elementary radiator and to those of the aerial system ; on the other hand, in formulas more amenable to mathematical treatment. These simplifications yield a simpler relationship of the three aforementioned quantities. Four of the current distributiong dealt with in the literature ate selected to show on hand of a few concrete examples, the values taken up by the newly introduced constants. Lastly, a generalisation of the solutions is attempted in seeking the current distribution which gives the highest geometrical gain in case of varioug numbers of components anda prescribed geometrical quality. Mathematically, the originaI problem is reduced to ah extremum problem with given auxiliary conditions. I/1. IntroductionFora long time papers have been published dealing with the theory of the so-called "supergain" gr super-directive antennae. Its essence is that with finite dimensions of the antenna any desired gain can be obtained. This end is achieved by means of continuous current distribution, or by the juxtaposition of a sufficient number of discrete radiators. The present paper deals only with the theory of the discrete radiators.SCH~LXU~OFr [2] was the first to take up this problem. He evolved a method for linear equidistant arrays whereby substantial gains ate obtainable, he did, however, not deal with the upper limit of gain in case of a constant number of elements for variable current distributions. He mentions, all the same, that with a marked increase in gain both radiation eff/ciency and band width decrease. DOLP• [3] took up the problem of maximum gain taking for his point of departure the requirements of radar technique and setting himself the task of determining the minimum main beato width at a given side-lobe attenuation. The angular resolving power of the locator depends indeed not on the gain but

Enhanced Directivity From Subwavelength Infrared/Optical Nano-Antennas Loaded With Plasmonic Materials or Metamaterials

“…The power radiation patterns in the spherical coordinate system for any resonance of order excited in the plane (i.e., by a dipole oriented in the direction and placed off axis along ) may be written as (3) where are the associated Legendre polynomials [41]. 2 The spherical harmonic of order n, in fact, interacts with and it is excited by the (n 01)th gradient of the field at the location of the particle [42].…”

“…By inspection you may notice that when isotropic and homogeneous media are considered, or more in general when the sufficient conditions (A.2) are satisfied, the equations lead to an algebraic system independent of space variables, that grants for the resonance the usual conditions for the resonances (A. 3) analogous to (2) but in which the radial permittivities take the place of the corresponding homogeneous values. Notice that the necessary conditions (A.2) are not easily obtainable in the spherical geometry, unless the medium is isotropic.…”

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“…Among those well-established theories and technologies, superdirectivity [20][21][22][23][24] is a huge attraction to the researchers. This concept claims that a small size array can perform as high directivity as a largesize array, while the directivity of the large-size array is achieved by conventional beamforming.…”

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“…In the past decades, the so-called superdirective array [4][5][6][7][8][9] has drawn numerous researchers. It is claimed that a small size array using superdirective beamforming method can perform as high directivity as a large-size array using conventional beamforming, which means that the expensive vast aperture HF receive array can be replaced by a lowcost small array without sacrificing gain.…”