Patent Publication Number: US-10312597-B2

Title: Ferrite-enhanced metamaterials

Description:
BACKGROUND INFORMATION 
     1. Field 
     The present disclosure relates generally to metamaterials. More particularly, the present disclosure relates to a method and apparatus for adjusting a resonance of a metamaterial structure using a tunable element associated with the metamaterial structure. 
     2. Background 
     A metamaterial may be an artificial composite material engineered to have properties that may not be currently found in nature. A metamaterial structure may be an assembly of multiple individual metamaterial cells that are formed from conventional materials. These conventional materials may include, but are not limited to, metals, metal alloys, plastic materials, and other types of materials. 
     The refractive index for a metamaterial cell is determined by the electric permittivity and magnetic permeability of the metamaterial cell. The refractive index determines how an electromagnetic wave propagating through the metamaterial cell is bent, or refracted. A negative index metamaterial (NIM) is a metamaterial that provides a negative index of refraction over a particular frequency range that is typically determined by the resonance of the metamaterial. This frequency range is typically a band of frequencies centered at or near a resonant frequency of the metamaterial. The frequency range over which the negative index of refraction is provided by a metamaterial structure may be dependent on various factors including the orientation, size, shape, and pattern of arrangement of the metamaterial cells that form the metamaterial structure. 
     A metamaterial structure may take the form of a two-dimensional or three-dimensional periodic structure of self-resonant metamaterial cells that are each typically self-resonant within the same frequency range, which may be a limited or narrow frequency range. The aggregate effect provided by this type of metamaterial structure may be used to focus electromagnetic energy in a manner similar to an optical lens. 
     While the negative index of refraction effects of metamaterial structures provide a powerful means of directing electromagnetic energy, these metamaterial structures have a limited operational frequency range. Increasing the range of frequencies over which a negative index of refraction may be provided by a particular metamaterial structure may be useful in certain applications. Therefore, it would be desirable to have a method and apparatus that take into account at least some of the issues discussed above, as well as other possible issues. 
     SUMMARY 
     In one illustrative embodiment, an apparatus comprises a metamaterial cell and a tunable element associated with the metamaterial cell. The metamaterial cell has a negative index of refraction. Tuning a set of electromagnetic properties of the tunable element adjusts a resonance of the metamaterial cell. 
     In another illustrative embodiment, a metamaterial structure comprises a plurality of meta-units. A meta-unit in the plurality of meta-units comprises a metamaterial cell and a tunable element associated with the metamaterial cell. Tuning at least one of an electric permittivity or a magnetic permeability of the tunable element adjusts a resonance of the metamaterial cell. Further, adjusting the resonance for at least a portion of the plurality of meta-units adjusts a frequency range over which the metamaterial structure provides a negative index of refraction for focusing electromagnetic energy. 
     In yet another illustrative embodiment, a method is provided for tuning a metamaterial cell. A set of electromagnetic properties of a tunable element associated with the metamaterial cell may be tuned. A resonance of the metamaterial cell may be adjusted in response to the set of electromagnetic properties being tuned. A range of frequencies over which the metamaterial cell provides a negative index of refraction may be changed in response to the resonance of the metamaterial cell changing. 
     The features and functions can be achieved independently in various embodiments of the present disclosure or may be combined in yet other embodiments in which further details can be seen with reference to the following description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features believed characteristic of the illustrative embodiments are set forth in the appended claims. The illustrative embodiments, however, as well as a preferred mode of use, further objectives and features thereof, will best be understood by reference to the following detailed description of an illustrative embodiment of the present disclosure when read in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is an illustration of an isometric view of an energy directing system in accordance with an illustrative embodiment; 
         FIG. 2  is an illustration of a top isometric view of a meta-unit in accordance with an illustrative embodiment; 
         FIG. 3  is an illustration of a bottom isometric view of a meta-unit in accordance with an illustrative embodiment; 
         FIG. 4  is an illustration of a side view of a meta-unit and a tuning device in accordance with an illustrative embodiment; 
         FIG. 5  is an illustration of a bottom view of another configuration for a meta-unit in accordance with an illustrative embodiment; 
         FIG. 6  is an illustration of a top isometric view of a meta-unit in accordance with an illustrative embodiment; 
         FIG. 7  is an illustration of a top isometric view of a meta-unit in accordance with an illustrative embodiment; 
         FIG. 8  is an illustration of a top view of a top isometric view of another configuration for a meta-unit in accordance with an illustrative embodiment; 
         FIG. 9  is an illustration of a process for tuning a metamaterial cell in the form of a flowchart in accordance with an illustrative embodiment; 
         FIG. 10  is an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell in the form of a flowchart in accordance with an illustrative embodiment; 
         FIG. 11  is an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell in the form of a flowchart in accordance with an illustrative embodiment; 
         FIG. 12  is an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell in the form of a flowchart in accordance with an illustrative embodiment; and 
         FIG. 13  is an illustration of a process for focusing electromagnetic energy in the form of a flowchart in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The illustrative embodiments recognize and take into account different considerations. For example, the illustrative embodiments recognize and take into account that it may be desirable to have a method and apparatus that enable adaptive tuning of the resonance of metamaterial cells for the purposes of varying the range of frequencies over which the metamaterial cell provides a negative index of refraction, for enabling the directing of electromagnetic energy in a desired direction. 
