This application is a National Phase application filed under 35 USC § 371 of PCT Application No. PCT/GB2015/050788 with an International filing date of Mar. 18, 2015 which claims priority of GB Patent Application 1413125.4 filed Jul. 24, 2014. Each of these applications is herein incorporated by reference in its entirety for all purposes.
The present invention relates to a lens design method and a radiation source substrate.
Antennas are well-known for communication and radar systems. Antennas act as a transducer between electromagnetic wave propagation in free space and guided electromagnetic wave propagation in transmission lines. It is possible to design antennas to concentrate the radiated electromagnetic energy in a principal direction and conversely receive electromagnetic energy from a principal direction.
The ability of an antenna to concentrate the transmitted energy in a particular direction is commonly known as directivity or gain. It is common to speak of gain as a function of angle or direction which leads to a so-called radiation pattern for a given antenna. The radiation pattern will typically comprise a main beam within which the majority of the electromagnetic energy is concentrated and a plurality of side lobes or minor beams which diminish in energy as the angular separation from the main beam increase.
The far-field radiation pattern, namely the radiation pattern far from the antenna where the wavefronts are substantially planar (and the E and H-field of the electromagnetic field are in phase) is a key design specification when creating an antenna. It is found that a highly directive antenna is usually bulky, heavy and often expensive. In situations where it is required to steer a beam, then phased antenna arrays are often employed, however scanning range is often angularly limited to avoid significant side lobes developing in the radiation pattern. Therefore, it is desirable to tailor a far-field radiation pattern for a given antenna.
In accordance with the present invention as seen from a first aspect there is provided a lens design method for designing a lens to reshape an actual far-field radiation pattern of a radiation source to a preferred far-field radiation pattern, the method comprising:
Advantageously, the method provides for the characterisation of a lens to create a preferred far-field radiation pattern for a given source of electromagnetic radiation.
In an embodiment, the corresponding near-field radiation pattern is derived from the preferred far-field radiation pattern using a mathematical expansion of the electric (E) and magnetic (H) fields, such as a Wilcox expansion. The actual near-field radiation pattern of the radiation source may also be derived from the actual far-field radiation pattern using a similar mathematical expansion of the E and H-fields.
The actual near-field pattern is mapped to the near-field pattern derived from the preferred far-field pattern by satisfying boundary conditions for the E and H-fields, as required by Maxwell's equations. The transfer relationship preferably maps the E and H-field of the actual near-field radiation pattern (EZ, iHZ) to the derived near-field radiation pattern)(E(0)Z, iH(0)Z) and comprises a transfer matrix, comprising tensor values of the required permittivity and permeability of the lens. The transfer relationship preferably comprises:
where εTT/v2=μTT/u2=εTT(0) and εZZ/u2=εZZ/v2=εZZ(0), ε and μ representing the permittivity and permeability respectively, and Φ is the difference in polarisation angle between the respective field components, namely between EZ and E(0)Z, and between Hz and H(0)Z.
In accordance with the present invention as seen from a second aspect, there is provided a lens for reshaping an actual far-field radiation pattern of a radiation source to a preferred far-field radiation pattern, the lens being designed according to the method of the first aspect.
In accordance with the present invention as seen from a third aspect, there is provided a computer program product comprising computer program elements configured to execute the method of the first aspect.
Spiral antennas are widely used in airborne and satellite borne applications such as communications, broadcasting, navigation, remote sensing and globe system positioning due to the wide bandwidth and circular polarization properties of the antenna, which avoid the Faraday rotation effect when radio wave propagates through the ionosphere. In one particular configuration, as illustrated in
The Archimedean spiral antenna, hereinafter referred to simply as spiral antenna, has a bidirectional radiation pattern, whereby radiation generated by the antenna 40 propagates outwardly either side of the plane of the spiral, along an axis of the spiral. The radiation pattern (not shown) comprises two maxima along the axis of the antenna 40, one on each side of the spiral antenna. However, in practice one of them is redundant as only the radiation pattern propagating away from one side of the spiral antenna 40 is used in applications. As such, spiral antennas typically waste useful radiation energy. Moreover, it is found that the redundant radiation pattern often causes interferences to other components of an electronic system (not shown) disposed proximate thereto. These drawbacks are also typical of other forms of antenna, where it is desirable to concentrate or direct the generated radiation along a particular direction.
