Metamaterial system and uses thereof

Abstract

A metamaterial system comprises a metamaterial having a multiplicity of structures made of a first material distributed to form a periodic pattern within a bulk made of a second material. One of the first and the second materials is metallic and the other one of the first and the second materials is dielectric. The system optionally and preferably comprises a magnetic field source forming a magnetic field within the metamaterial, wherein the magnetic field is selected to ensure that an electrical permittivity of the metamaterial is negative.

Description

[0001] METAMATERIAL SYSTEM AND USES THEREOF

[0002] RELATED APPLICATION

[0003] This application claims the benefit of priority of U.S. Provisional Patent Application No. 63 / 632,105 filed on April 10, 2024, the contents of which are incorporated herein by reference in their entirety.

[0004] FIELD AND BACKGROUND OF THE INVENTION

[0005] The present invention, in some embodiments thereof, relates to a metamaterial and, more particularly, but not exclusively, to a system having a metamaterial with negative electrical permittivity and to uses thereof.

[0006] Electricity is the presence and flow of electric charges. These charges can be positive or negative. When there is an imbalance of positive and negative charges in a region, an electric field is created. An electric field exerts a force on charges within the field. When a material is placed in an electric field, the electric field exerts a force on the charges within the material, causing them to shift slightly from their equilibrium positions. This shift in charges is called polarization. The degree to which a material can be polarized by an electric field is determined by a quantity known as electrical permittivity and denoted 8. The permittivity of the vacuum, denoted so, is a fundamental constant in physics and has a value of approximately 8.85 x 1012F / m. In the c.g.s. unit system, s is dimensionless.

[0007] The polarization of a material creates an additional electric field, which opposes the original field. This reduces the overall electric field strength within the material. The total electric field in the material is the sum of the original field and the field created by the polarization. The relationship between the electric field, E, and the polarization P in a material is described by the electric displacement field, D. The electric displacement field is defined as D = soE + P. In a linear, homogeneous, isotropic material with instantaneous response to changes in the electric field, the polarization P is linearly proportional to the electric field E via P = (s - 8o)E, and so, for these materials the relation between the electric displacement field and the electric field is given by D = sE.

[0008] Materials with a high electric permittivity are said to be good dielectrics because they significantly reduce the electric field strength within the material.

[0009] The permittivity s appears also in the law of the electrostatic Coulomb interaction of charged particles F = (l / s)(qiq2 / r3)r, where F is the force applied by one particle on the other, r is a vector connecting the two particles and qi and q2 are their electrical charges. When the vectors F and r are parallel to each other, the force is a repulsive force, and when these vectors are antiparallel to each other, the force is an attractive force. Thus, when s > 0, like charges repel each other and unlike charges attract each other. Further, the magnitude of the force (the strength of the Coulomb interaction between the particles) is reduced or enhanced depending on the value of 8.

[0010] Metamaterials are artificially engineered materials that have properties not found in naturally occurring materials. They are typically composed of repeating patterns of structures at scales smaller than the wavelengths of the phenomena they are designed to influence. The properties of metamaterials are derived both from the inherent properties of their constituent materials and from the geometrical arrangement of those constituent materials.

[0011] SUMMARY OF THE INVENTION

[0012] According to an aspect of some embodiments of the present invention there is provided a metamaterial system. The system comprises a metamaterial comprises a multiplicity of structures made of a first material distributed to form a periodic pattern within a bulk made of a second material, wherein one of the first and the second materials is metallic and the other one of the first and the second materials is dielectric; and a magnetic field source forming a magnetic field within the metamaterial, wherein the magnetic field is selected to ensure that an electrical permittivity of the metamaterial is negative.

[0013] According to some embodiments of the invention the first material is metallic and the second material is dielectric.

[0014] According to some embodiments of the invention the first material comprises bismuth.

[0015] According to some embodiments of the invention the first material is dielectric and the second material is metallic.

[0016] According to some embodiments of the invention a largest diameter of the structures is less than half of a periodicity parameter of the periodic pattern.

[0017] According to some embodiments of the invention a largest diameter of the structures is more than a quarter of a periodicity parameter of the periodic pattern.

[0018] According to some embodiments of the invention the structures are spherical.

[0019] According to some embodiments of the invention the structures are ellipsoidal.

[0020] According to some embodiments of the invention the structures are cylindrical.

[0021] According to some embodiments of the invention the structures are non-hollow.

[0022] According to some embodiments of the invention the magnetic field source is configured to generate a static magnetic field.

[0023] According to some embodiments of the invention the magnetic field source is configured to generate a static magnetic field having a strength of at least 0.1 T. According to some embodiments of the invention the system comprises a space characterized by a positive electrical permittivity adjacent to a surface of the metamaterial forming an interface therebetween.

[0024] According to some embodiments of the invention there are at least two interfaces between the space and the metamaterial.

[0025] According to some embodiments of the invention the space is a vacuum space.

[0026] According to some embodiments of the invention the system comprises atomic nuclei within the space, wherein the negative electrical permittivity of the metamaterial induces fusion between the atomic nuclei.

[0027] According to some embodiments of the invention the atomic nuclei comprise deuterium and the fusion is by a deuterium-deuterium reaction.

[0028] According to some embodiments of the invention the atomic nuclei comprise deuterium and tritium and the fusion is by a deuterium-tritium reaction.

[0029] According to some embodiments of the invention the atomic nuclei comprise tritium and the fusion is by a tritium-tritium reaction.

[0030] According to some embodiments of the invention the system comprises atoms within the space, wherein the negative electrical permittivity of the metamaterial induces ionization of the atoms.

[0031] According to some embodiments of the invention the system comprises liquid within the space, wherein the negative electrical permittivity of the metamaterial induces chemical reaction within the liquid.

[0032] According to an aspect of some embodiments of the present invention there is provided a nuclear propulsion system, comprises the metamaterial system as delineated above and optionally and preferably as further detailed below.

[0033] According to an aspect of some embodiments of the present invention there is provided a vehicle, being propelled by the nuclear propulsion system as delineated above and optionally and preferably as further detailed below.

[0034] According to an aspect of some embodiments of the present invention there is provided a power plant, comprises the metamaterial system as delineated above and optionally and preferably as further detailed below.

[0035] According to an aspect of some embodiments of the present invention there is provided a particle accelerator, comprises the metamaterial system as delineated above and optionally and preferably as further detailed below. According to an aspect of some embodiments of the present invention there is provided a method of generating energy, comprises introducing atomic nuclei into the vacuum space of the system as delineated above and optionally and preferably as further detailed below, so as to induce fusion between the atomic nuclei.

[0036] According to an aspect of some embodiments of the present invention there is provided a method of ionizing atoms or molecules, comprises introducing atoms into the space of the system as delineated above and optionally and preferably as further detailed below, so as to induce ionization of the atoms or molecules.

[0037] According to an aspect of some embodiments of the present invention there is provided a method of generating current, comprises introducing charged particles of like charges into the space of the system as delineated above and optionally and preferably as further detailed below, and applying an electric field to the space.

[0038] According to an aspect of some embodiments of the present invention there is provided a method of inducing a chemical reaction between molecules, comprises introducing the molecules into the space of the system as delineated above and optionally and preferably as further detailed below.

[0039] According to some embodiments of the invention the method is executed at room temperature.

[0040] Unless otherwise defined, all technical and / or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and / or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.

[0041] Implementation of the method and / or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and / or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system.

[0042] For example, hardware for performing selected tasks according to embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to exemplary embodiments of method and / or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and / or data and / or a non-volatile storage, for example, a magnetic hard-disk and / or removable media, for storing instructions and / or data. Optionally, a network connection is provided as well. A display and / or a user input device such as a keyboard or mouse are optionally provided as well.

[0043] BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0044] Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced.

[0045] In the drawings:

[0046] FIG. 1 a schematic illustration, of a metamaterial system, according to some embodiments of the present invention;

[0047] FIG. 2A schematically shows a sketch of l / s vs. 8 with discontinuity at s = 0 when s is assumed as real.

[0048] FIG. 2B schematically shows real (solid line) and imaginary (dashed line) parts of s=sMxxvs. o / op for a dimensionless magnetic field H=OCT=20.

[0049] FIG. 2C schematically shows A real part of l / s vs. Re s when the existence of the imaginary part of s is taken into account. The numerical values of s are taken from the branch AB shown in FIG. 2B.

[0050] FIGs. 3A-B are Similar to FIGs. 2A and 2B, respectively, except for the macroscopic dielectric permittivity seof a conductor-insulator composite with conducting elliptical inclusions shown in the inset. Results are obtained by Clausius-Mossotti (CM) and dilute (dil.) approximations vs. o / op. OPT=40. In FIG. 3B, the numerical values of s are taken from the Clausius-Mossotti approximation branch AB shown in FIG. 3B.

[0051] FIG. 4 is a schematic illustration showing a side view of a thin slab with two point unlike charged qi and q2, where the thin slab has permittivity si creating a bound electron-hole pair (exciton). Not all lines of the electrostatic forces are inside the slab. Therefore, the interaction between the point charges does not follow the Coulomb law. The permittivity of the surrounding medium is 82. FIG. 5 is a schematic illustration of two point charges -qi and -q2 in a slab with permittivity 81 above an infinitely thick medium with permittivity 82. The horizontal component of the Coulomb force F|| between charges -qi and -q2 is calculated using the method of images.