     The illustrative embodiments recognize and take into account that it may be desirable to tune the resonance of a metamaterial cell to thereby adjust the frequency range over which a metamaterial cell provides a negative index of refraction. In particular, it may be desirable to have a method and apparatus for performing this tuning without having to change the physical structure or geometric configuration of the metamaterial cell. 
     Thus, the illustrative embodiments provide a method and apparatus for controlling a metamaterial cell. In one illustrative example, a tunable element is associated with a metamaterial cell having a negative index of refraction. A set of electromagnetic properties of a tunable element may be tuned to adjust a resonance of the metamaterial cell. A direction in which electromagnetic energy passing through the metamaterial cell is focused is controlled based on the tuning of the set of electromagnetic properties of the tunable element. The set of electromagnetic properties of the tunable element may include, for example, an electric permittivity, a magnetic permeability, or both. 
     A plurality of metamaterial cells that form a metamaterial structure may be tuned as described above to provide an aggregate negative refractive index effect that enables electromagnetic energy to be focused in a desired direction. The direction in which the electromagnetic energy is focused may be easily changed by adjusting the resonance of one or more metamaterial cells of the plurality of metamaterial cells. 
     In the different illustrative examples, the base terms of “adjust,” “change,” and “tune,” and the various derivatives of these base terms may be used interchangeably. In other words, tuning a resonance may mean the same as adjusting the resonance or changing the resonance. Similarly, tuning an electromagnetic property may mean the same as changing or adjusting that electromagnetic property. 
     Referring now to the figures and, in particular, with reference to  FIG. 1 , an illustration of an isometric view of an energy directing system is depicted in accordance with an illustrative embodiment. In this illustrative example, energy directing system  100  may be used to direct and focus electromagnetic energy. 
     As depicted, energy directing system  100  includes metamaterial structure  102 . Metamaterial structure  102  is comprised of plurality of meta-units  104 . In this illustrative example, plurality of meta-units  104  may be arranged to form a grid. For example, without limitation, a first portion of plurality of meta-units  104  is arranged substantially parallel to first axis  106  and may be configured to receive electromagnetic energy that propagates in a direction substantially parallel to axis  106 . A second portion of plurality of meta-units  104  is arranged substantially parallel to second axis  108  and may be configured to receive electromagnetic energy that propagates in a direction substantially parallel to axis  108 . In this illustrative example, second axis  108  and first axis  106  are perpendicular to each other. 
     Metamaterial structure  102  may be used to direct and focus electromagnetic energy  110 . In particular, metamaterial structure  102  may be used to control propagation path  112  of electromagnetic energy  110  that passes through metamaterial structure  102 . For example, metamaterial structure  102  may be used to focus electromagnetic energy  110  in a desired direction. In other words, metamaterial structure  102  may be used to form focused electromagnetic energy  114  that is directed towards a particular point  116  in space. 
     Energy directing system  100  may operate in a reflection mode, a transmission mode, or both. In the transmission mode, electromagnetic energy  110  passes through metamaterial structure  102  and may be focused by metamaterial structure  102  towards the particular point  116  in a manner similar to a transmission lens effect. Metamaterial structure  102  is configured to allow electromagnetic energy  110  to pass through metamaterial structure  102  with reduced loss. 
     In the reflection mode, metamaterial structure  102  is used to reflect electromagnetic energy  110  in a particular direction and may focus a beam of electromagnetic energy  110  towards a particular point in space in a manner similar to a reflection lens effect. Metamaterial structure  102  is configured to prevent the passage of electromagnetic energy  110  through metamaterial structure  102 . 
     In one illustrative example, metamaterial structure  102  includes plurality of meta-units  104 . Meta-unit  118  may be an example of one of plurality of meta-units  104 . In this illustrative example, each other meta-unit of plurality of meta-units  104  is implemented in a manner similar to meta-unit  118 . However, in other illustrative examples, one or more other meta-units in plurality of meta-units  104  may be implemented differently from meta-unit  118 . 
