Radio-frequency telecommunication hardware

Abstract

an antenna system comprising an antenna configured for radiating over a frequency bandwidth, the antenna having an electrically conducting layer with slot pairs defined in the electrically conducting layer, wherein each of the slot pairs includes a first slot disposed perpendicularly to a second slot, wherein the slot pairs are disposed in a spiral arrangement and are configured to radiate electromagnetic waves, wherein the spiral arrangement is divided into sections, wherein each section includes a group of the slot pairs that are configured to radiate a frequency sub-band of the frequency bandwidth, and wherein the frequency sub-bands are different.

Description

RADIO-FREQUENCY TELECOMMUNICATION HARDWARE Technical Field

[0001] The present invention relates generally to radio-frequency hardware and, in particular, to an antenna system that has a steerable beam. Summary

[0002] Disclosed are antenna arrangements that enable a steerable beam.

[0003] According to a first aspect of the present disclosure, there is provided an antenna system comprising: an antenna configured for radiating over a frequency bandwidth, the antenna having an electrically conducting layer with slot pairs defined in the electrically conducting layer, wherein each of the slot pairs includes a first slot disposed perpendicularly to a second slot, wherein the slot pairs are disposed in a spiral arrangement and are configured to radiate electromagnetic waves, wherein the spiral arrangement is divided into sections, wherein each section includes a group of the slot pairs that are configured to radiate at a frequency sub- band of the frequency bandwidth, and wherein the frequency sub-bands are different.

[0004] Other aspects are also disclosed. Brief Description of the Drawings

[0005] At least one embodiment of the present invention will now be described with reference to the drawings and appendices, in which:

[0006] Fig.1 shows an antenna system according to the present disclosure;

[0007] Fig.2 shows the antenna of the antenna system shown in Fig.1;

[0008] Fig.3 shows a close up of the antenna of Fig.2;

[0009] Figs.4A and 4B show the feed component of the antenna system shown in Fig.1;

[0010] Figs.5A to 5C show another arrangement of the feed component of Figs.4A and 4B to electronically steer the beam of the antenna system of Fig.1; AH25(44380117_1)

[0011] Figs.6A to 6I show results of the antenna system of Fig.1 with a dielectric layer disposed above the antenna system;

[0012] Fig. 7 shows a comparison of the directivity of the antenna system of Fig. 1 with and without synchronising the phases of the electromagnetic fields radiated by the two spirals of the antenna of Fig.1;

[0013] Figs.8A and 8B show a metasurface;

[0014] Figs.9A to 9B and 10A to 10E show a cell used for the metasurface of Figs.8A and 8B;

[0015] Fig.11 shows an illustration of the channels of the cell of Figs.9A to 9B and 10A to 10E;

[0016] Fig.12 shows a first alternative cell used for the metasurface of Figs.8A and 8B;

[0017] Fig.13A shows a second alternative cell used for the metasurface of Figs.8A and 8B;

[0018] Figs.13B and 13C show components of alternative cells used for the metasurface of Figs.8A and 8B;

[0019] Fig.14 shows an antenna system using the metasurface shown in Figs.8A to 13 and the antenna system of Fig.1;

[0020] Figs.15A and 15B show the beam steering and beam null creation / formation of the antenna system of Fig.1 with the feed component of Figs.5A to 5C;

[0021] Figs.16A and 16B show two beam scanning patterns of the antenna system shown in Fig.14;

[0022] Figs.17A and 17B show examples of 2ndorder metasurface;

[0023] Figs.18A and 18B show an antenna system utilising the 2ndorder metasurface of Figs. 17A and 17B; AH25(44380117_1)

[0024] Figs.19A to 19E show the near-field phase distribution generated by the antenna system of Figs.18A and 18B and Fig.19F shows the radiation pattern generated by the antenna system of Figs.18A and 18B;

[0025] Fig.20 shows another antenna system utilising the 2ndorder metasurface of Figs.17A and 17B; and

[0026] Fig.21 shows a flowchart for designing the antenna of Fig.2. Detailed Description

[0027] Where reference is made in any one or more of the accompanying drawings to steps and / or features, which have the same reference numerals, those steps and / or features have for the purposes of this description the same function(s) or operation(s), unless the contrary intention appears. Circularly Polarised Antenna System 100

[0028] Fig.1 shows an antenna system 100 having an antenna 110 and a feed component 130. The antenna 110 will be described in detail hereinafter in relation to Figs.2 and 3. The feed component will be described in detail hereinafter in relation to Figs.4A to 4B and 5A to 5C.

[0029] Fig.1 also shows an attachment component 102 to attach the antenna 110 to the feed component 130. The attachment component 102 shown in Fig.1 has a ring-shaped component disposed on the outer edge of the antenna 110. The ring-shaped component has voids that are configured to receive screws, such that the screws hold the ring-shaped component, the antenna 110, and the feed component 130 together. There are other possible attachment means (e.g., nuts and bolts, glue, etc.) for attaching the antenna 110 to the feed component 130, which will not be discussed hereinafter as a skilled person would understand how to do so. The attachment component 102 should be made from materials that would not affect the radiation pattern of the antenna component 110.

[0030] Fig.2 shows the antenna 110 having an electrically conducting layer 112 with slot pairs 120 defined in the layer 112. The layer 112 is made from an electrically conductive material (such as metal). The layer 112 may also have other shapes such as square, rectangular, and the like. Each of the slot pairs 120 comprises a first slot 122A that is perpendicular to a second slot 122B in the slot pair 120 (see Fig.3). The slots 122A and 122B are designed such that AH25(44380117_1)each slot pair 120 radiates a circularly polarised wave in a particular direction (e.g., broadside). The first and second slots 122A and 122B are voids that are defined in the layer 112. The slot pairs 120 are disposed in a spiral arrangement as shown in Fig.2. Hereinafter, the term “slots 122” refers to all first and second slots 122A and 122B of all slot pairs 120, while the term “slot 122” refers to one of either the first slot 122A or second slot 122B of the slot pairs 120.

[0031] Fig.2 shows that the slot pairs 120 define two spirals 124A and 124B. In another arrangement, the slot pairs 120 may be disposed in one spiral only (e.g., 124A or 124B). In another arrangement, the spirals 124A and 124B may be one continuous spiral. In another arrangement, the slot pairs 120 are disposed in two or more spirals. Antenna 110 can also be made by etching slot pairs 120 on an electrically conducting layer deposited on a dielectric substrate.

[0032] The spirals 124A and 124B shown in Fig.2 are called piecewise or section-wise Archimedean spirals, which are modified Archimedean spirals.

[0033] Fig.2 shows that the spiral 124A has 5 loops where a loop is defined in the polar coordinates (r, φ) as starting from r=xn, φ=0° to r=xn+radial gapn, φ=0°, where x is the starting coordinate of a loop of the spiral 124A, n is the loop number of the spiral 124A, and the radial gap is the distance from the starting coordinate of a loop to the ending coordinate of that loop wherein the distance of a radial gap is between the centre of a slot pair 120 at the starting coordinate and that at the ending coordinate (see Fig.3 for an illustration of the radial gap 128 between the first and second loops of the spiral 124A). Similarly, the spiral 124B has 6 loops defined in the same coordinates (r, φ) as starting from r=yn, φ=0° to r=yn+radial gapn, φ=0°, where y is the starting coordinate of a loop of the spiral 124B, n is the loop number of the spiral 124B, and the radial gap is the distance from the starting coordinate of a loop to the ending coordinate of that loop.

[0034] The piecewise Archimedean spiral is designed using the equation: r = a(i) + b(i) . φ where (r, φ) refer to the polar coordinates of the spiral 124A or 124B, a(i) and b(i) refer to constants, and i refers to a section of the spiral 124A or 124B. In the arrangements shown in Fig.1 to Fig.3, each section is one complete loop of the spiral, but other ways of spiral sectioning are possible. AH25(44380117_1)

[0035] Although the spirals 124A and 124B are shown with 5 and 6 loops respectively, other numbers of loops for each of the spirals 124A and 124B may be used.

[0036] Figs.4A and 4B show a cross-section of the antenna system 100. Fig.4A shows the entire cross-section of the antenna system 100. Fig.4B shows a close-up version of the cross- section shown in Fig.4A.

[0037] Figs.4A and 4B show a terminal 305, a monopole 307, a first waveguide 310, an aperture 317, a second waveguide 315, and absorbers 320. The terminal 305 is configured to receive radio-frequency signals from an external source (not shown) and transmits the received radio-frequency signals to the monopole 307 coupled to and located at the other end of the terminal 305. The monopole 307 is disposed within the first waveguide 310 such that the monopole 307 couples the electromagnetic waves from the terminal 305 to the first waveguide 310. The coupled electromagnetic waves then travel away radially from the location of the monopole 307. The surface of the first waveguide is electrically conductive (e.g., made from metal, a material coated with metal, etc.) to enable propagation of the radially propagating electromagnetic waves toward the aperture 317, which is disposed at the end of the first waveguide 310. The second waveguide 315 is disposed at the other end of the aperture 317, such that the electromagnetic waves from the first waveguide 310 are transmitted to the second waveguide 315 at the aperture 317. The surface of the second waveguide 315 is also electrically conductive (e.g., made from metal, a material coated with metal, etc.). However, one or more of the surfaces of the second waveguide 315 are corrugated such that the one or more surfaces have raised regions 319. The raised regions 319 slow the propagation of electromagnetic waves travelling through the second waveguide 315. Both of the first and second waveguides 310 and 315 are radial waveguides that are connected to each other via the aperture 317. Although only one aperture 317 is shown, more than one aperture 317 can be used to couple the first waveguide 310 to the second waveguide 315.

[0038] The second waveguide 315 then couples to the slot pairs 120, such that as the electromagnetic waves radially propagating in the second waveguide 315 cross each loop of the spiral 124A or 124B, a portion of the energy radiates through the slot pairs 120. When the electromagnetic waves reach the ends of the second waveguide 315, these electromagnetic waves are absorbed by the absorbers 320, which are located at the inner end and outer end of the second waveguide 315. In one arrangement, each of the absorbers 320 is formed by layers of absorbers. AH25(44380117_1)

[0039] To electronically steer the beam radiated by the antenna 110, a plurality of monopoles 307 with a particular configuration is used in the feed component 130. Figs.5A to 5C show a monopole arrangement having one central monopole 307A with four monopoles 307B to 307E disposed at a concentric circle surrounding the central monopole. The four monopoles 307B to 307E are also spaced equally along the concentric circle. In another arrangement, the number of monopoles and associated terminals may be more or less than described above. In another arrangement, the central terminal and monopole shown in Figs.5A to 5C are removed and a dielectric or metal passive cylinder is inserted, which is found to provide less mutual coupling between the monopoles and terminals.