[0052] FIG. 6A-D show numerically calculated real (solid line) and imaginary (dashed line) parts of 8(e)xxof periodic array of conducting spheres vs. dimensionless frequency o / op. FIG. 6A corresponds to magnetic field H=0, while 80= 1. Localized surface plasmon resonances (LSPR) appear at a frequency Ores = coP((l-pi)n / so)1 / 2. FIG. 6B is similar to FIG. 6 A except for 80= 10. FIG. 6C is similar to FIG. 6A except for H=20 and 80= 1. Due to the applied field, the LSPR splits into the two branches, one of which (Ores,-) shifts by A01 to smaller values of o / op, while the other one (Ores,+) shifts in the opposite direction by Ao 2. FIG. 6D is similar to FIGs. 6A-C except for H=20 and 8o=lO. Due to the applied field the LSPR splits into two branches, one of which (Ores,-) shifts by A03 which is larger than in FIG. 6C due to parameter 8o=lO. In all graphs, the radii of the spheres R=0.45 a, where a is the distance between the sphere centers, OPT=40, and Shost = 82=1. The vertical dashed lines are eye guides which indicate the appearance of the LSPR. The arrows indicate the shifts of the resonances.

[0053] FIGs. 7A-D are similar to FIGs. 6A-D, respectively, except for a periodic array of infinitely long conducting circular cylinders. In FIG. 7A H=0, and 8o=l. The LSPR appears at the frequency Ores / op»0.45, where the depolarization factor nxof the circular cylinder is 1 / 2. In FIG. 7B 8o=lO. The LSPR shifts approximately by A01 to smaller frequencies due to parameter s0=10. Ores / oP~0.14. In FIG. 7C, H=20 and 8o=l. The LSPR shifts by A02 to larger frequency. Ores / oP~0.67. In FIG. 7D, the cylinders are of finite length Z=0.6a, where a is the distance between cylinder centers. H=20, and 8o=lO. The LSPR appear at smaller frequencies. Since the cylinders have final length, the behavior of the LSPR is qualitatively similar to behavior in the case of sphere. In all figures the radii of the cylinders R=0.4a, OT=40, and 8host=82=l. The vertical dashed lines indicate the calculated values of the LSPR frequencies.

[0054] FIG. 8 shows two resonance branches ores,- / opand ores,+ / opvs. Oc / opfor two values of the ratios n / so=l / 3 (upper curve) and nso=l / 3O (lower curve). Note that for oc / op» (4n / so)1 / 2its value approaches (n / so)1 / 2 / (oc / op) and therefore limCBc / coP^0o(ores- / op)→0.

[0055] FIG. 9 shows 8evs. o / opfor values oc / op=10 and oc / op=100. The resonance (with the negative values of se) appear arbitrary close to the zero frequency (o / op~0) but strictly at the zero frequency (o / op=0) the effective permittivity is se=8o(l+pi / n). DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

[0056] The present invention, in some embodiments thereof, relates to a metamaterial and, more particularly, but not exclusively, to a system having a metamaterial with negative electrical permittivity and to uses thereof.

[0057] Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and / or methods set forth in the following description and / or illustrated in the drawings and / or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways.

[0058] Referring now to the drawings, FIG. 1 illustrates a metamaterial system 10, according to some embodiments of the present invention. System 10 comprises a metamaterial 12 having a multiplicity of structures 14 made of a first material distributed to form a periodic pattern within a bulk 16 made of a second material.

[0059] Representative examples of types of periodic patterns suitable for the present embodiments, include without limitation, Representative examples of types of periodic patterns suitable for the present embodiments, include without limitation, square lattices, rectangular lattices, hexagonal lattices, triangular lattices, honeycomb lattices, kagome lattices, rhombic lattices, oblique lattices, centered rectangular lattices, centered square lattices, pyramidal lattices, diamond cubic lattices, hexagonal close-packed lattices, face-centered cubic lattices, body-centered cubic lattices, simple cubic lattices, gyroid lattices, Schwarz P surfaces, Schwarz D surfaces, Lidinoid surfaces, Schoen IWP surfaces, Neovius surfaces, Fischer-Koch S surfaces, Schwarz H surfaces, Schoen F-RD surfaces, and combinations thereof. The periodic pattern of metamaterial 12 can be characterized by a periodicity parameter shown at 18. When the periodic pattern is a lattice, periodicity parameter 18 can be the largest diameter of a unit cell of the lattice.

[0060] A unit cell of a lattice is the smallest repeating building block that, when translated through the lattice vectors, can reproduce the entire lattice structure. The unit cell contains one or more lattice points and is characterized by its dimensions, angles between the lattice vectors, and the positions of the lattice points within the cell. For example, when the periodic pattern is a cubic lattice, the unit cell is a cube with structures 14 at the corners of the cube, and may also include additional structures within the volume of the cube. In this case, periodicity parameter 18 is the length of the cube's edge.

[0061] In the simplest case, the periodicity parameter 18 is the distance between the nearest neighbor structures 14, as illustrated in FIG. 1. The skilled person would appreciate that this correspond to a primitive cubic lattice. One of the first and second materials is metallic and the other one of first and second materials is dielectric. Specifically, in some embodiments of the present invention structures 14 are metallic and bulk 16 is dielectric, and in some embodiments of the present invention structures 14 are dielectric and bulk 16 is metallic.

[0062] Representative examples of metallic material suitable for any of the above embodiments, include without limitation, aluminum, copper, silver, gold, nickel, titanium, tungsten, chromium, molybdenum, tantalum, zirconium, hafnium, vanadium, niobium, tin, lead, bismuth, indium, gallium, zinc, iron, cobalt, manganese, beryllium, magnesium, lithium, and alloys or combinations thereof. These metals are useful due to their favorable electromagnetic properties, such as high electrical conductivity and low losses at optical and microwave frequencies. Other metals are also contemplated.

[0063] Representative examples of dielectric material suitable for any of the above embodiments, include without limitation, silicon dioxide, silicon nitride, silicon oxynitride, aluminum oxide, titanium dioxide, zirconium dioxide, hafnium dioxide, tantalum pentoxide, magnesium oxide, yttrium oxide, boron nitride, aluminum nitride, gallium nitride, silicon carbide, and combinations thereof. These dielectric materials are useful due to their compatibility with micro- and nanofabrication processes. Other dielectrics are also contemplated.

[0064] Structures 14 are optionally and preferably non-hollow, but embodiments in which one or more of structures 14 are hollow are also contemplated.

[0065] Structures 14 can have any geometrical shape. The shape can be rounded (e.g., a spherical shape, an ellipsoidal shape, an ovoid shape, a toroidal shape, a spheroidal shape, a paraboloidal shape, a hyperboloidal shape, a capsule shape, a rounded rectangular shape, a rounded triangular shape, a rounded pentagonal shape, a rounded hexagonal shape, a rounded octagonal shape, a rounded star shape, a rounded heart shape, a rounded cross shape, a rounded crescent shape, a rounded tear-drop shape, a rounded trapezoid shape, a rounded rhomboid shape, a rounded kite shape, a rounded lemon shape, a rounded lune shape, a rounded polygonal shape, a rounded polyhedral shape, a rounded prismatic shape, a rounded pyramidal shape, a rounded frustum shape, a rounded conical shape, a rounded helical shape, a rounded spiral shape, a rounded Mobius strip shape, a rounded Klein bottle shape, a rounded torus knot shape), or formed of planar surfaces (e.g., a cubic shape, a rectangular prismatic shape, a triangular prismatic shape, a pentagonal prismatic shape, a hexagonal prismatic shape, an octagonal prismatic shape, a star prismatic shape, a cross prismatic shape, a trapezoidal prismatic shape, a rhomboid prismatic shape, a kite prismatic shape, a pyramidal shape, a frustum shape, a wedge shape, a tetrahedral shape, an octahedral shape, a dodecahedral shape, an icosahedral shape, a Platonic solid shape, an Archimedean solid shape, a Johnson solid shape, a zonohedron shape, a prism shape, an antiprism shape, a parallelepipedal shape, a polyhedral shape, a prismatoid shape, a bipyramidal shape, a trapezohedron shape, a rhombohedron shape), or formed of at least one curved surface and at least one planar surface (e.g., a cylindrical shape, a conical shape, a frustoconical shape, a paraboloidal shape, a hyperboloidal shape, a spherical wedge shape, a spherical lune shape, a spherical triangle shape, a spherical rectangle shape, a spherical pentagon shape, a spherical hexagon shape, a spherical octagon shape, a spherical polygon shape, a spherical polyhedron shape, a toroidal wedge shape, a toroidal lune shape, a toroidal triangle shape, a toroidal rectangle shape, a toroidal pentagon shape, a toroidal hexagon shape, a toroidal octagon shape, a toroidal polygon shape, a toroidal polyhedron shape, a rounded prismatic shape, a rounded pyramidal shape, a rounded frustum shape, a rounded bipyramidal shape, a rounded trapezohedron shape, a rounded rhombohedron shape, a rounded zonohedron shape, a rounded prism shape, a rounded antiprism shape, a rounded parallelepipedal shape, a rounded prismatoid shape).

