Composite material with powered resonant cells

[0001] This patent specification relates generally to the propagation of electromagnetic radiation and, more particularly, to composite materials capable of exhibiting negative effective permeability and/or negative effective permittivity with respect to incident electromagnetic radiation.

[0002] Substantial attention has been directed in recent years toward composite materials capable of exhibiting negative effective permeability and/or negative effective permittivity with respect to incident electromagnetic radiation. Such materials, often interchangeably termed artificial materials or metamaterials, generally comprise periodic arrays of electromagnetically resonant cells that are of substantially small dimension (e.g., 20% or less) compared to the wavelength of the incident radiation. Although the individual response of any particular cell to an incident wavefront can be quite complicated, the aggregate response the resonant cells can be described macroscopically, as if the composite material were a continuous material, except that the permeability term is replaced by an effective permeability and the permittivity term is replaced by an effective permittivity. However, unlike continuous materials, the resonant cells have structures that can be manipulated to vary their magnetic and electrical properties, such that different ranges of effective permeability and/or effective permittivity can be achieved across various useful radiation wavelengths.

[0003] Of particular appeal are so-called negative index materials, often interchangeably termed left-handed materials or negatively refractive materials, in which the effective permeability and effective permittivity are simultaneously negative for one or more wavelengths depending on the size, structure, and arrangement of the resonant cells. Potential industrial applicabilities for negative-index materials include so-called superlenses having the ability to image far below the diffraction limit to λ/6 and beyond, new designs for airborne radar, high resolution nuclear magnetic resonance (NMR) systems for medical imaging, and microwave lenses.

[0004] One issue that arises in the realization of useful devices from such composite materials, including negative index materials, relates to substantial losses experienced by the incident electromagnetic signal when propagating through the composite material. Accordingly, it would be desirable to reduce signal losses in such composite materials. It would be further desirable to provide a general approach to reducing such losses that can be applied to a variety of composite materials operating across a variety of different spectral ranges.

[0005] In accordance with an embodiment, a composite material is provided, the composite material being configured to exhibit a negative effective permittivity and/or a negative effective permeability for incident radiation at an operating wavelength, the composite material comprising an arrangement of electromagnetically reactive cells of small dimension relative to the operating wavelength, wherein each cell includes an externally powered gain element for enhancing a resonant response of that cell to the incident radiation at the operating wavelength.

[0006] A method for propagating electromagnetic radiation at an operating wavelength is also provided, comprising placing a composite material in the path of the electromagnetic radiation, the composite material comprising resonant cells of small dimension relative to the operating wavelength, the resonant cells being configured such that the composite material exhibits a negative effective permittivity and/or a negative effective permeability for the operating wavelength. Power is provided to each of the resonant cells from an external power source, each resonant cell being configured to couple at least a portion of that power into a resonant response thereof for reducing net losses in the electromagnetic radiation propagating therethrough

[0007] A composite material for propagating electromagnetic radiation at an operating wavelength is also provided, comprising a periodic pattern of resonant cells of small dimension relative to the operating wavelength. The resonant cells are configured such that the composite material exhibits at least one of a negative effective permittivity and a negative effective permeability at the operating wavelength. Each resonant cell is configured to receive power from an external power source different than a source of the propagating electromagnetic radiation, and to couple at least a portion of that power into its resonant response for reducing net losses in the propagating electromagnetic radiation.

[0008] Also provided is an apparatus configured to exhibit at least one of a negative effective permittivity and a negative effective permeability for incident radiation of at least one wavelength, the apparatus having an arrangement of electromagnetically reactive cells of small dimension relative to that wavelength. The apparatus includes means for transferring external power not arising from the incident radiation itself to each of the cells. The apparatus further includes means for transferring external power not arising from the incident radiation itself to each of the cells.

