GB2433842A

GB2433842A - An artificially structured dielectric material

Info

Publication number: GB2433842A
Application number: GB9615714A
Authority: GB
Inventors: John Brian Pendry; Anthony James Holden
Original assignee: Marconi Caswell Ltd; GEC Marconi Ltd; Marconi Co Ltd; Marconi UK Intellectual Property Ltd
Current assignee: Marconi UK Intellectual Property Ltd
Priority date: 1995-08-02
Filing date: 1996-07-18
Publication date: 2007-07-04
Anticipated expiration: 2016-07-18
Also published as: GB2433842B; GB9615714D0; FR2928780A1; GB9515803D0

Abstract

The material comprises a network of conductive channels, the mean distance between interconnections (a) and the radius (r) of the channels being selected such that the material has a predetermined dielectric constant for incident radiation of a specific frequency or frequency band. The channels 1 may be wires or fibres or even colloidal particles embedded in a dielectric matrix. The material is arranged to have a plasma frequency at the frequency or in the frequency range of expected incident radiation. The plasma frequency is that frequency at which the dielectric constant is zero and thus the material acts as a reflector. The material may be used for radomes, absorbers or resonant cavities.

Description

AN ARTIFICIALLY STRUCTURED DIELECTRIC MATERIAL

The present invention relates to an artificially structured dielectric material (that is a material which is at least a dielectric at certain frequencies, but not necessarily dielectric at DC), and method for making same, more particularly but not exclusively to such a material having a zero or negative dielectric constant in predetermined frequency bands.

In certain applications it would be advantageous if the dielectric constant of a material could be tailored for a particular application, at least for a specific frequency range.

Such a material would be particularly advantageous in applications such as radomes enabling the dielectric constant of the radome material to be matched to that of air in order to maximise transmission.

Natural materials are known which have a zero or negative dielectric constant for radiation of particular frequencies, for example metals. The frequency at which the dielectric constant of a material is zero is known as the plasma oscillation frequency w and in metals this occurs in the optical range, resulting in metals being good reflectors of light.

An explanation for the above properties can be obtained by considering the atomic structure of a metal in accordance with the Jellium model. According to this model the metal can be considered to comprise positive ions arranged in a fixed lattice structure and approximated as a uniform "jelly" of fixed positive charge, with the wealdy bound "free electrons", or valence electrons, forming an associated electron gas or fluid which is free to move. In such a model the electron gas will have a preferred rest point relative to the positive background, where the net electric charge is zero. An applied electric field will cause the electron cloud to drift in a constant direction over the positive background until it is stopped by a restoring force created by the imbalance in the net electric charge as a function of position. The system behaves like a driven harmonic oscillator and as the frequency of the applied field is increased a point is reached at which the field changes at the resonant frequency of the oscillator ("rings"). At this point the electron gas will simply oscillate at the resonant frequency of oscillation of the gas being the plasma frequency In general a band of plasma nodes will exist with varying wavelengths and a corresponding dispersion. At frequencies significantly above the plasma frequency the electron gas cannot respond quickly enough to the field and the contribution to the dielectric constant saturates to a value associated with the bound polarisable charge on the ions.

There are certain applications where it would be desirable to reduce the plasma frequency to infrared or microwave frequencies and below. This would make it possible to produce materials having a desired dielectric constant at a specific frequency, which material could form the basis of a highly efficient microwave absorbing structure with applications such as radar absorbing material for stealth and general radar installations.

A designable dielectric constant could also be used in radome materials with good free space matching characteristics. However the plasma frequency is given by: 2 -ne -* (1) 0 m where n is the density of electrons, e the charge on an electron and m* the effective mass of the electron. is the dielectric constant of free space in SI units. Reduction of the plasma frequency by reducing electron density n is feasible down to the infrared band but materials with low n and suitably high mobility are not available for lower frequencies.

According to a first aspect of the present invention there is provided an artificially structured dielectric material comprising an interconnected network of conductive channels (which term in the context of this specification covers all types of substantially linear conductive but not necessarily straight paths, including conductive wires and fibres), the diameter of the channels and mean distance between interconnections being selected such that the composite material has a plasma frequency, as seen by the incident radiation at a predetermined frequency, or within a predetermined frequency band, whereby the material has a real part of the dielectric constant for the incident radiation less than or equal to zero for incident radiation below or at the frequency or frequency band of the incident radiation.

The present invention exploits the electromagnetic properties of conducting channels.