In an endeavour to improve the efficiency of antennas, including spiral antennas 40, and minimise unwanted interference, antennas are typically mounted within a housing 51, but spaced from a rear wall 51a of the housing 51. So-called cavity backed spiral antennas 50 may comprise absorbing materials or metamaterials (not shown), for example, disposed within the housing 51 between the spiral antenna 40 and the rear wall 51a to minimise interference. However, this does not improve the efficiency of the spiral antenna 40, since half of the radiated energy is simply absorbed within the material (not shown) and wasted, and such cavity backed antennas are often bulky and occupy a significant volume.
In order to capture and use the energy radiated rearwardly of the spiral antenna 40, it is known to mount a perfect electrical conductor (PEC) 52 within the housing at the rear of the spiral antenna 40. The active region of the spiral antenna, namely the radiative zones along the arms 41, 42, is approximately the area circled by one wavelength in perimeter, the length of which varies with frequency. Accordingly, in order to reflect the rearwardly propagating radiation outwardly of the housing 51, the PEC is typically formed into a truncated cone shape 52, as illustrated in
A problem with such PEC cones 52 however, is that the resulting spiral antenna 40 has a poor bandwidth.
In accordance with the present invention as seen from a fourth aspect, there is provided a radiation source substrate for manipulating at least a portion of a radiation pattern of a radiation source, the substrate comprising material parameters which vary within the substrate to create a refractive index gradient for manipulating at least a portion of the radiation generated by the radiation source.
The substrate may comprise a host first material within which is disposed at least one second dispersed material, wherein a density of the at least one second dispersed material varies across the substrate to create the refractive index gradient.
In an embodiment, the substrate comprises a plurality of material parameters which are separated into a plurality of concentrically arranged regions of the substrate, the regions being centred on an axis of the radiation source and comprising a respective material parameter.
In an embodiment, the material parameters of the substrate are determined according to the method of the first aspect.
In accordance with the present invention as seen from a fifth aspect, there is provided a radiation generating arrangement, the arrangement comprising a substrate according to the fourth aspect and a radiation source disposed upon the substrate.
In an embodiment, the radiation source comprises a spiral antenna.
Embodiments of the present invention will now be described by way of example only and with reference to the accompanying drawings, in which:
Referring to
The method comprises determining the preferred far-field radiation pattern of the source at step 110 and then deriving a near-field radiation pattern from the preferred or desired far-field radiation pattern of the source at step 120.
The method 100 subsequently comprises transforming the actual near-field radiation pattern of the source to the derived near-field radiation pattern at step 130 by a transfer relationship that comprises material parameters which characterise the lens, and subsequently determining the material parameters at step 140.
Referring to
The electromagnetic fields in the space surrounding a radiation source, such as an antenna, are known to satisfy the homogenous Hemholtz equation and so the electric and magnetic fields at a distance r from an antenna 20 (as illustrated in
where An and Bn are vector angular functions dependent on the far-field radiation pattern of the antenna, and k=ω(εμ)1/2 is the wavenumber. The series expansions in equation 1 are based on a model where the space surrounding the antenna 20 is divided into an infinite number of concentric, spherical shells 21 of increasing radius, with the antenna located at the centre, as illustrated in
The far-field radiation pattern can be regarded as the asymptotic limits of the above series expansions and can be expressed as:
Equation 2 is the zeroth-order term of a Wilcox expansion, however, it is to be appreciated that other mathematical expansions may be used, for example with a spectral approach, the Weyl expansion may be used. The Wilcox expansion provides a spatial domain analysis, and the boundaries between the various shells are not strictly defined, but taken only as indicators in the asymptotic sense.