     Each of plurality of meta-units  104  may include a metamaterial cell and a tunable element. In particular, the metamaterial cell provides a negative index of refraction for electromagnetic energy  110  that is within a particular frequency range. When electromagnetic energy  110  is not within the particular frequency range, electromagnetic energy  110  may be scattered by metamaterial structure  102 . This type of scattering effect may be used to filter out undesired frequencies of electromagnetic energy  110  that propagates through the metamaterial structure  102 . 
     The negative index of refraction provided by each meta-unit in plurality of meta-units  104  may produce an aggregate effect. This aggregate effect may also be referred to as an aggregate negative refractive index effect. The aggregate effect of the negative index of refraction provided by each meta-unit in plurality of meta-units  104  controls the shaping of electromagnetic energy  110  that propagates through metamaterial structure  102  such that electromagnetic energy  110  may be focused towards point  116  in space. 
     Each meta-unit in plurality of meta-units  104  may be tuned to adjust or vary the negative index of refraction response produced by the metamaterial cell of that meta-unit. Individual meta-units or groups of meta-units in plurality of meta-units  104  may be tuned to produce an aggregate effect that focuses electromagnetic energy  110  in the desired direction. 
     In one illustrative example, tuning a meta-unit, such as meta-unit  118 , includes tuning a set of electromagnetic properties of the tunable element of meta-unit  118 . The set of electromagnetic properties may include one or more electromagnetic properties. In one illustrative example, the set of electromagnetic properties may include electric permittivity, magnetic permeability, or both. 
     Tuning the electric permittivity, the magnetic permeability, or both of a tunable element of meta-unit  118  adjusts the resonance of the metamaterial cell of meta-unit  118 . Changing the resonance of the metamaterial cell causes the frequency range at which a negative index of refraction is provided by meta-unit  118  to change. 
     With reference now to  FIG. 2 , an illustration of a top isometric view of a meta-unit is depicted in accordance with an illustrative embodiment. In this illustrative example, meta-unit  200  may be an example of one implementation for any one of plurality of meta-units  104  in  FIG. 1 . In one illustrative example, meta-unit  200  may be an example of one manner in which meta-unit  118  in  FIG. 1  may be implemented. 
     As depicted, meta-unit  200  includes metamaterial cell  201  and tunable element  202 . Metamaterial cell  201  may include base  203 , magnetic resonator  204 , and conductive structure  206 . Base  203 , magnetic resonator  204 , and conductive structure  206 . 
     Base  203  may be comprised of any material or combination of materials that is transparent to an electromagnetic field having a natural frequency of metamaterial cell  201 . In one illustrative example, base  203  takes the form of a dielectric substrate. 
     As depicted, magnetic resonator  204  and conductive structure  206  are disposed on side  210  and side  212 , respectively, of base  203 . Magnetic resonator  204  may be implemented in different ways. In one illustrative example, magnetic resonator  204  takes the form of dual split ring resonator  214 . In other illustrative examples, magnetic resonator  204  may take the form of some other type of device that produces negative index of refraction for electromagnetic energy within a given frequency range. For example, without limitation, magnetic resonator  204  may take the form of a single split ring resonator, a Swiss roll capacitor, an array of metallic cylinders, a capacitive array of sheets wound on cylinders, some combination thereof, or some other type of device. 
     As depicted, when magnetic resonator  204  takes the form of dual split ring resonator  214 , magnetic resonator  204  includes outer split ring  216  and inner split ring  218 , which are concentric split rings. In other words, dual split ring resonator  214  has plurality of splits  220 . Outer split ring  216  and inner split ring  218  may be etched or formed onto side  210  of base  203 . Outer split ring  216  and inner split ring  218  affect or control the electromagnetic energy that propagates through meta-unit  200 . 
     Conductive structure  206  is positioned relative to magnetic resonator  204 . Conductive structure  206  may be electrically conductive. In this illustrative example, conductive structure  206  takes the form of an electrically conductive post or rod. In particular, conductive structure  206  may take the form of a metallic post. However, in other illustrative examples, conductive structure  206  may be implemented using a conductive piece of wire, a conductive plate, or some other type of electrically conductive element. 
     Tunable element  202  is associated with metamaterial cell  201 . Tunable element  202  may be implemented in different ways such that tunable element  202  is associated with metamaterial cell  201  in different ways. In this illustrative example, tunable element  202  is associated with conductive structure  206 . 
     As used herein, when one component is “associated” with another component, the two components are physically associated with each other. For example, a first component, such as tunable element  202 , may be considered to be associated with a second component, such as conductive structure  206 , by being at least one of secured to the second component, bonded to the second component, mounted to the second component, welded to the second component, fastened to the second component, disposed on the second component, deposited on the second component, or connected to the second component in some other suitable manner. The first component also may be associated with the second component indirectly using a third component. Further, the first component may be considered to be associated with the second component by being formed as part of the second component, as an extension of the second component, or both. 