When electrons are constrained to narrow channels, a large inductive effect is produced, slowing the electrons in their trajectories. This can be interpreted as the magnetic vector potential A adding an electromagnetic term to the mass of an electron in bulk material m* (in the equation of motion). This is a modification to the momentum of a

particle j in a magnetic field where:

IL = m + e A_j C = m e ff (2) where e is the charge on an electron, y is the velocity of the electron, and c is the velocity of light.

From equation (2) above it can be seen that the apparent momentum of an electron increases due to the inductive effect and thus the electron behaves as though it has a higher effective mass mCfe Substituting mCf which is greater than m* due to the inductance of the thin conducting channels, for m* in equation (2) reduces o and therefore the present invention enables a material to be manufactured with a predetermined plasma frequency. The radius of the channels, r, and average distance between interconnections, a, can be determined by considering all the electrons to be confined in the channels such that when any current flows a strong magnetic field is established around the channels, given by: n ye H(R)= = I (3) 2itR 2itR where I is the current flowing in the channel, R is distance from the channel, n 1is the number of electrons per unit length of wire, and v is the mean electron velocity. This

field can be expressed as:

H(R)&01Vx A(R) (4) where t n ye A (R) = in (aIR) (5) 2t a' being the average spacing between interconnections, or in a lattice structure the lattice constant.

From classical mechanics, electrons in a magnetic field have an additional contribution to their momentum of eA, and therefore the extra momentum per unit length of the wire is: ji e2n2 v e n 1A ( r) = 0 1 n ( a / r) = m c fffl 1v (6) 2t - 0e 2 eff -in (aIr) (7) 2ic In practice this is the dominant contribution throughout the frequency bands of interest and the actual mass m of the electron will henceforward be omitted.Substituting meff for m in equation 1: 2 2 -2 -2 c 2 -_________ -________________ -(8) em eff ej,i 01n (air) a 21n (air) Preferably a and r are selected such that the packing fraction of the network is less than ten percent, and with a' being of the same order but substantially less than the selected wavelength. r is a free parameter, but to tune the structure it must be substantially smaller than a to ensure that the magnetic field can penetrate and see the individual wires. r is also limited by technological achievability -hence a and r must be balanced to optimise the structure.

The network is preferably three dimensional in structure and interconnected, so that the structure does not decompose into, isolated planes so that the flow of electronic current is not disrupted.

The energy storage capacity of the proposed structure (per unit volume) can be increased by coating the wires with a high-magnetic permeability (.t) material. This increases the magnetic energy stored and also confines the field, allowing a higher wire density. Real materials with high pt also have high, but this is in practice not serious because the magnetic field will be confined to the coating whereas the electric field spreads throughout the spaces. However there can be problems with conductivity at interconnections of the channels.

Whilst it is possible for the coating to be applied in such a way as to allow the conductive channels to be connected beneath it, this can be inconvenient. However, it is probably that a wealdy conductive coating could allow effective "shorting" across itself where conductive channels cross, whilst also carrying insignificant current axially.

(This is harder to achieve at high frequencies where current tends to be confined to the surface.) Helical wires allow axial capacitive conduction between turns and are, to an extent, self-spacing. This is a manufacturing option, requiring fewer cross-connections.

According to a second aspect of the invention, there is provided a method of producing an artificially structured dielectric material, the method comprising determining a frequency or frequency band for which it is desired that the material has a dielectric constant equal to or less than zero; determining the plasma frequency; and forming a network of interconnected channels in a dielectric media, selecting the diameter of the channels and mean distance between interconnections such that the composite material has the desired plasma frequency, as seen by incident radiation at the determined frequency or within the determined frequency band, and whereby the material has a real part of the dielectric constant for the incident radiation less than or equal to zero for incident radiation below or at the frequency or frequency band of the incident radiation.

Examples of structured materials in accordance with the present invention will now be described, by way of example only, with reference to the accompanying drawings of which: Figure 1 is a schematic illustration of a lattice structure in accordance with the present invention; Figures 2 to 6 illustrate various methods by which a lattice structure in accordance with the present invention can be fabricated; and Figure 7 illustrates the dispersion relation for surface plasma waves between two sheets of metal.

Referring to Figure 1 there is illustrated a regular cubic lattice structure comprising a number of conductive stainless steel fibres 1, each of a length large compared to the fibre periodicity a. The value of a determines wavelength range of operation and for microwave applications at J band a is approximately equal to 3mm. Typically the diameter of the fibre r should be less than 1/10th of the spacing a, and for higher frequency operation the value of a needs to be reduced. At infrared frequencies an appropriate value for r could be as little as mm making this a natural limit of the technique's applicability. The lattice period a' is selected to be appropriate for the selected frequency range and this is typically around the effective plasma frequency given by equation 8.