The angular vector of the electric field An (and analogously, the magnetic field Bn) can be represented as:
where Xim is the vector spherical harmonic denoted by l, m, η=(μ/ε)1/2 is the wave impedance and aE(l, m) and aM(l, m) are the coefficients of the expansion of the transverse electric and magnetic modes (TEim, TMim), respectively.
The relations illustrated in equation 3 provide for a relationship between the far-field pattern and the entire space surrounding the antenna 20, namely a relationship between the far-field and the near-field. In this respect, the Wilcox series is derived from the multipole expansion and the variation of the angular vector fields An and Bn are directly determinable in terms of the spherical far-field modes of the antenna. Accordingly, the derivation of the near-field radiation patter at step 120 is mathematically described as a series of higher-order TE and TM modes, those modes being uniquely derived by the content of the far-field radiation pattern.
In an embodiment, the derivation of the actual near-field radiation pattern from the actual far-field pattern is obtained at step 121 using a similar method to that at step 110. In an alternative embodiment, the derivation of the actual near-field radiation pattern may be directly determined at step 122 by making suitable measurements. Once the actual near-field radiation pattern is known, the near-field variation of the E and H-field around the antenna is mapped or transformed to the derived near-field radiation pattern (which ultimately generates the preferred far-field radiation pattern) at step 130.
For a 2-dimensional, in-plane electromagnetic wave propagating in the x-y plane, then assuming that the material properties of the lens and the E and H-field parameters are invariant in the z-direction, Maxwell's equations (in Heaviside-Lorentz units) can be expressed as:
∇×(μTT−1·∇×{circumflex over (z)}EZ)=k02εZZ{circumflex over (z)}EZ, ∇×(εTT−1·∇×{circumflex over (z)}HZ)=k02μZZ{circumflex over (z)}HZ (4)
where μTT and εTT are 2×2 symmetric tensors for the transverse permittivity and permeability, respectively and k0 is the wave number in a vacuum. The derived near-field radiation pattern, as represented by the E and H-field parameters (E(0)Z, iH(0)Z) can then be mapped to the actual E and H-field (EZ, iHZ) of the antenna source by a 2×2 transfer matrix relation at step 131, as shown below:
where εTT/v2=μTT/u2=εTT(0) and εZZ/u2=εZZ/v2=εZZ(0), and Φ is as defined above.
Maxwell's equations are still valid on the transformed fields (EZ, iHZ), within any physical medium which satisfies equation 5, namely any lens having a medium which comprises the required variation in permittivity and permeability as specified by the respective tensor matrix.
The near-field radiation pattern comprises a more complicated field pattern compared with the far field pattern owing to the reactive nature of the E and H-field proximate the antenna. In order to sufficiently map the derived near-field radiation pattern to the actual near-field radiation pattern of the antenna, it is beneficial to represent the physical domain across which the mapping occurs, namely the lens 30 (as illustrated in
The material parameters for the lens 30 are determined at step 140 from the calculated values of ε and μ, and thus u and v. The parameters are output as a representative signal to the processor 11 which subsequently interrogates a catalogue of various values of ε and μ and the corresponding material composition stored in the memory at step 141, to determine a material composition of the lens which provides the desired field transformation. The physical dimensions of the lens 30 are then chosen at step 142 depending on the preferred physical requirements of the antenna beam and/or receiving aperture, for example.
Referring to
Referring to
In order to create a substrate 60 which offers a similar performance to the conventional cavity backed antenna 50 illustrated in
The original permittivity and permeability tensors are defined in equation (8) and (9) as:
where I is the unitary matrix.