[0066] The largest diameter of structures 14 is typically less than half the periodicity parameter 18, and preferably more than a quarter of periodicity parameter 18, e.g., from about 0.3X to about 0.45X, or from about 0.3X to about 0.4X, or where X is periodicity parameter 18.

[0067] In some embodiments of the present invention structures 14 are nanostructures.

[0068] As used herein the term "nanostructure" refers to a three-dimensional body which is made of a solid substance, and which, at any point over its external surface, has at least one cross- sectional dimension and, in some embodiments, two orthogonal cross-sectional dimensions, and in some embodiments, three orthogonal cross-sectional dimensions, less than 1 micron, or less than 500 nanometers, or less than 200 nanometers, or less than 150 nanometers, or less than 100 nanometers, or even less than 70, less than 50 nanometers, less than 20 nanometers, less than 10 nanometers, or less than 5 nanometers, or less than 4 nanometers, or less than 3 nanometers, or less than 2 nanometers, e.g., about 1 nanometer.

[0069] The periodic structure, periodicity parameter, and shape and size of structure 14 are optionally and preferably selected to ensure a predetermined frequency dependence of the electrical permittivity s(o) of metamaterial 12. Preferably, these quantities are selected to ensure that the electrical permittivity s(o) is negative for a predetermined range of frequencies o. Such a predetermined range can include the range 0 < o < op, where opis the plasma frequency of free electrons in the metallic material of metamaterial 12. The Inventors found that when a system of electrically charged particles which rotates or vibrates at a frequency that is within the predetermined range of frequencies (e.g., rotates or vibrates at a frequency o satisfying range 0 < o < op) is placed at the vicinity of metamaterial 12 which was configured to have s(o) < 0 at this range, the force between particles of the system having like electrical charges (forces between negatively charged particles or forces between positively negatively charged particles) become attractive, and the force between particles of the system having unlike electrical charges (forces between negatively charged particles and positively charged particles) become repulsive.

[0070] The rotation or vibration frequency of the electrically charged particles at the vicinity of metamaterial 12 can be due to thermal motion of the particles and / or be induced by applying to the particles an oscillating electric or electromagnetic field, in which case the rotation or vibration frequency of the electrically charged particles depends on (e.g., equal to) the the oscillation frequency of the electric of electromagnetic field. Thus, in some embodiments of the present invention system 10 comprises an electric or electromagnetic field generator 28 for applying an oscillating electric or electromagnetic field to a region at the vicinity of metamaterial 12.

[0071] The inventors have also found that even in case in which the periodic structure, periodicity parameter, and shape and size of structure 14 do not ensure s(o) < 0 for the predetermined range of frequencies, a negative electrical permittivity over the predetermined range can still be achieved by applying a magnetic field or electric field (e.g., gate voltage) to metamaterial 12.

[0072] Thus, in some embodiments of the present invention, system 10 comprises a magnetic field source 20 forming a magnetic field within metamaterial 12, wherein the magnetic field is selected to ensure that the electrical permittivity of metamaterial 12 is negative, optionally and preferably for any frequency within the predetermined frequency range. Magnetic field source 20 can be a permanent magnet of an electromagnet, as desired. Preferably, magnetic field source 20 is configured to generate a static magnetic field. Typical strength of the magnetic field within metamaterial 12 is at least 0.1 T, or at least 0.2 T, or at least 0.3 T, or at least 0.4 T, or at least 0.5 T, or at least 0.6 T, or at least 0.7 T, or at least 0.8 T, or at least 0.9 T, e.g., about 1 T or more. Magnetic field source 20 can be configured to generate a dipole magnetic field or a multipole configuration. The present embodiments encompasses any number of magnetic poles, including but not limited to dipole, quadrupole, hexapole, octupole, or higher-order multipole fields. The strength and / or number and / or orientations of the magnetic poles are preferably adjusted to ensure the predetermined frequency dependence of the electrical permittivity metamaterial 12. Preferably, strength and / or number and / or orientations of the magnetic poles are selected to ensure that the s(o) is negative for the predetermined range of frequencies o.

[0073] System 10 optionally and preferably comprises a space 22 characterized by a positive electrical permittivity adjacent to a surface 24 of metamaterial 12 forming an interface between metamaterial 12 and space 22. In embodiments in which system 10 comprises electric or electromagnetic field generator 28, generator 28 is preferably configured to apply the oscillating electric or electromagnetic field to space 22.

[0074] Preferably, the sum of the (positive) electrical permittivity characterizing space 22 and the (negative) electrical permittivity characterizing metamaterial 12 is positive.

[0075] In some embodiments of the present invention there are two or more interfaces between space 22 and metamaterial 12. FIG. 1 illustrates an example embodiment with two interfaces. This can be achieved, for example, by providing metamaterial as two parts separated from each other by a gap, so that the gap enacts space 22. Other configurations with more or less than two interfaces are also contemplated.

[0076] Space 22 serves for receiving electrically charges particles, such as, but not limited to, elementary particles (e.g., electrons, protons), nuclei, and molecules. The Inventors found that electrically charges particles experience a force that is influenced both by the permittivity of space 22 and by the permittivity of metamaterial 12. In particular, when the electrically charges particles within space 22 rotate or vibrate at a frequency within the predetermined frequency range, the force between particles having like electrical charges are attractive, and the force between particles having unlike electrical charges are repulsive.

[0077] The width of space 22 (as measured perpendicularly to surface 24) is preferably selected to allow the particles to rotate about their carter of mass. For example, when space 22 is configured to receive atoms the width of space 22 is at least two times their Bohr radius. Preferably, but not necessarily, the width of space 22 is from 1 nm to about a micron, but other widths are also contemplated in some embodiments of the present invention.

[0078] Space 22 can be a vacuum space (in which case its electrical permittivity is electrical permittivity of the vacuum), or it may contain a medium which can be gas, liquid or solid medium, provided that the medium allows for the particles to rotate or vibrate at a frequency within the predetermined frequency range. In some embodiments of the present invention space 22 comprises a metal.

[0079] Metamaterial system 10 of the present embodiments offers a wide range of potential applications, particularly in the manipulation of particle species placed in space 22. Any of the applications described below can be executed at any temperature, e.g., from about 10 °C to about 100 °C, e.g., at room temperature (about 25 °C).

[0080] One such application is the facilitation of nuclear fusion reactions, where fusion fuel, such as deuterium and / or tritium and / or lithium can be introduced into space 22, and wherein the necessary conditions for fusion to occur are ensured by the attractive forces between the nuclei of the fuel, causing the nuclei to fuse together, releasing energy in the process. For example, a mixture of deuterium and tritium gas can be introduced into space 22 in which case reaction involves the fusion of a deuterium nucleus (consisting of one proton and one neutron) with a tritium nucleus (consisting of one proton and two neutrons) to form a helium-4 nucleus and a neutron. Alternatively, a tritium gas can be introduced into space 22 in which case reaction involves the fusion of two tritium nuclei, each containing one proton and two neutrons, to form a helium-4 nucleus, two neutrons, and energy. This reaction has a higher energy yield compared to the D-T reaction. Still alternatively, a deuterium gas can be introduced into space 22 in which case reaction involves the fusion of two deuterium nuclei, each containing one proton and one neutron. This reaction has two possible outcomes, a helium-3, a neutron and energy, or a tritium, a proton, and energy.

[0081] Additional fusion reaction which system 10 can facilitate include, without limitation, deuterium-helium fusion, helium-helium fusion, tritium-helium fusion, deuterium-lithium fusion, proton-lithium fusion, helium-lithium fusion, and proton-boron fusion.

[0082] According to preferred embodiments of the present invention the nuclear fusion is induced in vacuum, in which case space 22 is a vacuum space. Alternatively, the nuclear fusion can be induced in a medium, in which case space 22 comprises this medium, where the nuclear fuel (e.g., deuterium, tritium, lithium, helium, boron, etc.) is dissolved in the medium.

[0083] The energy released from nuclear fusion reactions according to some embodiments of the present invention can be harnessed for many applications. For example, a power plant comprising system 10 can distribute energy over a grid. Another example is propulsion, whereby the energy released from nuclear fusion reactions is used for propelling vehicles. Representative examples of vehicles suitable for the present embodiments include, without limitation, an aerial vehicle (e.g., a drone, an aircraft, a jet airplane, a helicopter, an unmanned aerial vehicle, a passenger aircraft, a cargo aircraft), a ground vehicle (e.g., an automobile, a motorcycle, a truck, a tank, a train, a bus, an unmanned ground vehicle), an aqueous or subaqueous vehicle (e.g., a boat, a raft, a battleship, a submarine), an amphibious vehicle, a semi-amphibious vehicle, a spacecraft, and the like. The fusion energy allows high specific impulses and thrust-to-weight ratios, far surpassing the capabilities of conventional chemical rockets or jet engines. This is particularly useful in space exploration, air travel, marine travel, and efficient transportation of goods and people around the globe.