Inserting the following values in equation 8, = 4it x iO, = 1.602 x r = 1.0 x 10 gives a = 15mm, o.,, (calculated) = 2.57 GHz, a = 5mm, (calculated) = 8.2 GHz, a = 3mm, o (calculated) = 14.09 Ghz.

These have been checked by detailed numerical analysis.

Referring to Figures 2 and 3 there is illustrated one method by which a structure in accordance with the present invention can be fabricated. The method comprises laying conducting fibres 1 along dielectric fibre 2 to form a composite fibre 3, a number of such composite fibres 3 being subsequently stacked as illustrated in Figure 3 to form a fully 3-D conducting cubic lattice. Alternative methods of forming a regular lattice structure are envisaged such as 3-D knitting or weaving or by a modified velvet process.

The dielectric fibres 2 can be glass fibres.

In one practical material demonstration a multi layer sandwich structure 4 was constructed, as shown in Figure 4, consisting of 20 micron diameter wires made from gold plated copper laid in straight lines with 5mm spacing between the lines and separated by a 3mm polymer sheet from the next layer of wires 7 laid at right angles to the first. The sandwich is completed by a succession of further 3mm sheets separating wires laid alternately at right angles. This produced a 3D unit cell of dimension 5mm x 5mm x 6mm. This was measured using normal incidence microwave plane waves in the 2-18GHz frequency band and found to demonstrate the predicted plasma frequency at 9GHz, with a negative value of the real part of the dielectric constant in a frequency band below this plasma frequency. The broadening of this response depended on the resistivity of the wires at the measurement frequency which was reduced by gold coating.

Regardless of the manufacturing technique, care needs to be taken to arrange the fibres in all three dimensions in such a manner to ensure good electrical contact is established between the conductive fibres 1 where they intersect.

The structure need not be a regular lattice structure but alternatively could be a random array of interconnecting conductive fibres comprising bunches of fibres arranged in a matrix material, such as a dielectric liquid which could subsequently be set to produce a pseudo regular lattice, the length of the conductive fibres and packing fraction being selected to provide an average spacing a, with electrical connection also occurring at a pseudo periodic interval a and the conducting fibres provide conduction in all three dimensions on roughly the given period. In a regular lattice structure modest bowing of the conducting fibres would not significantly affect the properties of the material.

An alternative pseudo random array can be constructed by arranging short conducting fibres of between 3-12mm in length by suspension in a dielectric liquid. Again, the packing fraction and the length of the fibres must be such as to provide pseudo periodic conduction paths in all three dimensions with good electrical contact being established between the fibres on an average pseudo period a.

Yet another alternative method of producing an artificially structured dielectric material would be by encouraging conductive polymers or polymer-like chains of appropriate diameter to form a pseudo periodic lattice in three dimensions with good electrical conductivity and good electrical contact at the "modes". This could be achieved by biological, chemical or electrochemical process such as for example a 3-D version of the Langmuir-Blodgett films.

Another technique by which a structure in accordance with the present invention could be fabricated is by using laser modelling or direct wet-dry etch processing of metal substrates producing an appropriate honeycomb structure which can then produce the desired 3-D conducting lattice with appropriate periodicity and channel diameter.

Alternatively the structure can be fabricated by weaving a series of conductive fibres into a 3-D structure as illustrated in Figure 5 comprising a number of straight sectioned helix interlocked to keep the fibres under tension and provide connections at each vertex. Such a structure could be self supporting with the wires pre-tinned and subsequently baked in order to fix the structure and ensure good electrical contact.

A structure in accordance with the present invention could also be formed from a number of polyhedra each comprising conductive channels on their edges with the side either being open or made of dielectric sheet with the conducting fibre formed from conductive material on the edge of the sheets, a tetrahedron being illustrated in Figure 6. A number of these can then be arranged together either in an ordered pile or random heap.

Open foams, where only the bubble intersections remain, might be baked to give a carbon or even metal network with the desired characteristics.

Channels could be made of a rigid, non-conducting core with a thin highly-conductive coating. At high frequencies, where current is confmed to the wire surface, this could give a lighter, stronger structure than a solid wire version, but with identical electrical properties.

The foregoing describes a few methods by which a structure in accordance with the present invention could be fabricated but it will be realised that any suitable manufacturing technique may be used to provide such a structure.

An artificially structured material in accordance with the present invention has a number of applications. The surface modes of materials in accordance with the invention, and other modes easily created by further structuring of the geometry of material in accordance with the invention have a very high density of states and often have a resonant nature. It is therefore envisaged that it will be possible to generate high local intensities of microwaves for modest input power providing a means of generating microwaves in very small volumes without the need for a conventional resonant cavity.