     As used herein, the phrase “at least one of,” when used with a list of items, means different combinations of one or more of the listed items may be used and only one of the items in the list may be needed. The item may be a particular object, thing, step, operation, process, or category. In other words, “at least one of” means any combination of items or number of items may be used from the list, but not all of the items in the list may be required. 
     For example, without limitation, “at least one of item A, item B, or item C” or “at least one of item A, item B, and item C” may mean item A; item A and item B; item B; item A, item B, and item C; or item B and item C. In some cases, “at least one of item A, item B, or item C” or “at least one of item A, item B, and item C” may mean, but is not limited to, two of item A, one of item B, and ten of item C; four of item B and seven of item C; or some other suitable combination. 
     In one illustrative example, tunable element  202  takes the form of a ferromagnetic material that is disposed on a portion of conductive structure  206 . For example, without limitation, the ferromagnetic material may be disposed on at least one side of conductive structure  206 . 
     In one illustrative example, the ferromagnetic material may be embedded within conductive structure  206  on the side of conductive structure  206  that is not facing base  203 . In another illustrative example, ferromagnetic material may be deposited on conductive structure  206  using additive manufacturing processes to form tunable element  202 . In some cases, tunable element  202  may take the form of one or more layers of ferromagnetic material that have been painted on the side of conductive structure  206  that is not facing base  203 . 
     The magnetic permeability of tunable element  202  may be tuned to adjust the resonance of metamaterial cell  201 . For example, tuning device  222  may be used to change the magnetic permeability of tunable element  202 . 
     In this illustrative example, tuning device  222  includes magnetic device  224  having first end  226  and second end  228 . In other illustrative examples, tuning device  222  may be implemented using more than one magnetic device. 
     Magnetic device  224  may be external to meta-unit  200  and may be used to apply a magnetic field to tunable element  202 . Applying a magnetic field to tunable element  202  may affect the magnetic permeability of tunable element  202 , which may, in turn, affect the resonance of metamaterial cell  201 . 
     For example, without limitation, the magnitude or level of the magnetic field that is applied to tunable element  202  may be adjusted to thereby change the magnetic permeability of tunable element  202 . Changing the magnetic permeability of tunable element  202  causes the resonance of metamaterial cell  201  to change, which in turn, changes the frequency range over which metamaterial cell  201  provides a negative index of refraction. 
     Turning now to  FIG. 3 , an illustration of a bottom isometric view of meta-unit  200  from  FIG. 2  is depicted in accordance with an illustrative embodiment. In this illustrative example, side  212  of base  203  may be more clearly seen. 
     With reference now to  FIG. 4 , an illustration of a side view of meta-unit  200  and tuning device  222  from  FIG. 2-3  is depicted in accordance with an illustrative embodiment. In this illustrative example, tuning device  222  is used to apply magnetic field  400  to tunable element  202 . Magnetic field  400  may be controlled by tuning device  222  to change the magnetic permeability of tunable element  202 , thereby changing the resonance of metamaterial cell  201  of meta-unit  200 . 
     As one illustrative example, as the magnitude of magnetic field  400  increases, the magnetic dipoles within tunable element  202  may align. This alignment may increase the effective magnetic flux through magnetic resonator  204  and shift the resonance of metamaterial cell  201  to thereby lower the frequencies of electromagnetic energy for which a negative index of refraction is provided. 
     With reference now to  FIG. 5 , an illustration of a bottom view of another configuration for a meta-unit is depicted in accordance with an illustrative embodiment. In this illustrative example, meta-unit  500  may be another example of an implementation for at least one of plurality of meta-units  104  in  FIG. 1 . In particular, meta-unit  500  may be another example of one implementation for meta-unit  118  in  FIG. 1 . 
     As depicted, meta-unit  500  includes metamaterial cell  501  and tunable element  502 . Metamaterial cell  501  may be implemented in a manner similar to metamaterial cell  201  in  FIGS. 2-4 . 
     As depicted, metamaterial cell  501  includes base  503  having first side  505  and second side  504 . First side  505  is shown in phantom view in this illustrative example. 
     Metamaterial cell  501  further includes magnetic resonator  506 , which is shown in phantom view and is disposed on first side  505 . Metamaterial cell  501  also includes conductive structure  508 . Conductive structure  508  is associated with second side  504  of base  503 . In this illustrative example, conductive structure  508  may be implemented differently from conductive structure  206  in  FIGS. 2-4 . 
     In this illustrative example, conductive structure  508  comprises first conductor  510  and second conductor  512 , both of which are electrically conductive. First conductor  510  and second conductor  512  take the form of a first electrode and a second electrode, respectively, which are disposed on second side  504  of base  503 . In one illustrative example, first conductor  510  and second conductor  512  may be three-dimensionally printed on base  503 . 