[0018] FIG. 1 illustrates a composite material 100 according to an embodiment. Composite material 100 comprises one or more planar arrays 102, each formed upon a semiconductor substrate 104. Each planar array 102 comprises an arrangement of resonant cells 106, each having a dimension that is small (e.g., 20 percent or less) than an operating wavelength. As used herein, operating wavelength refers to a wavelength or range of wavelengths of incident radiation 101 for which negative effective permittivity and/or negative effective permeability are to be exhibited in the composite material 100. Thus, by way of non-limiting example, where the desired operating wavelength lies in the mid-infrared region near 10 μm, both the dimension of each resonant cell 106 and the distance between planar arrays 102 should be less than about 2 μm/n, with better performance being exhibited where that dimension is about 1 μm/n or less, where n represents the refractive index of the material. It is to be understood that references to operating wavelengths herein generally refer to free space wavelengths, and that dimensions in the context of operating wavelength on a substrate are to be scaled, as appropriate, according to the refractive index of the substrate at the operating wavelength.

[0019] It is to be appreciated that FIG. 1 represents a simplified example for clarity of description, showing only a single set of planar arrays 102 aligned along a direction of propagation of the incident radiation 101. In other embodiments a second set of planar arrays can be provided perpendicular to the first set of planar arrays 102 for facilitating negative effective permittivity and/or negative effective permeability for more directions of propagation. In still other embodiments, a third set of planar arrays can be provided perpendicular to both the first set and second sets of planar arrays for facilitating negative effective permittivity and/or negative effective permeability for even more directions of propagation.

[0020] It is to be further appreciated that one or more additional sets of composite and/or continuous-material planes can be placed between the planar arrays 102 without departing from the scope of the present teachings. By way of example, planar arrays consisting of vertical conducting wires on a dielectric support structure can be interwoven with planar arrays 102 to provide a more negative effective permittivity for the overall composite material 100. It is to be further appreciated that the number of resonant cells 106 on the planar arrays 102 can be in the hundreds, thousands, or beyond depending on the overall desired dimensions and the desired operating wavelength.

[0021] As illustrated in FIG. 1, each resonant cell 106 comprises a solenoidal resonator 108 that includes a pattern of conducting material having both capacitive and inductive properties and being designed to interact in a resonant manner with incident radiation at the operating wavelength. In the particular example of FIG. 1 the conducting material is formed into a square split ring resonator pattern, but other patterns can be used including, for example, circular split ring resonator patterns, swiss roll patterns, or other patterns exhibiting analogous properties.

[0022] Each resonant cell 106 is further provided with a gain element 110 having an amplification band that includes the operating wavelength, the gain element 110 being coupled to receive power from an external power source. The gain element 110 is positioned and configured so as to enhance a resonant response of the resonant cell to the incident radiation at the operating wavelength. Losses in the propagating radiation are reduced by virtue of a coupling of the externally provided power into the response of the resonant cells 106.

[0023] In the particular example of FIG. 1, the gain element 110 comprises optical gain elements positioned near the notches of the square split rings, in a manner similar to a configuration that is shown more closely in FIG. 4. Optical gain elements 110 are pumped using pump light from an external optical power source 114 such as a laser. Optical waveguides 112 are used to transfer the pump light to the optical gain elements 110. The optical gain elements 110 are positioned such that a substantial amount of the resonant field occurring in the solenoidal resonator 108 intersects a substantial portion of the optical gain material. The amount of pump light should be kept below an amount that would cause the optical gain elements 110 to begin lasing on their own.

