Patent Publication Number: US-7911386-B1

Title: Multi-band radiating elements with composite right/left-handed meta-material transmission line

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from U.S. provisional application Ser. No. 60/802,947, filed on May 23, 2006, incorporated herein by reference in its entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with Government support under Contract N00014-01-1-0803 awarded by the U.S. Navy/Office of Naval Research. The Government has certain rights in this invention. 
    
    
     INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC 
     Not Applicable 
     NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION 
     A portion of the material in this patent document is subject to copyright protection under the copyright laws of the United States and of other countries. The owner of the copyright rights has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the United States Patent and Trademark Office publicly available file or records, but otherwise reserves all copyright rights whatsoever. The copyright owner does not hereby waive any of its rights to have this patent document maintained in secrecy, including without limitation its rights pursuant to 37 C.F.R. §1.14. 
     A portion of the material in this patent document is also subject to protection under the maskwork registration laws of the United States and of other countries. The owner of the maskwork rights has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the United States Patent and Trademark Office publicly available file or records, but otherwise reserves all maskwork rights whatsoever. The maskwork owner does not hereby waive any of its rights to have this patent document maintained in secrecy, including without limitation its rights pursuant to 37 C.F.R. §1.14. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention pertains generally to communications antennas, and more particularly to dual-band and multi-band antennas formed from composite right/left-handed transmission lines. 
     2. Description of Related Art 
     To satisfy the demands of compact and versatile wireless communication systems, a compact and dual-band and multi-band antenna is desirable. Antennas of this nature are required in various wireless systems, such as GSM/DCS cellular communication systems, and synthetic aperture radar (SAR) systems. Traditional dual-band antennas have been implemented by modifying a conventional microstrip patch antenna by operating it at different harmonics, adding an additional resonator, or by reactively loading the patch antenna with shorting pins. These antennas function at two different frequencies but have similar radiation patterns at each frequency. These dual-band methods have additional drawbacks, including that the operational frequencies are limited to integer multiples of the fundamental mode by operating at different harmonics, while the physical size requirement increases when adding another resonator. In the case of reactive loading, the placement and the number of required shorting pins is not easily determined. 
     Accordingly, a need exists for a system and method of creating compact dual-band and multi-band antennas which are not subject to the size, pattern and operational limits of conventional antenna radiators. These needs and others are met within the present invention, which overcomes the deficiencies of previously developed antenna system and methods. 
     BRIEF SUMMARY OF THE INVENTION 
     The drawbacks associated with conventional dual-band and multi-band antennas can be overcome by implementing dual-band and multi-band antennas with a composite right/left-handed (CRLH) meta-material transmission line (TL) which has several unique features such as a nonlinear dispersion relation. For the sake of simplicity of description, the radiating elements according to the invention are referred to as “antennas”, however, it should be appreciated that both antennas and resonators are similarly formed while being subject to different signal feed configurations. 
     Recent research into meta-materials based on periodic unit-cells for microwave applications has grown rapidly with the verification of left-handed (LH) meta-materials. In particular, the transmission line approach of LH meta-materials has led to the realization of the composite right/left-handed (CRLH) transmission line (TL) which includes LH and right-handed (RH) attributes. The CRLH TL has many unique properties such as supporting a fundamental backward wave (anti-parallel group and phase velocities) and zero propagation constant (β=0) with zero or non-zero group velocity at a discrete frequency. The backward wave property of the CRLH TL and other LH-based TLs has been used to realize novel, small half-wavelength resonant antennas. The infinite wavelength property (β=0, ω≠0) of the CRLH TL has been used to realize several size-independent resonant structures such as the zeroeth-order resonator and infinite wavelength series divider. 
     The operational frequencies of the dual-band CRLH half-wavelength antenna implemented in S. Otto, C. Caloz, A. Sanada, and T. Itoh, “A dual-frequency composite right/left-handed half-wavelength resonator antenna,”  Asia - Pacific Microwave Conference , December 2004 are not harmonics of each other because of the nonlinear dispersion relation of the CRLH TL. Since the dispersion relation of the CRLH TL is strictly determined by its unit-cell, the operational frequencies of the antenna can be controlled by modifying the unit-cell and/or the number of unit-cells. Unlike other reactively loaded dual-band and multi-band antenna approaches, the CRLH TL approach offers a more straight-forward design approach based on the dispersion relation of the CRLH TL unit-cell. 
     Accordingly, an aspect of the invention is a dual-mode compact microstrip antenna based on the fundamental backward wave supported by a composite right/left-handed (CRLH) meta-material transmission line (TL). The physical size and operational frequencies of the antenna are determined by the unit-cell of the CRLH meta-material. For example, this antenna is capable of monopolar radiation at one resonant frequency and patch-like radiation at another resonant frequency. 
     Additionally, since an infinite wavelength occurs when the propagation constant is zero, the frequency of the antenna does not depend on its physical length, but only on the reactance provided by its unit-cell. Therefore, the physical size of the antenna can be arbitrary; this is useful in realizing electrically small or electrically large antennas. By properly designing the unit-cell, the radiation pattern of the antenna at the infinite wavelength frequency can also be tailored. 
     Accordingly, another aspect of the invention is that the CRLH TL unit-cell provides a general model for the required unit-cell consisting of a series capacitance, a series inductance, a shunt capacitance, and a shunt inductance. The shunt resonance of the CRLH TL unit-cell determines the infinite wavelength frequency and thus the operational frequency of the antenna. As a result, a CRLH TL unit-cell without series capacitance referred to as an inductor-loaded TL unit-cell can also be used to realize the antenna. By modifying the equivalent shunt capacitance and/or shunt inductance circuit parameters of the unit-cell, the operational frequency and the physical size of the realized antennas can be controlled. 
     Furthermore, the unique “equal amplitude/phase” electric-field distribution of an infinite wavelength excited on the antenna gives rise to monopolar radiation pattern. In one embodiment, a dual-mode microstrip antenna includes a plurality of composite right/left-handed transmission line unit-cells which form a resonator. Each unit-cell of the resonator comprises a conductive patch (e.g., preferably metal) connected to a ground plane through a via, and in which the antenna radiates in a monopolar pattern. In one embodiment, the unit-cells are spaced apart by a gap. In one embodiment, the left-hand (LH) attribute of capacitance C L  arises in response to a gap between each of the unit-cells, while inductance L L  arises in response to the via. In one embodiment, right-hand (RH) attributes are due to the current flow (L R ) on the unit-cell and from an electric field between the metal patch and the ground plane (C R ). In one embodiment, changing the equivalent circuit parameters of the unit-cell, the operational frequencies of the antenna can be controlled without changing its physical size. In one embodiment, the antenna is capable of monopolar radiation at a first resonant frequency and patch-like radiation at a second resonant frequency. In one embodiment, the operational frequencies of the antenna are not constrained to be harmonics of one other, and the operational frequencies of the antenna are controlled by modifying the dispersion relation of the CRLH unit-cell. In one embodiment, physical size and operational frequencies of the antenna are determined by the configuration of the CRLH meta-material unit-cell. 
     At least one embodiment of the invention is a multi-mode resonant radiating element, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells configured for operation at multiple radio frequency bands; (b) each unit-cell comprising a conductive patch connected to a ground plane through a via connection, wherein a plurality of unit-cells form a resonator; (c) wherein the radiating element radiates an i th  radiation pattern at the i th  resonant frequency, and a j th  radiation pattern at a different j th  resonant frequency; and (d) wherein said i th  radiation pattern is of a different shape than said j th  radiation pattern. 
     At least one embodiment of the invention is a dual-mode resonant radiating element, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells configured for operation at an infinite wavelength; (b) each said unit-cell comprising a conductive patch connected to a ground plane through a via; and (c) said plurality of unit-cells forming a resonator; (d) wherein said radiating element radiates a first radiation pattern at a first resonant frequency, and a second radiation pattern at a second resonant frequency; and (e) wherein said first radiation pattern differs (e.g., different pattern shape) from said second radiation pattern. It will be appreciated that the radiating element may comprise a resonator and/or an antenna depending on the feed configuration adopted. 
     At least one embodiment of the invention may be a dual-mode resonant antenna, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells; (b) each said unit-cell comprising a conductive patch connected to a ground plane through a via; and (c) said plurality of unit-cells forming a resonator. The antenna radiates a first radiation pattern at a first resonant frequency, and a second radiation pattern at a second resonant frequency. In a preferred embodiment the first radiation pattern provides a different shape than the second radiation pattern. In at least one embodiment the first radiation pattern is a monopolar radiation pattern, and the second radiation pattern is a patch-like radiation pattern. The first resonant frequency operates at n=0 supporting an infinite wavelength of the CRLH TL. The second resonant frequency (e.g., determined by dispersion relation and number of unit-cells) operates at n=−1 supporting a half-wavelength of the CRLH TL. The antenna, or resonator, operates in response to the fundamental backward wave of the CRLH TL, in which the supported wavelength is proportional to the operational frequency and the infinite wavelength supported by the CRLH TL at a finite frequency. One significant advantage is that the first and second resonant frequencies of the antenna are not limited to being harmonics of one another. 
     Each of the unit-cells within the antenna/resonator comprises a plurality of vias connecting at least one conductive plate to a ground plane. In at least one embodiment, a conductive plate serves across a number of unit cells. In another embodiment, separate conductive plates (e.g., separated by a non-conductive gap) are coupled to each of the vias, or alternatively a group of vias. 