[0084] Another application of system 10 include generation of electrical current. The inventor found that due to the attractive forces between like particles, electrons that are introduced into space 22 can form electron pairs. Each individual electron in the pair is an electron, hereby the formed pair is a boson. As bosons, the electron pairs can occupy the same quantum state, which means that they can all condense into the lowest energy state available. This results in a collective behavior of the pairs, known as a Bose-Einstein condensate. In this state, the pairs can move coherently, without scattering or energy loss, leading to the resistance-free flow of electrical current. Thus, upon application of electrical field to space 22, an essentially resistance-free current is generated, and so space 22 serves as a superconductive medium. Since the attraction between electrons is not phonon-mediated, it can optionally and preferably occur at room temperature. According to preferred embodiments of the present invention the electrical current is generated in a material, in which case space 22 comprises the material. For example, system 10 can comprise a slab 26 in contact with metamaterial 12, wherein space 22 is within slab 26. Representative examples of materials suitable for use as slab 26 in embodiments in which system 10 serves for generating electrical current include, without limitation, bismuth strontium calcium copper oxide (also known as BISCO), yttrium barium copper oxide (also known as YBCO), e.g., YBaiCusO?, LaHw, La2-xBaxCuO4, Pb, Sn, Ta, Al, Zn, W, PbTaSe2, PbMo6S8, Bi(2212), Bi(2223), and SnAs.

[0085] The essentially resistance-free current can reduce energy losses in power transmission and be used in electrical devices which enjoy higher efficiency. In addition, the collective behavior of the pairs as bosons can be exploited for applications in quantum computing, where the coherent movement of the pairs can be used to create stable and scalable quantum bits (qubits) for quantum information processing.

[0086] System 10 can also promote ionization of atoms or molecules. When particle species, such as atoms or molecules that rotate or vibrate at frequencies within the predetermined frequency range, are placed in space 22, they can be subjected to a ionization process. In this process, the particles experience a repulsive force between unlike charges, such as electrons and nuclei. This repulsive force can overcome the binding energy of the electrons to the nucleus, causing the electrons to be stripped away from the atom or molecule, resulting in ionization. The ability of system 10 ionize particle species is useful in many applications. For example, system 10 can be used to create localized and controllable plasma regions, which have applications in material processing, surface modification, and chemical analysis. The ionized particles in the plasma can be used to etch or deposit materials on a substrate, or to modify the surface properties of a material, such as its wettability or adhesion.

[0087] Additionally, the ionized particles can be analyzed using techniques such as mass spectrometry or optical emission spectroscopy, providing valuable information about the composition and properties of the material. Focalized plasma regions can be used in light sources, such as, but not limited to, as extreme ultraviolet or soft X-ray lasers. The ability of system 10 to ionize particle species can be combined with other manipulation techniques, such as magnetic confinement or RF heating, to create plasma-based devices and systems. For example, system 10 can be used to generate a plasma, which can then be confined and heated using magnetic fields or RF waves to create a plasma source useful in, e.g., plasma propulsion, and plasma processing.

[0088] System 10 of the present embodiments can also be used to facilitate chemical reactions in space 22. When particle species, such as atoms or molecules, that rotate or vibrate at frequencies within the predetermined frequency range, are placed in space 22 they experience forces that facilitate chemical reactions. In this process, the particle species experience an attractive force between like charges, such as electrons or ions, which attractive force can bring the particles closer together, increasing the probability of chemical reactions occurring. The ability of system 10 to facilitate chemical reactions in space 22 is useful in many applications. For example, system 10 can be used as a localized reaction zone, which has applications in chemical synthesis, catalysis, and material processing. The attractive force between like charges can bring reactant molecules closer together, increasing the rate and selectivity of the chemical reaction. This cab be used to synthesize novel compounds or materials, or to enhance the efficiency of existing chemical processes.

[0089] System 10 can also be used in particle accelerators. When particle species, such as electrons or protons, that rotate or vibrate at frequencies within the predetermined frequency range, are placed in space 22 they experience attractive force between like charges, causing the particle species to accelerate towards each other, gaining kinetic energy in the process. The ability of system 10 to accelerate particles can be useful, for example, in scientific research, medical therapy, or industrial processing. The attractive force between like charges can accelerate particles to high energies over short distances, reducing the size and cost of the accelerator compared to conventional designs.

[0090] A particle accelerator employing system 10 can be used in high-energy physics research. The ability to create attractive forces between like charges in space 22 allows the acceleration of particles to elevated energies in a more compact and efficient manner compared to conventional accelerators. This is useful in the study of fundamental particles and their interactions at energy scales that may optionally and preferably be higher than those currently achieved by conventional accelerators. The charge attraction mechanism in space 22 can improve beam focusing, and increase luminosity, enhancing the precision and sensitivity of collider experiments. A particle accelerator employing system 10 can be used in accelerator-driven systems, such as subcritical nuclear reactors or accelerator-driven transmutation of nuclear waste. A particle accelerator employing system 10 can be used in medical and industrial applications. For example, it can be used to generate electron or ion beams for cancer radiation therapy, allowing for more precise targeting of tumors while minimizing damage to healthy tissue. In industry, the accelerator can use in materials processing, such as ion implantation for semiconductor fabrication or surface modification of materials.

[0091] As used herein the term “about” refers to ± 10 %

[0092] The terms "comprises", "comprising", "includes", "including", “having” and their conjugates mean "including but not limited to".

[0093] The term “consisting of’ means “including and limited to”.

[0094] The term "consisting essentially of" means that the composition, method or structure may include additional ingredients, steps and / or parts, but only if the additional ingredients, steps and / or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure.

[0095] As used herein, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. For example, the term "a compound" or "at least one compound" may include a plurality of compounds, including mixtures thereof.

[0096] Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

[0097] Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases “ranging / ranges between” a first indicate number and a second indicate number and “ranging / ranges from” a first indicate number “to” a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween.

[0098] It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements.

[0099] Various embodiments and aspects of the present invention as delineated hereinabove and as claimed in the claims section below find experimental support in the following examples.

[0100] EXAMPLES

[0101] Reference is now made to the following examples, which together with the above descriptions illustrate some embodiments of the invention in a non limiting fashion.

[0102] I. INTRODUCTION

[0103] The relation between the electric displacement D and the electric field E

[0104] D = ε • E (1) shows that at negative £ (in this Example 8 is measured in c.g.s. units and is therefore a dimensionless quantity), the directions of D and E are opposite. The permittivity £ appears also in the law of the electrostatic Coulomb interaction of charged particles qi and q?. at a distance r:

[0105] The Coulomb interaction can be reduced or even enhanced by changing £ in the positive region [4]. It follows logically from Eq. (2) that the force F should reverse its direction when £ is negative. Therefore like charges attract each other, while unlike charges repel each other. The consequence of this can lead to unexpected physical properties and fantastic technical applications. Although Coulomb’s law and the superposition principle for electric fields in vacuum are completely equivalent to Maxwell’s equations for electrostatics, it is not obvious that the permittivity in Eq. (1) and in Eq. (2) is the same. This is somewhat similar to the situation in mechanics where the inertial mass (F = ma) and gravitational mass are not the same and their identity was used to form the theory of general relativity. The appearance of the relative permittivity in the Coulomb law is usually explained phenomenologically as a result of the polarization of the medium.

[0106] The possibility to change repulsion of like charges to attraction is discussed very rarely in the literature. One of the first authors who pointed to the possibility of using negative permittivity to change repulsion to attraction was V. L. Ginzburg [5]. However, he mentioned this only in order to illustrate qualitatively the appearance of Cooper pairs in superconductors. In the article by D. A. Kirzhnits [6] it was stated explicitly: “There exists in principle a class of substances within which the static interaction of the electrons has the character not of repulsion, as in vacuo, but of attraction.” The latter prediction is probably already verified experimentally, at least partially. In a recent publication [7] the observation of attraction between electrons was reported in the system of bubble and stripe phases at negative permittivity.

[0107] Other publications about this problem include [8-13] (attraction of metal nanoparticles

[0014] in an electrolyte solution

[0015] are not consider herein). This problem can also be extended to the case of ions and nuclei. E.g., in Ref.

[0016] it was recently reported that6Li nuclei may be bound into Cooper-pair-like states (using a 2D optical dipole trap).

[0108] This Example discuss whether electrons can attract each other when the permittivity is negative (the spin dependence of this is ignored for the sake of simplicity). As will be shown, this can be realized not only in the static regime but also at nonzero frequency. Negative values of permittivity are achieved according to some embodiments of the present invention due to the localized surface plasmon resonances (LSPR) in metamaterials. These resonance frequencies can be varied over a wide range by application of static magnetic or electric fields.

[0109] I this Example, the magnetic field H is expressed in dimensionless units. The value of the magnetic field B in dimensioned units (e.g., Tesla) can be obtained using the relation H=pB, where p. is the characteristic electron mobility of the electrons in the metallic material of metamaterial 12. Values of the electron mobility is readily available in the literature. For example, at temperature of about 300K, the electron mobility of bismuth about 104cm2 / V-s, the electron mobility of gold is about 40 cm2 / V- s, the electron mobility of silver is about 50 cm2 / V-s, the electron mobility of copper is about 43 cm2 / V-s. and the electron mobility of aluminum is about 30 cm2 / V-s.