[0024] By way of example and not by way of limitation, where the desired operating wavelength lies in the near-infrared region near the 1.3 μm–1.55 μm range, the optical gain material 110 can comprise bulk active InGaAsP and/or multiple quantum wells according to a InGaAsP/InGaAs/InP material system. In the latter case, the semiconductor substrate 104 can comprise a top layer of p-InP material 100 nm thick, a bottom layer of n-InP material 100 nm thick, and a vertical stack therebetween comprising 5–12 (or more) repetitions of undoped InGaAsP 6 nm thick on top of undoped InGaAs 7 nm thick. Where the desired operating wavelength lies in the near-infrared region near the 1.3 μm–1.55 μm range, the resonant cell dimension should be less than about 300 nm, with better performance being exhibited where that dimension is about 150 nm or less. Using known photolithographic techniques including ion implantation, disordering, passivation, etc., and other known techniques as used in VCSEL (vertical cavity surface emitting laser) fabrication and/or SOA (semiconductor optical amplifier) fabrication, the other elements of the planar array 102 such as the optical waveguides 112 can be formed, including the generally inactive areas of the substrate 104. Material systems such as GaAs/AlGaAs, GaAs/InGaAsN, and InGaAs/InGaAlAs can be used for operating wavelengths in the 780 nm–1.3 μm range. In alternative embodiments, the entire wafer can comprise optically active material using one or more of the optical pumping schemes described infra.

[0025] FIG. 2 illustrates a composite material 200 according to an embodiment in which a common optical beam is used to provide power to one or more resonant cells. A planar array 202 comprising a semiconductor substrate 204, resonant cells 206, solenoidal resonators 208, and optical gain elements 210 are provided in a manner analogous to the embodiment of FIG. 1. However, a pump light source 214 is used to provide a beam of pump light to the planar array 202 from out-of-plane. Empty-space vias (not shown) can optionally be formed into the back of substrate 204 to reduce attenuation of the pump light on its way to the active layers of the optical gain elements 210.

[0026] FIG. 3 illustrates a composite material according to an embodiment in which the optical pump light is provided along the edges of the planar arrays 302, the pump light propagating inside the wafer to the optical gain material regions. Other methods for providing pump light to the optical gain elements can be used without departing from the scope of the present teachings.

[0027] FIG. 4 illustrates a resonant cell 400 of a composite material according to an embodiment having a first spatial arrangement of optical gain material similar to that of FIG. 1. Resonant cell 400 comprises a solenoidal resonator including an outer ring 402 and an inner ring 404, and optical gain elements 406 and 408. In one embodiment for which the operating wavelength is 10 μm, the pitch (i.e., center-to-center spacing) of the resonant cells is 1093 nm, the width of each of the inner and outer rings 402 and 404 is 115 nm, the notch width A is 115 nm, the inter-ring gap width B is 115 nm, the inner dimension C of the inner ring 404 is 288 nm, and the outer dimension D of the outer ring 402 is 977 nm. For operating wavelengths in approximately the 3–30 μm range, the optical gain elements 406 and 408 can comprise mid-infrared (MIR) lead salt lasers, such as PbS/PbSrS multi-quantum well lasers or PbSnTe/PbEuSeTe buried heterostructure diode lasers, with the particular structure and materials being selected such that amplification band of the optical gain material encompasses the desired operating wavelength.

[0028] The position of the optical gain material relative to the solenoidal resonator can be varied, provided that a substantial amount of its resonant field intersects a substantial portion of the optical gain material. FIG. 5 illustrates a resonant cell 500 of a composite material according to an embodiment having a second spatial arrangement of optical gain elements 506 and 508. FIG. 6 illustrates a resonant cell 600 of a composite material according to an embodiment having a third spatial arrangement of optical gain material 606.

[0029] When optical gain materials are used to power the resonant cells, any of a variety of different wavelengths of operation can be achieved by selecting the appropriate gain material having an amplification band including the desired wavelength of operation. The choice of optical gain materials is not necessarily limited to that of optical lasers. Indeed, the wavelength of operation can extend well down the spectrum, even down to the microwave frequencies. In one embodiment, for example, an operating wavelength of 1.5 cm (20 GHz) is provided by using an optical gain medium of ruby (Cr-doped Al₂O₃) known to be used in K-band traveling-wave ruby masers. In this case, the dimension of the resonant cells is on the order of 1.5 mm, and the ruby substrate is about 1 mm thick. Unlike with the other optical gain media described supra in which the pump wavelength generally lies in the amplification band, the ruby material would be pumped at about 50 GHz due to Zeeman splitting. Other differences include temperature control requirements, as the ruby gain material usually requires operation at liquid helium temperatures. Nevertheless, operation at microwave wavelengths represents an appealing embodiment of a composite material with powered resonant cells, because of the many practical applications (e.g., MRI, radar) in which microwave radiation is used.