[0040] In one arrangement, when transmitting electromagnetic waves from the monopoles 307A to 307E to the antenna 110 via the waveguides 310 and 315, the respective terminals 305 provided radio-frequency signals of different amplitudes and phases to the respective monopoles 307. The varying amplitudes and phases to the different monopoles 307A to 307E create a beam null(s) / minima in specific directions, effectively steering null(s) electronically within a small solid angle at specific directions by changing the amplitudes and phases. In another arrangement, the varying amplitudes and phases of the radio-frequency signals to the different monopoles 307 create a beam peak in a specific direction, effectively steering the beam peak electronically within a small solid angle at specific directions by changing the amplitudes and phases of the radio-frequency signals. Changes to the phases and amplitudes of the electromagnetic waves provided to the multiple terminals 305 change the two- dimensional electromagnetic field distribution within the radial waveguides 310 and 315. This in turn change the radiation characteristics of the antenna 110 including its radiation pattern, beam peak direction, direction of any pattern nulls, antenna directivity, antenna gain, pattern beamwidth, side-lobe level, and cross-polarisation level.

[0041] When the antenna system is in the transmitting mode, the input to the antenna system 100 is split into multiple radio-frequency channels and each channel is passed through a phase shifter and, where required, a variable attenuator / amplifier before providing each channel to each terminal 305. This way, RF electromagnetic waves with appropriate amplitudes and phases are applied to each terminal 305 to steer the transmitting beam electronically within a relatively small solid angle, to create beam peaks(s) / maxima and / or null(s) / minima in specific directions, or to steer beam peak(s) or null(s) electronically within a relatively small solid angle.

[0042] Changes to the phases and amplitudes of the electromagnetic waves input at multiple terminals 305 change the two-dimensional electromagnetic field distribution within the radial waveguides 310 and 315. This, in turn, change the radiation characteristics of the antenna 110 AH25(44380117_1)including its radiation pattern, beam peak direction, direction of any pattern nulls, antenna directivity, antenna gain, pattern beamwidth, side-lobe level, and cross-polarisation level.

[0043] When receiving electromagnetic waves at the antenna 110, appropriate amplitudes and phases are applied to the received electromagnetic waves at the terminals 305. The received electromagnetic waves are then combined at the output of the terminals 305. The amplitudes and phases applied at the terminals 305 steer the main receiving beam electronically within a small solid angle, create a receiving beam nulls / minima in specific directions, or create and steer the null(s) of the receiving beam electronically within a small solid angle (null steering). This effectively changes the radiation characterises of the receiving antenna 110 including its radiation pattern, beam peak direction, direction of any pattern nulls, antenna directivity, antenna gain, pattern beamwidth, side-lobe level, and cross-polarisation level.

[0044] When the antenna system 100 is in the receiving mode, each output of each terminal 305 in multiple radio-frequency channels is passed through a variable phase shifter and, where required, a variable attenuator / amplifier. This way, appropriate amplitudes and phases are applied to the electromagnetic waves coming out of the terminals 305. The outputs of the terminals 305 are then combined to form one output, to steer the receiving beam electronically within a relatively small solid angle, to create beam peaks(s) / maxima and / or null(s) / minima in specific directions, or to steer beam peak(s) or null(s) electronically within a relatively small solid angle (null steering). This effectively changes the radiation characterises of the receiving antenna system including its radiation pattern, beam peak direction, direction of any pattern nulls, antenna directivity, antenna gain, pattern beamwidth, side-lobe level, and cross- polarisation level.

[0045] Fig.15A illustrates electronic beam steering of a 4-monopole feed arrangement (similar to the monopoles 307B to 307E shown in Figs.5A to 5C, but without the monopole 307A). Monopoles 307D and 307E are along the x-axis and monopoles 307B and 307C are along the y-axis. The electromagnetic waves applied to monopoles 307B and 307E are phase-shifted by the same amount relative to reference phase of the electromagnetic waves applied to monopoles 307C and 307D, which have the same phase of 0 reference. When the phase shift of monopoles 307B and 307E is 00, the antenna system beam is almost along broadside as shown by the solid line. When the phase shift of monopoles 307B and 307E is 900, the beam steers to approximately 10zenith angle as shown by the dotted line. When the phase shift of monopoles 307B and 307E is 1800, the beam has a null very close to the broadside direction, as shown by the broken line. For other values of phase shift, other patterns with different beam peaks or nulls result. The directions of beam peaks or nulls are changed by changing the phase AH25(44380117_1)shift. If variable attenuators or variable-gain amplifiers are provided in addition to variable phase shifters, more electronic control of the radiation pattern parameters including beamwidth is possible through amplitude weighting.

[0046] In one alternative arrangement, phase shifting and amplitude weighting is applied to the channel corresponding to each terminal 305 at the digital level. When the antenna system 100 is in the receiving mode, each channel includes an analog-to-digital converter and a digital phase shifter that is implemented in digital signal-processing hardware or software. Additionally, each channel may include a RF receiver, one or more amplifiers, one or more filters, a mixer, and / or an RF-to-IF converter between the terminal and the analog-to-digital converter. When the antenna system 100 is in the transmitting mode, each channel includes a digital-to-analog converter and a digital phase shifter that is implemented in digital signal-processing hardware or software. Additionally, each channel may include a RF transmitter, one or more amplifiers, one or more filters, a mixer, and / or an IF-to-RF converter between the digital-to-analog converter and the terminal.

[0047] In one alternative arrangement, when the antenna system 100 is in the receiving mode, output of each of the terminals 305 are applied to an amplitude detector or power detector followed by an analog-to-digital converter and digital hardware or software / firmware. Additionally, each channel may include an RF receiver, one or more amplifiers, one or more filters, a mixer, and / or an RF-to-IF converter between the terminal and amplitude detector. Each channel produces a digital value that represents the amplitude of the signal received by the beam corresponding to that terminal at that instant in time. By comparing these numbers, the digital sub-system (hardware, firmware and / or software) determines extremely quickly and precisely the instantaneous direction (in polar or rectangular coordinates) of any radio- frequency source that is emitting the received signals, for example a non-geostationary satellite such as a CubeSat or other low-earth-orbit (LEO) satellite, or a moving drone, for example for tracking purposes.

[0048] Other monopole arrangements with varying numbers and configurations are also possible. Similar to the discussion above, for transmission, the amplitudes and phases of the radio-frequency signals provided to the terminals 305 are varied to change the beam or null direction of the antenna 110. In the receiving mode, different amplitudes and phases are applied at the terminals 305 to change the beam or null direction of the antenna 110.

[0049] In the arrangement shown in Fig.5C, the centre conducting monopole 307A is extended as a probe to couple its field to the first waveguide 310 and launch the AH25(44380117_1)electromagnetic waves in the first waveguide 310. The top part of one or multiple monopoles 307A to 307E may be enlarged as shown in Fig.5C to improve impedance matching with less reflections at the input(s). Other types of coupling arrangements are also possible, e.g. microstrip, suspended strip. In an alternative arrangement, the centre terminal 305 and the centre monopole 307A in the five-terminal antenna arrangement is replaced by a cylinder made out of conducting or dielectric or other material to reduce the mutual coupling between the remaining four monopoles 307B to 307E.

[0050] The feed component 130 has been described above for transmission of electromagnetic waves. The feed component 130 can also receive electromagnetic waves. The reverse operation of that described above occurs when the feed component 130 receives electromagnetic waves at the antenna 110.

[0051] In another arrangement for electronic steering, each of the monopoles 307A to 307E provide a particular radiation pattern at the output of the antenna system 100. Selecting one of the monopoles 307A to 307E selects one of the radiation pattern outputs at the antenna system 100. Fig.15B shows a radiation pattern produced by the central monopole 307A (shown in Figs. 5A to 5C) on φ = 00cut plane by the solid line. As can be seen, the beam is pointing very close to broadside, i.e. θ = 00direction. The radiation pattern produced by the monopole 307D on the same φ = 00cut plane is shown by the broken line. This beam points towards θ = 2.60direction. The radiation pattern produced by the monopole 307E on the same φ = 00cut plane is shown by the dotted line. This beam points towards θ = -2.60direction. The antenna system beam can be electronically changed rapidly between the three beams using an electronic switch attached to the respective terminals 305 of the five monopoles 307A to 307E and selecting one of these three terminals 305 for transmission or reception. The other two monopoles 307B and 307C are along the y-axis and therefore not on the φ = 00plane, so the monopoles 307B and 307C do not produce significant radiation on this plane cut, but the monopoles 307B and 307C produce significant radiation on the φ = 900cut plane. The beam on the φ = 900cut plane can be changed by switching between the respective terminals 305 of the monopoles 307A, 307B, and 307C. On other cut planes such as φ = 450, beam can be electronically changed by selecting one out of all 5 terminals 305. The reason for this beam direction change is each terminal 305 produces a different phase distribution in the waveguide(s) 315 that has radiating slots. Thus, each terminal 305 excites the radiating slots with different phases.

[0052] The above electronic beam steering is a discrete selection between a few available radiation patterns. In an alternative arrangement (discussed previously), electronic beam AH25(44380117_1)steering is achieved continuously using (variable) phase shifters, (variable) attenuators, and (variable) gain amplifiers connected to the terminals 305. Design of Antenna 110

[0053] Discussion now turns to the design of the antenna 110. A slot is a known antenna element and the design of which is not covered in the present disclosure as a skilled person would understand how to do so. Further, although rectangular slots are shown in Figs.1 to 3, other shapes may be used. A method 2100 of designing the antenna 110 is shown in Fig.21. The method 2100 commences at step 2110 by determining an initial spiral for the design of the spiral 124A or 124B. The initial spiral may be an Archimedean spiral. Other spirals may also be used for the initial spiral. As described hereinbefore, the spiral used in the present disclosure is a piecewise Archimedean spiral based on the equation: r = a(i) + b(i) . φ, where i refers to a section of the spiral 124A or 124B and b(i) is the radial advance of the spiral per one degree of advance of φ. The shape of the initial spiral can be determined once the number of sections per loop is determined at step 2120. The parameter b(i) = radial_gapn / 360 where radial_gapn is the radial gap (in degrees) of the nthloop to which the ithsection belongs to. Although in general it is possible to change b(i) from section to section even within one loop, here it is changed from loop to loop for convenience. The initial radial gap is determined hereinafter in step 2140.

[0054] The method 2100 then proceeds from step 2110 to step 2120.

[0055] In step 2120, the initial spiral is divided into sections. The initial spiral is divided into arbitrary sections, where each section is designed to radiate optimally at a particular frequency sub-band of the overall frequency bandwidth of the spiral 124A (or 124B). For example, if the spiral 124A is intended to operate with a frequency bandwidth of 10.65 GHz to 12.75 GHz (i.e., 2.1 GHz frequency bandwidth), then the frequency bandwidth is divided into frequency sub- bands (e.g., 3 to 30) corresponding to the number of sections. In one example, 11 frequency sub-bands are used for a 2.1 GHz bandwidth from 10.65 to 12.75 GHz. The 11 frequency sub- bands may be centred along the frequencies of 10.7, 10.9, 11.1, 11.3,11.7, 11.9,12.0,12.1, 12.3, 12.5 and 12.7 GHz. These 11 frequencies are then the design frequencies for the respective sections of the initial spiral. According to this example, the first section has slot pairs 120 designed to operate in a particular frequency sub-band (i.e., 11.9 GHz for this example) for that section. AH25(44380117_1)

[0056] Each section may be a quarter of a loop, half of a loop, other fraction of a loop, one loop, or multiple loops of the initial spiral.

[0057] The fraction of power radiated by the antenna 110 is determined by the frequency of the propagating electromagnetic waves and the dimensions of the slots 122. The length of the slots 122 in a specific section of the spiral 124A or 124B is designed to radiate well at a specific frequency sub-band that is within a wide operating frequency band of the antenna 110. The lengths of the slots 122 in different sections are different in general, as those different sections are designed in general to operate in different frequency sub-bands. Two subsections in the same spiral may be tuned to the same sub-band e.g. loop 6 and loop 8 in Spiral B in Table 1 below. The sections as a whole are designed to cover the entire operating frequency bandwidth of the antenna 110. Therefore, the lengths of the slots 122 are changed from section to section to radiate optimally at different frequency sub-bands, to cover the entire range of operating frequencies as opposed to one design frequency. Accordingly, the lengths of the slots 122 are either increased or decreased from section to section as an abrupt or step change, as opposed to changing continuously from one slot pair 120 to the adjacent slot pair 120. The operating bandwidth of the antenna 110 is divided into a several (e.g., 3-30) narrower frequency sub- bands. Each section is intended to radiate optimally in one of these frequency sub-bands (but will also radiate less efficiently in other sub-bands).

[0058] As discussed in step 2110, the piecewise Archimedean spiral is designed using the determined number of sections. Once the number of sections is determined in step 2120, the number of sections is used to determine the shape of the spiral 124A or 124B using the equation provided in step 2110.

[0059] The method 2100 then proceeds from step 2120 to step 2130.

[0060] In step 2130, the slots 122 for each section are designed according to the frequency sub-band for the respective section. The difference between radial (r) coordinates of the two slot pairs in each section is set initially to quarter of the guided wavelength of the wave in the waveguide at the centre frequency of the section sub-band. The method 2100 then proceeds from step 2130 to step 2140.

[0061] In step 2140, initial radial gaps of the initial spiral are determined. The radial gaps affect the radiation beam of the antenna 110. Amending the radial gaps of the loops of the spiral synchronizes the phases of the beams radiated by the different sections, enabling a wider operating bandwidth of the overall antenna 110. Although the slot pairs 120 of each section in AH25(44380117_1)the initial spiral are designed to radiate optimally in one frequency sub-band (referred to as the first frequency sub-band for ease of reference) within a wide operating bandwidth, slightly longer or shorter slots 122 in other sections also radiate reasonably well at the first frequency sub-band and their radiation interfere with the radiation from the section that is specifically designed for the first frequency sub-band. Accordingly, initial radial gap is changed from loop to loop to make the radiation from multiple sections at each considered frequency point (within the wide operating band) approximately in phase. Several such frequency points within the operating band are considered, depending on the target bandwidth of the antenna and design complexity, for example 10 – 20 frequency points. The initial radial gap of a loop is determined by determining the design frequency (which can be an average of the centre frequency points of the sections in the loop) and setting the initial radial gap to be one guided wavelength of that design frequency.

[0062] In one example, a loop in the spiral 124A has 4 sections operating in frequency sub- bands with centre points of 11, 11.25, 11.5, and 11.75 GHz. The design frequency is determined as the average of the centre frequency points, which is 11.375 GHz. The initial radial gap for this loop is therefore one guided wavelength of this design frequency.

[0063] The method 2100 concludes at the conclusion of step 2140. The method 2100 is repeated for designing multiple spirals.

[0064] Once the spiral 124A is designed, then the design (using the method 2100) can be expanded to include an additional spiral 124B. When both the spirals 124A and 124B are placed in proximity to each other (as shown in Fig.2), then there is radiation interference from each other and the radiation from all spirals 124A and 124B need to be synchronised. In other words, the radiation from the spirals 124A and 124B is made to be at least approximately in- phase over the entire operating band in the desired direction of the main beam. To synchronize the radiation beams of two spirals 124A and 124B, either the spiral 124A or 124B is shifted inward or outward. The shift is performed by modifying the starting position (i.e., xn or yn) of either the spiral 124A or 124B by a certain value. As described hereinbefore, a loop of the spiral 124A is defined in the polar coordinates (r, φ) as starting from r=xn, φ=0° to r=xn+radial gapn, φ=0°. The shift alters the equations to starting from r=xn + shift, φ=0° to r= (xn+shift) +radial gapn, φ=0°, where shift is either a positive value (for outward shift) or a negative value (for inward shift). Similar shift can be performed to the spiral 124B. AH25(44380117_1)

[0065] When synchronizing the radiation beams of the spiral 124A and 124B, it may be possible to shift (inward or outward) the spiral 124A or 124B, or to shift (inward or outward) both the spiral 124A and 124B.

[0066] Once the spirals 124A and 124B are synchronized, the length of the slots 122 in each section (which has been set approximately to radiate optimally in its frequency sub-band) and the radial gaps 128 of the spirals 124A and 124B are iteratively adjusted until the desired antenna performance such as the gain, directivity, radiation efficiency, VSWR, and the like is achieved over the desired wide bandwidth for the whole antenna 110. If only one spiral 124A or 124B is used in the design, the iterative adjustment of the lengths of the slots 122 and the radial gaps 128 is also performed to optimize the gain, directivity, radiation efficiency, VSWR, and the like of the spiral 124A or 124B.

[0067] When two or more spirals 124A and 124B are used, the radiation phases of the spirals 124A and 124B need to be re-synchronized by shifting (inward or outward) of the spiral 124A or 124B after each iteration of the slot lengths and radial gaps. This process is repeated until the desired parameters of the antenna 110 are achieved.

[0068] The antenna design process described above does not follow an analytical formula for the slot length variation or a “coupling factor” that is determined only at one frequency. Advantageously, the above described wideband design method leads to a wide frequency bandwidth of operation of the antenna system 110 with high gain, high directivity, high radiation efficiency, low reflections at the input terminal, and good axial ratio over said wide frequency bandwidth.

[0069] The following is an example describing the design of the spirals 124A and 124B (once each spiral has been designed using the method 2100) with a beam direction toward the broadside (i.e., φ= 0, θ = 0 in spherical coordinates), where φ refers to the same angle as the polar coordinates discussed above and θ is the elevation angle from the plane of the antenna 100. First, the phase of the co-polar radiation (e.g., right hand circular polarization (RHCP)) of the spiral 124A is determined. Such a determination may be performed using simulation software. If other antennae are present, then the radiation produced by other antennae are simulated to be absorbed. The phase of the spiral 124A is determined at a far location along the main beam direction at many sample frequency points (say 10 – 100 frequency points) within the operating bandwidth. The same process is performed for the spiral 124B at the same far-field location. From the phase of each of the spirals 124A and 124B at the far location, the AH25(44380117_1)phase difference between the radiation of the spirals 124A and 124B at each sample frequency point within the antenna operating band is determined.

[0070] The phase of the radiation of the spiral 124A or 124B is changed by shifting the entire spiral (i.e., either 124A or 124B) radially outward or inward. For example, when the wave propagation in the second waveguide 315 is inward (i.e., from the aperture 317 toward the centre of the antenna 110), the phase of the radiation produced by slot pairs 120 coupled to the second waveguide 315 is increased by an amount P degrees by shifting all slot pairs 120 in the spiral 124A or 124B outward by an amount that is equal to (P / 360) x Lambda_g where Lambda_g is the guided wavelength at that specific sample frequency. P can be positive or negative. A negative P means decreasing the phase of radiation from the spiral 124A or 124 and this is achieved by shifting the entire slot pairs 120 in an inward-travelling waveguide inward (i.e., by decreasing by (|P| / 360) x Lambda_g the r-coordinates of all slot pairs 120 in that spiral 124A or 124B where |P| denotes the absolute value of P). For waves travelling outwards in the second waveguide 315 (i.e., from the aperture 317 toward the edge of the antenna 110), the opposite is true, so the r-coordinates of all slot pairs 120 in the spiral 124A or 124B are increased by (|P| / 360) x Lambda_g when P is negative.

[0071] In summary, the design of antenna 110 includes designing the spiral 124A alone and then 124B alone. The phase difference or phase error Ph_error(f) = Ph_124B(f)-Ph_124A(f) at all frequency points is then determined, where Ph_error(f) is the phase difference or phase error, Ph_124B(f) is the phase of the spiral 124B radiation at different frequencies f, and Ph_124A(f) is the phase of the spiral 124A radiation at different frequencies f. To synchronise the two spirals 124 and 124B, or to make the phase error zero, Ph_124A is increased or Ph_124B is decreased by Ph_error by shifting the spiral 124A or 124B.

[0072] When determining the shifts of spiral 124A or 124B or both, it is possible to aim to maximise a selected antenna performance figure (e.g., gain, directivity) at a specific frequency, or to improve a selected antenna performance figure over a specific frequency band. For example, if maximum directivity improvement is to be achieved at a specific frequency, say f=12.7 GHz, then the spiral 124A or 124B is shifted by the value that is required to make the radiation of the two spirals exactly in phase at 12.7 GHz, which is S(12.7) = 2.5mm as shown in Table 2 below. On the other hand, if overall directivity improvement across a specific frequency band is to be achieved, then several frequency points are selected within that band, the shift required to make the radiation in-phase at each of those frequency points is determined individually as described in previous paragraphs, and an averaged (e.g. simple average, mean, or a weighted average) value of those is selected for the shift. In the example shown in Table 2, AH25(44380117_1)an average shift value of 1.5mm is required to synchronize the two spirals across the whole band.AH25(44380117_1)Table 2

[0073] The directivity of the antenna 110 having the spirals 124A and 124B before and after spiral synchronisation are compared across the operating bandwidth of 10.7-12.7 GHz (shown in Fig.7). In this example, synchronisation was applied to maximise the directivity at a specific frequency of 12.7 GHz due to the low directivity around that frequency. Fig.7 shows the directivity before synchronisation in dotted line, and the directivity after radiation synchronisation by spiral shifting is shown in continuous line.

[0074] Table 1 below shows the design of the spirals 124A and 124B, wheren the spiral 124A has 6 loops and the spiral 124B has 9 loops. For each spiral 124A and 124B, each section is one loop and accordingly the value of n indicating the loop number corresponds to the section number. The loops in each spiral are counted starting from the spiral end that is closer to the aperture 317. In Spial 124A n=1 loop in the largest loop and in Spiral 124B n=1 loop is the smallest. The width of all slots is 2mm.AH25(44380117_1)Table 1

[0075] To reduce the variation of gain of the antenna 110 across the operating frequency band, a layer of dielectric is placed above the antenna 110. The distance between the antenna 110 and the dielectric layer is referred to as an air gap. The dielectric layer thickness, dielectric constant, and the air gap are varied in an iterative manner to achieve high antenna gain with very little variation, as well as the required axial ratio, over the operating frequency bandwidth.

[0076] The air gap can be filled with vacuum or with dielectrics such as foam, artificial dielectric with an effective dielectric constant, and the like. In one arrangement, the air gap is zero. In another arrangement, an artificial dielectric is placed in the air gap where the artificial dielectric is made from small sections (that are smaller than the wavelength of the maximum AH25(44380117_1)operating frequency band) of different dielectric materials using methods such as 3D printing / additive manufacturing.

[0077] Fig.6A show the realised gain of the antenna system 100 in continuous lines with triangles. When the dielectric layer (with a thickness of 2mm and dielectric constant of 2.32) is disposed above the antenna 110, the realised gain of the antenna system 100 is shown in continuous line in Fig.6A. When a dielectric layer with a thickness of 1.6mm and dielectric constant of 2.32 is used, the realised gain of the antenna system 100 is shown in dotted lines. As can be seen, the realised gain of the antenna system 100 is improved in the mid-band frequencies (i.e., from 11.3 GHz to 12.4 GHz) when the dielectric layer is used.

[0078] Fig.6B shows the realised gain of the antenna system 100 with the 2mm dielectric layer. Fig.6C shows the antenna gain (IEEE) of the antenna system 100 with the 2mm dielectric layer. Fig.6D shows the axial ratio versus frequency of the antenna system 100 with the 2mm dielectric layer. Fig.6E shows the polarisation discrimination (i.e., the difference between the Right-Hand circular polarisation (RHCP) gain and the Left-Hand circular polarisation (LHCP) cross-polar gain in the broadside direction) of the antenna system 100 with the 2mm dielectric layer. Fig.6F shows the input reflection coefficient at the terminal 305 of the antenna system 100 with the 2mm dielectric layer. Fig.6G shows the voltage standing wave ratio (VSWR) at the terminal 305 of the antenna system 100 with the 2mm dielectric layer. Fig. 6H shows the normalised radiation patterns at φ =0° at frequencies of 10.7 GHz, 11.7 GHz, and 12.7 GHz. Fig.6I shows the normalised radiation patterns at φ =90° at frequencies of 10.7 GHz, 11.7 GHz, and 12.7 GHz.

[0079] Figs.8A and 8B show a 1storder metasurface 1000 having cells 900. Fig.8A show the top view of the metasurface 1000, while Fig.8B show a perspective view of the metasurface 1000. The metasurface 1000 shown in Fig.8A and 8B has a square shape. It is possible to make metasurfaces of other shapes such as rectangular, circular, oval, hexagonal or octagonal. Each cell 900 is a phase-shifting cell that converts one type of circular polarisation to another type (e.g., LHCP to RHCP or RHCP to LHCP). The cell 900 (and alternative arrangements of cell 900) will be described hereinafter in relation to Figs.9A to 9B to 13. The cells 900 are disposed adjacent to other cells 900 to form the metasurface 1000.

[0080] Each cell 900 is configured to receive electromagnetic waves on one end (e.g., the top) of the cell 900, converts the polarisation, and transmit the electromagnetic waves with converted polarisation on the other end (e.g., the bottom) of the cell 900. The cells 900 as shown in Fig. AH25(44380117_1)9A is a square and, as shown in Fig.8A, is arranged in a square lattice to form the metasurface 1000. However, it is possible to form other 2D arrangements, such as hexagonal or triangle.

[0081] When the cell 900 is rotated by X degrees, the resulting conversion in the phase shift of the electromagnetic field transmitting through the cell 900 is 2X degrees. For example, the metasurface 1000 has identical cells 900 in the y-direction so each cell 900 in the y-direction produces the same phase shift. Along the x-direction, each cell 900 is rotated by 30 degrees relative to the previous cell 900. This produces an approximately linear transmission phase gradient in the x-direction, that is 60 degrees per metasurface period, which is close to half a wavelength at the centre frequency of the operating band. For the operating band centre frequency of 11.7 GHz (per the example shown in Fig.7), the half wavelength is 12.8mm and length of the cell (per the example shown in Fig.7) and the metasurface period are 11.2mm. The metasurface 1000 is a 1storder metasurface because its transmission phase shift varies approximately linearly in a particular direction, in this example in the x-direction.

[0082] The main beam direction of any antenna can be tilted by placing the metasurface 1000 of linear transmission phase gradient (also known as 1st order transmission phase metasurface) above the antenna. For example, the zenith angle (θ) of the beam is changed by the metasurface 1000. By rotating the metasurface 1000 about its axis, the azimuth angle (φ) of the beam is also changed dynamically to any angle (i.e., 0 – 360 degrees). This is known as 1D beam steering.

[0083] Fig.14 shows two metasurfaces 1000A and 1000B disposed above the antenna system 100. When each of the two metasurfaces 1000A and 1000B is rotated around its axis of rotation, both the zenith angle (θ) and the azimuth angle (φ) of the beam of the antenna 100 is changed dynamically. Although the antenna system 100 is shown in Fig.14, other antenna systems radiating circularly polarised electromagnetic waves may be used instead of the antenna system 100.

[0084] By placing two metasurfaces 1000A and 1000B in close proximity with each other and above the antenna system 100, the tilt of the beam (the zenith angle (θ)) can be increased or decreased depending on the orientation of the second metasurface 1000B relative to the first metasurface 1000A. By rotating the two metasurfaces 1000A and 1000B independently, the main beam direction can be changed in both spherical coordinate directions (i.e., azimuth and zenith angles). The zenith (θ) angle of the main beam can be changed over a wide range for example between -60 to +60 degrees whereas the azimuth (φ) angle of the main beam can be changed over the entire 0 to 360 degree range. The arrangement shown in Fig.14 is known as AH25(44380117_1)2D beam steering or complete beam steering. The arrangement shown in Fig.14 only requires the metasurfaces 1000A and 1000B to be rotated to steer the beam, while the base antenna (e.g., 100) as well as its RF terminal connection are completely stationary.

[0085] In one example, each of the two metasurfaces 1000 is continuously rotated rapidly but at two different speeds, the resulting antenna beam scans a large field-of-view (e.g., with an apex angle of 1200) rapidly. These metasurfaces 1000 require small motors with low power consumption for rotation. Due to the low power consumption, this method provides a means to scan a large volume of RF sources in a large field of view and automatically determine the directions of those RF sources. Example applications of this arrangement are remote sensing, navigation, and “Signals of Opportunity” applications.

[0086] In an alternative arrangement, one of the metasurfaces 1000A or 1000B includes phase correction. Such a phase correction means that the metasurfaces 1000A or 1000B is no longer a first-order metasurface.

[0087] Figs.16A and 16B show two different scanning patterns for the arrangement shown in Fig.14.

[0088] For simplicity, let us assume that the two metasurfaces 1000A and 1000B are identical, each metasurface 1000A or 1000B has a linear phase gradient ofOne metasurface 1000A rotates at a constant speed of ^1rad / s and the other metasurface 1000B at ^2, both start rotating at the same time t=0 and the two metasurfaces 1000A and 1000B are aligned when the rotation starts. ^1and ^2can be positive or negative. Then the angular position of the first metasurface 1000A at time t is ^1t radians and the second metasurface 1000B is ^2t. The zenith angle of the beam of this antenna system at time t is given byand the azimuth angle of the beam of this antenna system at time t is given by ^^^^^^^^(^^) = tan−1[(^^^^^^^^1^^ + ^^^^^^^^2^^) / (^^^^^^^^1^^ + ^^^^^^^^2^^) ]

[0089] Fig.16A shows the scanning pattern (^^^^^^^^(^^) in solid line, ^^^^^^^^(^^)in dotted line) versus time over a 1 second period for a radio-frequency scanning system operating at 11.7 GHz with the following parameters: ^ = 0.5236 deg. / cm; rotation speed of the metasurface 1000B (i.e., AH25(44380117_1)the one with the slower speed) = 3600 / s; rotation speed of the metasurface 1000A (i.e., the one with the faster speed) = 7200 / s. The horizontal axis in Fig.16A is time in seconds. The entire field of view comprising zenith angles from -250to +250and azimuth angles from 00to 3600are scanned in about one second.

[0090] Fig.16B shows an alternate scanning pattern in which the zenith angle changes faster than the azimuth angle of the beam. Many other scanning patterns are possible by changing the parameters in the system.

[0091] In addition to steering the beam of the antenna system or a null in its radiation pattern over a very large angle range by mechanically rotating the metasurfaces, which is relatively slower, the beam of the antenna system or a null in the radiation pattern can be steered electronically much faster over a relatively smaller angle range using a base antenna with multiple input or output terminals and following the terminal switching method, variable phase shifter method or digital beam steering method disclosed previously. Such hybrid mechanical / electronic beam steering has the advantages of low power consumption due to low power consumption of mechanical rotation when compared with fully electronically steered phased arrays with similar antenna gains, which require a large number of (e.g., a few thousands) of phase shifters, amplifiers and up / down converters. When compared with fully mechanical beam steering, hybrid method has the capability to correct the beam peak or beam null direction extremely quickly (using only a few electronic or digital phase shifters / switches).

[0092] Using the cell 1200 with variable phase shifters, 1D or 2D beam steering can be achieved with only one metasurface 1000A or 1000B, and without any mechanical rotation, tilting or any other mechanical movement. This is achieved by varying the phase shifts of the variable phase shifters in each cell 1200 to achieve the required two-dimensional phase distribution at the output plane of the metasurface 1000. For example, an equal additional phase shifts of Pintra degrees applied to both channels C1 and C2 of the cell 1200 directly advance the phase of the output field of that cell 1200 by the same amount Pintra degrees. When using these cells, the sequential rotation of cells in metasurface 1000, 1000A or 1000B is not required because the transmission phase shift provided by cell rotation can also be provided by the intra-cell phase shifters. A special case of metasurface 1000 that has no cell rotation and zero phase gradient can be used. In addition to the beam direction, other characteristics of the radiation pattern including the beam shape can be changed and optimised due to the additional flexibility and degree of freedom offered by variable intra-cell phase shifters. Such beam steering and beam shaping can be achieved dynamically and extremely rapidly due to high speed of electronics compared to relatively slower mechanics. AH25(44380117_1)

[0093] Using the cells 1200 with variable phase shifters as well as variable amplifiers and / or variable attenuators, the two-dimensional amplitude distribution of the near field at the output plane of the metasurface 1000 can also be changed in addition to the phase distribution at this plane, enabling one to synthesize almost any beam shape, beam direction, beam nulls, etc. The sequential rotation of cells in metasurface 1000, 1000A or 1000B is not required because the transmission phase shift provided by cell rotation can also be provided by the intra-cell phase shifters. A special case of metasurface 1000 that has no cell rotation and zero phase gradient can be used. I

[0094] Fig.9A shows one arrangement of a cell 900. The cell 900 includes 5 layers 910, 920, 930, 940, and 950. Each of the layers 910 to 950 contains components for receiving electromagnetic waves, converting the polarisation of the received electromagnetic waves, and transmitting the electromagnetic waves with the converted polarisation. Figs.10A to 10E show the top views of each of the layers 910 to 950.

[0095] Fig.9B shows diagrams showing the operation of the cell 900 of Fig.9A.

[0096] The cell 900 has two electromagnetic channels: channel C1 for first electromagnetic waves with a first incident linear polarisation (LP1), and channel C2 for electromagnetic waves with a second incident linear polarisation (LP2) that is orthogonal to the first electromagnetic waves LP1. Fig.11 illustrates block diagrams showing the theoretical components of the cell 900. Each channel C1 and C2 includes a receptor 1110A or 1110B, a phase shifter Pc1or Pc2, and an emitter 1120A or 1120B. The receptors 1110A and 1110B are configured to receive electromagnetic waves. The phase shifters Pc1or Pc2are configured to phase shift the received electromagnetic waves. The emitters 1120A or 1120B are configured to radiate the phase- shifted electromagnetic waves. In the arrangement shown in Figs.9A and 9B, the cell 900 has two internal pathways to provide the required phase shifts, one for the channel C1 and the other for channel C2. Mutual coupling between the two pathways is reduced by appropriate selection of the layout or other means to reduce cross coupling between the two channels C1 and C2.

[0097] The first layer 910 of the cell 900 includes a dielectric laminate 912 and a patch disposed on the top surface of the dielectric laminate 912 (see Fig.10A). The patch is made of electrically conducting material and is formed by two orthogonal receptors 1110A and 1110B. The receptor 1110A has a rectangular shape that is longer vertically to receive electromagnetic waves with polarisation in the vertical axis. The receptor 1110B has a rectangular shape that is longer horizontally to receive electromagnetic waves with polarisation in the horizontal axis. AH25(44380117_1)

[0098] The second layer 920 includes an electrically conducting surface 922, voids 924, and vias 926 (see Fig.10B). The electrically conducting surface 922 may be disposed on the bottom layer of the dielectric laminate 912 or the top surface of the dielectric laminate 932 of the third layer 930. The voids 924 are then defined in the electrically conducting surface 922, so that the vias 926 can pass through the electrically conducting surface 922. The vias 926 are made from electrically conducting material to connect the top of the receptor 1110A or the right side of the receptor 1110B to electrically conducting lines 934 (discussed below in relation to Fig.10C).

[0099] The third layer 930 includes two dielectric laminates 932 and electrically conducting lines 934 (see Fig.10C). The electrically conducting lines 934 (e.g., strip lines) are disposed in the middle of the two dielectric laminates 932 so that they are sandwiched between the two dielectric laminates. In one arrangement, one dielectric laminate is used and the electrically conducting lines 934 are disposed in the middle of the single dielectric laminate. As discussed hereinbefore, one end of the electrically conducting lines 934 is connected to the vias 926. The other end of the electrically conducting lines 934 connect to the vias 946 (discussed below in relation to Fig.10D).

[0100] The fourth layer 940 is similar to the second layer 920. The fourth layer 940 includes an electrically conducting surface 942, voids 944, and vias 946 (see Fig.10D). The electrically conducting surface 942 may be disposed on the bottom layer of the dielectric laminate 932 or the top surface of the dielectric laminate 952 of the fifth layer 950. The voids 944 are then defined in the electrically conducting surface 942, so that the vias 946 can pass through the electrically conducting surface 942. The vias 946 are made from electrically conducting material to connect the electrically conducting lines 934 to the emitters 1120A and 1120B (discussed below in relation to Fig.10E).

[0101] The fifth layer 950 is similar to the first layer 910. The fifth layer 950 includes a dielectric laminate 952 and a patch disposed on the bottom surface of the dielectric laminate 952 (see Fig.10E). The patch is made of electrically conducting material and is formed by two orthogonal emitters 1120A and 1120B. The emitter 1120B has a rectangular shape that is longer vertically to emit electromagnetic waves with polarisation in the vertical axis. The emitter 1120A has a rectangular shape that is longer horizontally to emit electromagnetic waves with polarisation in the horizontal axis.

[0102] Although the above arrangement describes the use of four dielectric laminates 912, 932, and 952, it is possible to use one dielectric laminate to form the cell 900. In another AH25(44380117_1)arrangement, more than four dielectric laminates may be used. In another arrangement, air or foam gaps are disposed between layers.

[0103] The above arrangement enables the top side of the receptor 1110A (aligned to receive Ey field) to be connected to the left side of the emitter 1120A (aligned to output -Ex field) via a via 926, electrically conducting line 934, and via 946, to form the first channel C1. Similarly, the right side of the receptor 1110B (aligned to receive Ex field) is connected to the bottom side of the emitter 1120B (aligned to output -Ey field) via a via 924, electrically conducting line 934, and via 946, to form the second channel C2. Fig.9B shows the connections in block diagrams, where the electrically conducting lines 934 together with the vias 926 and 946 act as phase shifters PS.

[0104] The conducting surfaces 922 and 942 act as electromagnetic shields to isolate the fields from the input side (i.e., receptors 1110A and 1110B) of the cell 900 and the output side (i.e., emitters 1120A and 1120B) of the cell 900.

[0105] In other arrangements, a co-planar waveguide or a substrate-integrated waveguide (SIW) may be used instead of the electrically conducting lines 934. The co-planar waveguide or SIW may be used with an electromagnetic coupler to the receptor 1110A or 1110B and another electromagnetic coupler to the emitter 1120A or 1120B. Then, the length of the waveguide, together with the couplers, provide a constant phase shift for that channel C1 or C2 at each frequency.

[0106] The arrangement shown in Figs.9A, 9B, and 10A to 10E provide a 180-degree differential phase shift between the two orthogonal channels C1 and C2. The input field of the first channel C1 is polarised along the x-axis as the receptor 1110A is aligned along the x-axis (see Fig.9B for the axes orientation). The C1 phase shifter or pathway (formed by the electrically conducting line 934 and vias 926 and 946) has a phase shift PS from the receptor 1110A to the emitter 1120A. The receptor 1110A receives electromagnetic waves in the positive x-direction. The receptor 1110A is then connected to the emitter 1120A, which is rotated by 90 degrees in relation to the receptor 1110A. The output field of the emitter 1120A has a linear polarisation in the negative y-direction. The polarisation vector rotation between the input field and the output field is 90 degrees anticlockwise. This is equal to the 90-degree anticlockwise physical rotation between the receptor 1110A and corresponding emitter 1120A.

[0107] Similar to the first channel C1, the input field of the second channel C2 is polarised along the y-axis as the receptor 1110B is aligned along the y-axis (see Fig.9B for the axes AH25(44380117_1)orientation). The C2 phase shifter or pathway (formed by the electrically conducting line 934 and vias 926 and 946) has a phase shift PS from the receptor 1110B to the emitter 1120B. The receptor 1110B receives electromagnetic waves in the positive y-direction. The receptor 1110A is then connected to the emitter 1120B, which is rotated by 90 degrees in relation to the receptor 1110B. The output field of the emitter 1120B has a linear polarisation in the negative x-direction. The polarisation vector rotation between the input field and the output field in C2 is 90 degrees clockwise. This difference in rotation direction is the key difference between the channels C1 and C2 that produces the aforementioned 180-degree differential phase shift between the two channels C1 and C2.

[0108] The main difference between the two channels C1 and C2 is, in the second channel C2, the output of the phase shifter / pathway is connected to the opposite side of the emitter 1120B – left side in the example as opposed to the right side. This swapping of emitter connection point flips the direction of the output polarisation vector from positive x-direction to the negative-x direction, effectively producing an additional phase shift of 180 degrees in the channel C2 relative to the channel C1. This differential phase shift is implemented by geometry so the differential phase shift is frequency-independent and equal to 180 degrees at all frequencies. The polarisation vector rotation between the input field and the output field in the channel C1 is 90 degrees anticlockwise as a result of 90-degree anticlockwise physical rotation between the receptor 1110B and the emitter 1120B. On the contrary, the polarisation vector rotation between the input field and the output field in the channel C2 is 90 degrees clockwise, which is due to the 90-degree anticlockwise physical rotation between the receptor 1110B and the emitter 1120B followed by 180-degree polarisation rotation due to the swapping of the connection point from right to the left side of the emitter 1120B. In other words, if the channel C1 is rotated clockwise by 90 degrees to make the receptor 1110A aligned with the receptor 1110B, the connection point in the emitter 1120A is on the right-hand side. The rotation angle between a receptor 1110A or 1110B and the corresponding emitter 1120A or 1120B is arbitrary as long as the same rotation is maintained for both channels C1 and C2 and the connection point is swapped in only one of the channels. For example, Fig.13B shows an alternative arrangement where the rotation between a receptor 1110A or 1110B and the corresponding emitter 1120A or 1120B is zero in both channels C1 and C2, and the connection point is swapped only in the channel C2. Connection point swapping is done either at the emitter end as shown, or at the receptor end to obtain the differential phase shift of 180 degrees. Fig.13C shows another alternative arrangement where a phase shifter of 180 degrees is added in the channel C2, but this arrangement has a narrow bandwidth due to the use of the 180-degree phase shifter, which normally produces exactly 180 phase shift only at one frequency or within a narrow frequency band. AH25(44380117_1)

[0109] A key advantage of the cell 900 is that, except from swapping the connection points, the two channels C1 and C2 are identical. The channels C1 and C2 have identical phase shifts (PS) due to identical patch lengths apart for the differential 180-degree shift provided by connection swap, and also identical attenuation due to any RF losses in conductors and dielectrics. Therefore, the two channels C1 and C2 are almost perfectly balanced. Further, the cell 900 is passive as the cell 900 does not contain active RF components and is therefore reciprocal (i.e., electromagnetic waves can propagate through the cell 900 in the opposite direction, thereby the emitters 1120A or 1120B become receptors and vice versa).

[0110] Fig.12 shows an alternative cell 1200 to cell 900. As discussed hereinbefore, the cell 900 does not have any active components. The alternative cell 1200 shown in Fig.12 includes one or more active RF components.

[0111] The cell 1200 includes receptors / emitters 1210A, 1210B, 1210C, 1210D, amplifiers 1230A, 1230B, 1230C, 1230D, variable phase shifters 1240A, 1240B, 1240C, 1240D, and switches 1250A, 1250B, 1250C, 1250D.

[0112] The first channel C1 is formed by the receptor / emitter 1210A connected to the input of the switch 1250A. The switch 1250A is a single-pole double-throw switch where the single-pole is referred to herein as the first terminal and the double-throw are referred to as the second and third terminals respectively. The switch 1250C is similar to the switch 1250A and the terminals of the switch 1250C are referred to in a similar manner as the terminals of the switch 1250A. The switch 1250A connects the receptor / emitter 1210A to either the receiving or transmitting path by switching between the two outputs. In the receiving path, the second or third terminal of the switch 1250A connects to the amplifier 1230A, which in turn connects to the variable phase shifter 1240A. The variable phase shifter 1240A then connects to the second or third terminal of the switch 1250C, which in turn connects to the receptor / emitter 1210C. When the first channel C1 is in receiving mode, the electromagnetic waves are received by the emitter / receptor 1210A. The switch 1250A then directs the received electromagnetic waves to the amplifier 1230A, the phase shifter 1240A, the switch 1250C, and the emitter / receptor 1210C.

[0113] In the transmitting path of the first channel C1, the second or third terminal of the switch 1250A connects to the amplifier 1230B, which in turn connects to the variable phase shifter 1240B. The variable phase shifter 1240B then connects to the second or third terminal of the switch 1250C, which in turn connects to the receptor / emitter 1210C. When the first channel C1 is in transmitting mode, the electromagnetic waves are received by the AH25(44380117_1)emitter / receptor 1210C. The switch 1250C then directs the received electromagnetic waves to the phase shifter 1240B, the amplifier 1230B, the switch 1250A, and the emitter / receptor 1210A.

[0114] Similar to the first channel C1, the second channel C2 is formed by the receptor / emitter 1210B connected to the input of the switch 1250B. The switch 1250B is a single-pole double- throw switch (similar to the switch 1250A) to connect the receptor / emitter 1210B to either the receiving or transmitting path. Similar to the switch 1250A, the single-pole of the switch 1250B is referred to herein as the first terminal, while the double-throw of the switch 1250B are referred to as the second and third terminals respectively. The switch 1250D is similar to the switch 1250B and the terminals of the switch 1250D are referred to in a similar manner as the terminals of the switch 1250B. In the receiving path, the second or third terminal of the switch 1250B connects to the amplifier 1230C, which in turn connects to the variable phase shifter 1240C. The variable phase shifter 1240C then connects to the second or third terminal of the switch 1250D, which in turn connects to the receptor / emitter 1210D. When the second channel C2 is in receiving mode, the electromagnetic waves are received by the emitter / receptor 1210B. The switch 1250B then directs the received electromagnetic waves to the amplifier 1230C, the phase shifter 1240C, the switch 1250D, and the emitter / receptor 1210D.

[0115] In the transmitting path of the second channel C2, the second or third terminal of the switch 1250B connects to the amplifier 1230D, which in turn connects to the variable phase shifter 1240D. The variable phase shifter 1240D then connects to the second or third terminal of the switch 1250D, which in turn connects to the receptor / emitter 1210D. When the second channel C1 is in transmitting mode, the electromagnetic waves are received by the emitter / receptor 1210D. The switch 1250D then directs the received electromagnetic waves to the phase shifter 1240D, the amplifier 1230D, the switch 1250B, and the emitter / receptor 1210B.

[0116] The variable phase shifters 1240A to 1240D may use electrically controlled phase shifters or optically controlled phase shifters or any other type of variable phase shifters to enable dynamic control of the phase shifts in each channel independently or dependently.

[0117] The amplifiers 1230A and 1230C are low-noise amplifiers, with a fixed or variable gain, to improve signal-to-noise ratio and bit error rates during reception. The amplifiers 1230B and 1230D are power amplifiers, with a fixed or variable gain, to improve overall system performance or radiated electromagnetic field strength during transmission. Although the amplifiers 1230A to 1230D are active RF components that are non-reciprocal, the switches AH25(44380117_1)1250A to 1250D enable the operation of the cell 1200 in both directions for receiving and transmitting modes.

[0118] When the cell 1200 is implemented in the metasurface 1000, the cell 1200 does not need to be rotated to achieve a linear transmission phase gradient in a certain direction. The variable phase shifters 1240A to 1240D can be tuned to provide the necessary linear transmission phase gradient in that particular direction.

[0119] Fig.13A shows an alternative cell 1300. The cell 1300 includes two receptors 1310A and 1310B, electrically conducting lines 1330A and 1330B, a phase shifter 1340, and two emitters 1320A and 1320B. The cell 1300 may be manufactured in a similar manner to the cell 900 (i.e., using dielectric laminates).

[0120] The receptor 1310A is aligned with the negative x-axis because it is parallel to x-axis and the connection point is towards the negative x direction (see Fig.13 for the axes orientation). The left side of the receptor 1310A is connected to the left side of the emitter 1320A via an electrically conducting line 1330A (which has a phase shift PS dependent on the inherent property of the line 1330A). This combination forms the first channel C1. The receptor 1310A is configured to receive electromagnetic waves with polarisation along the negative x- axis. The received electromagnetic waves are then phase shifted by the phase shift PS. The phase shifted electromagnetic waves are then transmitted by the emitter 1320A.

[0121] The receptor 1310B is aligned with the positive y-axis. The bottom side of the receptor 1310B is connected to the bottom side of the emitter 1320B via an electrically conducting line 1330B (which has a phase shift PS dependent on the inherent property of the line 1330B) and the phase shifter 1340. The phase shift of both of the electrically conducting lines 1330A and 1330B are the same. The phase shifter 1340 adds a 180° phase shift to the electromagnetic waves received by the receptor 1310B. This combination forms the second channel C2. The receptor 1310B is configured to receive electromagnetic waves with polarisation along the y- axis. The received electromagnetic waves are then phase shifted by the phase shift PS plus 180°. The phase shifted electromagnetic waves are then transmitted by the emitter 1320B.

[0122] As discussed above, the cell 900 adds a 180° phase shift due to the use of geometry. On the other hand, the phase shifter 1340 adds or subtracts 180° phase shift by using a passive or active RF component. In one arrangement, the phase shifter 1340 comprises an electrically conducting line that is longer or shorter by half-a-guided wavelength. For example, the electrically conducting line 1330B is made shorter or longer than that of the electrically AH25(44380117_1)conducting line 1330A by half-a-guided wavelength. In another arrangement, the phase shifter 1340 is an active phase shifter. In another arrangement, the phase shifter 1340 is a combination of an active RF phase shifter and differential length.

[0123] The differential phase delay of plus or minus 180 degrees in one channel C1 or C2 relative to the other channel C1 or C2 converts the polarisation of the field received by the receptors 1310A and 1310B from LHCP to RHCP, and vice versa (similarly, for the receptors of the cells 900 and 1200). Consequently, a LHCP incident wave at the receptors 1310A and 1310B results in a RHCP wave transmitted by the emitters 1320A and 1320B. Likewise, a RHCP incident wave at the receptors 1310A and 1310B results in a LHCP wave transmitted by the emitters 1320A and 1320B.

[0124] Figs.17A and 17B show a 2ndorder metasurface 1700 having cells 900. Fig.17A shows one arrangement of the cells 900. Fig.17B shows another arrangement of the cells 900. Although the cells 900 are shown, other cells 1200 or 1300 or any other phase transformation cells may be used for the 2ndorder metasurface 1700. The 2nd-order metasurface 1700 is implemented by cascading the cells 900 adjacent to each other. A 2nd- order metasurface is a metasurface that has a 2nd-order transmission phase distribution in at least one lateral dimensions. In this case, the 2nd-order metasurface 1700 has a 2nd-order transmission phase distribution in the radial (r) direction and no phase variation in the ^ direction in cylindrical coordinates.

[0125] The cells 900 are arranged to have one central cell 900A surrounded by multiple first loop cells 900B. Each of the first loop cells 900B is rotated by X1 degrees relative to the central cell 900A, to achieve a particular phase shift. Similarly, the first loop cells 900B are surrounded by multiple second loop cells 900C. Each of the second loop cells 900C is rotated by X2 degrees relative to the first loop cell 900B.

[0126] Any type of tessellating grid can be used such as a square grid, hexagonal grid, or a triangular grid. Although a square grid and square cells are equally possible (per the example shown to implement the metasurface 1000), hexagonal grid is more convenient to implement the metasurface 1700 with a rotationally symmetric transmission phase distribution. The features of the cell 900 are as described hereinbefore but the two ground planes and all dielectric laminates in the cell 900 are shaped to a hexagon.

[0127] As described hereinbefore, when the cell 900 is rotated by X degrees, transmission phase shift changes by 2X degrees. The central cell 900A is not rotated in this example, which AH25(44380117_1)gives the reference transmission phase shift of zero at r=0. The 1stloop of six cells 900B have their centres along the r=0.985 cm circle because the length of the cells 900B scaled to the operating frequency of 14.25 GHz is 0.985 cm. By substituting r = 0.985 cm, ^^^^^^= 2.049890 / cm2and ^^^^^^=0 in equation [3] (described hereinafter), the phase shift required at this radius is found to be 1.990. So, all the first loop cells 900B are rotated by 1.990 / 2 = 0.990with respect to the central cell 900A. The 2ndloop of 12 cells 900C have their centres along the r = 1.971 cm circle. From equation [3], the phase shift required at this radius is 7.960. So, all these twelve cells 900C are rotated by 7.960 / 2= 3.980relative to the central cell. This continues until the edge of the metasurface 1700 is reached.

[0128] Fig.18A shows an antenna system 1800 having a 2ndorder antenna system 1810 and the second order metasurface 1700. A 2nd-order antenna system is an antenna that has a 2ndorder near-field phase distribution in at least one lateral dimensions. The 2nd-order antenna system 1810 is an antenna that has a 2ndorder near-field phase distribution in the radial (r) direction and no phase variation in the ^ direction in cylindrical coordinates. The second order metasurface 1700 is disposed above the 2ndorder antenna system 1810. To achieve beam steering, either the 2ndorder antenna system 1810 or the metasurface 1700 is moved laterally (without rotational movement) in the x-y plane (i.e., the plane of the metasurface 1700 and the antenna system 1810. Only the 2ndorder antenna system 1810 or the metasurface 1700 needs to be moved to change the elevation (θ) angle and the azimuth (φ) angle of the beam of the antenna system 1810. Fig.18A shows that the metasurface 1700 is larger than the antenna system 1810 so that, when the 2ndorder antenna system 1810 or the metasurface 1700 is moved relative to each other, the 2ndorder antenna system 1810 stays underneath the metasurface 1700.

[0129] The term “2ndorder” used in relation to Figs.17 to 20 should not be confused with order related to the signal amplitude such as non-linearity, higher-order amplitude distortion, intermodulation, and the like. All RF components considered herein are assumed to be at least substantially linear (or 1storder) with respect to amplitude. Amplitude non-linearity is assumed to be negligible unless it is stated otherwise.

[0130] The antenna system 1800 requires only one moving component (i.e., either the antenna system 1810 or the metasurface 1700) in the lateral plane to fully steer a beam in 2D. Rotational or tilting movement of the 2ndorder antenna system 1810 or the metasurface 1700 is not required. The movement of either the 2ndorder antenna system 1810 or the metasurface 1700 may be performed by a mechanical system. AH25(44380117_1)

[0131] The 2ndorder antenna system 1810 has a radially 2nd-order near-field phase distribution in a cylindrical coordinate system (r, φ, z), as shown by the broken line in Fig.19A. The radially 2nd-order near-field phase distribution of the antenna system 1810 is shown by the solid line in Fig.19A. It matches the radially 2nd-order transmission phase distribution of the metasurface 1700. In other words, the phases of both vary in proportion to r2but in opposite ways, which is described hereinafter in the appendix. On the other hand, neither the near-field phase of the 2ndorder antenna system 1810 nor the transmission phase of the metasurface 1700 change with the φ coordinate.

[0132] Fig.18B shows a top view of Fig.18A. Fig.18B shows an example of the 2ndorder antenna system 1810 being moved relative to the metasurface 1700. Although both the metasurface 1700 and the 2ndorder antenna system 1810 has a circular shape, other shapes such as rectangular, octagonal, hexagonal, square, and the like may be used. Fig.18B shows that the centre of the antenna system 1810 is offset by a radial shift Spover an azimuth angle φRrelative to the centre of the metasurface 1700.

[0133] The discussion below holds for both arrangements when the 2ndorder antenna system 1810 or the metasurface 1700 is moved. That is, the 2ndorder antenna system 1810 is shifted and the metasurface 1700 is stationary, and vice versa. The radial shift Spdetermines the zenith angle (θ) of the beam (θSYS) according to the equation:

[0134] where k0 is the free-space wave number at the frequency of the electromagnetic field, ^^^^^^is the 2ndorder coefficient of the metasurface described in the appendixand the rotation angle of the centre of the 2ndorder antenna system 1810 with respect to the coordinate origin (φR), shown in Figs.18B, determines and in fact is equal to the azimuth angle of the beam (φSYS):

[0135] The mechanical lateral two-dimensional shifting system (for the 2ndorder antenna system 1810 and / or the metasurface 1700) can operate in either a rectangular (x,y) coordinate system or a cylindrical (r, φ) coordinate system. The operation in the cylindrical coordinates is easier to understand and accordingly the discussion below will be conducted in the cylindrical coordinates. For ease of explanation, the 2ndorder antenna system 1810 will be described to be moving relative to the metasurface 1700. However, the discussion below also applies to the metasurface 1700 moving relative to the 2ndorder antenna system 1810. AH25(44380117_1)

[0136] In summary, as will be shown below, a radial shift (^^^^) of the 2ndorder antenna system 1810 relative to the metasurface 1700 changes the zenith (θSYS) angle of the system beam and the rotary shift of the antenna system 1800 changes the azimuth angle (φSYS) of the system beam. Similarly, a radial shiftof the metasurface 1700 relative to the 2ndorder antenna system 1810 changes the zenith (θSYS) angle of the system beam and the rotary shift of the metasurface 1700 changes the azimuth angle (φSYS) of the system beam.

[0137] The transmission phase ^^^^^^(^^, φ) of the 2ndorder metasurface 1700 at a point (r, φ) is given by^^^^^^(^^, φ) = ^^^^^^^^2+ ^^^^^^[3] where ^^^^^^and ^^^^^^are constants which can be negative or positive. ^^^^^^can also be zero but ^^^^^^cannot be zero. The transmission phase changes in proportion to r2in the radial direction but does not change with φ. The transmission phase has rotational symmetry. The solid line inFig. 19A shows the radially 2nd-order variation of the transmission phaseφ) for ^^^^^^ = -2.04989 degrees / cm2and ^^^^^^=0. Fig.19A shows the transmission phase when the radial shift Spis zero.

[0138] The near-field phase distribution ^^^^^^(^^, φ) of the 2nd-order antenna system 1810 in Fig. 19A, which is “2nd-order phase matched” to the metasurface 1700 disposed above, at a point (r, φ) is given by^^^^^^(^^, φ) = −^^^^^^^^2+ ^^^^^^[4] where ^^^^^^is another constant. The near-field phase distribution also changes in proportion to r2in the radial direction but in the opposite way due to the negative sign. Mathematically speaking, its second order term is additively inverted. It also does not change with φ. The near-field phase distribution also has rotational symmetry. The constants ^^^^^^and ^^^^^^play no role in beam steering and can be arbitrary. The broken line in Fig.19A shows the radially 2nd-order variationof near-field phase distribution ^^^^^^(^^, ϕ) for ^^^^^^ = -2.04989 degrees / cm2and ^^^^^^=0.

[0139] The near-field phase distribution of the 2ndorder antenna system 1810 in equation [4] is implemented in one of the following ways.

[0140] One implementation is changing the design of an antenna system to have radially 2ndorder near-field phase. In one example, the antenna system 100 (of Fig.1) is modified to produce radially 2ndorder near-field phase. The antenna system 100 produces approximately AH25(44380117_1)uniform near-field phase distribution due to the spirals 124A and 124B. When the slot-pair locations in the spirals 124A and 124B are adjusted, a radially 2nd-order near-field phase can be produced. This is achieved by moving each slot-pair radially inwards or outwards until the phase of the antenna system 100 matches the required value at a particular location. First, the required shift of each of the slot-pair locations is estimated. The near-field phase distribution of the antenna is simulated and shift of the slot-pair locations is re-adjusted iteratively, if required, until the required 2ndorder near-field phase distribution is achieved. Other types of antennas and arrays with fixed beams can be modified in this manner to produce a 2nd-order near-field phase distribution instead of a nearly uniform phase distribution.

[0141] Fig.20 shows an alternative antenna system 1810, where the 2ndorder antenna system 1810 comprises the antenna system 100 with a second phase-transformation metasurface 1820. The second phase-transformation metasurface 1820 converts the near-field phase distribution of the antenna 100 to the required 2nd-order near-field phase distribution. This second metasurface is permanently attached to the antenna system 100. Although the antenna system 100 is shown in Fig.20, other antennae may be used.

[0142] The 2nd-order beam steering system 1800 shown in Figs.18A and 20 work for both circularly-polarised and linearly-polarised 2nd-order antenna system 1810.

[0143] A phase of X degrees is the same as a phase of X +n(360) degrees where n is any negative or positive integer. Replacing a large value of phase X by a smaller equivalent value X +n(360) by selecting n such that X +n(360) is within a smaller range such as 0-3600or -1800to +1800is called phase wrapping. Hence, large phase values are not required to be implemented as effectively 2nd-order phase distribution in the 2nd-order antenna system 1810 or the metasurface 1700. Instead, the implemented phase can be wrapped to smaller phase values as shown in Fig.19B. The unwrapped phase shift is shown by the solid line of Fig.19B. The wrapped phase shift is shown by the broken line of Fig.19B.

[0144] Fig.19C illustrates the phase of the 2nd-order antenna system 1810 at the input plane of the metasurface 1700 (broken line), the unwrapped phase shift of the metasurface 1700 (solid line), and the antenna system 1800 output phase at the output plane of the metasurface 1700 (dotted line). Fig.19C has a lateral shift of zero (Sp = 0). This is a 1D cut along the x-z plane of the actual rotationally symmetric 2D phase distributions. In this example, the 2nd-orderantenna system 1810 radiates at 14.25 GHz; ^^^^^^ = −^^^^^^ = − 357.721 deg / m2, and all otyher constant coefficients are zero. As shown by the dotted line, the output phase of the antenna system 1800 (at the output plane of the metasurface 1700) is zero in the region above the 2nd- AH25(44380117_1)order antenna system 1810 (-11cm<x<11cm), thus the resulting system far-field beam is along the broadside direction (θ SYS = 0). The near field of the antenna system 1810 outside this region is relatively weak and has no significant contribution to the far field.

[0145] The present disclosure now describes steering the beam of the antenna system 1800 by approximately 210to the direction of θ SYS = 210, φ SYS = 00. By substituting the values for ^^^^^^^^, θ SYS and k0 for 14.25 GHz in equation [1] (described hereinbefore), the required radial shift in cylindrical coordinates is determined to be Sp =~-15 cm. From equation [2] (described hereinbefore), the rotation of the 2nd-order antenna system 1810 relative to coordinate origin is 00. When the 2nd-order antenna system 1810 is shifted by 15cm, the system output phase at the output plane of the metasurface 1700 is shown by the dotted line in Fig.19D. The output phase of the antenna system 1800 is similar to the output phase of the antenna system shown in Fig. 14 because it has a linear phase gradient. This linear phase gradient of 61.50 / cm at 14.25 GHz creates a far-field beam in the direction of θ SYS = 210, φ SYS = 00. Fig.19F shows a simulated result of the beam steering discussed in this paragraph.

[0146] As mentioned previously, when designing the 2nd-order antenna system 1810 and the metasurface 1700 to have the required 2nd-order phase distributions, the phases of both the antenna system 1810 and the metasurface 1700 can be wrapped to simplify implementation. In Fig.19E both the near-field phase (broken line) of the 2nd-order antenna system 1810 and the transmission phase of the metasurface 1700 (solid line) have been wrapped to a range between -3600and 00. Still the spatially linear variation of the system output phase versus x can be noted in the “saw-tooth” graph (dotted line) Fig.19E. Industrial Applicability

[0147] The arrangements described are applicable to the telecommunication, sensing and navigation industries.

[0148] The foregoing describes only some embodiments of the present invention, and modifications and / or changes can be made thereto without departing from the scope and spirit of the invention, the embodiments being illustrative and not restrictive.

[0149] In the context of this specification, the word “comprising” means “including principally but not necessarily solely” or “having” or “including”, and not “consisting only of”. Variations of the word "comprising", such as “comprise” and “comprises” have correspondingly varied meanings. AH25(44380117_1)Appendix A Theory of 2nd-order MetaSteering In this section, the base antenna is the 2ndorder antenna system 1810 (referred to as BA) and the 2ndorder metasurface is the metasurface 1700 (referred to as MS). For ease of understanding, first consider the case with no relative shift between the 2nd-order metasurface (MS) and the 2nd-order base antenna (S^ = 0 in Fig.18A). Suppose in this case the2D phase distribution created by the 2nd-order base antenna (BA) at a point ( ^^, ^^ ) on the inputplane of the metasurface is given bywhere ^^^^^^^^is the 2nd-order coefficient of BA spatial phase distribution in the x-direction, ^^^^^^^^is the 2nd-order coefficient of BA spatial phase distribution in the y-direction, ^^^^^^^^is the 1st- order coefficient of BA spatial phase distribution in the x-direction, ^^^^^^^^is the 1st-order coefficient of BA spatial phase distribution in the y-direction, ^^^^^^is an arbitrary constant,and ^^, ^^ are standard Cartesian coordinates. ^^^^^^^^ , ^^^^^^^^ and ^^^^^^ are not required for this beamsteering; they can be zero. On the other hand, at least one of the 2nd-order coefficients is essential for the claimed method of beam steering, and the base antenna needs to be designed to produce such a spatial 2nd-order near-field phase distribution. Many aperture antennas and arrays, including slot-pair spiral arrays claimed here, can be designed to produce such uncommon phase distributions. Alternatively, the 2D near-field phase distribution of any aperture antenna can be transformed into a 2nd-order distribution by inserting a fixed phase-transformation metasurface between the base antenna and the large metasurface as described previously (Fig.20).Suppose the phase shift of the spatially 2nd-order phase shifting metasurface at ( ^^, ^^ ) is given bywhere ^^^^^^^^is the 2nd-order coefficient of the MS transmission phase in the x-direction, ^^^^^^^^is the 2nd-order coefficient of the MS transmission phase in the y-direction, ^^^^^^^^is the 1st-order coefficient of MS transmission phase in the x-direction, ^^^^^^^^is the 1st-order coefficient of MS transmission phase in the y-direction, and ^^^^^^is an arbitrary constant. Again, ^^^^^^^^, ^^^^^^^^and AH25(44380117_1)^^^^^^are not required for this beam steering method; they can be zero. On the other hand, at least one of the 2nd-order coefficients is essential for the claimed method of beam steering, and the metasurface must be designed to produce such a 2nd-order transmission phase distribution. Most metasurfaces, including the one claimed above, can be designed to produce such 2nd-order transmission phase distributions. The system output near-field phase distribution is the phase distribution at the output plane of the metasurface, given by^^^^^^^^(^^, ^^) = ^^^^^^(^^, ^^) + ^^^^^^(^^, ^^) (3)Now we enforce the condition that 2nd-order phase coefficients of the metasurface are negatives of the 2nd-order phase coefficients of the base antenna. Mathematically this means^^^^^^^^ = −^^^^^^^^ and ^^^^^^^^ = −^^^^^^^^ (4)We refer this as the condition for “2nd-order phase matching”. Substitution of this, and equations (1) and (2) in equation (3) leads toNote that as a result of phase matching, the undesirable second order phase terms containing x2and y2cancel out, and the output phase distribution is similar to that of an ideal 1st-order antenna system with a directed beam. The zenith (^SYS) and azimuth (^SYS) angles of the antenna system beam direction in polar coordinates are given bywhere k0is the free-space wave number. Now, to steer the antenna system beam, we laterally shift either the metasurface or the base antenna while keeping the other fixed. Without any loss of generality, suppose we shift the metasurface by a distance of Sxin the x-direction and also by a distance of Syin the y-direction. Consequently, the phase shift distribution of the metasurface also changes, and now it is given by: AH25(44380117_1)Now the output phase distribution of the antenna system becomes^^^^^^^^(^^, ^^) = ^^^^^^(^^, ^^) + ^^^^^^(^^, ^^)Note that the condition for 2nd-order phase matching, given in equation (4), has been substituted and as a result, the undesirable second order phase terms containing x2and y2cancel out again. This is essential because any 2nd-order phase terms in the antenna system output near field distribution distorts the radiation pattern. Now the spatial phase distribution at the output of the metasurface does not have any 2ndorder components. It only has 1st-order (linear) components containing x and y, and a constant term. In other words, the output has a spatially linear phase distribution, just like an ideal antenna system with one or two 1st-order metasurfaces that were mentioned previously. These 1st-order terms steer the antenna beam in 2D, producing complete beam steering, as described below. To determine the beam direction, let us organise the above equation as follows:The zenith (^SYS) and azimuth (^SYS) angles of the antenna system beam direction are now given by AH25(44380117_1)For the special case wherewhich means there is no net 1st-order phase distribution at the MS output,For another special case where the 2nd-order coefficients are equal in x and y directions, i.e.^^^^^^^^ = ^^^^^^^^ = ^^^^^^, (19)the zenith angle of the beam is given byis the radial shift of the MS from the coordinate centre in cylindrical ordinates (ρ, ϕ, z). Denoting this by S^, we reach the following expression for the zenith angle of the beam (^SYS) when the MS is shifted radially by a distance of S^^The azimuth angle of the beam (^SYS) is now given by^^ = tan−1 (^^^^^^^^) (23) Note that ^SYS is equal to angle by which the MS centre is rotated with respect to the coordinate origin, shown by ^R in Fig.18B. AH25(44380117_1)In the special case where there is no relative lateral shift between the MS and the BA, i.e. Sx=Sy=S^ =0, from equation (22), ^SYSis zero that means the beam is along the z-axis, which is also known as the broadside direction of the antenna system. AH25(44380117_1)

Claims

CLAIMS:

1. An antenna system comprising: an antenna configured for radiating over a frequency bandwidth, the antenna having an electrically conducting layer with slot pairs defined in the electrically conducting layer, wherein each of the slot pairs includes a first slot disposed perpendicularly to a second slot, wherein the slot pairs are disposed in a spiral arrangement and are configured to radiate electromagnetic waves, wherein the spiral arrangement is divided into sections, wherein each section includes a group of the slot pairs that are configured to radiate at a frequency sub-band of the frequency bandwidth, and wherein the frequency sub-bands are different.

2. The antenna system of claim 1, wherein the spiral arrangement includes loops, wherein the loops are separated by a radial gap.

3. The antenna system of claim 2, wherein the radial gap is determined to synchronize the phases of beams radiated by the different sections of the spiral arrangement.

4. The antenna system of any one of claims 1 to 3, wherein the spiral arrangement includes one or more spirals.

5. The antenna system of claim 4, wherein the spiral arrangement includes two spirals, wherein one of the spirals is shifted inward or outward to synchronize radiation beams of the two spirals.

6. The antenna system of any one of claims 1 to 5, further comprising: a feed arrangement comprising: a terminal configured for receiving radio frequency signals; a monopole configured for coupling to the terminal; and a waveguide configured for coupling to the monopole and the slot pairs, such that the slot pairs radiate the electromagnetic waves.

7. The antenna system of claim 6, wherein the waveguide comprises: a first waveguide configured for coupling to the monopole; a second waveguide configured for coupling to the first waveguide via an aperture, wherein the second waveguide is configured for coupling to the slot pairs. AH25(44380117_1)8. The antenna system of claim 7, wherein the second waveguide comprises a corrugated surface.

9. The antenna system of claim 7 or 8, wherein the second waveguide comprises absorbers at one end of the second waveguide.

10. The antenna system of any one of claims 6 to 9, wherein the terminal comprises a plurality of terminals configured for beam steering the electromagnetic waves radiated by the slot pairs.

11. The antenna system of any one of claims 1 to 10, further comprising: a dielectric layer disposed above the antenna.

12. The antenna system of any one of claims 1 to 11, further comprising: two metasurfaces disposed above the antenna, wherein the two metasurfaces are rotatable for beam steering the electromagnetic waves radiated by the slot pairs.

13. The antenna system of claim 12, wherein the metasurface comprises cells, wherein each cell is configured for receiving electromagnetic waves having a polarisation, converting the polarisation of the received electromagnetic waves, and transmitting the converted electromagnetic waves, wherein the cells along a direction of the metasurface is rotated to phase shift the electromagnetic waves in the direction.

14. The antenna system of claim 13, wherein each cell comprises two sets of receptor / emitter configurations for two orthogonal polarisations.

15. The antenna system of any one of claims 1 to 11, further comprising: a second order metasurface disposed above the antenna.

16. The antenna system of claim 15, wherein the second order metasurface or the antenna is shifted relative to the other to beam steer the electromagnetic waves radiated by the slot pairs. AH25(44380117_1)

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