     Tunable element  502  is implemented differently in meta-unit  500  as compared to tunable element  202  in meta-unit  200  in  FIGS. 2-4 . In this illustrative example, tunable element  502  takes the form of a fluid mixture that is located between first conductor  510  and second conductor  512 . In this illustrative example, the fluid mixture may be held in reservoir  514  formed between base  503 , first conductor  510 , second conductor  512 , and cover  515 . Cover  515  may take the form of a sheet of transparent plastic in this illustrative example. 
     In some illustrative examples, reservoir  514  may take the form of a channel or cavity that is formed within base  503  for holding the fluid mixture that forms tunable element  502 . In some cases, the fluid mixture may be held in a plastic box, a box comprised of dielectric material, or some other type of structure disposed between first conductor  510  and second conductor  512 . 
     In this illustrative example, the fluid mixture that forms tunable element  502  comprises plurality of liquid crystals  516 . In this manner, reservoir  514  is filled with plurality of liquid crystals  516 . Plurality of liquid crystals  516  may inherently have anisotropic geometry. In other words, each liquid crystal molecule of plurality of liquid crystals  516  may have a geometry that is directionally dependent. For example, without limitation, each liquid crystal of plurality of liquid crystals  516  may have a rod-type shape, a cigar-type shape, an oblate shape, or some other type of elongated shape. 
     Tuning the electric permittivity of plurality of liquid crystals  516  changes the resonance of metamaterial cell  501 . The electric permittivity of plurality of liquid crystals  516  may be changed by applying an electric field to plurality of liquid crystals  516  using a tuning device (not shown). Applying an electric field to plurality of liquid crystals  516  may change an electric permittivity of plurality of liquid crystals  516 , which may thereby change a resonance of metamaterial cell  501 . 
     With reference now to  FIG. 6 , an illustration of a top isometric view of meta-unit  500  from  FIG. 5  is depicted in accordance with an illustrative embodiment. In this illustrative example, first side  505  may be more clearly seen. As depicted, magnetic resonator  506  is disposed on first side  505  of base  503 . 
     Magnetic resonator  506  includes outer split ring  600  and inner split ring  602 , which are concentric. In this manner, magnetic resonator  506  takes the form of dual split ring resonator  604 . 
     In this illustrative example, plurality of liquid crystals  516  that form tunable element  502  is held within reservoir  514  formed between base  503 , first conductor  510 , second conductor  512 , and cover  515 . First conductor  510 , second conductor  512 , and cover  515  may be substantially flush with second side  504  of base  503  in that first conductor  510 , second conductor  512 , and cover  515  do not protrude or extend past second side  504 . In some cases, reservoir  514  may be considered to be formed as a channel within base  503 . 
     Tuning device  606  may be used to apply an electric field to tunable element  502 . In this illustrative example, tuning device  606  takes the form of an alternating current bias voltage source that can be controlled to generate voltage that can be varied. In other illustrative examples, tuning device  606  may take the form of some other type of controllable voltage source. 
     In this illustrative example, tuning device  606  is connected to first conductor  510  through line  608  and is connected to second conductor  512  through line  610 . Tuning device  606  may be used to apply a voltage to first conductor  510  and to second conductor  512 , which may create a potential difference between first conductor  510  and second conductor  512 . This potential difference results in an electric field being applied to plurality of liquid crystals  516  that form tunable element  502 . Changing the voltage applied to first conductor  510  and to second conductor  512  may change the magnitude or level of the electric field applied to plurality of liquid crystals  516 . 
     Applying an electric field to plurality of liquid crystals  516  affects the electric permittivity of plurality of liquid crystals  516 . Thus, changing the voltage applied to first conductor  510  and second conductor  512  changes the electric permittivity of plurality of liquid crystals  516 , thereby changing the resonance of metamaterial cell  501 . 
     With reference now to  FIG. 7 , an illustration of a top isometric view of meta-unit  500  from  FIGS. 5-6  having reservoir  514  that is located outside of base  503  is depicted in accordance with an illustrative embodiment. In this illustrative example, reservoir  514  is located at, and attached to, second side  504  of base  503 . First conductor  510  and second conductor  512  protrude out past second side  504  of base  503 . 
     With reference now to  FIG. 8 , an illustration of a top isometric view of another configuration for a meta-unit is depicted in accordance with an illustrative embodiment. In this illustrative example, meta-unit  800  may be another example of an implementation for at least one of plurality of meta-units  104  in  FIG. 1 , including, but not limited to, meta-unit  118  in  FIG. 1 . 
