Electromagnetic waveguide

Abstract

There is disclosed an electromagnetic waveguide comprising: two metamaterials having different topological properties, such that the metamaterials are configured to confine electromagnetic fields along a boundary defined between the two metamaterials when in operative proximity; wherein: each metamaterial comprises a set of unit cells arranged in a side-by-side arrangement extending in a direction along the boundary; and each metamaterial comprises at least two unit cells in a direction perpendicular to a point along a boundary section.

Description

[0001] Electromagnetic waveguide

[0002] Field This specification concerns electromagnetic (EM) waveguides, which uses a photonic topological insulator to control propagation of EM waves.

[0003] Background EM waveguides play a significant role in many of the digital and wireless systems that are central to modern life. As the nature of these systems expands to encompass the millimetre wave and sub-THz regimes there is an increasing demand for more efficient and compact components. These higher frequency bands are more affected by atmospheric attenuation necessitating higher- powered beams to propagate a signal the same distance. More efficient waveguiding components have hence become increasingly desirable. Moreover, reduction in component size and weight is increasingly at a premium in both the civil and defence sectors; compact waveguiding structures able to conform to tightly curved paths therefore being of increasing value.

[0004] In the growing field of metamaterials, a photonic topological insulator is a known device where the bulk material behaves as an electrical insulator while its external edge surfaces behave as an electrical conductor. This means that electrons can move along certain directions along the edge surfaces of the material only. Further, the global topology of the material’s energy band structure can be categorized by a non-zero Chern number (the so-called “topological invariant”) that does not depend on the shape of the surfaces of the material. Accordingly, such materials are said to be “topologically protected” in that these conducting surface states are observed regardless of impurities or small changes to the shape of the material. For example, the conducting edge states of the material is resistant to a wide range of distortions (e.g. damage or change in direction) to the material. Such materials are accordingly the subject of active research in the field of EM waveguides, as those skilled in the art seek to utilise their surface and edge modes to guide an EM wave efficiently and with reduced demands in respect of volume and weight. Aspects of the present invention are concerned with a waveguide which incorporates a topological insulator to address the foregoing. Summary

[0005] According to an aspect of the present invention, there is provided an electromagnetic waveguide. The waveguide comprises: two metamaterials having different topological properties (e.g. by virtue of having different Chern numbers), such that the metamaterials are configured to confine electromagnetic fields along a boundary defined between the two metamaterials when in operative proximity; wherein: each metamaterial comprises a set of unit cells arranged in a side-by- side arrangement extending in a direction along the boundary; and each metamaterial comprises at least (and in preferred embodiments exactly) two unit cells in a direction perpendicular to (e.g. a point or points along) a boundary section.

[0006] Each metamaterial may be regarded as a photonic topological insulator. Each unit cell may comprise two, e.g. complementary, metasurfaces separated by a thickness of dielectric material. The thickness of the dielectric material may be selected based on a predetermined relationship between the thickness and a bandwidth (e.g. band gap and thus frequency of electromagnetic wave to be) supported by the photonic topological insulator.

[0007] In embodiments, the thickness of dielectric material between the metasurfaces has a value within the range 0.1 mm to 2mm. This gives bandwidths of up to 6Ghz.

[0008] The two metamaterials may have different topological properties in that: each unit cell has the same structure; and the unit cells in the first metamaterial have a first vertical orientation and the unit cells in the second metamaterial have a second vertical orientation opposite the first vertical orientation (i.e. flipped by 180 degrees). Each unit cell may comprise three layers: a first layer comprising a first planar pattern of conducting regions and insulating regions: a second dielectric layer stacked on the first layer; and a third layer comprising a second planar pattern (arrangement) of conducting regions and insulating regions.

[0009] The first planar pattern of unit cells may comprise a central conducting region and an outer insulating region. The second planar pattern of unit cells in the second metamaterial may comprise a central insulating region and an outer conducting region.

[0010] The boundary section may comprise an input terminal at one end and an output terminal at another end, so as to define a waveguide between them, e.g. to supply an electromagnetic wave to the boundary section. In further embodiments, the electromagnetic waveguide is configured to operate as an antenna. This is achieved, in embodiments, where: at least one unit cell is a modified unit cell in that it has a different bandgap to another one of the unit cells, to permit radiation of an EM field from the waveguide via the modified unit cell.