[0110] II. IMAGINARY PART OF THE PERMITTIVITY IN THE CASE OF ANOMALOUS DISPERSION

[0111] A. Imaginary part of £

[0112] The work of Kirzhnits [6] was based mainly on the study of the Kramers -Kronig relations. Let us check here the possibility of zero and negative values of the relative permittivity £ in the Coulomb law from first principles. At first glance Eq. (2) should not be correct at negative values of £ since it has a discontinuity at £ = 0 as it is shown by the sketch in FIG. 2A. However, in the case of anomalous dispersion (namely, when it is possible to obtain zero or negative values of £), the permittivity inevitably has an imaginary part

[0017] . In the case of normal dispersion, the imaginary part is usually small. Even from numerical calculations (see FIGs. 2B) it follows that when the real part of £ vanishes, its imaginary part essentially differs from zero. These dependences are calculated using the Drude model of the metal permittivity tensor [see Eq. (Al) in Appendix A]. The real part of the inverse permittivity, i.e., the value of Re(l / £), passes continuously through zero, as shown in FIGs. 2C. This is because for complex permittivity £ = E' + is" the inverse permittivity also has a zero real part Re(l / s) = £ / (s'2+ s"2) when s'= 0.

[0113] FIGs. 3A-B show dependences of the effective macroscopic permittivity seand Re(l / se) but obtained for a dielectric-conductor metamaterial. Results are obtained by using the dilute and Clausius-Mossotti approximations (see Eqs. ( 16)-( 19), (34) below and Refs. [18, 19]).

[0114] B. Non-Hermitian problem

[0115] The presence of the imaginary part of permittivity s complicates the theory of considered phenomenon. In quantum mechanical description, the Hamiltonian in the Schrodinger equation becomes non-Hermitian when the permittivity is complex. This also means that the solution is not be stationary and damped [20, 21]. This can be seen directly from the time-dependent Schrodinger equation for a pair of quantum particles (see below)

[0022] where ip = ip(r,t) is the wave function, V' - iV"= e2 / [(s'+ is ") | r | ] is the complex Coulomb potential, r is the distance, h = h / (2n) is Planck’s constant, and / Zehis the reduced mass of a pair of particles “e” and “h” (see below). Multiplying the above Schrodinger equation by ip* and the complex

[0116] $P i V / . J — _v"0conjugated equation by ip one get obtains dt ' h r , where p = ip*ip is the particle

[0117] = ...HL. density and J is the current density. Therefore, in the steady state the particle density is attenuated by V ".

[0118] The influence of the imaginary part of the Coulomb potential can be illustrated also in the framework of Newton dynamics. The potential in Newton’s second law (written along the x-axis) can be expanded in series near the initial position Ro:

[0119] Up to the term linear in x one has where arctan

[0120] . The solution of this is where xiis the amplitude of the “oscillations”. Thus, the imaginary part of the Coulomb potential (due to imaginary part of permittivity £) leads, as in optics, to damping. Whether the imaginary part of the permittivity £ prevents or helps the pairing of particles requires additional consideration. Meanwhile, from FIG. 6C and FIGs. 7B-C it can be seen that it is possible to find frequencies for which £ < 0 and £ — 0. For simplicity and without loss of generality we consider everywhere below the case £ 0.

[0121] III. ELECTRON OSCILLATION AND WANNIER EXCITONS

[0122] Kirzhnits [6] and others [8-10] considered the static situation when the permittivity should be taken at zero frequency. The static case corresponds to an attraction of particles strictly along a straight line. According to classical mechanics

[0023] , this is possible only when their angular momentum M is strictly equal to zero. If M is nonzero, then the particles move along elliptical trajectories so that within the framework of classical mechanics the fall of a particle to the center is impossible. Although a negative value of £ in the static regime [i.e., £(0) < 0] is possible in metamaterials by application of magnetic [18, 19, 24-33] or electric

[0034] fields (see Sec. IV below), it is more convenient to use for this purpose permittivity at nonzero frequency a> which can be realized in the case of oscillating or rotating charges. If, for example, the point charges are rotating one about the other (around a common center like in the case of the Wannier excitons [35-40]) then from outside it looks like oscillations of the dipole moment, i.e. oscillations of the electric field. In this case the permittivity £, as a response of the surrounding media to the perturbation caused by charge oscillations, can be used at the frequency of these oscillations. One needs only to check whether the permittivity £ at these frequencies can reach negative values. The situation is similar to a problem in the theory of Wannier excitons: which £ should be used in the Coulomb interaction of a hole with an electron. As was shown in Refs. [35, 41] and

[0042] , when the radius of the exciton orbit (electron-hole pair) is small and therefore the frequency of rotation is large then the permittivity is taken as £ = 1, since the valence electrons of the crystal cannot follow the rapid motion of the electron-hole pair. By contrast, when the orbit radius is large the rotation frequency is small and the value of £ is the low frequency permittivity. As will be shows in Sec. IV, negative values of £ can be achieved in the entire range of frequencies 0 < a)P. When the frequency of exciton oscillation is smaller than the plasma frequency ropthe permittivity is negative (see Sec. IV and Appendix A).

[0123] The case of rotation of an electron around a hydrogen nucleus is often considered as a simple classical exercise. This can be treated as electric oscillations. From elementary evaluations (mev2 / rB= e'yrB7-. where re is the Bohr radius, meis the electron mass) one can find the angular frequency of electron rotation rad / sec. Similarly, one can find the frequency co ex of rotation of electron and hole around their common center of mass in the case of the Wannier-Mott exciton [35-38] (i.e., a pair of electron and hole).

[0124] A. Modification of the Coulomb law in slabs: Method of images

[0125] In this Example it is assumed that the exciton is located in a thin dielectric slab (with positive permittivity £i > 0) which is placed between two metal-dielectric media (with negative permittivity £2 < 0), see FIG. 4. Since not all lines of the electrostatic forces are inside the slab (see FIG. 4 and Refs. [43-46]) the interaction between the point charges does not follow the usual Coulomb law. Therefore the Coulomb interaction depends not only on the permittivity £i but also on £2. Therefore, when £2 < 0, the attraction between electron and hole can be changed to repulsion and the repulsion between electrons can be changed to attraction. This can be shown for example by the method of images [17, 47]. In general this method is applied for the static case. However, when the relaxation time T of electrons of the media with negative permittivity (see media with £2 in FIG. 4 and FIG. 5) is much less than the inverse frequency l / a> of the rotation (or oscillation) of the point charges (-qi and -qz in FIG. 5) in the media with £1 (i.e., when T « 1 / ro), the induced image-charges in the medium with £2 (~^1 and +*?2 in FIG. 5) have sufficient time to form and the image method is appropriate.

[0126] Similar to Ref.

[0010] this Example considers a system of two media: a dielectric slab with £1, placed on the top of the thick semiconductor slab with £2 (see FIG. 5). Above a dielectric slab with £1 it is possible to consider another thick slab with £2 like in Ref.

[0010] , but in this Example it is assumed that this medium with £2 is a vacuum, which is easier to realize experimentally. Two point charges q\ and qz (qi = qi) are placed in a slab £1 at the distance L each from each other. The distance from the charges qi and qz to the lower medium £2 (and therefore from the induced charges q\ and q'z to the lower interface) is h. In the semiconductor due to the ESPR the negative permittivity £2 < 0 can be achieved, while in the dielectric £1 > 1. A point charge qi induces a point charge q\ in medium £2, while the point charge q\ induces in its turn a point charge in the medium £1 (see FIG. 5). The horizontal component of the Coulomb force acting on the point charge qz is (see FIG. 5): where:

[0127] When 4h2 / L2« 1, Eq. (5) simplifies to the form

[0128] From Eq. (6) it follows that the like charges can attract each other when £2 < 0 while £i+£2 > 0. In this case, charges with different signs repel each other.

[0129] B. Exciton-like electron-electron bound pairs

[0130] According to Ref.

[0035] , a pair of unlike charged electron and hole can be roughly viewed when considering only one excited electron and one hole in a crystal, and take into account the remaining emitted electrons and atomic cores by introducing a periodic potential that determines only the isotropic masses of an electron and a hole, etc. If one further assumes that an electron and a hole in such a medium interact according to the Coulomb law (-e2 / £reh), then the Schrodinger equation for the electron-hole system has the following form where fehis the distance between the electron and the hole, T is the wave-function, and meand nih are the electron and hole masses, respectively. This equation is written in the so-called effective mass approximation and is similar to the equation for the hydrogen atom

[0048] . The quantummechanical expression for the effective Bohr exciton radius [35-38] is where / Zeh = memh / (me+rnh) is the reduced mass of the exciton. This differs from the hydrogen

[0131] Bohr radius

[0048] by the presence of the permittivity £ in the numerator. In semiconductors the typical permittivity £ is of order £ — 10 and, therefore, the rotation frequency of the electron-hole pair is of order a>ex — 1.3 • 1015sec-1, which is smaller than a>e. This can be compared with the quantum estimation a)ex= (angular momentum) / (mass- radius2) (see Ref.

[0035] ):

[0132] 61ex = h / flehR. (9)

[0133] For an exciton with an effective mass / ieh= me / 2 in a crystal with gap energy EG = 2 eV and radius r = 5 Bohr radii one obtains a>ex~ 3 • 1015sec-1, which is close to the classical estimation.

[0134] The linear velocity of the electron in an exciton can be estimated by 1.4- 105m / sec according to:

[0135] This is much less than one percent of the light speed 3- 108m / sec. Therefore the above classical estimates are reasonable.