[0030] FIG. 7 illustrates a resonant cell 700 of a composite material according to an embodiment in which optical gain elements 706 and 708 are electrically pumped. In this embodiment, optical power is provided to the resonant cell 700 (e.g., using the optical waveguides 112 of FIG. 1) and then converted into local electrical power using photodiodes 701 and 702. This local electrical power is then provided to pump circuitry (not shown) for pumping the optical gain elements 706 and 708. The need for electrical wires for carrying external electrical power to the resonant cells is avoided, which is advantageous because such power-carrying electrical wires can potentially confound the operation of the overall composite material. For devices with small-scale resonant cells the optical waveguides 112 can be formed in the semiconductor substrate material, while for devices with larger-scale resonant cells the optical waveguides 112 can comprise optical fibers.

[0031] FIG. 8 illustrates a resonant cell 800 of a composite material according to an embodiment comprising an electrical amplification circuit to enhance the resonant response. Although applicable at a variety of operational wavelengths, the embodiment of FIG. 8 is particularly advantageous for microwave wavelengths in the <0.4 cm to >15 cm range (greater than 80 GHz down to 2 GHz or less). For an operational frequency of 2 GHz, the dimension A of the outer ring 802 in FIG. 8 is on the order of 1.5 cm. The electrical amplification circuit comprises a field effect transistor 806 and a phase control circuit 808 coupled among the outer ring 802 and inner ring 804 as shown. Electrical power is provided using the optical waveguide/photo diode circuit of FIG. 7 (not shown in FIG. 8).

[0032] FIG. 9 illustrates a resonant cell 900 of a composite material according to an embodiment similar to that of FIG. 8, except that a tunnel diode 906 is used instead of a field effect transistor. The tunnel diode 906, which is coupled with a phase control circuit 908 among the outer ring 902 and inner ring 904 as shown, is biased to operate in its negative resistance region. Electrical power is also provided using the optical waveguide/photo diode circuit of FIG. 7 (not shown in FIG. 9).

[0033] According to another embodiment, a composite material is provided, the composite material being configured to exhibit a negative effective permittivity and/or a negative effective permeability for incident radiation at an operating wavelength, the composite material comprising an arrangement of powered resonant cells, wherein the gain elements of resonant cells lying farther along a direction of propagation of the incident radiation are configured to provide a smaller amount of gain than the gain elements of resonant cells lying nearer along a direction of propagation. As compared to an embodiment having the same overall gain but having the farther and nearer gains being the same, the embodiment having the nearer gains being greater than the farther gains has a reduced overall noise figure.

[0034] Whereas many alterations and modifications of the embodiments will no doubt become apparent to a person of ordinary skill in the art after having read the foregoing description, it is to be understood that the particular embodiments shown and described by way of illustration are in no way intended to be considered limiting. By way of example, while some embodiments supra are described in the context of negative-index materials, the features and advantages of the embodiments are readily applicable in the context of other composite materials. Examples include so-called indefinite materials (see WO 2004/020186 A2) in which the permeability and permittivity are of opposite signs.

[0035] By way of further example, powered resonant cells can be implemented on only a portion of a larger composite material, or with a subset of the possible directions of an anisotropic composite material, or interleaved in one or more directions with a continuous material as part of a larger composite material, without departing from the scope of the embodiments. By way of still further example, various parameters and/or dimensions of the composite material layers, or additional layers of composite or continuous materials, can be modulated in real-time or near-real time without departing from the scope of the embodiments. Thus, reference to the details of the described embodiments are not intended to limit their scope.