In the 2D case, equation (7) can be simplified as:
Accordingly, upon substituting equations 8, 9 and 10 into equation 6, the permittivity and permeability tensors of the transformed space can be expressed as:
The geometry of the cavity backed antenna 40 with PEC cone 52 illustrated in
The mapping relationship between the original (x-y) coordinate system and the new coordinate (u, v) system is described in equation (13), where b is constant and a is the compression ratio in v direction.
u=x; v=ay+b (13)
For x∈[−d1,0], a=1 and for x∈[−d3, −d2], a=0.4804. However, when x∈[−d2, −d1], a it is not a constant value, but rather a variable defined by equation (14):
Within a discretized step x∈[xi,xi+1], a can be treated as a constant. Accordingly, the following relations can be set:
Therefore, using equations 10, 11 and 12, the following relations can be derived:
The permittivity and permeability tensor components for the substrate can thus be expressed as:
The permittivity and permeability tensors in the thin flat substrate 60 of the radiation generating arrangement 80 are determined by equation (19)-(24). Since the compression ratio a is not a constant when x∈[−d2,−d1], then for practicality reasons, the spatial variation in material properties of the substrate must be discretized if such a device is fabricated. Accordingly, there is a trade-off between the size of the discretization step and the complexity of fabrication, with a smaller step offering a better correlation in the material parameter (and thus refractive index) profile across the substrate with with the derived spatial profile, and thus an improved performance of the arrangement 80 compared with the conventional cavity backed antenna 50, but an increased manufacturing complexity.
The substrate 60 illustrated in
The performance of the radiation generating arrangement 80 according to the above described embodiment, with the substrate 60 being discretised into ten concentric regions 61a-j, has been shown to be comparable with the conventional cavity backed antenna 50, but comprises only half the thickness. Accordingly, it is evident that the radiation generating arrangement 80 and substrate 60 provides for an improved control and manipulation of radiation patterns.
Number | Date | Country | Kind |
---|---|---|---|
1413125.4 | Jul 2014 | GB | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/GB2015/050788 | 3/18/2015 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
---|---|---|---|
WO2016/012745 | 1/28/2016 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
3755815 | Stangel et al. | Aug 1973 | A |
6335710 | Faulk et al. | Jan 2002 | B1 |
7119739 | Struckman | Oct 2006 | B1 |
7911407 | Fong et al. | Mar 2011 | B1 |
7929147 | Fong | Apr 2011 | B1 |
20040008149 | Killen | Jan 2004 | A1 |
20050030240 | Rawnick et al. | Feb 2005 | A1 |
20070285322 | Nyshadham et al. | Dec 2007 | A1 |
20080238810 | Winsor | Oct 2008 | A1 |
20140320361 | Liu | Oct 2014 | A1 |
Number | Date | Country |
---|---|---|
102694232 | Sep 2012 | CN |
2738878 | Jun 2014 | EP |
2004008570 | Jan 2004 | WO |
2013013467 | Jan 2013 | WO |
Entry |
---|
Wilcox “An Expansion Theorem for Electromagnetic Fields”, Communication on Pure and Applied Mathematics, vol. IX, 115-134, California Institute of Technology, 1956. |
International Search Report and Written Opinion of PCT Application No. PCT/GB2015/050788, dated Jun. 19, 2015, 14 pages. |
Yuya Akatsuchi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Makoto Ohkado, Tsuyoshi Nomura: “Design of a far-infrared lens based on topology optimization”, 10th World Congress on Structural and Multidisciplinary Optimization, May 19, 2013-May 24, 2013, XP002741165, Orlando, FL, Retrieved from: http//ww2.mae.ufl.edu/mdo/Papers/5326.pdf. |
Wei Xiang Jiang Et Al: “Planar reflector antenna design based on gradiant-index metamaterials”, Microwave and Millimeter Wave Technology (ICMMT), 2010 International Conference on, IEEE, Piscataway, NJ, May 8, 2010, pp. 431-433, XP031717221, ISBN: 978-1-4244-5705-2. |
Search Report of Great Britain Application No. GB1413125.4, dated Jan. 9, 2015, 5 pages. |
Number | Date | Country | |
---|---|---|---|
20170162944 A1 | Jun 2017 | US |