Electromagnetic waveguide

Abstract

An electromagnetic waveguide comprises two metamaterials (first metamaterial 11 and second metamaterial 12) having different topological properties (e.g. by virtue of having different Chern numbers),

Description

Field 5 This specification concerns electromagnetic (EM) waveguides, which uses a photonic topological insulator to control propagation of EM waves. Background 10 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- 15 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. 20 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. 25 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 30 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 35 volume and weight. Aspects of the present invention are concerned with a waveguide which incorporates a topological insulator to address the foregoing. 5 Summary 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), 10 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 15 cells in a direction perpendicular to (e.g. a point or points along) a boundary section. Each metamaterial may be regarded as a photonic topological insulator. 20 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. 25 In embodiments, the thickness of dielectric material between the metasurfaces has a value within the range 0.1mm to 2mm. This gives bandwidths of up to 6Ghz. The two metamaterials may have different topological properties in that: each unit 30 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. 5 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. 10 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. According to a further aspect of the present invention, there is provided a method 15 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 20 output terminal at another end of the boundary section. 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 25 parameter described herein may be applied to any aspect and / or combined with any other feature or parameter described herein. Brief Description of the Drawings 30 Embodiments of the invention will now be described by way of non-limiting example with reference to the accompanying drawings, in which: 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 35 present invention; 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; 5 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; io Figure 4 is a graph which illustrates the transmission and reflection characteristics of the waveguide of Figure 1; 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 15 accordance with a second embodiment of the present invention; and 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. 20 Like reference numerals are used to denote like features throughout the drawings. Detailed Description 25 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. The waveguide 10 comprises a first metamaterial 11 and a second metamaterial 30 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. 5 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), io 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. 15 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 20 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. 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 25 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 0.1mm and 2mm giving bandwidth of up to 6GHz. The strong coupling between the first layer 20 and the third layer 24 lifts trivial 30 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 35 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. The planar pattern of the first layer 20 is the inverse of the planar pattern of the 5 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 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 io 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. The outer insulating region 28 of the first layer 20 and the outer conducting region 15 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 20 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. It will be appreciated that the thickness 212 of the dielectric layer 22 may be varied 25 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 cross-30 coupling effects increasing the closer the complementary metasurface layers 20, 24. Merely as an example, the bandwidth increases from 8.2 GHz for a 1mm 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 35 bandwidth to be supported by the photonic topological insulator. With reference again to Figure 1, the set of unit cells 14 in the first metamaterial 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 5 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 io 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 12 may be regarded as having an upside-down orientation. 15 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 20 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. 25 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 30 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 5 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. The waveguide 10 comprises an input terminal 16 at a first end 17 of the interface io 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 15 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). 20 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. The graph is a scattering parameters graph, which shows the input-output 25 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 30 the input reflection coefficient and S22 is for the output reflection coefficient. 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 35 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. The Applicant has recognised that transmission effectiveness of the bound edge 5 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. io 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 15 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 20 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 25 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. As best shown in Figure 1, each metamaterial 11,12 comprises, at all points along 30 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 35 the boundary 13. 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 5 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 by virtue of being structurally the same but inversed (i.e. vertically flipped by 180 degrees) with respect to the unit cells in the other metamaterial, for example. io 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 15 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. 20 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. 25 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 30 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. Further, the waveguide of the present invention is able to confine and guide EM 35 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. It will be appreciated that whilst various aspects and embodiments of the present 5 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

1. 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; andeach 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 0.1mm 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; andthe 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; anda 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; andthe 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.

10. 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; andreceiving the electromagnetic wave at an output terminal at another end of the boundary section.

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