     As depicted, meta-unit  800  includes metamaterial cell  801  and tunable element  802 . Metamaterial cell  801  may be implemented in a manner similar to metamaterial cell  201  in  FIGS. 2-4  and metamaterial cell  501  in  FIGS. 5-7 . 
     Metamaterial cell  801  includes base  803  having first side  804  and second side  806 . Metamaterial cell  801  further includes magnetic resonator  808 . Magnetic resonator  808  may take the form of, for example, without limitation, a dual split ring resonator. Additionally, metamaterial cell  801  includes conductive structure  810 . Conductive structure  810  comprises conductive post  811 , first electrode  812 , and second electrode  814 . 
     Tunable element  802  takes the form of fluid mixture  815  in this illustrative example. Fluid mixture  815  is present between first electrode  812  and second electrode  814 . Fluid mixture  815  is held within reservoir  816  formed between first electrode  812  and second electrode  814 . 
     Fluid mixture  815  comprises plurality of liquid crystals  818  and plurality of magnetic nanoparticles  820 . Plurality of magnetic nanoparticles  820  may be dispersed among plurality of liquid crystals  818 . 
     Plurality of magnetic nanoparticles  820  belong to a class of nanoparticles that can be manipulated using magnetic field gradients. A magnetic nanoparticle of plurality of magnetic nanoparticles  820  may comprise at least one of iron, nickel, cobalt, some other type of magnetic element, or a chemical compound that includes at least one of iron, nickel, cobalt, a ferromagnetic material, or some other type of magnetic element. In some illustrative examples, nanoparticles may include a silica or polymer protective coating to protect against chemical or electrochemical corrosion. 
     In one illustrative example, plurality of magnetic nanoparticles  820  take the form of a plurality of ferromagnetic nanoparticles. These ferromagnetic nanoparticles may take the form of a plurality of nanoferrite particles. Further, such nanoparticles may comprise nanoferrite particles, barium ferrite particles, or other suitable ferrite materials. 
     An electric field may be applied to plurality of liquid crystals  818  to change an electric permittivity of plurality of liquid crystals  818 . For example, without limitation, tuning device  606  from  FIG. 6  may be used to apply a voltage to first electrode  812  through line  608  and second electrode  814  through line  610 . Applying a voltage to first electrode  812  and second electrode  814  creates a potential difference between these electrodes and thereby, an electric field across fluid mixture  815 . The voltage may be controlled and varied by tuning device  606 . Changing the voltage applied to first electrode  812  and second electrode  814  changes the potential difference between these electrodes, which changes the magnitude of the electric field applied across fluid mixture  815 , which thereby changes the electric permittivity of plurality of liquid crystals  818 . 
     Additionally, applying the electric field to plurality of liquid crystals  818  causes a first alignment of plurality of liquid crystals  818  to change. The change in the first alignment of plurality of liquid crystals  818  may cause a corresponding change in a second alignment of plurality of magnetic nanoparticles  820 . The change in the second alignment of plurality of magnetic nanoparticles  820  may change the magnetic permeability of plurality of magnetic nanoparticles  820 . 
     The change in the electric permittivity of plurality of liquid crystals  818  and the change in magnetic permeability of plurality of magnetic nanoparticles  820  together cause a change in the resonance of metamaterial cell  801 . In this manner, the resonance of metamaterial cell  801  may be custom-tuned. 
     In some cases, a ferromagnetic material (not shown) may be disposed on conductive post  811 . An external magnetic device, such as magnetic device  224  in  FIG. 2 , may be used to apply a magnetic field to the ferromagnetic material that changes the magnetic permeability of the ferromagnetic material, which, in turn, changes the resonance of metamaterial cell  801 . In some cases, the magnetic field may also affect the magnetic permeability of plurality of magnetic nanoparticles  820 . 
     The ratio of plurality of magnetic nanoparticles  820  to plurality of liquid crystals  818  in fluid mixture  815  may be tuned. For example, the ratio of plurality of magnetic nanoparticles  820  to plurality of liquid crystals  818  may be selected such that fluid mixture  815  maintains a liquid viscosity and has a desired amount of flow. In one illustrative example, fluid mixture  815  may have a 1:1 ratio by weight of plurality of magnetic nanoparticles  820  to plurality of liquid crystals  818 . In another illustrative example, fluid mixture  815  may have a ratio of plurality of magnetic nanoparticles  820  to plurality of liquid crystals  818  that is between 1:1 and 10:1. 
     As described in  FIGS. 1-8 , the resonance of a metamaterial cell may be changed in different ways by tuning the electric permittivity, magnetic permeability, or both of a tuning element that is associated with the metamaterial cell. The process of adaptively tuning the resonance of a metamaterial cell using a tunable element may be repeated for one or more meta-units in, for example, plurality of meta-units  104  in  FIG. 1 . In this manner, the aggregate effect produced by plurality of meta-units  104  in metamaterial structure  102  may be custom-tailored for a customized frequency range of electromagnetic energy  110 . 