[0136] The values of used above ex ~ 1.3 - 1015sec-1or C9ex~ 3 • 1015sec-1are smaller than the plasma frequency &)P: where No is the concentration of free electrons in the metal. Since for typical metals such as aluminum or silver No is approximately 1023cm-3, the plasma frequency of Eq. (10) is of order a)P— 1.5 • 1016sec-1(which is in the ultraviolet region). At frequencies a) > a)Pthe metal permittivity £m— 1 since the electrons of the surrounding media are unable to follow the electric field oscillations.

[0137] Since the frequency of the exciton oscillations roex is much smaller than the plasma frequency a>P, the permittivity £ in Eq. (8) can differ from 1. By tuning the LSPR with an applied magnetic field [18, 24-27, 29-31] or an applied gate voltage

[0034] , the permittivity £2 can be made negative at the frequency &)ex(see Sec. IV below). Since the interaction between two point charges in a thin dielectric film with £1 depends also on the permittivity of a thin conducting film with £2, this leads to breakup of electron-hole pairs (cold electrostatic exciton dissociation) and creation of electron-electron pairs (similar to Cooper pairs). Since the masses of the electron and the hole can r:> — be different, the exciton hydrogenic Rydberg constant ex (see Ref.

[0035] ) for the electron-hole pairs and the electro-electron pairs can also be different and the process of exciton destruction and creation of electron-electron pairs can be experimentally observable directly in the optical spectra of the same sample. The electron-electron system with negative permittivity £ is also similar to positronium

[0049] , but without annihilation. Two electrons can form a bound state but cannot enter into a fusion reaction since unlike protons, electrons interact only via the weak and electromagnetic interaction.

[0138] Another interesting phenomenon which can appear at negative permittivity £e< 0, is the ionization of atoms which is a consequence of repulsion of the atomic nucleus and its electron shell.

[0139] C. Nuclei-nuclei bound pairs

[0140] Substituting a proton mass (instead an electron mass) into expression for Bohr radius a value of order 3- 10-14m is obtained (for |s| = 1). This value is close to the 10-15m, where the strong forces begin to act. Thus, nuclear fusion can be realized by the system of the present embodiments.

[0141] The estimation of the rotation frequency of deiterium-tritium pair gives

[0142] For example, for = 1 the frequency CODT IS of the order 1019which is lager than the cop, and for = 3 the frequency CODT IS of the order 0.51018which is smaller than the cop. It is nevertheless noted that it is preferred to apply other approaches, such as, but not limited to, relativistic quantum mechanics in order to provide estimation for the case of nuclei.

[0143] IV. ANALYTICAL AND NUMERICAL FORMALISM - RESONANCES.

[0144] The negative permittivity £ needed for achieving attraction of like charges can be obtained in insulator-conductor metamaterials with appropriate nanostructures. The frequencies at which negative values of £ are achieved can be manipulated by an applied static magnetic [19, 24-31] field B or electric gate voltage

[0034] . The theory and formalism of this are presented briefly below (taking into account all parameters in general form). This Example uses a quasi-static approximation in which the wave vector k = 0. In this approximation the wavelength is greater than the characteristic sizes of the nanostructures of the metamaterials. This approximation is used in many situations. The description of the more general case when |k| > 0 can be found e.g., in Refs. [4, 50],

[0145] This Example considers a two-constituent insulator-conductor composite medium made of two uniform materials with permittivity tensors ’- land dent local permittivity tensors of this medium can be written as: where Here the following characteristic or indicator function of the / '-constituent was used:

[0146] When the inclusions form a periodic lattice, this description is suitable, provided the lattice constant is much smaller than the wavelength, so that the sample can be considered homogeneous on the scale of the electromagnetic wavelength. Following [19, 24-31, 34], this Example chooses a scheme where the composite medium occupies the entire volume in between the infinitely conducting plates of a parallel plate capacitor. The plates are taken to be infinitely large, and the distance between them is taken to be finite but large compared to any scale of inhomogeneity of the system. Keeping the medium fixed, the orientation of the plates is selected to be perpendicular to any of the coordinate axes. Denoting by <pW the local potential field that results when the plates are perpendicular to the raaxis, a potential difference equal to their distance apart is applied between them. The volume averaged electric field is then (ycpW) = Vra= ea, where eais a unit vector in the radirection. The potential field <pW is the solution of the partial differential equation for the electric displacement namely and the boundary condition = raat the capacitor plates.

[0147] The bulk effective electric permittivity tensor is defined by where the angular brackets denote a volume average:

[0148] The case of a single inclusion of ellipsoidal or cylindrical shape can be solved exactly when H = a>cT = 0.

[0047] Extensions of that solution for the case were described in Refs. [19, 24-29]. For a dilute system it follows that where pi = Vmc / V is the volume fraction of the inclusions. When B II z (i.e., when d£xz =d£yz = o£zx = 6szy= 0) the matrix / takes the form [18, 31]: where nx, ny, and nzare the depolarization factors

[0047] of the inclusion. The subscripts “2” in the host permittivity tensors2are omitted for simplicity.

[0149] A. Insulating host and conducting ellipsoidal inclusions

[0150] Consider the case of insulating host and dilute conducting ellipsoidal inclusions. From Eqs. ( 16)-( 18) one can write, for example, an expression for the xx-component of the permittivity tensor

[0151] , (19) where the host is insulator with &<x, £yy- and Ezz permittivity tensor components (the off diagonal components zXy = £xz = £yx = £zx = 0 vanish). The permittivity tensor components of the conducting inclusions are indicated with superscript “inc”, while taking, from Eq. (Al), the limit

[0152] The resonance frequencies correspond to the case where the determinant D(co) in Eqs. (17)- (18) is equal to zero. Substituting Eq. (Al) in the limit a>r » 1 into Eq. (18) and equating it to zero, one obtains an equation for the resonance frequency <Wes. This condition can be rewritten as where the definitions a = (1 - nx)Exx + com and ft = (1 - ny)Ejy + zonyare introduced, and where EO is the dielectric constant of the background ionic lattice [see Eq. (Al)]. This can be simplified to the form of a bi-quartic equation

[0153] The solutions of Eq. (21) are

[0154] The resonance (23) is called the “cyclotron resonance”. From Eq. (24) for H = 0 one obtains the frequency which is known as the LSPR. When H > 0, this splits into two resonances: a “magneto-plasma resonance” (denoted by M~) and a “magnetoplasma shifted cyclotron resonance” (denoted by m+) [19, 24-30]. Eq. (24) can be expanded in the limits a>c / o)p

[0155] « 1 and cop / coc « 1. For a weak magnetic field (i.e., for a>P» aic) one gets

[0156] Tlx — Tly = Tl and Exx — Eyy — E0, (28) it follows from Eqs. (26)-(27) that

[0157] (note that for the sphere nx= ny= nz= n = 1 / 3). The situation with Eq. (25) is more complicated under the conditions (28) since for these parameters vanishes. One needs to put conditions (28) into Eqs. (21)-(22), then these resonances take simple forms (see also FIG. 8):

[0158] From this one obtains an approximate expression in the limit coc« O)P:

[0159] The resonances (29), (30), and (32) are observed when the conductivity relaxation time T satisfies a>r > 1. Such resonances were studied both experimentally and theoretically [51, 52, 18, 19, 24-30],

[0160] From Eq. (31) it follows that when ^'P , the resonance value

[0161] FIG. 9 shows the dependence of seon co / cop for two values coc / cop = 10 and coc / cop = 100 calculated using Eq. (19). The resonance (with the negative values of se) can appear arbitrary close to the zero frequency (co / cop ~ 0) but strictly at the zero frequency a> / a>p= 0 the effective permittivity is positive and equal t

[0162] When the applied magnetic field vanishes (&)c= 0), the expression for the resonance frequency follows directly from The expression for <Wes in the Clausius-Mossotti approximation has a similar form, obtained by the substitution

[0163] B. Cylindrical inclusions

[0164] When the cylinder axis is along they axis then the depolarization factor in this direction is zero: ny= 0. When the magnetic field is directed parallel to the z-axis, B II z, Eq. (17) simplifies and there are resonances when the denominator D(co) = &a- nx6sxx, or D(co) = sZz - nz6szz vanishes.

[0165] When the elliptical cylinders are conducting and the host is insulating, the expression for the resonance frequency can be obtained directly from Eq. (24) by substituting ny= 0:

[0166] Thus, the value of res increases monotonically with the application of a magnetic field a>c. rorescan be decreased by decreasing the depolarization factor nxfrom 0.5 to 0 and by increasing so.

[0167] The present embodiments also contemplate the case of insulating cylinders inside a conducting host at nonzero magnetic field H [19, 24-30].

[0168] C. Results

[0169] FIGs. 6A-D show numerically calculated real (solid line) and imaginary (dashed line) parts ,(e) of t xx of a periodic array of conducting spheres (of radii R = 0.45a, where a is the distance between the centers of neighboring spheres) vs. the dimensionless frequency a> / a>P. The LSPR appears at the frequency given by Eq. (34). Notice the shifts from these values due to large sphere radii when the dilute or Clausius-Mossotti approximation are not in a good quantitative agreement. Larger -(e) values of the radii lead to deeper negative values of at the resonances in all cases of FIGs. 6A-

[0170] D. FIG. 6A shows the case of zero magnetic field H = 0. The LSPR appears at frequency G)res / G)p — 0.45 [see Eq. (34)]. In the numerical calculation this resonance is shifted to lower frequencies due to large sphere radius R = 0.45a. Changing so [see Eq. (Al)] to the value so = 10 shifts the resonance by Aon to the lower frequency G)res / G)p — 0.17. Application of an external magnetic field H = G)cT = / Ze|B| [see Eq. (Al)] can decrease the resonance frequency. FIG. 6C shows the case H = 20 (when so = 1). The LSPR splits in this case into two branches, one of which [tores-, see Eq. (30)] shifts by Ao)2 towards a lower frequency, while the other one [o)res+, see Eq. (29)] shifts in the opposite direction by A co 3. After substitution of the parameters, the Inventors obtained o)res- / o)p 0.35 and o)res+ / o)p — 0.85. Using both parameters H= 20 and £0= 10 leads to a greater shift. FIGs. 7A-D are similar to FIGs. 6A-D but for a periodic array of infinitely long conducting cylinders (with radii 0.4a) vs. dimensionless frequency a> / a>P. FIG. 7A shows the case of zero magnetic field H= 0, with £o= 1. The LSPR appears at the frequency given by Eq. (35), where the depolarization factor mof the circular cylinder is 1 / 2. FIGs. 7B-D are similar, mutatis mutandis, to FIGs. 6A-D. Note that when the cylinders are not infinite but have finite length (see, e.g., FIG. 7D with length / = 0.6a), the LSPR appears at lower frequencies than predicted by Eq. (35). This is entirely due to the finite length of the cylinder, when the behavior of the LSPR is qualitatively similar to the case of a sphere.

[0171] V. CONCLUSIONS

[0172] This Example demonstrated that using the LSPR it is possible to reach negative values of the permittivity £ in a wide range of frequencies a) by application of magnetic or electric fields. This can lead to attraction of like charged particles instead of repulsion and can be observed experimentally as destruction of electron-hole pairs and creation of hole-hole or electron-electron pairs similar to Cooper pairs.

[0173] APPENDIX A

[0174] Drude approximation for the permittivity tensor

[0175] In the quasi-static regime the electric permittivity tensor of a metal, ’ Af has the form [19,

[0176] 24- 31] where the conductivity tensor C is taken in the free-electron Drude approximation (with a static magnetic field B II z), so is the scalar dielectric constant of the background ionic lattice and I is the unit tensor.

[0177] The magnetic field enters through the Hall-to-Ohmic resistivity ratio H = pn / p = (Jyx / (Jxx = pe\ B | = a>cT, where o)c= eB / mc is the cyclotron frequency, r is the conductivity relaxation time, is the plasma frequency, No is the charge carrier concentration, m is the effective mass of the charge carriers, and peis the electron Hall mobility. [19, 24-31] Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. It is the intent of the applicant(s) that all publications, patents and patent applications referred to in this specification are to be incorporated in their entirety by reference into the specification, as if each individual publication, patent or patent application was specifically and individually noted when referenced that it is to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting. In addition, any priority document(s) of this application is / are hereby incorporated herein by reference in its / their entirety.

[0178] REFERENCES

[0179] [1] V. G. Veselago, Electrodynamics of substances with simultaneously negative values of e and p, Sov. Phys. Usp. 10 509-5014 (1968). [Usp. Fiz. Nauk 92, 517-526 (1964)].

[0180] [2] J. B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 3966 (2000).

[0181] [3] T.W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Extraordinary optical trans-mission through sub-wavelength hole arrays, Nature (London) 391, 667 (1998).

[0182] [4] Karakasoglu and Fan, Controlling the electrostatic Coulomb interaction using metamaterials, Phys. Rev. B 93, 075433 (2016).

[0183] [5] V. L. Ginzburg, Phys. Usp. 43, 573-583 (2000).

[0184] [6] D. A. Kirzhnits, Sov. Phys. Usp. 19, 530-537 (1976).

[0185] [7] B. Friess, Y. Peng, B. Rosenow, F. von Oppen, V. Umansky, K. von Klitzing and J. H. Smet, arXiv: 1608.05210 or arXiv: 1608.05210vl [cond-mat.mes-hall].

[0186] [8] C. W. Chu, F. Chen, J. Shulman, S. Tsui, Y.Y. Xue, W. Wen and P. Sheng, A negative dielectric constant in nano-particle materials under an electric field at very low frequencies, SPIE Proc. 5932, pp. 31 (2005). Edited by I. Bozovic, and P. Pavuna (Optics & Photonics, San Diego, California, USA).

[0187] [9] V. N. Smolyaninova, C. Jensen, W. Zimmerman, J. C. Prestigiacomo, M. S. Osofsky, H. Kim, N. Bassim, Z. Xing, M. M. Qazilbash, and I. I. Smolyaninov, Enhanced superconductivity in aluminum-based hyperbolic metamaterials, Sc. Rep. 6, 34140 (2016).

[0188]

[0010] A. A. Rangelov and N. Karchev, Coulomb interaction revised in the presence of material with negative permittivity, arXiv:0910.5307v3 [physics. class-ph] 26 Nov 2010.

[0189]

[0011] V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, and P.P.J. M. Schram, Kramers-Kronig relations for the dielectric function and the static conductivity of Coulomb systems, EPL 90, 10003 (2010).

[0190]

[0012] A. Hamo, A. Benyamini, I. Shapir, I. Khivrich, J. Waissman, K. Kaasbjerg, Y. Oreg, F. von Oppen, and S. Hani, Electron attraction mediated by Coulomb repulsion, Nature 535, 395- 400 (2016)

[0191]

[0013] F. Castles, J. A. J. Fells, D. Isakov, S. M. Morris, A. A. R. Watt, and P. S. Grant, Active Metamaterials with Negative Static Electric Susceptibility, Advanced materials 32, 1904863 (2020).

[0192]

[0014] X. Li, C. Li, X. Gao, and D. Huang, Like-charge attraction between two identical dielectric spheres in a uniform electric field: a theoretical study via a multiple -image method and an effective-dipole approach, J. Mater. Chem. A 12, 6896-6905 (2024).

[0015] A. P. dos Santos and Y. Levin, Like-Charge Attraction between Metal Nanoparticles in a 1:1 Electrolyte Solution, Phys. Rev. Lett. 122, 248005 (2019).

[0193]

[0016] M. Holten, L. Bayha, K. Subramanian, S. Brandstetter, C. Heintze, P. Lunt, P. M. Preiss, and S. Jochim, Observation of Cooper pairs in a mesoscopic two-dimensional Fermi gas, Nature 606, 287-291 (2022).

[0194]

[0017] J. D. Jackson, Classical electrodynamics (1962).

[0195]

[0018] D. J. Bergman and Y. M. Strelniker, Magneto-transport in conducting composite films with a disordered columnar microstructure and an in-plane magnetic field, Phys. Rev. B 60, 13016-13027 (1999).

[0196]

[0019] Y. M. Strelniker, D. Stroud, and A. O. Voznesenskaya, Control of Extraordinary Light Transmission Through Perforated Metal Films Using Liquid Crystals, Eur. Phys. J. B 52, 1-7 (2006).

[0197]

[0020] H. C. Baker and R. L. Singleton, Jr., Non-Hermitian quantum dynamics, Phys. Rev. A 42, 10-17 (1990).

[0198]

[0021] C. M. Bender, D. C. Brody, and H. F. Jones, Complex Extension of Quantum Mechanics, Phys. Rev. Let. 89, 270401 (2002).

[0199]

[0022] J. P. Sun, G. I. Haddad, P. Mazumder, J. N. Schulman, Resonant Tunneling Diodes: Models and Properties, Proc. IEEE 86, 641 (1998).

[0200]

[0023] L. D. Landau, E. M. Lifshitz, Mechanics: Volume 1 (Course of Theoretical Physics).

[0201]

[0024] D. J. Bergman and Y. M. Strelniker, Anisotropic ac electrical permittivity of a periodic metal-dielectric composite film in a strong magnetic field, Phys. Rev. Lett. 80, 857-860 (1998).

[0202]

[0025] Y. M. Strelniker and D. J. Bergman, Magneto-Optical Properties of Metal-Dielectric Composites with a Periodic Microstructure, Eur. Phys. J AP 7, 19-24 (1999).

[0203]

[0026] Y. M. Strelniker and D. J. Bergman, Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field, Phys. Rev. B 59, R12763- R12766 (1999).

[0204]

[0027] Y. M. Strelniker, Theory of Optical Transmission through Elliptical Nanohole Arrays, Phys. Rev. B76, 085409 (2007).

[0205]

[0028] Y. Fleger, M. Rosenbluh, Y. M. Strelniker, D. J. Bergman, and A. N. Lagarkov, Controlling the optical spectra of gold nano-islands by changing the aspect ratio and the inter-island distance: theory and experiment, Eur. Phys. J. B 81, 85-93 (2011).

[0029] Y. M. Strelniker and D. J. Bergman, Strong angular magneto-induced, anisotropy of Voigt effect in metal-dielectric metamaterials with periodic nanostructures, Phys. Rev. B 89, 125312 (2014).

[0206]

[0030] Y. M. Strelniker and D. J. Bergman, Surface versus localized plasmons in an assembly of metaldielectric parallel flat slabs in the presence of an in-plane magnetic field, Phys. Rev. B 102, 035302 (2020).

[0207]

[0031] Y. M. Strelniker and D. J. Bergman, Transmittance and transparency of subwavelength- perforated conducting films in the presence of a magnetic field, Phys. Rev. B 77, 205113 (2008).

[0208]

[0032] M. Tornow, D. Weiss, K. von Klitzing, K. Eberl, D. J. Bergman, and Y. M. Strelniker, Anisotropic magnetoresistance of a classical antidot array, Phys. Rev. Lett. 77, 147-150 (1996).

[0209]

[0033] G. J. Strijkers, F. Y. Yang, D. H. Reich, C. L. Chien, P. C. Searson, Y. M. Strelniker, and D. J. Bergman, Magnetoresistance anisotropy of a Bi antidot array, IEEE T. Magm. 37, 2067 (2001).

[0210]

[0034] Y. M. Strelniker and D. J. Bergman, Gate-tuning of the surface plasmons and their optical properties, In D. P. Tsai, T. Tanaka, and Y-J. Lu (Eds.), Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XX [1219706] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 12197) (2022).

[0211]

[0035] R. S. Knox, Theory of Excitons, Acad. Press-New York and London (1963).

[0212]

[0036] G. H. Wannier, The structure of electronic excitation levels in insulating crystals, Phys. Rev. 52, 191 (1937).

[0213]

[0037] N. F. Mott, Conduction in polar crystals, pt. 2, Trans. Farad. Soc. 34, 500 (1938).

[0214]

[0038] G. Dresselhaus, Effective mass approximation for excitons, J. Phys. Chem. Solids 1, 14 (1956).

[0215]

[0039] V. N. Piskovoi, E. F. Venger, and Ya. M. Strelniker, Theory of Polaritons in Bounded Spatially Dispersive Media, Phys. Rev. B 66, 115402 (2002).

[0216]

[0040] Ya. M. Strelniker, Theory of inelastic low-energy electron scattering with generation of surface and bulk excitons in molecular crystals, Phys. Stat. Sol. B 149, 603-613 (1988).

[0217]

[0041] H. Haken and W. Schottky, Die behandlung des Exzitons nach der Vielelektronentheorie, Z. Phys. Chem. Neue Folge 16, 218-244 (1958).

[0218]

[0042] H. Haken, Die Theorie des Exzitons imfesten Ko'rper, Fortschritte der Physik 6, 271-334 (1958).

[0043] V. L. Ginzburg and V. V. Kelle, Surface Excitons of Electron-hole Type and Collective Phenomena Associated with Them, JETP. Lett. 17, 306-308 (1973) [ZhETF Pis. Red. 17, 428-431 (1973)].

[0219]

[0044] L. V. Keldysh, Exciton in Semiconductor-Dielectric Nanostructures, Phys. Stat. Sol. (a) 164, 3-12 (2001).

[0220]

[0045] L. V. Keldysh, Soviet Phys. - J. Exper. Theor. Phys. Lett. 29, 716 (1979).

[0221]

[0046] E. V. Shornikova, D. R. Yakovlev, N. A. Gippius, G. Qiang, B. Dubertret, A. H. Khan, A. D. Giacomo, I. Moreels, and M. Bayer, Exciton Binding Energy in CdSe Nanoplatets measured by One- and Two-Photon Absorption, Nano Lett. 21, 10525-10531 (2021).

[0222]

[0047] L. D. Landau, L. P. Pitaevskii, E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, Oxford, 1984).

[0223]

[0048] L. D. Landau, L. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd Edition, Butterworth, Heinemann.

[0224]

[0049] V. B. Berestetskii, L. P. Pitaevskii, E.M. Lifshitz, Quantum Electrodynamics: Volume 4 (Course of Theoretical Physics).

[0225]

[0050] D. J. Bergman, Eigenstates of Maxwell’s equations in multiconstituent microstructures, Phys. Rev. A 105, 062213 (2022).

[0226]

[0051] G. Dresselhaus, A. F. Kip, and C. Kittel, Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals, Phys. Rev. 98, 368-384 (1955).

[0227]

[0052] G. Dresselhaus, A. F. Kip, and C. Kittel, Plasma Resonance in Crystals: Observations and Theory, Phys. Rev. 100, 618 -625 (1955).

[0228]

[0053] L. D. Landau, E.M. Lifshitz, The Classical Theory of Field, 4th revised English edition. Pergamon Press, Oxford (1987).

[0229]

[0054] H. A. Lorentz, 2nd edition (1915); reprint, Dover, New York (1952). (p. 158).

[0230]

[0055] Y. M. Strelniker and D. J. Bergman, Manipulation of the Optical Properties of a Plasmonic Metamaterial Film by an External Transverse Voltage Springer Proceedings in Mathematics & Statistics, 457 (2024). Editors: F. Willot, J. Dirrenberger, S. Forest, D. Jeulin, A. V. Cherkaev. Continuum Models and Discrete Systems CMDS-14, Paris, France, June 26-30, 2023

[0231]

[0056] Y. M. Strelniker and D. J. Bergman, Phys. Rev. B 110, 085305 (2024).

Claims

WHAT IS CLAIMED IS:

1. A metamaterial system, comprising; a metamaterial comprising a multiplicity of structures made of a first material distributed to form a periodic pattern within a bulk made of a second material, wherein one of said first and said second materials is metallic and the other one of said first and said second materials is dielectric; and a magnetic field source forming a magnetic field within said metamaterial, wherein said magnetic field is selected to ensure that an electrical permittivity of said metamaterial is negative.

2. The system according to claim 1, wherein said first material is metallic and said second material is dielectric.

3. The system according to claim 2, wherein said first material comprises bismuth.

4. The system according to claim 1, wherein said first material is dielectric and said second material is metallic.

5. The system according to claim 1, wherein a largest diameter of said structures is less than half of a periodicity parameter of said periodic pattern.

6. The system according to any of claims 2-4, wherein a largest diameter of said structures is less than half of a periodicity parameter of said periodic pattern.

7. The system according to claim 1, wherein a largest diameter of said structures is more than a quarter of a periodicity parameter of said periodic pattern.

8. The system according to any of claims 2-6, wherein a largest diameter of said structures is more than a quarter of a periodicity parameter of said periodic pattern.

9. The system according to any of claims 1-8, wherein said structures are spherical.

10. The system according to any of claims 1-8, wherein said structures are ellipsoidal.

11. The system according to any of claims 1-8, wherein said structures are cylindrical.

12. The system according to any of claims 1-11, wherein said structures are non-hollow.

13. The system according to claim 1, wherein said magnetic field source is configured to generate a static magnetic field.

14. The system according to any of claims 2-12, wherein said magnetic field source is configured to generate a static magnetic field.

15. The system according to claim 13, wherein said magnetic field source is configured to generate a static magnetic field having a strength of at least 0.1 T.

16. The system according to claim 14, wherein said magnetic field source is configured to generate a static magnetic field having a strength of at least 0.1 T.

17. The system according to claim 1, comprising a space characterized by a positive electrical permittivity adjacent to a surface of said metamaterial forming an interface therebetween.

18. The system according to any of claims 2-16, comprising a space characterized by a positive electrical permittivity adjacent to a surface of said metamaterial forming an interface therebetween.

19. The system according to claim 17, wherein there are at least two interfaces between said space and said metamaterial.

20. The system according to claim 18, wherein there are at least two interfaces between said space and said metamaterial.

21. The system according to any of claims 17-20, wherein said space is a vacuum space.

22. The system according to any of claims 17-21, comprising atomic nuclei within said space, wherein said negative electrical permittivity of said metamaterial induces fusion between said atomic nuclei.

23. The system according to claim 22, wherein said atomic nuclei comprise deuterium and said fusion is by a deuterium-deuterium reaction.

24. The system according to claim 22, wherein said atomic nuclei comprise deuterium and tritium and said fusion is by a deuterium-tritium reaction.

25. The system according to claim 22, wherein said atomic nuclei comprise tritium and said fusion is by a tritium-tritium reaction.

26. The system according to any of claims 17-21, comprising atoms within said space, wherein said negative electrical permittivity of said metamaterial induces ionization of said atoms.

27. The system according to any of claims 17-21, comprising liquid within said space, wherein said negative electrical permittivity of said metamaterial induces chemical reaction within said liquid.

28. A nuclear propulsion system, comprising the metamaterial system according to any of claims 22-25.

29. A vehicle, being propelled by the nuclear propulsion system of claim 28.

30. A power plant, comprising the metamaterial system according to any of claims 22- 25.

31. A particle accelerator, comprising the metamaterial system according to any of claims 1-21.

32. A method of generating energy, comprising introducing atomic nuclei into the vacuum space of the system according to claim 21, to induce fusion between said atomic nuclei.

33. A method of ionizing atoms or molecules, comprising introducing the atoms or molecules into the space of the system according to any of claims 17-21, so as to induce ionization of the atoms or molecules.

34. A method of generating current, comprising introducing charged particles of like charges into the space of the system according to any of claims 17-21, and applying an electric field to said space.

35. A method of inducing a chemical reaction between molecules, comprising introducing the molecules into the space of the system according to any of claims 17-21.

36. The method according to any of claims 32-35, being executed at room temperature.

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