[0011] The modified unit cell may have a different structure to that of the other unit cell, such that it will have a different bandgap to the other unit cell.

[0012] The set of unit cells in each metamaterial may comprise at least one conducting region and at least one insulating region. The set of unit cells in a or each metamaterial may comprise at least one modified unit cell wherein the conducting region has a cut-out section to permit radiation of an EM field from the waveguide through the cut-out section. The at least one modified unit cell may be located at the perimeter of the metamaterial, e.g. in operative proximity to the boundary.

[0013] The at least one modified unit cell may comprise plural modified unit cells which form a single row of adjacent unit cells perpendicular to the boundary; and the remaining rows perpendicular to the boundary may comprise unmodified unit cells, e.g. which do not have a cut-out section.

[0014] The cut-out section may comprise an adjustable conducting material to fill the cut- out section. The adjustable conducting material may be operable to switch between a conducting state and a non-conducting state to selectively either prevent or allow radiation to be emitted through the cut-out section.

[0015] The adjustable conducting material may be operable (e.g. controllable) to dynamically set or adjust the capacitance across the cut-out section and thus control an aspect of the radiation pattern.

[0016] The adjustable conducting material may be a diode, e.g. a varactor diode. The adjustable conducting material may be a phase change material.

[0017] According to a further aspect of the present invention, there is provided a method of using the electromagnetic waveguide of any preceding statement, comprising: bringing the two metamaterials into operative proximity so as to define an interface path for confining electromagnetic fields along a boundary between the two metamaterials; supplying an electromagnetic wave to an input terminal which is at one end of the boundary section; and receiving the electromagnetic wave at an output terminal at another end of the boundary section. In further embodiments, the method comprises using the waveguide as an antenna.

[0018] The skilled person will appreciate that except where mutually exclusive, a feature or parameter described in relation to any one of the above aspects may be applied to any other aspect. Furthermore, except where mutually exclusive, any feature or parameter described herein may be applied to any aspect and / or combined with any other feature or parameter described herein.

[0019] Brief Description of the Drawings Embodiments of the invention will now be described by way of non-limiting example with reference to the accompanying drawings, in which:

[0020] Figure 1 is a schematic diagram illustrating a top-down view and a side cross- sectional view of an EM waveguide in accordance with an embodiment of the present invention;

[0021] Figure 2 is a schematic diagram illustrating top-down view and a side cross- sectional view of a unit cell in a first metamaterial of the EM waveguide, in accordance with an embodiment of the present invention;

[0022] Figure 3 is a schematic diagram illustrating top-down view and a side cross- sectional view of a unit cell in a second metamaterial of the EM waveguide in accordance with an embodiment of the present invention;

[0023] Figure 4 is a graph which illustrates the transmission and reflection characteristics of the waveguide of Figure 1 ;

[0024] Figure 5 is a schematic diagram illustrating a top-down view and a side cross- sectional view of a unit cell in a first metamaterial of the EM waveguide, in accordance with a second embodiment of the present invention;

[0025] Figure 6 is a schematic diagram illustrating top-down view and a side cross- sectional view of a unit cell in a second metamaterial of the EM waveguide in accordance with the second embodiment of the present invention;

[0026] Figure 7 is a schematic diagram illustrating a top view of the waveguide configured to operate as an antenna in accordance with an embodiment of the present invention;

[0027] Figure 8 is a schematic diagram illustrating a top-down view and a side cross- sectional view of a unit cell in the second metamaterial of the waveguide of Figure 7; and Figure 9 is a schematic diagram illustrating a top-down view and a side cross- sectional view of a unit cell of the second metamaterial of the waveguide, in accordance with another embodiment of the present invention. Like reference numerals are used to denote like features throughout the drawings.

[0028] Detailed Description

[0029] Figure 1 is a schematic diagram illustrating an EM waveguide in accordance with an embodiment of the present invention. The Figure shows a top-down view and a side cross-sectional view of the waveguide.