     The illustrations of energy directing system  100  in  FIG. 1 , meta-unit  200  in  FIGS. 2-4 , meta-unit  500  in  FIGS. 5-7 , and meta-unit  800  in  FIG. 8  are not meant to imply physical or architectural limitations to the manner in which an illustrative embodiment may be implemented. Other components in addition to or in place of the ones illustrated may be used. Some components may be optional. 
     In some illustrative examples, conductive structure  810  in  FIG. 8  may include conductive post  811  and a pair of conductive plates instead of first electrode  812  and second electrode  814 . In some cases, meta-unit  800  may be implemented using some other type of magnetic resonator  808  other than a dual split ring resonator. In some illustrative examples, a tuning device may include both a magnetic device and a controllable voltage source. 
     With reference now to  FIG. 9 , an illustration of a process for tuning a metamaterial cell is depicted in the form of a flowchart in accordance with an illustrative embodiment. The process illustrated in  FIG. 9  may be implemented to tune a resonance of a metamaterial cell in a meta-unit such as one of plurality of meta-units  104  in  FIG. 1 . 
     The process may begin by tuning a set of electromagnetic properties of a tunable element associated with the metamaterial cell (operation  900 ). A resonance of the metamaterial cell is adjusted in response to the set of electromagnetic properties being tuned (operation  902 ). 
     A range of frequencies over which the metamaterial cell provides a negative index of refraction is changed in response to the resonance of the metamaterial cell changing (operation  904 ), with the process terminating thereafter. In other words, the process described in  FIG. 9  may be used to change the set of electromagnetic properties of a tunable element associated with a metamaterial cell to adjust a resonance of the metamaterial cell, and to thereby, adjust a frequency range over which the metamaterial cell yields a negative index of refraction. 
     With reference now to  FIG. 10 , an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell is depicted in the form of a flowchart in accordance with an illustrative embodiment. The process illustrated in  FIG. 10  may be used to implement operation  900  in  FIG. 9 . 
     The process may begin by applying an electric field to a fluid mixture located between a first conductor and a second conductor associated with a metamaterial cell in which the fluid mixture comprises a plurality of liquid crystals (operation  1000 ). Operation  1000  may be performed by, for example, applying a voltage to the first conductor and the second conductor to create a potential difference between the first conductor and the second conductor. Changing the voltage applied changes the potential difference created, which changes the electric field. 
     An electric permittivity of the plurality of liquid crystals is changed in response to the electric field being applied to the fluid mixture (operation  1002 ), with the process terminating thereafter. The extent to which the electric permittivity of the plurality of liquid crystals changes is determined by the level of the voltage applied to the first conductor and the second conductor. Thus, the electric permittivity of the plurality of liquid crystals may be finely tuned by controlling the voltage applied to the first conductor and the second conductor. 
     With reference now to  FIG. 11 , an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell is depicted in the form of a flowchart in accordance with an illustrative embodiment. The process illustrated in  FIG. 11  may be used to implement operation  900  in  FIG. 9 . 
     The process may begin by applying an electric field to a fluid mixture located between a first conductor and a second conductor associated with a metamaterial cell in which the fluid mixture comprises a plurality of liquid crystals and a plurality of magnetic nanoparticles (operation  1100 ). Operation  1100  may be performed by, for example, applying a voltage to the first conductor and the second conductor, which creates a potential difference between the first conductor and the second conductor. Changing the voltage changes the potential difference, which changes the electric field. 
     An alignment of the plurality of liquid crystals is changed in response to the electric field being applied to the fluid mixture (operation  1102 ). An alignment of the plurality of magnetic nanoparticles is changed in response to the alignment of the plurality of liquid crystals changing (operation  1104 ). A magnetic permeability of the plurality of magnetic nanoparticles is changed in response to the alignment of the plurality of magnetic nanoparticles changing (operation  1106 ), with the process terminating thereafter. 
     With reference now to  FIG. 12 , an illustration of a process for tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell is depicted in the form of a flowchart in accordance with an illustrative embodiment. The process illustrated in  FIG. 12  may be used to implement operation  900  in  FIG. 9 . 
     The process may begin by applying a magnetic field to a ferromagnetic material associated with a conductive structure that is part of a metamaterial cell (operation  1200 ). Operation  1200  may be performed by, for example, using an external magnetic device to apply the magnetic field. A magnetic permeability of the ferromagnetic material is changed in response to the magnetic field being applied to the ferromagnetic material (operation  1202 ), with the process terminating thereafter. 