With a negative dielectric constant there is the possibility of surface modes satisfying eff + 1 = 0. Such modes might couple to external electromagnetic radiation making possible emitter or detector applications over a wide band of frequencies.

The surface modes of the material also offer the possibility of several novel waveguides, the modes on two surfaces in close proximity interacting to give a symmetric and antisymmetric mode with dispersion. This is illustrated in Figure 7 which shows the dispersion relation for surface plasma waves between two sheets of metal. The antisymmetric mode tends to zero at small q and the symmetric mode tends to the bulk plasma frequency. Unlike a conventional waveguide, the group velocity of a material in accordance with the invention is controlled by the plasma frequency and may be much less than the velocity of light. In waveguides consisting of two parallel plates of material in accordance with the invention the group velocity may be much less than the velocity of light, and offers the possibility for constructions of novel mm wave filters.

Another possible application of the material is to levitation devices. This arises because of the plasma frequency Re(eff) =0 offering novel boundary conditions. An infinitely conducting material (or a good metal) requires the electric field to lie (nearly) perpendicular to the surface. A material obeying the above equation requires the electric field (at &) to lie parallel to the surface in the same way that a superconductor (ji = 0) requires magnetic fields to be parallel (at DC). At the plasma frequency the material repels rather than attracts lines of electric force and therefore is repelled from strong electric fields and may therefore be suitable for applications in levitation devices.

Probably the greatest potential application of this new material arises from the ability to engineer a low or zero dielectric constant material at particular frequency bands by balancing the background environment dielectric material with the negative dielectric constant matrix to provide the desired dielectric constant. This may be used to provide the "perfect" radome material with = 1, thereby matched to air for matching out electromagnetic waves to and from transmit/receive antennas. The material also offers a low dielectric constant substrate for microwave devices and circuits to reduce capacitance while offering other properties such as high thermal conductivity, and smaller size (reduced intracircuit coupling). It could also be used to make the RF phase uniform across a large circuit.

A further application of a material in accordance with the present invention is as a microwave absorbing material. Metal colloids at optical frequencies are known to be extremely efficient absorbers of optical radiation, the so called gold-blacks being one example. These colloids are believed to achieve this absorption by the creation of a photonic band gap structure formed from the strongly resonant states based around the surface plasma frequency of the constituent metal spheres. By forming similar colloid-like structures from the material in accordance with the present invention strong absorption may be achieved in the selected frequency band. The diameter of the particles would need to be on a scale large compared to the lattice spacing a' of the conducting fibres but small compared to the wavelength of the incoming electromagnetic radiation.

Claims

CLAIMS

1. An artificially structured dielectric composite material comprising an interconnected network of conductive channels, the diameter of the channels and mean distance between interconnections being selected such that the composite material has a plasma frequency, as seen by the incident radiation at a predetermined frequency, or within a predetermined frequency band, whereby the material has a real part of the dielectric constant for the incident radiation less than or equal to zero for incident radiation below or at the frequency or frequency band of the incident radiation.

2. A material as claimed in claim 1 wherein the interconnected network is embedded in a matrix material.

3. A material as claimed in claim 2 wherein the packing fraction of the network is less than ten per cent of the matrix material.

4. A material as claimed in any preceding claim wherein the specific frequency or frequency band is below the optical frequency band.

5. A material as claimed in any preceding claim wherein the fibres are metallic.

6. A material as claimed in any preceding claim wherein the fibres are superconducting.

7. A material as claimed in any preceding claim wherein the interconnected network is arranged as a regular lattice structure.

8. A material as claimed in any preceding claim wherein the conductive channels have a surface coating of a material with a high magnetic permeability relative to the material of the channel.

9. A material substantially as hereinbefore described with reference to the accompanying figures.

10. A method of producing an artificially structured dielectric composite material, the method comprising: determining a frequency or frequency band for which it is desired that the material have a dielectric constant equal to or less than zero; determining the plasma frequency; and forming a network of interconnected channels in a dielectric media, selecting the diameter of the channels and mean distance between interconnections such that the composite material has the desired plasma frequency, as seen by incident radiation at the determined frequency or within the determined frequency band, and whereby the material has a real part of the dielectric constant for the incident radiation less than or equal to zero for incident radiation below or at the frequency or frequency band of the incident radiation.

11. A method as claimed in claim 10 comprising embedding the conductive channels in a matrix material.

12. A method as claimed in any one of claims 10 to 11 comprising arranging the channels in a regular lattice structure.

13. A method as claimed in any one of claims 10 to 12 comprising placing the conductive channels on non-conductive rods of material and arranging the rods such that the channels form an interconnected network.