     At least one embodiment of the invention may be a dual-mode microstrip antenna, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells; (b) said plurality of unit-cells forming a resonator; (c) each said unit-cell comprising a metal patch connected to a ground plane through a via. The antenna radiates according to a first pattern, such as monopolar. Left-hand (LH) attributes arise in response to both the gap between the unit-cells, which provides capacitance C L , and the current through the via, which provides inductance L L . Right-hand (RH) attributes are due to the current flow on the unit-cell from which inductance (L R ) arises, and from an electric field between the conductive patch (e.g., metallic) and the ground plane from which capacitance (C R ) arises. In response to changing the equivalent circuit parameters of the unit-cell, the operational frequencies of the antenna can be controlled without changing its physical size. The antenna/resonator is capable of monopolar radiation at a first resonant frequency and patch-like radiation at a second resonant frequency. 
     At least one embodiment of the invention is a dual-mode resonant radiating element, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells configured for operation in two frequency bands; (b) a plurality of separate conductive patches; (c) a ground plane; and (d) a plurality of vias coupled between each of said plurality of conductive patches and said ground plane forming a composite right/left-handed (CRLH) transmission line unit-cell implementation; (e) wherein the vias of each unit-cell provide inductance L L  as a left-handed (LH) attribute; (f) wherein said unit-cells are spaced apart by a gap from which capacitance C L  arises as a left-handed (LH) attribute; (g) wherein right-handed (RH) attributes arise in response to inductance L R  from current flow on the unit-cell, and in response to capacitance C R  from an electric field between the conductive patch and the ground plane; (h) wherein each said unit-cell, in said plurality of units-cells, comprises a single patch coupled through a single via to said ground plane; (i) wherein said radiating element radiates a monopolar radiation pattern at a first resonant frequency, and a patch-like radiation pattern at a second resonant frequency; and (j) wherein the first and second resonant frequencies are not constrained to being harmonics of one another. 
     At least one embodiment of the invention is a dual-mode resonant radiating element, comprising: (a) a plurality of composite right/left-handed (CRLH) transmission line (TL) unit-cells configured for operation in two frequency bands; (b) at least one conductive patch; (c) a ground plane; and (d) a plurality of vias coupled between said at least one conductive patch and said ground plane forming an inductor-loaded transmission line (TL); (e) wherein the via provides an inductance L L  as a left-handed (LH) attribute; (f) wherein right-handed (RH) attributes arise in response to inductance L R  from current flow on the unit-cell, and in response to capacitance C R  from an electric field between the conductive patch and the ground plane; (g) wherein said radiating element radiates a monopolar radiation pattern at a first resonant frequency, and a patch-like radiation pattern at a second resonant frequency; and (h) wherein the first and second resonant frequencies are not constrained to being harmonics of one another. 
     An aspect of the invention is a compact dual-band and multi-band radiating element based on CRLH meta-material transmission line. 
     Another aspect of the invention is that the radiating element can be configured as an antenna and/or resonator in response to feed configuration. 
     Another aspect of the invention is an antenna supporting differently-shaped radiation patterns for each of its bands. 
     Another aspect of the invention is an antenna configured for monopolar radiation at one resonant frequency and patch-like radiation at another resonant frequency. 
     Another aspect of the invention is an antenna having an arbitrary physical size, which need not be related to its operating wavelengths. 
     Another aspect of the invention is an antenna based on the fundamental infinite wavelength property of the CRLH TL. 
     Another aspect of the invention is an antenna based on the fundamental backward wave of the CRLH TL. 
     Another aspect of the invention is an antenna which does not require reactively loading with shorting pins. 
     Another aspect of the invention is an antenna whose operating frequencies are not limited to integer multiples of the fundamental mode in response to operating at different harmonics. 
     Another aspect of the invention is an antenna in which the operational frequencies of the antenna are not harmonics of each other. 
     Another aspect of the invention is an antenna where the operational frequencies of the antenna can be controlled by modifying the dispersion relation of the CRLH unit-cell. 
     Another aspect of the invention is an antenna where the physical size and operational frequencies are determined by CRLH meta-material unit cell design. 
     Another aspect of the invention is an antenna whose operating frequencies do not depend on physical length and/or size constraints, but only on the reactance of its unit-cell. 
     Another aspect of the invention is an antenna/resonator having a dispersion relation determined by the structure of its constituent unit-cells. 
     Another aspect of the invention is an antenna whose supported wavelength is proportional to the operational frequency and the infinite wavelength supported by the CRLH TL at a finite frequency. 
     Another aspect of the invention is a multi-mode compact microstrip antenna based on the fundamental backward wave supported by a composite right/left-handed (CRLH) meta-material transmission line (TL). 
     Another aspect of the invention is an antenna using a CRLH TL unit-cell comprising a series capacitance, a series inductance, a shunt capacitance, and a shunt inductance. 
     Another aspect of the invention is a CRLH TL unit-cell where the shunt resonance determines the infinite wavelength frequency and thus the operational frequency of the antenna. 
     Another aspect of the invention is an antenna using a CRLH TL unit-cell in which modification of equivalent shunt capacitance and/or shunt inductance of the unit-cell changes the operational frequency and/or physical size. 
     Further aspects of the invention will be brought out in the following portions of the specification, wherein the detailed description is for the purpose of fully disclosing preferred embodiments of the invention without placing limitations thereon. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) 
       The invention will be more fully understood by reference to the following drawings which are for illustrative purposes only: 
         FIG. 1  is a schematic of a one-dimensional CRLH meta-material TL with N cells according to an aspect of the present invention. 
         FIG. 2  is a graph of a dispersion curve for a CRLH TL composed of N unit cells according to an aspect of the present invention. 
         FIG. 3  is a schematic of a CRLH TL resonator according to an embodiment of the present invention. 
         FIG. 4  is a graph of resonance peaks for the CRLH TL of  FIG. 3 . 
         FIG. 5  is a schematic of a CRLH TL antenna according to an embodiment of the present invention. 
         FIG. 6  is a graph of return loss for the antenna of  FIG. 5 . 
         FIG. 7  is a graph of monopolar radiation pattern for a CRLH TL according to an aspect of the present invention. 
         FIG. 8  is a graph of a patch-like radiation pattern of a CRLH TL according to an aspect of the present invention. 
         FIG. 9A  is a schematic of an infinitesimal circuit model RH TL according to an aspect of the present invention. 
         FIG. 9B  is a schematic of an infinitesimal circuit model LH TL according to an aspect of the present invention. 
         FIG. 9C  is a schematic of a dispersion diagram of an RH TL and LH TL according to aspects of the present invention. 
         FIG. 10A  is a schematic of a CRLH TL with LC unit cell of length p according to an aspect of the present invention. 
         FIG. 10B  is a graph of dispersion showing fundamental RH and LH modes according to an aspect of the present invention. 
         FIG. 11A  is a schematic of a four-cell open-ended resonator with a CRLH TL unit cell according to an aspect of the present invention. 
         FIG. 11B  is a schematic of a four-cell open-ended resonator with no series capacitance components according to an aspect of the present invention. 
         FIG. 12  is a graph of resonance peaks of open-ended resonators shown in 
         FIG. 11A , and  FIG. 11B . 
         FIG. 13A  is a schematic of an inductor-loaded TL having an LC of length p according to an aspect of the present invention. 
         FIG. 13B  is a graph of dispersion for the TL of  FIG. 13A . 
         FIG. 14A  is a schematic of a conventional microstrip patch antenna which is resonant along the Y direction and which supports half-wavelength. 
         FIG. 14B  is a schematic of a CRLH patch antenna which is resonant along the Y direction and which supports an infinite-wavelength. 
         FIG. 15  is a schematic of a microstrip CRLH TL based on a high-impedance surface according to an aspect of the present invention. 
         FIG. 16A  is a schematic of a CRLH TL antenna of two unit-cells according to an aspect of the present invention. 
         FIG. 16B  is a schematic of an inductor-loaded TL two unit-cell implementation according to an aspect of the present invention. 
         FIG. 17  is a graph of dispersion for the CRLH and inductor-loaded unit cells of  FIG. 16A  and  FIG. 16B . 
         FIG. 18A  is a graph of the real part (R) of CRLH antenna input impedance according to an aspect of the present invention. 
         FIG. 18B  is a graph of the imaginary part (X) of CRLH antenna input impedance according to an aspect of the present invention. 
         FIG. 19A  is a graph of the real part (R) of inductor-loaded TL antenna input impedance according to an aspect of the present invention. 
         FIG. 19B  is a graph of the imaginary part (X) of inductor-loaded TL antenna input impedance according to an aspect of the present invention. 
         FIG. 20  is a graph of return loss for the CRLH and inductor-loaded two unit cell antennas according to aspects of the present invention. 
         FIG. 21A  is a 3D graph of electric field distribution beneath a two unit cell 
       CRLH antenna according to an aspect of the present invention, shown at half-wavelength mode. 
         FIG. 21B  is a 3D graph of electric field distribution beneath a two unit cell CRLH antenna according to an aspect of the present invention, shown at infinite-wavelength mode. 
         FIGS. 22A-22D  are graphs of CRLH radiation patterns according to an aspect of the present invention, showing x-z, y-z, and x-y planes as well as cross-polarizations normalized to co-polarizations. 
         FIGS. 23A-23B  are graphs of inductor-loaded antenna radiation patterns according to an aspect of the present invention, showing x-z and y-z planes. 
         FIGS. 24A-24B  are graphs of two unit-cell CRLH antenna radiation patterns according to an aspect of the present invention, showing x-z and y-z planes. 
         FIGS. 25A-25B  are graphs of four unit-cell inductor-loaded antenna radiation patterns according to an aspect of the present invention, showing x-z and y-z planes. 
         FIGS. 26A-26B  are graphs of six unit-cell CRLH antenna radiation patterns according to an aspect of the present invention, showing x-z and y-z planes. 
         FIGS. 27A-27B  are graphs of six unit-cell inductor-loaded antenna radiation patterns according to an aspect of the present invention, showing x-z and y-z planes. 
         FIG. 28  is a schematic of an enlarged aperture monopolar antenna according to embodiment of the present invention. 
         FIG. 29A  is a graph of return loss for the monopolar antenna of  FIG. 28 . 
         FIG. 29B  is a graph of the radiation pattern for the monopolar antenna of  FIG. 28 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring more specifically to the drawings, for illustrative purposes the present invention is embodied in the apparatus generally shown in  FIG. 1  through  FIG. 29B . It will be appreciated that the apparatus may vary as to configuration and as to details of the parts, and that the method may vary as to the specific steps and sequence, without departing from the basic concepts as disclosed herein. 
     1. Dual-Mode Microstrip Antenna Based on Backward Wave. 