     With reference now to  FIG. 13 , an illustration of a process for focusing electromagnetic energy is depicted in the form of a flowchart in accordance with an illustrative embodiment. The process illustrated in  FIG. 13  may be implemented using metamaterial structure  102  in  FIG. 1  to focus electromagnetic energy  110 . 
     The process begins by tuning a set of electromagnetic properties of a tunable element associated with a metamaterial cell for at least one meta-unit in a plurality of meta-units that form a metamaterial structure (operation  1300 ). A resonance of the metamaterial cell is adjusted for the at least one meta-unit in response to the tuning (operation  1302 ). 
     A direction in which electromagnetic energy passing through the metamaterial structure is focused is controlled based on an aggregate effect of a negative index of refraction provided by each meta-unit in the plurality of meta-units that form the metamaterial structure (operation  1304 ), with the process terminating thereafter. In particular, the plurality of meta-units may be used to focus electromagnetic energy within a particular frequency range in a desired direction but to scatter electromagnetic energy outside of this particular frequency range. 
     The flowcharts and block diagrams in the different depicted embodiments illustrate the architecture, functionality, and operation of some possible implementations of apparatuses and methods in an illustrative embodiment. In this regard, each block in the flowcharts or block diagrams may represent a module, a segment, a function, and/or a portion of an operation or step. 
     In some alternative implementations of an illustrative embodiment, the function or functions noted in the blocks may occur out of the order noted in the figures. For example, in some cases, two blocks shown in succession may be executed substantially concurrently, or the blocks may sometimes be performed in the reverse order, depending upon the functionality involved. Also, other blocks may be added in addition to the illustrated blocks in a flowchart or block diagram. 
     Thus, the illustrative embodiments provide a method and apparatus for tuning the resonance of metamaterial cells. In particular, the frequency response of a metamaterial cell may be tuned by externally applying a magnetic field, an electric field, or both to a tunable element associated with the metamaterial cell. 
     In one illustrative example, a metamaterial cell may be tuned using ferromagnetic material that has been uniquely deposited onto a conductive post or mixed into a fluid mixture to control the total magnetic flux through the metamaterial cell. In some cases, the ferromagnetic material may take the form of a plurality of magnetic nanoparticles that are mixed with a plurality of liquid crystals in the fluid mixture. In another illustrative example, a metamaterial cell may be tuned using a plurality of liquid crystals by controlling a total electric field applied to the plurality of liquid crystals and, in some cases, around a conductive post associated with the metamaterial cell. 
     Increasing at least one of the capacitance or inductance of the metamaterial cell is the mechanism used to alter the resonance frequency of the metamaterial cell. Increasing at least one of the capacitance or inductance results in a lowering of the metamaterial cell resonant frequency. The extent to which the capacitance and inductance can be changed may be limited by the size of and physical material properties of the metamaterial cell. 
     The illustrative embodiments described may be used to facilitate the cost effective fabrication of ferrite-enhanced metamaterials and the fabrication of high gain metamaterial-based antennas. Further, the overall bandwidth of a negative index metamaterial-based antenna may be increased. The illustrative embodiments provide a method for tuning a negative index metamaterial-based antenna that facilitates the focusing of electromagnetic signals and the filtering out of undesired electromagnetic signals at the negative index metamaterial-based antenna. 
     The illustrative embodiments provide a method and apparatus that may facilitate the cost-effective fabrication of wideband adaptive impedance matching and filtering networks. Further, the type of adjustable inductor described by the illustrative embodiments may improve overall performance of radio frequency (RF) systems and may reduce power consumption as compared to currently available inductors. 
     The adjustable inductor described by the illustrative embodiments may enable an impedance matching and filtering network to be made smaller and lighter. Further, this adjustable inductor may simplify the mechanical structures and assembly process needed for the impedance matching and filtering network by reducing the number of circuit components required. 
     The adjustable inductor and adjustable capacitor described by the illustrative embodiments may be particularly useful in forming circuit networks in various systems that operate at radio frequencies. These systems may include, but are not limited to, cellular phones, satellite communication systems, televisions, radar imaging systems, and other types of systems that operate at radio frequencies. 
     In one illustrative example, a ferrite-enhanced negative index metamaterial (FENIM) structure may be used to build a high-gain, lightweight lens antenna that directs radiofrequency energy in much the same manner as an optical lens does with respect to focusing light. The ferrite-enhanced negative index metamaterial may be tuned to have a wider range of frequencies for which a desired aggregative negative refractive index effect is produced. 
     The description of the different illustrative embodiments has been presented for purposes of illustration and description, and is not intended to be exhaustive or limited to the embodiments in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. Further, different illustrative embodiments may provide different features as compared to other desirable embodiments. The embodiment or embodiments selected are chosen and described in order to best explain the principles of the embodiments, the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated.