An electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced electromechanical resonators disposed in or on the electromagnetic medium configured to control electromagnetic wave propagation properties in the electromagnetic composite metamaterial.

FIELD OF THE INVENTION

This invention relates generally to metamaterials and more particularly to an electromagnetic composite metamaterial for controlling electromagnetic wave propagation properties in the metamaterial.

BACKGROUND OF THE INVENTION

Metamaterials are artificial composites that achieve material performance beyond the limitation of uniform materials and exhibit properties not found in naturally-formed substances. Such artificially structured materials are typically constructed by patterning or arranging a material or materials to expand the range of electromagnetic properties of the material.

When an electromagnetic wave enters a material, such as a metamaterial, the electric and magnetic fields of the wave interact with electrons and other charges of the atoms and molecules of the material. These interactions alter the motion of the wave changing the electromagnetic wave propagation properties in the material, e.g., velocity, wavelength, direction, dispersion, impedance, index of refraction, and the like. The velocity and wavelength of the electromagnetic wave in a material is controlled by two parameters: electric permittivity (ε) and magnetic permeability (μ). The velocity of an electromagnetic wave in the material is governed by:

c=1μ⁢⁢ɛ(1)
and the wavelength of an electromagnetic wave in the material is governed by:

λ=cf=1f⁢μ⁢⁢ɛ(2)
where f is the frequency of the electromagnetic wave. As shown by equations (1) and (2), increasing the value of μ and/or ε in a metamaterial is one way to control electromagnetic wave propagation properties in the metamaterial, such as reducing the velocity and wavelength.

The dimensions of an antenna are usually determined by the frequency at which the antenna is designed to function. An ideal antenna is some multiple (or half multiple) of the electromagnetic wavelength such that the antenna can support a standing wave. Antennas usually do not satisfy this constraint because designers either require the antenna to be smaller than a particular wavelength, or the antenna is simply not allotted the required volume in a particular design. When an antenna is not at its ideal dimensions, reflections from the edges of the antenna interfere with the standing wave and the antenna loses efficiency. An antenna, or guided wave structure, is often used to capture information encoded on an electromagnetic wave. However, if the antenna is smaller than an incoming electromagnetic wavelength, the information is captured inefficiently and considerable power is lost. One way to overcome the aforementioned problems is to use a metamaterial and reduce the wavelength of the electromagnetic wave in the metamaterial of the antenna by increasing the value of μ and/or ε for the metamaterial of the antenna. Increasing μ and/or ε in a metamaterial allows for making ultra-miniature antennas, as well as also other smaller devices, such as phase shifters, beam steering devices, and the like.

Every material has a different value for μ and ε. One approach used in conventional metamaterials to reduce the wavelength or velocity in a material is to choose materials that naturally have high values for ε and μ. But, this often results in an impedance mismatch at the edges of the material. Impedance can be thought of as the resistance of a material to the propagation of electromagnetic waves. Impedance is described by the ratio of the magnetic component of an electromagnetic wave to its electrical component. In a non-conducting electromagnetic medium, this relationship is described by:

At the interface between two materials, it is the difference in impedances that leads to reflections and energy loss. When electromagnetic waves propagate through a material, some of the energy of electromagnetic waves turns to thermal energy. Choosing a material with a high value for ε is one way to reduce thermal losses. Ideally, one would decrease the wavelength in the metamaterial by choosing a high value for μ and choosing a high value for ε to reduce thermal losses while keeping the ratio of μ/ε the same to reduce impedance mismatch and reflections. However, in practice, this is not currently possible with conventional materials.

If the impedances of the two materials are matched, the energy exchange across the interface will be perfectly efficient. Therefore, one of the benefits of engineered materials and metamaterials is the ability to vary the permittivity and permeability of the material to achieve the desired wavelength, while keeping optimal impedance.

Any variation in a material on a length scale smaller than the wavelength of an incident electromagnetic wave looks as a continuous material to that electromagnetic wave. One way to engineer metamaterials is to include composite structures inside the material and keep the spacing between the structures small compared to the wavelength of the electromagnetic wavelength. Thus, composite metamaterials can be designed by combining materials where ε is optimized in one material and μ is optimized in another material such that the scales of the two materials are smaller than the wavelength of the electromagnetic wave. An electromagnetic wave therefore interacts with the composite as if it were a bulk material with the desired values of μ and ε.

One conventional metamaterial uses small circuits spaced smaller than the wavelength of an incoming electromagnetic wave. See “Composite Right/Left-Handed Transmission Line Metamaterials”, IEEE Microwave Magazine, 2004, ITOH, incorporated herein by reference. As disclosed therein, a metamaterial is comprised of periodic arrays of resonating elements, e.g., capacitor-inductor elements, arranged to couple effectively into an antenna or guided wave structure that modifies an electromagnetic wave.

However, the disadvantages of this metamaterial include electrical losses in the structure, the challenge of attaining the high inductance required to operate at the desired frequencies, and the large size of individual elements. These disadvantages limit the range of resonant frequencies that can be achieved and the minimum size the structure can achieve.

Another way to control electromagnetic wave propagation properties in a material is to use electromechanical resonators to convert the electrical energy of electromagnetic wave to mechanical energy, e.g., vibrations, and store the mechanical energy therein. If the electromechanical resonators were spaced in a medium such that the spacing between the electromechanical resonators was small compared to the wavelength of the electromagnetic wave, an innovative new electromagnetic composite metamaterial could be achieved.

BRIEF SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide a new electromagnetic composite metamaterial.

It is a further object of this invention to provide such an electromagnetic composite metamaterial that controls electromagnetic wave propagation properties using electromechanical resonators.

It is a further object of this invention to provide such an electromagnetic composite metamaterial which reduces the size of a device made of the metamaterial.

It is a further object of this invention to provide such an electromagnetic composite metamaterial which provides smaller unit elements.

It is a further object of this invention to provide such an electromagnetic composite metamaterial which increases the range of resonant frequencies that can be achieved with a device made of the metamaterial.

It is a further object of this invention to provide such an electromagnetic composite metamaterial which eliminates the problems associated with trying to match the electric permittivity and magnetic permeability.

It is a further object of this invention to provide such an electromagnetic composite metamaterial which virtually eliminates impedance mismatch and reflections.

The subject invention results from the realization that an electromagnetic composite metamaterial is effected, in one embodiment, with an electromagnetic medium and the plurality of spaced electromechanical resonators in or on the electromagnetic medium that control electromagnetic wave propagation properties. The small electromechanical resonators convert and store the electrical energy of the electromagnetic wave as mechanical energy, or vibrations, which provides for controlling the electromagnetic wave propagation properties in the metamaterial, e.g., velocity, wavelength, direction, dispersion, impedance, index of refraction, and the like. This reduces the size of a device made of the material, increases the range of resonant frequencies that can be achieved, virtually eliminates impedance mismatch and reflections, and eliminates the problems associated with manufacturing a metamaterial by choosing different values for μ and ε or using closely spaced arrays of capacitive-inductor unit cells.

This invention features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced electromechanical resonators disposed in or on the electromagnetic medium configured to control electromagnetic wave propagation properties in the electromagnetic composite metamaterial.

In one embodiment, the plurality of spaced electromechanical resonators in or on the electromagnetic medium control electromagnetic wave propagation properties that may be chosen from the group consisting of velocity, index of refraction, wavelength, direction, dispersion, and impedance. The electromagnetic medium may include a medium chosen from the group consisting of a solid material, a liquid, and a gas. One or more of the plurality of spaced electromechanical resonator may include at least one MEMS piezoelectric resonator. One or more of the plurality of spaced electromechanical resonators may include at least one MEMS frequency tunable electromechanical resonator. The operating frequency of the at least one MEMS frequency tunable electromagnetic resonators may be adjustable to change the electromagnetic wave propagation properties in metamaterial by applying at least one of electrostatic voltages, magnetic forces, thermal actuation, chemical actuation, or light induction. The at least one MEMS frequency tunable electromagnetic resonator may include at least one cantilever electromechanical resonator. The at least one MEMS frequency tunable electromechanical resonator may include at least one paddle electromechanical resonator. The at least one MEMS frequency tunable electromechanical resonators may include at least one tuning fork electromechanical resonator, or at least one disk electromechanical resonator. The at least one MEMS piezoelectric resonator may include a piezoelectric resonator chosen from the group consisting of: a surface acoustic wave piezoelectric resonator, a control mode piezoelectric resonator, a thickness mode piezoelectric resonator, a shear mode piezoelectric resonator, and a Lamé mode piezoelectric resonator. The plurality of spaced electromechanical resonators may be disposed in or on the electromagnetic medium in a lattice network arrangement. The plurality of spaced electromechanical resonators may be configured in one dimension in or on the electromagnetic medium. The plurality of spaced electromechanical resonators may be configured in two dimensions in or on the electromagnetic medium. The plurality of spaced electromechanical resonators may be configured in three dimensions in or on the electromagnetic medium. The plurality of spaced electromechanical resonators may be disposed in the electromagnetic medium. The plurality of spaced electromechanical resonators may be disposed on the electromagnetic medium. The plurality of spaced electromechanical resonators may be disposed at the interface between two electromagnetic media. The electromagnetic composite metamaterial may be configured as an antenna, a phase shifter, a delay element, a beam focusing device, a beam steering device, a frequency selective surface, an invisibility material, or a lens.

This invention also features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS electromechanical resonators disposed in or on the electromagnetic medium configured to control electromagnetic wave propagation properties in the electromagnetic composite metamaterial.

This invention further features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention also features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS piezoelectric electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention also features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS frequency tunable electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention further features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS cantilever electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention further features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS paddle electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention also features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS tuning fork electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

This invention further features an electromagnetic composite metamaterial including an electromagnetic medium and a plurality of spaced MEMS disk electromechanical resonators having an electromagnetic wave traveling therein disposed in or on the electromagnetic medium configured to control propagation properties of the electromagnetic wave in the electromagnetic composite metamaterial.

DETAILED DESCRIPTION OF THE INVENTION

One conventional metamaterial10,FIG. 1A, includes periodic array12of capacitive-inductive networks comprised of capacitive-inductive unit elements, e.g., capacitor-inductor unit elements14,16,18,20and22that are collectively spaced smaller than the wavelength of an electromagnetic wave. Each of unit elements14-22, e.g., element14,FIG. 1B, includes capacitor24and inductor26connected to ground28. As discussed in the Background section, capacitor-inductor unit elements14-22modify the electromagnetic propagation properties, e.g., the wavelength or velocity of an incoming electromagnetic wave so that metamaterial10forms a guided-wave structure or antenna. Metamaterial10achieves its behavior as a result of phase shifting through each of the individual elements14-22, signal interference from elements14-22, simple lump type element loading, and the like. The disadvantage of such a design is electrical losses in elements14-22, the difficulty in attaining high inductances in the small area of each element14-22, and the large size of individual elements14-22. The relatively low inductance achieved through the design limits the range of resonant frequencies as well as the minimum size that can be achieved with a device made of metamaterial10. The larger size of individual unit cells14-22resulting from inductance and the frequency requirements also limits the flexibility of the overall design, resulting in a large footprint and increased inductance and resistance.

In contrast, electromagnetic composite metamaterial30,FIG. 2Aof this invention, in one embodiment, includes electromagnetic medium32and a plurality of spaced electromechanical resonators34(an exemplary number of which are indicated) in or on electromagnetic medium32that control the electromagnetic wave propagation properties in electromagnetic metamaterial30. Electromagnetic medium32may be a solid material, a liquid, or gas. Each of the plurality of spaced electromechanical resonators34convert the electrical energy of an electromagnetic wave, e.g., electromagnetic wave36,FIG. 2B, to mechanical energy and store the energy mechanically as a physical vibrations. Each of the plurality of spaced electromechanical resonators34,FIG. 2A, are sized and closely spaced to each other so they are smaller than the wavelength of electromagnetic wave36. In one exemplary design, the size of each of the plurality of electromechanical resonators34is between about 10 to 100 μm and the spacing between each of plurality of electromechanical resonators34is about 1 to 100 μm. In one example, the size of electromagnetic wave36is about 30 m to 30 mm is at frequencies between about 10 MHz to 106 Hz. However, depending on the specific design of metamaterial30and the frequency of operation, the size of each of the plurality of electromechanical resonators34, the spacing between electromechanical resonators34, and the number of electromechanical resonators34used can vary significantly, as known to those skilled in the art.

In operation, electromagnetic wave36sees each of the plurality of electromechanical resonators34and the spaces there between as a continuous material. Once electromagnetic wave36has been converted and stored as mechanical energy, the plurality of spaced electromechanical resonators34are designed to control electromagnetic wave propagation properties in electromagnetic composite metamaterial30. In practice, in order to effectively control the electromagnetic wave propagation properties in composite metamaterial30, composite metamaterial30has a size which is at least on the order of the size of electromagnetic wave36FIG. 2B.

FIG. 2C, where like parts have been given like numbers, shows an example of piece31,FIG. 2Ametamaterial30with a plurality of electromechanical resonators34,FIG. 2Cconnected to each other by connection33. Connection33transfers energy between the electromechanical resonators34. Connection33may be a mechanical connection, e.g., a tether, or an electrical or electromagnetic connection, e.g., a wire or transmission line. In this example, the plurality of electromechanical resonators34are MEMs resonators, e.g., a piezoelectric resonator (discussed below).

Preferably, the electromagnetic wave propagation properties controlled by metamaterial30include velocity, index of refraction, wavelength, dispersion (spreading), phase shift, and impedance. Because the wavelength and/or velocity of electromagnetic wave36in metamaterial30can be reduced when it is converted to mechanical energy, the problems associated with the wavelength of an electromagnetic wave being too large for a device made of metamaterial30are eliminated. This provides the ability to manufacture smaller devices, e.g., ultra-miniature antennas, phase shifts, delay elements, beam focusing devices, beam steering devices, phase shifters, a frequency selective surface, an invisibility material, a lens, and the like, using metamaterial30. The small size of each of the plurality of spaced electromechanical resonators34also provides for making smaller similar type devices using metamaterial30. The electromagnetic wave propagation properties in metamaterial30can be controlled by changing the parameters of one or more or all of the plurality of spaced electromechanical resonators34, such as the size, shape, geometry and other various parameters associated with one or more of the plurality of spaced electromechanical resonators34. Thus, metamaterial30provides an innovative and effective way to control the electromagnetic wave propagation properties of a wave traveling through metamaterial30.

In one embodiment, one or more, or all, of the plurality of spaced electromechanical resonators34may include a micro-electro-mechanical system (MEMS) resonator, e.g., MEMS piezoelectric resonator40,FIG. 3, MEMS cantilever electromechanical resonator50,FIG. 4, MEMS paddle resonator70,FIG. 5, MEMS tuning fork resonator100,FIG. 6, or MEMS disk resonator110,FIG. 7(discussed in further detail below). As defined herein, MEMS resonators may include nanoelectromechanical systems (NEMS). MEMS resonators have small size, low loss, and adjustable resonant frequencies. Typical measured resonant frequencies of a MEMS resonator in accordance with this invention are in the range of about 10 MHz to 10 GHz. MEMS resonators are also very small, e.g., less than about 100 μm. Thus, when one or more, or all, of the plurality of spaced electromechanical resonator34are MEMS electromechanical resonators, they can be combined in areas smaller than the wavelength of electromagnetic wave36and provide the ability for complex behavior in a very small device.

Because metamaterial30does not rely on capacitor-inductor unit elements, the problems associated therewith are eliminated and the overall size of an antenna or guided-wave structure, or any device made of metamaterial30, can be significantly reduced. Moreover, because the plurality of spaced electromechanical resonators34may include MEMS electromechanical resonators, a higher range of resonant frequencies can be achieved. Additionally, because the plurality of spaced electromechanical resonators34convert the electric energy of electromagnetic wave36to mechanical energy and are spaced so that electromagnetic wave36sees them as a continuous material. This material can be designed to achieve desired values of μ and ε. the problems associated with mismatched μ and ε are eliminated. Thus, impedance mismatching and reflection can be virtually eliminated or significantly reduced.

As shown inFIG. 2C, each of the plurality of spaced electromechanical resonators34is a MEMS piezoelectric resonator, such as piezoelectric resonator40,FIG. 3. Piezoelectric resonator40has coplanar design and includes electrodes42and44with piezoelectric substrate46, e.g., aluminum nitride, or similar type material, sandwiched there between. In one example, electrodes42and44are made of 300 Å of chromium disposed over 150 Å of platinum and are 4 μm wide by 41 μm long. In this example, piezoelectric resonator40is disposed on a solid material, e.g., a wafer of silicon that functions as electromagnetic medium32,FIG. 2A, and is attached to the solid material by anchors. In other designs, piezoelectric resonator40may be disposed inside the solid material.

In operation, electric fields applied to electrodes42and44by electromagnetic wave36,FIG. 2B, create oscillating currents that stretch and compress the piezoelectric material46,FIG. 3, as shown by arrows48. This action converts the electric energy of electromagnetic wave36to mechanical vibrations. In one embodiment, piezoelectric resonator40may be a surface acoustic wave piezoelectric resonator, a contour mode piezoelectric resonator, a thickness mode piezoelectric resonator, a shear mode piezoelectric resonator, or a Lamé mode piezoelectric resonator. As known by those skilled in the art, variations in the size, geometry and spacing of electrodes42and44and the material chosen for piezoelectric substrate46provides numerous ways piezoelectric resonator40can convert electrical energy of electromagnetic wave36to mechanical energy to control the electromagnetic wave propagation properties in metamaterial30,FIG. 2A, e.g., velocity, index of refraction, wavelength, dispersion, impedance, and the like.

One or more, or all, of the plurality of electromechanical resonators34,FIG. 2A, may include a MEMS frequency tunable electromechanical resonator, such as electromechanical cantilever resonator50,FIG. 4. Electromechanical cantilever resonator50includes electrode52suspended over electrode54. Electrode52, typically rectangular in shape, is connected to base56by supporting member58. Electrode54is coupled to base56and is designed to remain stationary during operation. In this example, electromechanical cantilever resonator50is disposed on a solid material, e.g., a wafer of silicon that functions as electromagnetic medium32,FIG. 2A, and is attached to the solid material by supporting members. In other designs, electromechanical resonator50may be disposed inside the solid material32(not shown).

In operation, electrode52vibrates up and down in the direction indicated by arrows60in response to electromagnetic wave36,FIG. 2B. This action converts the electrical energy in electromagnetic wave36to mechanical energy to control the electromagnetic wave propagation properties in metamaterial30,FIG. 2B. In one design, the operating frequency of electromechanical cantilever resonator50is adjustable to change the electromagnetic wave propagation properties in metamaterial30by applying at least one of electrostatic voltages, magnetic forces, thermal actuation, chemical actuation and light-induction, as known by those skilled in the art. See, e.g., “Nanomechanics of Ultrathin Silicon Beams and Carbon Nanotube”, Ono, T. et al., Micro Electro Mechanical Systems, 2003, IEEE The Sixteenth Annual International Conference, pp. 33 to 36 (January 2003), and “Nanowire-Based Very-High-Frequency Electromechanical Resonator”, Husain, A. et al., Applied Physics Letters 83, 1240 (2003), both incorporated by reference herein.

In one embodiment, one or more, or all, of the plurality of electromechanical resonators34,FIG. 2A, may include at least one MEMS frequency tunable electromechanical resonator, such as electromechanical paddle resonator70,FIG. 5that can be tuned to adjust the electromagnetic wave propagation properties in metamaterial30,FIG. 2A. Paddle resonator70,FIG. 5, includes paddle72suspended over trench74by supporting rods76and78that approximately bisect opposite sides of paddle72. Rods76and78are connected to solid material80and82, respectively. Paddle resonator70is disposed on a solid material, e.g., a wafer of silicon which functions as electromagnetic medium32,FIG. 2A, and is attached to the solid material by anchors. In other designs, paddle resonator70may be disposed inside the solid material (not shown).

In operation, the electric fields of electromagnetic wave36cause wave paddle72,FIG. 5, to vibrate to convert and store the electric energy of wave36to mechanical energy which controls the electromagnetic wave propagation properties of metamaterial. There are several modes of vibration for paddle72, including shifting up and down, indicted by arrow88, to the left and right, indicated by arrow90or in a “seesaw” fashion, indicated by arrows92,94and96. The “seesaw” motion is also known as the torsional mode and occurs at the highest frequencies, as known by those skilled in the art. In one design, frequency tuning is achieved by applying a potential from conducting pad84in trench74underneath side86of paddle72. In one design, the operating frequency of paddle resonator70is adjustable to change the electromagnetic wave propagation properties in metamaterial30by applying at least one of electrostatic voltages, magnetic forces, thermal actuation, chemical actuation and light-induction, as known by those skilled in the art. See, e.g., “Temperature-Dependent Internal Friction in Silicon Nanoelectromechanical Systems,” Envoy, A. et al. Applied Physics Letters, Vol. 77 (15), pp. 2397 to 2399 (2000), incorporated by reference herein.

In another embodiment, one or more, or all, the plurality of electromechanical resonators34,FIG. 2A, may include at least one MEMS frequency tunable electromagnetic resonator, such as electromechanical tuning fork resonator100,FIG. 6. Tuning fork resonator100includes tuning fork102with electrodes104,105, and107disposed on the sides of tuning fork102. Tuning fork resonator100typically is disposed on a solid material, e.g., a wafer of silicon that functions as electromagnetic medium32,FIG. 2A, and is attached to the solid material by anchors, e.g., anchors109and111. In other designs, tuning fork100may be disposed inside the solid material (not shown).

In operation, the electric fields of electromagnetic wave36,FIG. 2B, cause tines113and115of tuning fork102,FIG. 6, to vibrate up and down in the opposite directions, e.g., into and out of the page as shown in the top view ofFIG. 6. This converts and stores the electrical energy of electromagnetic wave31as mechanical vibrations to control the electromagnetic wave propagation properties of metamaterial30. In one design, the operating frequency of tuning fork100is adjustable to change the electromagnetic wave propagation properties in metamaterial30by applying at least one of electrostatic voltages, magnetic forces, thermal actuation, chemical actuation and light-induction, as known by those skilled in the art. See, e.g., “Reduction in Thermoelastic Dissipation in Micromechanical Resonators by Disruption of Heat Transport,” Candler, R. W. et al., Proceedings of Solid State Sensors and Actuators, pp. 45 to 48 (2004), incorporated by reference herein.

In another example, one or more, or all, of the plurality of electromechanical resonators34,FIG. 2A, may include at least one MEMS frequency tunable electromagnetic resonator, such as disk resonator110,FIG. 7. Disk resonator110includes disk112disposed about electrodes160and162. Disk resonator110is disposed on a solid material, e.g., a wafer of silicon that functions as electromagnetic medium32,FIG. 2A, and is attached to the solid material by anchors. In other designs, disk resonator110may be disposed inside the solid material (not shown).

In operation, the electric fields of electromagnetic wave36cause disk112,FIG. 7, to expand and contract about its radius as shown by arrow116to effectively convert and store the electric energy of the electromagnetic wave to mechanical vibrations to control the electromagnetic wave propagation properties of the wave in metamaterial30.

In one design, the operating frequency of disk resonator110is adjustable to change the electromagnetic wave propagation properties in metamaterial30by applying at least one of electrostatic voltages, magnetic forces, thermal actuation, chemical actuation and light-induction, as known by those skilled in the art. See, e.g., “High-Q UHF Micromechanical Radial-Contour Mode Disk Resonators”, Clark, J. R., et al., Microelectromechanical Systems, Journal of, Volume 14, Issue 6, pp. 1298 to 1310 (December 2005), incorporated by reference herein.

The plurality of resonators34,FIG. 2, may be configured as a lattice network, such as lattice network130,FIG. 8. In one design, the plurality of electromagnetic resonators34are disposed in electromagnetic medium32, e.g., the ambient air, and are connected to each other by a variety of coupling mechanisms, including, but not limited to, electrical leads, transmission lines, mechanical coupling, or electromagnetic coupling through the surrounding medium32. In other designs, the plurality of electromechanical resonators34may be arranged in a lattice network disposed on the electromagnetic medium32, e.g., any solid, liquid, or gas.

The plurality of electromechanical resonators34,FIG. 2, may be disposed in a two dimensional arrangement on electromagnetic medium32, as shown inFIG. 9, or in a three dimensional arrangement and/or on electromagnetic medium32, as shown inFIG. 10. In one embodiment, the plurality of electromechanical resonators34,FIG. 2, may be disposed in a one dimensional arrangement, e.g., for an antenna, phase shifter, or circuit elements.