     A dual-mode CRLH radiating element (e.g., antenna and/or resonator), is described for compact communication systems that benefit from radiation pattern selectivity, such as terrestrial communication systems with satellite uplinks and wireless local-area-networks (WLANs). Radiating elements described herein are generally referred to, for the sake of simplicity, as antennas although they may be alternately configured as resonators. 
     Unlike the dual-band CRLH half-wavelength antenna of S. Otto, C. Caloz, A. Sanada, and T. Itoh, “A dual-frequency composite right/left-handed half-wavelength resonator antenna,”  Asia - Pacific Microwave Conference , December 2004, the present antenna configuration can support a different radiation pattern at each operational frequency. By way of example and not limitation, the radiation patterns comprise a monopolar radiation pattern at one resonant frequency and a patch-like radiation pattern (similar to the pattern produced by the dominant mode of a classical patch antenna) at another resonant frequency. The antenna is based on the fundamental backward wave of the CRLH TL in which the supported wavelength is proportional to the operational frequency and the infinite wavelength supported by the CRLH TL at a finite frequency. The ability of this antenna to generate two different radiation patterns depends on the field distributions supported by the CRLH unit-cell which is discussed in the following sections. 
     1.1 Composite Right/Left-Handed Transmission Line Theory. 
       FIG. 1  illustrates an equivalent circuit model of a CRLH TL, having a unit-cell consisting of an LH series capacitance (CO, an RH series inductance (L R ), an LH shunt inductance (L L ), and an RH shunt capacitance (C R ). The CRLH meta-material TL is a practical realization of a purely left-handed (LH) TL, which takes into account unavoidable parasitic right-handed (RH) effects. By cascading a CRLH unit-cell of length p, N times, a CRLH TL of length N*p can be realized. The resonant condition of the CRLH TL is determined by βL=nπ, where the resonance index, n, can be a negative integer, positive integer, or zero. 
       FIG. 2  depicts a dispersion diagram of a CRLH TL along with possible resonant operating points. By applying the Bloch-Floquet theorem to the CRLH TL unit-cell, the dispersion relation of the CRLH TL is determined to be 
                         n   ⁢           ⁢   π     N     =       cos     -   1       ⁡     (     1   -       1   2     ⁢     (         ω   L   2       ω   n   2       +       ω   n   2       ω   R   2       -       ω   L   2       ω   se   2       -       ω   L   2       ω   sh   2         )         )         ,       when   ⁢           ⁢   N     =   1             (   1   )               
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     Since the dispersion relation of the CRLH TL can be controlled by properly designing its unit-cell, it is particularly well-suited for realizing compact antennas (or large antenna structures). In general, the series resonance (ω se ) and the shunt resonance (ω sh ) of the CRLH unit-cell are not equal, thus resulting in a band-stop region. A fundamental backward wave (i.e., anti-parallel group and phase velocities) is supported at frequencies below the band-stop. It is this fundamental backward wave that is used to realize the antenna for operation at the n=0 and n=−1 resonances. By changing the dispersion relation of the CRLH TL by Eq. (1), these two frequencies can be controlled. Unlike a conventional microstrip patch antenna, the operational frequencies of the antenna are not harmonics of each other. In addition, both operational frequencies are based on the fundamental backward mode supported by the CRLH TL. 
     At the n=0 resonance, an infinite wavelength (β=0, ω≠0) is supported by the CRLH TL. The n=0 resonance frequency is determined by ω sh  when the terminals of the CRLH TL are open-circuited. This constant field distribution can be used to generate a monopolar pattern depending on the unit-cell implemented. For the n=−1 resonance mode, a half-wavelength is supported by the CRLH TL. The n=−1 frequency is determined by the dispersion relation of the CRLH unit-cell and the number of unit-cells used to implement the CRLH TL as given by Eq. (1). 
     1.2 CRLH-Based Radiating Element Realization. 
       FIG. 3  illustrates by way of example embodiment  10  a CRLH resonator on a base (substrate)  12  with ground plane  14 . The CRLH TL resonator shown coupled to input  16  and output  18  and constructed with three CRLH unit-cells  20   a ,  20   b  and  20   c , to verify the resonant operation frequencies of the CRLH unit-cell used to implement the resonator. Three resonance points occur in the backward mode region since three unit-cells are used to implement the resonator. 
     The CRLH unit-cell comprises a conductive patch  22  (e.g., a metallic patch) coupled to ground plane  14  by a via  24 . The patch structure is based on a mushroom structure, which was chosen because of its symmetry that readily lends itself toward generating a monopolar pattern as discussed below. The width  26  of each patch  22  is shown in relation to a gap  28  between the unit-cells which contributes the left-hand capacitance attribute C L  while via  24  contributes left-hand inductance attribute L L . The length  30  of a patch region is also marked in the figure, and represented by way of example as being at least twice the width. It should be noted, however, that the aspect ratio of the patch can be varied depending on the application and configuration of the unit-cells. 
     The RH attributes are due to the current flow (L R ) on the unit-cell and from the electric field between the metal patch and the ground plane (C R ). By changing the equivalent circuit parameters of the unit-cell, the operational frequencies of the antenna can be controlled without changing its physical size. By way of example and not limitation, the entire structure shown in the figure was implemented on RT/Duroid 5880 (∈ R =2.2, h=1.57 mm). Parameter extraction was performed on the CRLH unit-cell yielding C L =0.46 pF, C R =0.82 pF, L L =1.50 nH, and L R =0.29 nH. According to Eq. (1), the n=0 resonance occurs at 4.54 GHz and the n=−1 resonance occurs at 3.59 GHz. 
       FIG. 4  depicts resonant peaks for the embodiment shown in  FIG. 3 , with numerical and experimental resonance peaks; the n=0 resonance occurs at f 0 =4.00 GHz and the n=−1 resonance occurs at f −1 =3.55 GHz. The results obtained from Eq. (1) deviate from the numerical and experimental results because of the inaccurate parameters extracted from the unit-cell. 
       FIG. 5  illustrates an embodiment of an antenna based on the CRLH resonator of  FIG. 3 . A single feed line  16  for exciting the antenna, is shown having length  32  in relation to gap  34  between the feed-line and the first patch. 
       FIG. 6  depicts numerical and experimental return losses for the antenna of  FIG. 5 . The graph indicates a return loss of −10.21 dB and −9.2 dB are experimentally obtained at the dual frequencies of f 0 =4.00 GHz and at f −1 =3.57 GHz, respectively. 
     By way of example, the antenna size is λ/5×λ/5×λ/50 at a first frequency f 0  and λ/5.7×λ/5.7×λ/54 at a second frequency f −1 . At f 0 , an infinite wavelength is supported by the CRLH TL and the electric-field along the perimeter of the patch formed by the three CRLH unit-cells is a constant. Therefore, the equivalent magnetic current densities along the edges of the patch form a magnetic loop, from which a monopolar radiation pattern is expected. 
       FIG. 7  depicts an experimental confirmation of the monopolar radiation pattern obtained from the experimental test setup. A maximum gain of 2.3 dBi was achieved at f 0 , while at f −1 , the electric-field distribution is a half-wavelength and only two edges contribute to the radiation in similar manner to the dominant mode of a classical patch antenna, wherein a patch-like radiation pattern is expected. 
       FIG. 8  depicts an experimental confirmation of the patch-like radiation pattern at f −1 . A maximum gain of −2.5 dBi was achieved at frequency f −1 . 
     Accordingly, the embodiment described above is a dual-mode compact microstrip antenna based on the fundamental backward wave supported by a composite right/left-handed (CRLH) meta-material transmission line (TL). This antenna is capable of monopolar radiation at one resonant frequency and patch-like radiation at another resonant frequency. Unlike a conventional microstrip patch antenna, the operational frequencies of the antenna are not harmonics of each other and can be controlled by modifying the dispersion relation of the CRLH unit-cell. The physical size and operational frequencies of the antenna are determined by the unit cell of the CRLH meta-material. Numerical and experimental results of a three unit-cell CRLH-based antenna were presented to verify operation of the antenna. 
     2. Infinite Wavelength Resonant Antennas with Monopolar Radiation. 
     2.1 Introduction. 
     In the following discussion, the analysis and design of resonant, planar antennas based on the fundamental infinite wavelength property of the CRLH TL is described in detail. Since an infinite wavelength occurs when the propagation constant is zero, the frequency of the antenna does not depend on its physical length, but only on the reactance provided by its unit-cell. Therefore, the physical size of the antenna can be arbitrary (not constrained by wavelength), which is important toward realizing electrically small or electrically large antennas. By properly designing the unit-cell, the radiation pattern of the antenna at the infinite wavelength frequency can also be tailored. In particular, it is shown that the CRLH TL unit-cell is the general model for the required unit-cell which consists of a series capacitance, a series inductance, a shunt capacitance, and a shunt inductance. The shunt resonance of the CRLH TL unit-cell determines the infinite wavelength frequency and thus the operational frequency of the antenna. As a result, a CRLH TL unit-cell without series capacitance referred to as an inductor-loaded TL unit-cell can also be used to realize the antenna. By modifying the equivalent shunt capacitance and/or shunt inductance circuit parameters of the unit-cell, the operational frequency and the physical size of the realized antennas can be controlled. Furthermore, the unique “equal amplitude/phase” electric-field distribution of an infinite wavelength excited on the antenna gives rise to a monopolar radiation pattern. 
     The periodic design methodology described herein offers a straight-forward design approach based on the characteristics of a single unit-cell. Based on this periodic structure methodology, CRLH antennas with monopolar radiation patterns are numerically and experimentally verified, such as in response to models which consist, by way of example, of two, four, or six unit-cells. Inductor-loaded antennas with monopolar radiation patterns consisting by way of example having two, four, and six unit-cells are also investigated. The input impedance, gain, and radiation pattern as a function of the number of unit-cells are examined for both types of antennas. The effect of adding unit-cells in the non-resonant dimension of the antenna are also investigated. In addition, the choice of CRLH unit-cell or inductor-loaded unit-cell for dual-mode antenna configurations is discussed. 
     2.2 Theory. 
     Since the infinite wavelength antenna is based on a periodic design approach, a unit-cell capable of supporting an infinite wavelength is discussed in the following sub-section. In addition, the monopolar radiation pattern of the infinite wavelength antenna is presented. 
     2.2.1 Fundamental Infinite Wavelength Unit-Cell. 
       FIG. 9A  through  FIG. 9C  illustrates aspects of TL models and their dispersion characteristics. To realize a resonant-type planar antenna with no dependence on its physical size, a TL structure that supports an infinite wavelength at its fundamental mode is needed. First, infinitesimal lumped element circuit models are shown for a conventional RH TL model in  FIG. 9A , and for the LH TL model in  FIG. 9B . The lossless RH TL model consists of a series inductance per-unit length (L R ′) and a shunt capacitance per-unit length (C R ′), while the lossless LH TL consists of a series capacitance times-unit length (C L ′) and a shunt inductance (L L ′). The propagation constant of a TL is given by γ=α+jβ=√{square root over (Z′Y′)} where Z′ and Y′ are respectively the per-unit length impedance and the per-unit length admittance. Therefore the propagation constant for the lossless RH TL is given by:
 
β RH =ω√{square root over (C′ R L′ R )},  (3)
 
and for the lossless LH TL is
 
     
       
         
           
             
               
                 
                   
                     β 
                     LH 
                   
                   = 
                   
                     
                       
                         - 
                         1 
                       
                       
                         ω 
                         ⁢ 
                         
                           
                             
                               C 
                               L 
                               ′ 
                             
                             ⁢ 
                             
                               L 
                               L 
                               ′ 
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The dispersion diagram of the RH and LH TL are shown in  FIG. 9C . This diagram illustrates that neither a RH or LH TL structure can support an infinite wavelength at a non-zero frequency; the RH TL only has β=0 when ω=0, while the LH TL has β=0 when ω=∞. Therefore, a RH and LH TL cannot be used to realize a fundamental infinite wavelength resonant antenna. A practical realization of a LH TL, which includes unavoidable RH effects, known as a CRLH TL is able to support an infinite wavelength (β=0 when ω≠0) and therefore can be used to realize the antenna. 
       FIG. 10A  illustrates an equivalent circuit model for a CRLH TL unit-cell. By applying periodic boundary conditions related to the Bloch-Floquet theorem, the dispersion relation of the CRLH TL unit-cell is determined to be: 
                       β   ⁡     (   ω   )       =       1   p     ⁢       cos     -   1       ⁡     (     1   -       1   2     ⁢     (         ω   L   2       ω   2       +       ω   2       ω   R   2       -       ω   L   2       ω   se   2       -       ω   L   2       ω   sh   2         )         )           ,           (   5   )               
where
 
     
       
         
           
             
               
                 
                   
                     
                       ω 
                       L 
                     
                     = 
                     
                       1 
                       
                         
                           
                             C 
                             L 
                           
                           ⁢ 
                           
                             L 
                             L 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       ω 
                       R 
                     
                     = 
                     
                       1 
                       
                         
                           
                             C 
                             R 
                           
                           ⁢ 
                           
                             L 
                             R 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       ω 
                       se 
                     
                     = 
                     
                       1 
                       
                         
                           
                             C 
                             L 
                           
                           ⁢ 
                           
                             L 
                             R 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       ω 
                       sh 
                     
                     = 
                     
                       
                         1 
                         
                           
                             
                               C 
                               R 
                             
                             ⁢ 
                             
                               L 
                               L 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
       FIG. 10B  depicts a dispersion diagram for the CRLH TL unit-cell of  FIG. 10A . It should be appreciated that the CRLH TL supports a fundamental LH wave (phase advance) at lower frequencies and a RH wave (phase delay) at higher frequencies. 
     In general, the series resonance (ω se ) and the shunt resonance (ω sh ) are not equal and two non-zero frequency points with β=0 are present. These two points are referred to as infinite wavelength points and are determined by the series resonance and shunt resonance of the unit-cell as given in Eq. (6). By cascading a CRLH TL unit-cell of length p, N times, a CRLH TL of length L=N*p can be realized. The CRLH TL can be used as a resonator under the resonance condition: 
                     β   n     =       n   ⁢           ⁢   π     L             (   7   )               
where n is the resonance mode number and can be a positive or negative integer, or even zero. In the case where n=0, an infinite wavelength is supported and the resonance condition is independent of the length of the CRLH TL (i.e., number of unit-cells, N, can be arbitrary). In the case of open boundary conditions, the infinite wavelength frequency is determined by the shunt resonance frequency, ω sh . Since only the shunt resonance of the CRLH TL unit-cell determines the infinite wavelength frequency, the series components have no effect.
 
       FIGS. 11A through 11B  illustrate examples of four cell resonators. In  FIG. 11A  the resonator has the following parameters: C L =1.50 pF, L R =1.00 pF, C R =1.45 pF, and L L =1.95 nH, which corresponds to f sh =3.0 GHz. The open-ended resonator is coupled to the input/output port with capacitors of C c =0.01 pF.  FIG. 11B  depicts an open-ended resonator with the series capacitance CL components eliminated (CL becomes infinite). 
       FIG. 12  depicts the resonance peaks of the two open-ended resonators above, and demonstrates that only the shunt components determine the infinite wavelength resonance in the case of open boundary conditions. 
     Therefore, an inductor-loaded TL unit-cell with the same shunt components as the CRLH TL unit-cell has the same infinite wavelength frequency as the CRLH TL unit-cell. 
       FIG. 13A  illustrates a unit-cell of the inductor-loaded TL which has a propagation constant given by: 
     
       
         
           
             
               
                 
                   
                     β 
                     ⁡ 
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       p 
                     
                     ⁢ 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               1 
                               2 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     L 
                                     R 
                                   
                                   
                                     L 
                                     L 
                                   
                                 
                                 - 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   
                                     ω 
                                     R 
                                     2 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
       FIG. 13B  depicts the dispersion diagram plotted for the inductor-loaded TL of  FIG. 13A . The inductor-loaded TL has a DC-offset in similar manner as the CRLH TL, albeit the dispersion characteristics are quite different. It should be appreciated that phase advance or phase delay can occur for the CRLH TL, while only phase delay can occur for the inductor-loaded TL. Since the resonance condition of Eq. (7) is independent of the length of the CRLH TL or inductor-loaded TL at the infinite wavelength frequency, the open-ended resonators of  FIG. 11A  and  FIG. 11B  can be utilized according to the present invention for realizing size independent resonant antennas and resonators. Although the number of unit-cells used to realize an infinite wavelength resonator has no effect on its operational frequency f 0 , the input impedance of the structure is dependent on the number of unit-cells and is given by: 
                       Z   in     =         -     jZ   o       ⁢     cot   ⁡     (     β   ⁢           ⁢   l     )         ⁢     ≈     β   -&gt;   0       ⁢     1   NY         ,           (   9   )               
where Y is the admittance of the unit-cell, given by Y=j(ωC R −1/(ωL L )).
 
     2.2.2 Infinite Wavelength Antennas with Monopolar Radiation. 
     By using an open-ended resonator that supports an infinite wavelength, an infinite wavelength resonant antenna with an operational frequency independent of its physical size can be realized. Antennas having this configuration according to the invention can be made electrically large or small, the latter of which has been demonstrated previously with a patch-like pattern. In contrast, electrically large and small infinite wavelength antennas with monopolar radiation patterns are demonstrated herein. Various low-profile monopolar antennas have been realized based on reactive loading with shorting pins. However, the placement and number of shorting pins for these monopolar antennas were strictly based on numerical studies. 
       FIG. 14A  and  FIG. 14B  illustrate microstrip patch antennas of equal dimension which are shown in order to discuss the radiation mechanisms behind the antenna. First, a conventional microstrip patch antenna as shown in  FIG. 14A  is discussed. The patch antenna can be modeled as a square cavity with perfect magnetic conductor (PMC) walls. At its fundamental mode, the patch antenna supports a half-wavelength along its resonant length. Therefore, the non-zero equivalent magnetic current density at each radiating edge is given by:
 
 {right arrow over (M)}   S =−2 {circumflex over (n)}×{right arrow over (E)},   (10)
 
where {circumflex over (n)} is the unit normal to the edge, {right arrow over (E)} is the electric field at the edge, and the factor of two is due to the ground plane. It is the two equivalent magnetic current densities at the radiating edges of the patch antenna that contribute to its radiation pattern. Next consider the CRLH antenna shown in  FIG. 14B . Since the CRLH TL can support an infinite wavelength, the field distributions along the perimeter of the CRLH antenna are in-phase when operated at its infinite wavelength frequency. Therefore, the equivalent magnetic current densities at the edges described by Eq. (8) form a loop as shown in  FIG. 14B . It is this equivalent magnetic loop that produces the monopolar radiation pattern; a magnetic loop is an ideal electric dipole by duality. As a result, the infinite wavelength antennas are polarized in the theta-direction.
 
     2.3 CRLH TL Unit-Cell Realization. 
     As mentioned in section 2.2 the CRLH TL unit-cell is the general model for the monopolar unit-cell. To realize the required capacitances and inductances of the CRLH TL unit-cell model, a physical implementation has to be chosen. Lumped components or distributed structures can be used, but for radiation-type applications pure component-based structures are impractical due to their inability to radiate. Due to the popularity of microstrip technology for planar antennas, the CRLH TL unit-cell is based on microstrip. 
       FIG. 15  illustrates a CRLH embodiment  50  implemented as a two dimensional array on a ground plane  52  with unit cells, one of which is indicated at  54   a  comprising mushroom structures, which are one type of structure that can be utilized for realizing a CRLH TL. Each mushroom comprises a patch  56  (e.g., square) connected to ground plane  52  through a square metallic via  58  connected to the ground plane by a shorting post. The LH capacitance (CO of the mushroom is attributed to the edge coupling between the unit-cells and the LH inductance (L L ) of the mushroom is in response to the shorting post to ground. The RH effects are due to the capacitive coupling (C R ) between the patch and ground plane and the current flow atop the patch (L R ). By changing the physical properties of the mushroom unit-cell (e.g., patch size, shorting post radius, dielectric constant, and so forth), the equivalent capacitances and inductances can be controlled. When there is no gap between the mushroom unit-cells, the antenna structure an inductor-loaded TL. The interdigital-based CRLH TL unit-cell is another microstrip implementation of the CRLH TL unit-cell used for one-dimensional LH applications. The choice of the mushroom unit-cell over the interdigital-based unit-cell is for radiation pattern preference. In the case of the mushroom unit-cell, symmetrical boundary conditions similar to the center-shorted microstrip patch antenna exist and a monopolar radiation pattern is possible. In the case of the interdigital-based unit-cell antenna, a patch-like radiation is exhibited since there is only one radiating open-boundary. 
     2.4 Infinite Wavelength Resonant Antenna Realization. 
     In this section, several infinite wavelength antennas with monopolar radiation patterns are realized. The unit-cells for the antennas are based on a modified mushroom unit-cell, wherein the metallic patch can be rectangular and not need be a square. The size of the patch, the dielectric constant, the period of the unit-cell, the radius of the shorting post, and the number of unit-cells are all factors that control the dispersion curve of the unit-cell and in effect the resonant frequencies of the antenna. A CRLH TL unit-cell and an inductor-loaded TL unit-cell are used to realize the infinite wavelength antennas. Both types of unit-cells have similar shunt reactance and thus similar infinite wavelength frequency. To demonstrate this effect, antennas consisting of two, four, and six CRLH TL unit-cells and two, four, and six inductor-loaded TL unit-cells are realized. In the next sub-sections, the dimensions of the unit-cells, the input impedance of the antenna as a function of the number of unit-cells, and the radiation pattern/gain of the antennas are discussed. 
     2.4.1 Antenna Design. 
       FIG. 16A  and  FIG. 16B  illustrate general models  70 ,  70 ′ of CRLH TL and the inductor-loaded TL based infinite wavelength antennas, respectively, implemented on a circuit board (or substrate) material  72  having at least one ground plane  74 . In both figures, at least a first feed line  76  leads to unit cells  80   a ,  80   b . In  FIG. 16A  each unit cell comprises conductive patch  82  with conductive via  84  connecting it to the ground plane. A gap  86  is defined between the conductive patches for each unit cell in  FIG. 16A . In  FIG. 16B  a single conductive patch  82 ′ (no gaps) is connected to the ground plane with multiple vias  84 . The figures depict the use of proximity coupling as the feed network for the antennas. However, it should be recognized that different feed mechanisms can be adopted, while the feeding method can vary in response to the number of unit-cells (N) utilized. Feed line  76  is shown having length  86  and separated by a gap  88  from conductive patch  82 . 
     By way of example and not limitation, all the antennas described below are realized on a circuit board comprising a Rogers RT/Duroid 5880 material having a dielectric constant ∈ R =2.2 and thickness h=1.57 mm. The CRLH TL unit-cell measures 7.3×15 mm 2  with a period of 7.5 mm, while the inductor loaded TL unit-cell measures 7.5×15 mm 2  with a period of 7.5 mm. The radius of the shorting post is 0.12 mm for both unit-cells. Therefore, the infinite wavelength frequency for these unit-cells are very similar. 
       FIG. 17  depicts calculated dispersion diagrams for the unit-cells of  FIG. 16A  and  FIG. 16B  along with experimental resonant peaks of a five unit-cell open-ended resonator implementation. The infinite wavelength frequency for the CRLH TL unit-cell is 3.65 GHz and is 3.52 GHz for the inductor-loaded TL unit-cell as predicted by applying periodic boundary conditions on a single unit-cell. In contrast, the five unit-cell resonator implementation predicts an infinite wavelength frequency of 3.51 GHz and 3.50 GHz for the CRLH TL unit-cell and for the inductor-loaded TL unit-cell, respectively. By modifying the patch area or the radius of the shorting post of the unit-cell, the infinite wavelength frequency can be controlled. 
     2.4.2 Input Impedance. 
       FIGS. 18A-18B  and  FIGS. 19A-19B  depict computed impedance characteristics of a CRLH antenna according to the invention. The input impedance (Z in =R+jX Ω) of each antenna implementation is computed, such as utilizing Ansoft HFSS v10. A 50Ω line was directly attached to the input edge of each antenna and de-embedded to calculate the input impedance. The real part and imaginary component of the input impedance for the CRLH TL based antennas are shown in  FIGS. 18A and 18B , respectively. 
     The real part and imaginary component of the input impedance for the inductor-loaded TL based antennas are shown in  FIG. 19A  and  FIG. 19B , respectively. It should be appreciated that the resonant frequency of an antenna is generally defined as the frequency where the reactance is equal to zero. However, it can be observed from  FIG. 19B  that the reactance curve does not cross zero as the number of cells is increased. As a result, the resonant frequency of the antenna is defined as the frequency where the resistance reaches a maximum, independent of the value of reactance. The input impedance and corresponding infinite wavelength resonant frequency obtained from HFSS for the antennas are summarized in Table 1. 
     From Table 1, it can be observed that the infinite wavelength frequency increases slightly as the number of unit-cells increases. This characteristic arises in response to the additional mutual coupling between the unit-cells, which affects the resonance frequency. Although the inductor-loaded antennas do not have series capacitance, their infinite wavelength frequency is very similar to the CRLH antennas. In addition, the input impedance follows the trend predicted by Eq. (9); wherein the input impedance decreases as the number of unit-cells increases. Also, it is noted that the input reactance of the CRLH based antenna becomes capacitive as more unit-cells are added, while the input reactance of the inductor-loaded antenna becomes increasingly inductive with the addition of more unit-cells. 
     2.4.3 Two Unit-Cell Antenna Realization. 
     The input impedance for both the CRLH and inductor-loaded two unit-cell antennas is quite high for quarter wavelength matching. Therefore, proximity coupling is relied upon in these examples for matching both antennas to a 50Ω line as shown in the example of  FIG. 16A  and  FIG. 16B  having feed length  86  w 1 =15.0 mm and gap  88  w 2 =0.2 mm. 
       FIG. 20  depicts experimental return loss of the CRLH and inductor-loaded two unit-cell antennas, shown in  FIG. 16A  and  FIG. 16B . For the CRLH based antenna, a return loss of −12.34 dB is obtained at f 0 =3.38 GHz, while a return loss of −13.91 dB at f 0 =3.37 GHz is obtained for the inductor-loaded antenna. The electrical size of the antennas is λ/6×λ/6×λ/57 at f 0 . These results show that the two unit-cell antenna is not matched exactly at the predicted infinite wavelength frequency of Table 1, which is due to the high input resistance of the antenna. 
       FIG. 21A  and  FIG. 21B  depict electric-field distribution underneath the two unit-cell CRLH antennas, shown in  FIG. 16A  and  FIG. 16B , for the n=−1 (βl=−180°) and n=0 modes, respectively. 
     Ansoft HFSS was used to obtain these field plots. The n=−1 mode distribution shows that the electric-field is 180° out-of-phase corresponding to a half-wavelength. As a result, the equivalent magnetic current densities along the perimeter of the antenna for the n=−1 mode form a distribution comparable to  FIG. 14B  and the radiation pattern will be similar to a conventional patch antenna. The n=0 distribution shows that the electric-field is in-phase verifying that an infinite wavelength is supported. Therefore, the equivalent magnetic current densities along the perimeter of the antenna for the n=0 mode form a loop comparable to  FIG. 14B  and a monopolar radiation occurs. By using the n=−1 and n=0 mode, the antennas can be used in dual-mode applications. 
     The field distribution of the infinite wavelength antenna shown in  FIG. 21B  is similar to the TM 01  mode of a conventional circular patch antenna. However, the TM 01  mode is a higher order mode which makes the conventional circular patch antenna impractical for compact wireless devices. By placing a shorting post at the center of the conventional circular patch antenna, the TM 01  becomes the fundamental mode. In addition, a mode similar to TM 01  mode of the circular patch can be excited in non-circular patches, which are shorted in the center, to produce a fundamental monopolar radiation pattern. 
       FIGS. 22A-22D  and  FIGS. 23A-23B  illustrate radiation patterns for two unit cell CRLH and inductor-loaded antennas, respectively. The numerical and experimental radiation patterns of the CRLH and inductor-loaded antennas shown in these figures reveal the expected monopolar radiation pattern.  FIG. 22A  and  FIG. 22B  depict radiation patterns in the Z direction with Phi=0° (x-z plane) and Phi=90° (y-z plane), respectively.  FIG. 22C  depicts radiation in the X direction (x-y plane) with Theta=90°.  FIG. 22D  depicts cross-polarizations normalized to co-polarizations, shown with patterns in the x-z, y-z and x-y planes. 
     A maximum gain of 0.87 dBi and 0.70 dBi is experimentally obtained for the CRLH TL based antenna and for the inductor-loaded TL based antenna, respectively. In addition, the x-y plane radiation pattern and cross-polarization (normalized relative to co-polarization) of the CRLH antenna are shown in  FIG. 22C  and  FIG. 22D , respectively.  FIG. 22C  illustrates the omni-directional coverage in the x-y plane provided by the monopolar antenna, while  FIG. 22D  shows that the cross-polarization is less than the co-polarization. The inductor-loaded antenna has similar x-y plane and cross-polarization patterns. These patterns verify that the antennas are polarized in the theta-direction as discussed in Section 2.2.2. 
     2.4.4 Effect of Increasing the Number of Unit-Cells. 
     The embodiments of  FIG. 16A  and  FIG. 16B  are extended into four and six unit-cell antennas along the y-direction. In this example a single section quarter wavelength transformer is used to match each four and six unit-cell antenna to a 50Ω line. Only the real part of the input impedance shown in Table 1 is considered in the matching. The experimental infinite wavelength frequency, return loss, and gain of the two, four, and six unit-cell antennas are displayed in Table 2. The electrical size of the four unit-cell antennas is λ/6×λ/3×λ/53 at f 0  and the electrical size of the six unit-cell antennas is λ/6×λ/2×λ/53 at f 0 . Although the antennas become physically larger, the infinite wavelength frequency remains approximately constant. In addition, gain increases as the antenna becomes physically larger. The x-y plane and cross-polarization of the four and six unit-cell CRLH antennas are similar to those of the two unit-cell CRLH antenna and therefore are not shown. 
       FIG. 24A  through  FIG. 27B  depict radiation patterns for different antenna configurations. The predicted infinite wavelength frequencies of Table 1 show good agreement with the measured infinite wavelength frequencies of Table 2. The numerical and experimental radiation patterns for the CRLH and inductor-loaded four unit-cell antennas are shown in  FIGS. 24A-24B  and  FIGS. 25A-25B , respectively. While, the numerical and experimental radiation patterns for the CRLH and inductor-loaded four unit-cell antennas are shown in  FIGS. 26A-26B  and  FIGS. 27A-27B , respectively. The expected monopolar pattern is obtained. It should be noted, however, that the pattern is asymmetrical in the y-z plane, which can be attributed to the feed and that the antenna is operated in the fast-wave region as seen in  FIG. 18B  and  FIG. 21B , which means that the unit-cell is inherently radiative. This asymmetry can be eliminated by using a coaxial feed at the center of the antenna. 
     2.4.5 Effect of Increasing Unit-Cells in Non-Resonant Direction. 
       FIG. 28  illustrates a four inductor-loaded unit cell antenna embodiment  90  shown on a circuit board  92  (or substrate) having a ground plane  94 . A feed-line is shown with input section  96   a  coupled to a coupling region  96   b . One of the unit cells,  100   a , is shown comprising conductive plate  102  coupled through conductive via  104  to ground plane  94 . The feed line is shown with input length w 1    106  coupled to coupling region  96   b  having a span of I 1    108  and a width w 2    110 , separated from the unit cells by gap w 3    112 . 
     The previous sections showed the effect of adding unit-cells along the resonant length of the antenna. In this section, it is shown that unit-cells can be added to the non-resonant direction of the antenna to increase gain and to avoid the asymmetrical radiation pattern present in the six unit-cell antenna realizations with an edge feed. The antenna is depicted in  FIG. 28 , which consists of four inductor-loaded unit-cells in the y-direction and two inductor-loaded unit-cells in the x-direction forming a square antenna aperture. The inductor-loaded unit-cells are the same as the ones used to realize the antennas presented in Section 2.4.3 and Section 2.4.4. The feed utilized for the two unit-cell antennas is slightly modified with the addition of coupling region  96   b  in order to excite the entire structure. 
       FIG. 29A  through  FIG. 29B  depict numerical and experimental return loss of the enlarged antenna, along with experimental return loss for an enlarged aperture antenna, respectively. These graphs also depict the original two unit-cell inductor-loaded antenna for comparison. 
     An experimental return loss of −6.4 dB is obtained at f 0 =3.58 GHz. The shift in the infinite frequency is due to the increased mutual coupling attributed to the additional unit-cells. The electrical size of the antennas is λ/3×λ/3×λ/53 at f 0 . The experimental radiation patterns at f 0 =3.58 GHz are plotted in  FIG. 29B  and confirm the expected monopolar radiation pattern. A maximum gain of 5.72 dBi is obtained with a more symmetric radiation pattern than the six unit-cell antennas of Section 2.4.4. 
     The discussion above demonstrates the design of infinite wavelength resonant antennas based on periodic structures. The frequency of the antenna does not depend on its physical length, but only on the reactance provided by its unit-cell. In particular, the infinite wavelength supported by a composite right/left-handed unit-cell and an inductor-loaded unit-cell were used to realize several monopolar antennas. The infinite wavelength frequency is determined by the shunt resonance of the unit-cell. Since the physical length of the monopolar antenna is independent of the resonance phenomenon at the infinite wavelength frequency, a monopolar antenna can be arbitrary sized. To demonstrate these concepts, six antennas with differing numbers of unit-cells are numerically and experimentally realized with the composite right/left-handed unit-cell and an inductor-loaded unit-cell. Although, the resonant length of the antenna is increased by 200%, only a 4.7% frequency shift was obtained for the six unit-cell antenna in comparison to the two unit-cell antenna. 
     The analysis of resonant-type antennas based on the fundamental infinite wavelength supported by certain periodic structures has been presented. Since the phase shift is zero for a unit-cell that supports an infinite wavelength, the physical size of the antenna can be arbitrary; wherein antenna size is independent of resonance phenomenon. The operational frequency of the inventive antenna depends only on its unit-cell, while the physical size of the antenna depends on the number of unit-cells. In particular, the unit-cell is based on the composite right/left-handed (CRLH) meta-material transmission line (TL). It has been shown that the CRLH TL is a general model for the required unit-cell, which includes a non-essential series capacitance for the generation of an infinite wavelength. The analysis and design of the unit-cell has been discussed based upon field distributions and dispersion diagrams. It was also shown that the supported infinite wavelength can be used to generate a monopolar radiation pattern. Infinite wavelength resonant antennas have been realized with different numbers of unit-cells to demonstrate the infinite wavelength resonance. 
     Dual-band radiating structures were exemplified in the specification; however, one of ordinary skill in the art will appreciate that the teachings herein can be utilized in creating radiators having any desired number of discrete resonant frequencies. 
     Although the description above contains many details, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. Therefore, it will be appreciated that the scope of the present invention fully encompasses other embodiments which may become obvious to those skilled in the art, and that the scope of the present invention is accordingly to be limited by nothing other than the appended claims, in which reference to an element in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.” All structural, chemical, and functional equivalents to the elements of the above-described preferred embodiment that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Moreover, it is not necessary for a device or method to address each and every problem sought to be solved by the present invention, for it to be encompassed by the present claims. Furthermore, no element, component, or method step in the present disclosure is intended to be dedicated to the public regardless of whether the element, component, or method step is explicitly recited in the claims. No claim element herein is to be construed under the provisions of 35 U.S.C. 112, sixth paragraph, unless the element is expressly recited using the phrase “means for.” 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Input Impedance and Corresponding Resonant 
               
               
                 Frequency of CRLH Antennas 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 frequency 
                   
               
               
                 Cell Type 
                 No. Cells 
                 (GHz) 
                 Z in  = R + jX (Ω) 
               
               
                   
               
               
                 (CRLH) 
                 2 
                 3.47 
                 1060.1 + j0.0 
               
               
                   
                 4 
                 3.53 
                  410.0 − j15.0 
               
               
                   
                 6 
                 3.55 
                  253.0 − j73.0 
               
               
                 Inductor-loaded 
                 2 
                 3.44 
                  890.0 + j0.0 
               
               
                   
                 4 
                 3.51 
                  310.0 + j20.6 
               
               
                   
                 6 
                 3.53 
                  178.8 + j41.0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Results for Two, Four, and Six Unit-cell Antennas 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 frequency 
                 return loss 
                 peak gain 
               
               
                 Cell Type 
                 No. Cells 
                 (GHz) 
                 (dB) 
                 (dBi) 
               
               
                   
               
               
                 (CRLH) 
                 2 
                 3.38 
                 −12.34 
                 0.87 
               
               
                   
                 4 
                 3.52 
                 −17.33 
                 4.50 
               
               
                   
                 6 
                 3.55 
                 −11.17 
                 5.17 
               
               
                 inductor-loaded 
                 2 
                 3.37 
                 −13.91 
                 0.70 
               
               
                   
                 4 
                 3.49 
                 −20.50 
                 4.17 
               
               
                   
                 6 
                 3.53 
                 −35.02 
                 5.00