[0030] The waveguide 10 comprises a first metamaterial 11 and a second metamaterial 12, which are configured to be interfaced with one another to define a boundary 13 between the two metamaterials 11 , 12. Each metamaterial 11 , 12 is in the form of a photonic topological insulator (PTI) with EM duality. The PTI has a structure which comprises a set of unit cells 14, 15, one set forming each respective metamaterial 11 , 12. As best shown in Figures 2 and 3, each unit cell 14, 15 has the same structure comprising two complementary metasurfaces separated by a thickness of dielectric material. In this specific example, each unit cell 14, 15 comprises three stacked layers. A first metasurface layer 20 which comprises a conducting, e.g. Copper, region 26 and an insulating, e.g. dielectric (e.g. commercially-off-the- shelf (COTS) Rogers (TM) 5880), region 28. A second layer 22 which is a dielectric material, e.g. Rogers (TM) 5880, which is between the first layer 20 and the third layer 24. The third layer 24 is a metasurface comprising a conducting, e.g. Copper, region 26 and an insulating, e.g. dielectric (Rogers (TM) 5880), region 28. In both the first and third layers 20, 24, the conducting and insulating regions are arranged to lie in the same plane to form a planar arrangement or pattern of conducting and non-conducting regions. The conducting regions 26 abut and contact the insulating regions 28 in the same layer.

[0031] The first and third layers 20, 24, have EM properties that are complementary hence enabling a cross-coupling of transverse magnetic (TM) and transverse electric (TE) modes. This may be achieved by each layer of the unit cell 14, 15 being mutually shaped and symmetrical about a line of symmetry 210. In this case, the unit cells 14, 15 are hexagonal shaped, which may be particularly advantageous in that it allows for more symmetry points in the electronic band structure. Other symmetrical shapes (e.g. a square) are of course possible.

[0032] Further, the thickness 212 of the dielectric layer 22 is selected to be sufficiently low to allow for a strong effective magneto-electric coupling between the first layer 20 and the third layer 24. The thickness 214 of the third layer 24 and a thickness 216 of the first layer 20 are equal, and in this embodiment are set to a thickness value between 0.1 mm and 2mm giving bandwidth of up to 6GHz.

[0033] The strong coupling between the first layer 20 and the third layer 24 lifts trivial degeneracy to open a non-trivial band gap for the unit cell over a range of eigenfrequencies. The energy bands above and below the band gap can be described by a topological invariant called a spin-Chern number, where the spin- Chern number is non-zero, e.g. one. Such a structure facilitates the existence of edge modes within the bandgap and enables electrons to propagate along the edge surfaces. Further, such a structure is topologically protected in that these conducting surface states are observed regardless of impurities or changes to the shape of the material.

[0034] The planar pattern of the first layer 20 is the inverse of the planar pattern of the third layer 24. That is, where a given region in the third layer 24 of a unit cell 14 is a conducting region 26, a corresponding region (in terms of, e.g. planar, location) in the first layer 20 of the same unit cell 15 is an insulating region 28, and vice versa. The planar pattern in the first layer 20 comprises a central, hexagonal conducting region 26 and an outer insulating region 28 in the form of a ring with a hexagonal outer profile. In contrast, the planar pattern of the third layer 24 of the unit cell 15 comprises a central, hexagonal insulating region 28 and an outer conducting region 26 in the form of a ring with a hexagonal outer profile.

[0035] The outer insulating region 28 of the first layer 20 and the outer conducting region 26 of the third layer 24 have the same width 218, e.g. one millimeter, as measured in a planar direction from an inner edge which abuts the central region to an outer edge which is configured to abut an adjacent unit cell of the wider metamaterial. The total planar span 220 of the unit cell is set to be approximately one tenth of the wavelength of EM waves supported by the waveguide. The planar span 220 is defined as the distance between two parallel transverse edges 222 of the unit cell 14, 15, measured in a direction parallel to the plane of the third layer 24. In this embodiment, the planar span 220 is set to seven millimetres.

[0036] It will be appreciated that the thickness 212 of the dielectric layer 22 may be varied over a significant range not limited to 0.1-2mm. The Applicant has recognised that the thickness of the dielectric layer 22, and thus the separation of the first layer 20 and the third layer 24, affects the band gap size and consequently the bandwidth of the topologically protected surface mode frequencies. Indeed, the band gap will increase for decreasing values of thickness 212, due to the crosscoupling effects increasing the closer the complementary metasurface layers 20, 24. Merely as an example, the bandwidth increases from 8.2 GHz for a 1 mm thickness 212 to 11.4 GHz for a 200 micron thickness 212. Accordingly, the thickness 212 of the dielectric material in the second layer 22 is selected based on a predetermined (e.g. linear) relationship between the thickness and a bandwidth to be supported by the photonic topological insulator.

[0037] With reference again to Figure 1 , the set of unit cells 14 in the first metamaterial

[0038] 11 have a first vertical orientation and the set of unit cells 15 in the second metamaterial 12 have a second vertical orientation opposite the first vertical orientation (i.e. the second vertical orientation is flipped by 180 degrees from the first vertical orientation). That is, the unit cells in both metamaterials have the same vertical stack structure, except that the order by which materials are vertically stacked from bottom to top in the set of unit cells 14 in the first metamaterial 11 is the inverse of the order by which materials are vertically stacked from bottom to top in the set of unit cells 15 in the second metamaterial 11 . In other words, the unit cells 14 in the first metamaterial 11 may be regarded as having an upright orientation while the unit cells 15 in the second metamaterial

[0039] 12 may be regarded as having an upside-down orientation.

[0040] The set of unit cells 14, 15 forming a respective metamaterial 11 , 12 are arranged in a side-by-side arrangement. All of the unit cells 14, 15 forming a respective one of the metamaterials 11 , 12 lie in the same plane and have the same pitch between them and their adjacent unit cell 14. The pitch is equal to the planar span 220 of each unit cell, such that the transverse edge 222 of one unit cell 14, 15 abuts a transverse edge 222 of an adjacent unit cell 14, 15 to interlock the set of unit cells forming the metamaterial 11 , 12. In this way the unit cells 14, 15 define a regular and repeating structure across the metamaterial 11 , 12. However, in general the metamaterials need not be planar.

[0041] As stated above, the first metamaterial 11 and the second metamaterial 12 are configured to be interfaced with one another, in use, to define a boundary 13 between the two metamaterials 11 , 12. In that regard, it will be appreciated that the metamaterials may be movable between a first, disconnected position and a second, interfaced position (shown) at which the first metamaterial 11 and the second metamaterial 12 are arranged side-by-side in operative proximity to one another at the boundary 13. The transverse edges 222 of the respective metamaterials 11 , 12 face each other, and may be in physical contact along the boundary 13, when in the interfaced position. In other embodiments, such as that shown, there is a spacing between the two while remaining in operative proximity. As the two metamaterials 11 , 12 have different (e.g. inverse) topological properties, e.g. by virtue of unit cells in one metamaterial being vertically flipped with respect to the unit cells in the other metamaterial, topological edge modes at the boundary of the two metasurfaces 11 , 12 will be confined along the boundary line, enabling scatter-free propagation of the edge modes in a single direction along an interface path defined at the boundary 13 between the two metamaterials 11 , 12.

[0042] The waveguide 10 comprises an input terminal 16 at a first end 17 of the interface path between the metasurfaces 11 , 12, and an output terminal 18 at a second, opposite end 19 of the interface path. The input terminal 16 may be coupled to an EM signal source (not shown) via conventional waveguide means, e.g. using a coaxial cable, transmission line or rectangular waveguide, or even (e.g. dipole) antenna means, so as to supply an EM field to the input terminal 16. In use, the EM field will propagate from the input terminal 16 along the interface path (as shown by the arrows included in Figure 1) and will emerge at the output terminal 18. The output terminal 18 may comprise another conventional waveguide or antenna means, so as to receive the EM field. The output terminal 18 may further be connected to a detector (not shown). Figure 4 is a graph which illustrates the transmission and reflection characteristics of the waveguide 10 described above with respect to Figures 1 to 3.

[0043] The graph is a scattering parameters graph, which shows the input-output relationship of the waveguide 10 over a range of input signal frequencies. The scattering parameters are expressed in terms of the signal loss (expressed in decibels, dB) at each frequency. Specifically, S21 is with respect to the forward transmission (the signal from input terminal 16 to output terminal 18), S12 is for the reverse transmission (from output terminal 18 to input terminal 16), S11 is for the input reflection coefficient and S22 is for the output reflection coefficient.

[0044] From the scattering parameters graph, it can be seen that the waveguide 10 suffers minimal signal loss across a wide range of frequencies from about 17 GHz to about 24 GHz. Thus it will be appreciated that the band gap frequencies are from about 17 GHz to about 24 GHz, which matches the eigenfrequencies of the band gap. It can also be seen that the waveguide suffers little from input and output signal reflections (S11 , S22) often referred to as back-scattering.

[0045] The Applicant has recognised that transmission effectiveness of the bound edge waves, from the input terminal 16 to output terminal 18, are affected by the number of unit cells 14, 15 arranged side-by-side in directions 110, 111 , which are perpendicular to the boundary of the metamaterials 11 , 12, i.e. perpendicular to the transverse edge of the unit cells 14, 15 at the boundary 13. This is the case regardless of the structure, size, or shape of the unit cells and the interface path. For example it has been found that, should the set of unit cells 14, 15 in a given one of the metamaterials 11 , 12 comprise a single row of unit cells along the boundary 13, i.e. such that a single unit cell is present in directions 110, 111 perpendicular to the boundary 13, the EM fields would leak from the interface path to the point that the structure may no longer be regarded as a topological insulator. Further, the change in transmission effectiveness from the case where a set of unit cells has 1-cell width to the case where the set has a 2-cell width yields a noticeable increase in transmission, and correspondingly lower signal losses. Therefore, a minimum two unit cell width from the boundary is needed to maintain the strong topological protection of the band gap frequencies. However, the benefit for a structure with more than 2 unit cells in width from the boundary is limited as the transmission effectiveness show minimal improvements for more than two cell widths. Accordingly, arrangements where the set of unit cells 14, 15 in the metamaterial 11 , 12 comprises exactly two unit cells perpendicular to the boundary 13 are advantageous in that it strikes a balance between providing efficient transmission of EM waves, while minimizing the size, weight and complexity of the overall metamaterial and waveguide structure.

[0046] As best shown in Figure 1 , each metamaterial 11 , 12 comprises, at all points along a boundary section, exactly two unit cells 14, 15 in a direction 110, 111 perpendicular to the boundary 13. That is, the width of the set of unit cells 14, 15, as measured by the number of unit cells arranged side-by-side in the direction 110, 111 perpendicular to the boundary 13, is exactly two. In other words, the set of unit cells 14, 15 comprises exactly two rows of unit cells 14, 15 extending along the boundary 13.

[0047] While the invention has been described above as having unit cells where first and third layers have inversed planar patterns, this is not required. The unit cells need not have planar patterns of conducting and insulating regions. Indeed many different structures are possible and envisaged for the unit cells, as long as the two metamaterials 11 , 12 have different topological properties, e.g. different Chern numbers. Furthermore, it is noted here that the two metamaterials may be regarded as having different Chern numbers even if their magnitude is the same. For example, the metamaterials heretofore described may have a Chern number of the same magnitude but opposite signs, i.e. positive or negative Chern numbers of the same magnitude, and this is the case where the unit cells in both metamaterials are structurally the same but inversed (i.e. vertically flipped by 180 degrees).

[0048] In a further embodiment as shown in Figures 5 and 6, each unit cell may comprise a first conducting layer 20, a second dielectric layer 22 and a third conducting layer 24. The first conducting layer 20 and the second conducting layer 24 may be parallel, as shown. The unit cells 14 in the first metamaterial 11 are the topological inverse of the unit cells 15 in the second metamaterial 12. In this example, this is achieved by virtue of the second layer 22 of each unit cells 14 of Figure 5 comprising at least one conducting metal rod 50 which is electrically coupled to the third layer 24 and extends downwards through the dielectric material towards but separated from the first layer 20 by a dielectric region. Inversely, the second layer 22 of each unit cell 15 of Figure 6 comprises at least one conducting metal rod 60 which is electrically coupled to the first layer 20 and extends upwards through the dielectric material towards but separated from the third layer 26 by a dielectric region.

[0049] In view of the above, it is clear that the present invention provides a waveguide which has large bandwidth topological protection enabling scatter-free propagation of surface edge modes around arbitrary interface paths. The unit cells and thus metamaterials have the ability to be small, thin and compact with minimal loss in functionality. The simplicity of the design also allows for the seamless integrated incorporation of power-splitting and radiating mechanisms. That is, the structure of the waveguide lends itself well to being used for traditional waveguide applications.

[0050] Further, the waveguide of the present invention is able to confine and guide EM fields / waves along any arbitrarily shaped interface paths. Thus the invention is not limited to the same extent as conventional waveguides, i.e. in terms of the intricacy and acceptable level of curvature in their designs.

[0051] Another application of the waveguide of the present invention is in the field of antenna design. In particular, the waveguide may be configured to operate as an antenna as will now be described with respect to Figures 7 to 9.

[0052] As best shown in Figure 7, the waveguide 10 has substantially the same structural features as that shown and described with respect to Figures 1 to 3. That is, it comprises a first metamaterial 11 and a second metamaterial 12 having different topological properties (by virtue of having different Chern numbers), and which are configured to be interfaced to define a boundary 13 for confining EM waves between the two metamaterials 11 , 12. In the illustrated embodiment, the topological difference is achieved in that the two metamaterials comprise unit cells 14, 15 which have the same structure but opposite vertical orientations in the two metamaterials.

[0053] The waveguide 10 of Figure 7 differs from that of Figures 1 to 3 in that one of the metamaterials (the second metamaterial 12 in this embodiment) comprises a set of modified unit cells 15a which are adjacent to one another in a side-by-side arrangement along the boundary 13. The modified unit cells 15a may be identified by comparison with the remaining unit cells 15 in the second metamaterial 12 (or indeed the unit cells 14 of the first metamaterial 11) which may be regarded as unmodified unit cells 14, 15 having the same structure as that described above with respect to Figures 1 to 3. The unit cells 15a are modified in that the conducting region 26 in the third layer 24 comprises a cut-out section 80 where the conducting material is removed, i.e. there is a void or a gap of conducting material in that section. As best shown in Figure 8, the conducting material which in this example forms the hexagonal ring about the perimeter of the modified unit cell 15a is interrupted such that there is a void of conducting material along the length 81 of the cut-out section 80 between two termination points 82 and 83 on the conducting region 26. The cut-out section 80 exposes the dielectric material in the second layer 22. Within the wider metamaterial 12, the cut-out section 80 is at the perimeter of the metamaterial 12. It is in proximity to the boundary 13 and is located at or near to the transverse edge 222 of the second metamaterial 12 which faces the first metamaterial 11. In the embodiment shown, the cut-out sections 80 have the same planar positions in respective unit cells 15a.

[0054] The cut-out section 80 is provided to induce radiation of an EM field supplied to the waveguide at the input terminal 16, through the cut-out sections 80. Indeed it has been found that when an RF signal is supplied to the input terminal 16, the waveguide can emit a radiation pattern consistent with that expected from a leaky wave antenna. Without wishing to be bound by theory, the cut-out section 80 changes the behaviour of the unit cell 15a from one that is predominantly inductive, as is the case for the unmodified unit cell 15 where EM waves propagate along the edges at the boundary 13, to one that has a capacitance in series with that inductance for the modified unit cell 15a. The termination points 82 and 83 at opposite sides of the cut-out section 80 in effect forms a capacitor across the gap between them. The modified unit cell 15a will still have a bandgap which facilitates the existence of edge modes within the bandgap and enables electrons to propagate along the edge surfaces. However, the bandgap will have been shifted such that it no longer provides a bandgap response to confine EM waves at the frequencies that would otherwise be confined if the unit cell was unmodified. EM waves at that frequency can instead now propagate into space. That is, the modified unit cells 15a will have a different bandgap to that of the unmodified unit cells 14, 15. The extent by which the bandgap is shifted (different) is determined by the nature of the inductance and the capacitance of the unit cell, which depends upon the size of the cut-out section 80, i.e. the length 81 between the termination points 82, 83 of the conducting region 26 as measured across the cut-out section 80, at least in the first instance.

[0055] To prevent a large proportion of the power leaking into the metamaterial 12, in embodiments only the first row of unit cells 15a perpendicular to the boundary 13 comprise cut-out sections 80. However, the antenna function can be achieved in embodiments where more than one row of unit cells perpendicular to the boundary 13 cut-out sections 80, or indeed where at least one unit cell in one or more rows of both metamaterials comprises a cut-out section.

[0056] Outside of its bandgap, the capacitance across the cut-out section 80 changes the nature of the radiating modes that the structure will support, and in consequence the rate of power radiation along the structure, the direction of the beam and how quickly that beam changes direction with alteration in frequency. Accordingly, the length 81 of each cut-out section 80 may be predetermined and set at manufacture based on the desired operating frequency and bandwidth for the antenna. In the illustrated embodiment, the length 81 is 0.7mm, however suitable values may fall within a range up to 1.5mm. By setting the length 81 of the cut-out section 80, it is possible to tune the dispersion modes of the topological metasurface, hence giving the ability to set the frequency point at which the modes become leaky. In further embodiments, the antenna function of the waveguide 10 can be reconfigured and dynamically turned ON or OFF, e.g. in the field. Any form of dynamic alteration can be used but, as best shown in Figure 9, in embodiments this is achieved by providing adjustable conductors 91 in the cut-out section 80 instead of there being a void of material. That is, the cut-out section 80 comprises and is filled by a material 91 whose electrical conductivity can be modified and set by the user to in effect fully open or fully close a conductive path across the gap between the termination points 82, 83 of the conducting region 26. In other words, to selectively either introduce or remove a capacitance across the cut-out section 80, such that the cut-out section 80 is set to be either inductive or capacitive.

[0057] In the present embodiment, the cut-out sections 80 are filled with a phase change material, the electrical conductivity of which is locally variable under the application of heat, e.g. caused by incident photons. The system may further comprise a laser which is operable to irradiate the phase change material to dynamically control its conductivity. The phase-change material 91 may be any material that can be controlled to exist in two different phases, a crystalline phase and an amorphous phase, as solids at room temperature. In both phases, the atomic arrangement differs considerably between the amorphous and crystalline states, such that the material exhibits a large contrast in electrical conduction between those states. A suitable phase change material may be a chalcogenide- based phase change material such as germanium-tellurium, antimony-tellurium or germanium-antimony-tellurium (GST) mixtures. GST alloys, such as Ge1Sb4Te7, Ge1 Sb2Te4 and Ge2Sb2Te5, have been found to exhibit relatively fast crystallisation with a large electrical contrast. Thin film technology can be used for manufacture using such alloys, while colloidal techniques offer greater potential for control over thickness, conductivity and stability.

[0058] In alternative embodiments, the plural cut-out sections 80 are filled by and comprise diodes which are operable between an ON (i.e. inductive) state and an OFF (capacitive) state by the application of a voltage signal issued by a controller. That is, when a bias voltage is applied over the diode, then in effect the cut-out section 80 is closed and the energy is confined and carried along the boundary 13. However when the bias voltage is turned off, the cut-out section 80 does not confine the energy and a gap is in effect formed across the cut-out section 80 to allow the energy to leak. In embodiments, the diode is a Varactor diode or a PIN diode.

[0059] Other suitable materials 91 include but are not limited to photoconductive silicon or microfluidic systems with liquid metal or micro-electro-mechanical system switches. However, in preferred embodiments, optically-controlled conductors such as phase change materials, photoconductive silicon etc. are used as they do not require any control wires. By providing means to control whether the cut-out sections 80 are inductive or capacitive, the present invention is able to dynamically reconfigure the waveguide 10 between a first mode of operation in which EM waves at a first bandgap frequency are confined along the edges 222 of the metamaterial 12 and thus propagate along the boundary 13, and a second mode of operation in which those EM waves are deliberately radiated from the waveguide 10 through the unit cell 15a cut-out sections 80.

[0060] In further embodiments, where the adjustable conductor material 91 is received in the cut-out section 80, it is not only possible to reconfigure the waveguide 10 between the first mode and the second mode, but also to control and set the capacitance across the cut-out section 80 and thus control an aspect of the radiation pattern emitted thereby.

[0061] In particular, the capacitance across the cut-out section may be adjusted or set (by setting or changing the conductivity of the adjustable conductor material in the cut-out section) to change the effective cut-out gap size, and therefore change the frequency and direction of the radiation which is radiated through the cut-out section. For example, one can dynamically change the capacitance (effective gap size) to dynamically change the beam frequency. This enables the waveguide to be used as a frequency scanning antenna. Furthermore, by dynamically changing the capacitance, a beam at a fixed frequency can be scanned.

[0062] While the antenna function has been described above with respect to introducing a cut-out section in the conducting region of a unit cell, which correspondingly introduces a capacitance, the antenna function can be achieved using many different designs or modifications to the unit cell structures described herein, as long as the modified unit cells have a bandgap which is shifted relative to that of the other, unmodified unit cells in the same metamaterial or the other metamaterial of the wider waveguide structure.

[0063] It will be appreciated that whilst various aspects and embodiments of the present invention have heretofore been described, the scope of the present invention is not limited to the embodiments set out herein and instead extends to encompass all methods and arrangements, and modifications and alterations thereto, which fall within the scope of the appended claims.

Claims

Claims1. An electromagnetic waveguide, comprising: two metamaterials having different topological properties, such that the metamaterials are configured to confine electromagnetic fields along a boundary defined between the two metamaterials when in operative proximity; wherein: each metamaterial comprises a set of unit cells arranged in a side-by-side arrangement extending in a direction along the boundary; and each metamaterial comprises at least two unit cells in a direction perpendicular to a boundary section.

2. The electromagnetic waveguide of claim 1 , wherein each metamaterial comprises exactly two unit cells in a direction perpendicular to a boundary section.

3. The electromagnetic waveguide of claim 1 or 2, wherein each unit cell comprises two metasurfaces separated by a thickness of dielectric material.

4. The electromagnetic waveguide of claim 3, wherein: the thickness of the dielectric material is selected based on a predetermined relationship between the thickness and a bandwidth supported by the photonic topological insulator.

5. The electromagnetic waveguide of claim 3 or 4, wherein the thickness has a value within the range 0.1 mm to 2mm.

6. The electromagnetic waveguide of any preceding claim, wherein the two metamaterials have different topological properties in that: each unit cell has the same structure; and the unit cells in the first metamaterial have a first vertical orientation and the unit cells in the second metamaterial have a second vertical orientation opposite the first vertical orientation.

7. The electromagnetic waveguide of any preceding claim, wherein each unit cell comprises three layers:a first layer comprising a first planar pattern of conducting regions and insulating regions: a second dielectric layer; and a third layer comprising a second planar pattern of conducting regions and insulating regions.

8. The electromagnetic waveguide of claim 7, wherein: the first planar pattern of unit cells comprises a central conducting region and an outer insulating region; and the second planar pattern of unit cells in the second metamaterial comprises a central insulating region and an outer conducting region.

9. The electromagnetic waveguide of any preceding claim, wherein the boundary section comprises an input terminal at one end and an output terminal at another end, e.g. to supply an electromagnetic wave to the boundary section.

10. The electromagnetic waveguide of any preceding claim, wherein at least one unit cell is a modified unit cell in that it has a different bandgap to another one of the unit cells, to permit radiation of an EM field from the waveguide via the modified unit cell.

11. The electromagnetic waveguide of claim 10, wherein the modified unit cell has a different structure to that of the other unit cell, such that it will have a different bandgap to the other unit cell.

12. The electromagnetic waveguide of claim 10 or 11 , wherein: the set of unit cells in each metamaterial comprises at least one conducting region and at least one insulating region; the set of unit cells in a or each metamaterial comprises at least one modified unit cell wherein the conducting region has a cut-out section to permit radiation of an EM field from the waveguide through the cut-out section.

13. The electromagnetic waveguide of any one of claims 10-12, wherein the at least one modified unit cell is located at the perimeter of the metamaterial, e.g. in operative proximity to the boundary.

14. The electromagnetic waveguide of any one of claims 10-13, wherein: the at least one modified unit cell comprises plural modified unit cells which form a single row of adjacent unit cells perpendicular to the boundary; and the remaining rows perpendicular to the boundary comprise unmodified unit cells, e.g. which do not have a cut-out section.

15. The electromagnetic waveguide of any one of claims 12-14, wherein: the cut-out section comprises an adjustable conducting material to fill the cutout section; and the adjustable conducting material is operable to switch between a conducting state and a non-conducting state to selectively either prevent or allow radiation to be emitted through the cut-out section.

16. The electromagnetic waveguide of any one of claims 12-15, wherein the adjustable conducting material is operable to dynamically set or adjust the capacitance across the cut-out section and thus control an aspect of the radiation pattern.

17. The electromagnetic waveguide of claim 15 or 16, wherein the adjustable conducting material is a diode, e.g. a varactor diode.

18. The electromagnetic waveguide of claim 15 or 16, wherein the adjustable conducting material is a phase change material.

19. A method of using the electromagnetic waveguide of any preceding claim, comprising: bringing the two metamaterials into operative proximity so as to define an interface path for confining electromagnetic fields along a boundary between the two metamaterials; supplying an electromagnetic wave to an input terminal which is at one end of the boundary section; and receiving the electromagnetic wave at an output terminal at another end of the boundary section.