14. A method as claimed in any one of claims 10 to 13 comprising forming a random network of channels.

15. A method as claimed in any one of claims 10 or 11 comprising weaving the channels into a three dimensional structure.

16. A method as claimed in any one of claims 10 or 11 comprising knitting the channels into a three dimensional structure.

17. A method as claimed in any one of claims 10 to 15 comprising potting the channels in a matrix material.

18. A method as claimed in any one of claims 10 or 11 comprising arranging conductive channels in suspension in a dielectric liquid and subsequently permitting the liquid to set.

19. A method as claimed in claim 18 wherein the channels are between 3mm and 12mm in length.

20. A method as claimed in any one of claims 10 or 11 comprising forming the lattice structure by thin film techniques.

21. A method as claimed in any one of claims 10 or 11 comprising forming the lattice structure from a plurality of polyhedra having conductive edges.

22. A method as hereinbefore described with reference to the accompanying drawings.

Amendments to the claims have been filed as follows 1. An artificially structured dielectric composite material comprising a network of conductive channels, wherein a mean distance between conductive channels is substantially less than a wavelength of radiation of a selected frequency or frequency band at which the material is intended to be used and wherein the diameter of the channels is substantially less than the mean distance such that the composite material has a plasma frequency as seen by said radiation whereby the material has a real part of the dielectric constant which is less than or equal to zero for radiation below or at the selected frequency or frequency band.

2. A material as claimed in Claim 1 wherein the diameter of the channels is less than one tenth of the mean distance.

3. A material as claimed in Claim 1 or Claim 2 wherein the network is embedded in a matrix material.

4. A material as claimed in any preceding claim wherein the selected frequency or frequency band is below the optical frequency band.

5. A material as claimed in any preceding claim wherein the conductive channels are metallic.

6. A material as claimed in any preceding claim wherein the conductive channels c0 are superconducting.

7. A material as claimed in any preceding claim wherein the conductive channels are arranged as a regular lattice structure.

8. A material as claimed in any on of Claims 1 to 6 wherein the conductive channels are arranged as a random network.

9. A material according to any preceding claim wherein the conductive channels are woven into a three dimensional network.

10. A material according to any one of Claims 1 to 6 wherein the conductive channels are knitted into a three dimensional network.

11. A material according to any preceding claim wherein the conductive channels are interconnected.

12. A material as claimed in any preceding claim wherein the conductive channels have a surface coating of a material with a high magnetic permeability relative to the material of the channel.

13. A material substantially as hereinbefore described with reference to or substantially as illustrated in Figures 1, 2, 3, 4, 5 or 6 of the accompanying figures.

14. A method of producing an artificially structured dielectric composite material, the method comprising: selecting a frequency or frequency band for which it is desired that the material has a dielectric constant equal to or less than zero; forming a network of conductive channels in which a mean distance between conductive channels is substantially less than the wavelength of radiation of the selected frequency or frequency band and selecting the diameter of the channels to be substantially less than the mean distance between conductive channels such that the composite material has the desired plasma frequency as seen by radiation at the selected frequency or within the selected frequency band, and whereby the material has a real part of the dielectric constant which is less than or equal to zero said radiation below or at the selected frequency or selected frequency band.

15. A method as claimed in Claim 14 comprising embedding the conductive channels in a matrix material.

16. A method as claimed in Claims 14 or Claim 15 comprising arranging the channels in a regular lattice structure.

17. A method as claimed in any one of Claims 14 to 16 comprising forming the conductive channels on rods of non-conductive material and arranging the rods such that the channels form a network.

18. A method as claimed in any one of Claims 14, 15 or 16 comprising forming a random network of conductive channels.

19. A method as claimed in any one of Claims 14 to 18 comprising weaving the conductive channels into a three dimensional structure.

20. A method as claimed in any one of Claims 14 to 18 comprising knitting the conductive channels into a three dimensional structure.

21. A method as claimed in any one of Claims 14 to 20 comprising potting the conductive channels in a matrix material.

22. A method as claimed in Claims 14 or Claim 15 comprising arranging the conductive channels in suspension in a dielectric liquid and subsequently permitting the liquid to set.

23. A method as claimed in Claim 22 wherein the channels are between 3mm and 12mm in length.

24. A method as claimed in Claim 14 or Claim 15 comprising forming the network by thin film techniques.

25. A method as claimed in Claim 14 or Claim 15 comprising forming the network from a plurality of polyhedra having conductive edges.

26. A method as substantially hereinbefore described with reference to or substantially as illustrated in the accompanying drawings.