Patent Publication Number: US-9887465-B2

Title: Single-layer metalization and via-less metamaterial structures

Description:
PRIORITY CLAIMS AND RELATED APPLICATIONS 
     This application is a divisional application of U.S. application Ser. No. 12/250,477, filed Oct. 13, 2008, which claimed the benefit of priority of: U.S. Provisional Application No. 60/979,384, filed Oct. 11, 2007; U.S. Provisional Application No. 60/987,750, filed Nov. 13, 2007; U.S. Provisional Application No. 61/024,876, filed Jan. 30, 2008; and U.S. Provisional Application No. 61/091,203, filed Aug. 22, 2008, the benefit of priority of each of which is hereby presently claimed and each of which is hereby incorporated herein by reference. 
    
    
     BACKGROUND 
     This application relates to metamaterial structures. 
     The propagation of electromagnetic waves in most materials obeys the right handed rule for the (E, H, β) vector fields, where E is the electrical field, H is the magnetic field, and β is the wave vector. The phase velocity direction is the same as the direction of the signal energy propagation (group velocity) and the refractive index is a positive number. Such materials are “right handed” (RH). Most natural materials are RH materials. Artificial materials can also be RH materials. 
     A metamaterial (MTM) has an artificial structure. When designed with a structural average unit cell size p much smaller than the wavelength of the electromagnetic energy guided by the metamaterial, the metamaterial can behave like a homogeneous medium to the guided electromagnetic energy. Unlike RH materials, a metamaterial can exhibit a negative refractive index with permittivity ∈ and permeability μ being simultaneously negative, and the phase velocity direction is opposite to the direction of the signal energy propagation where the relative directions of the (E, H, β) vector fields follow the left handed rule. Metamaterials that support only a negative index of refraction with permittivity ∈ and permeability μ being simultaneously negative are pure “left handed” (LH) metamaterials. 
     Many metamaterials are mixtures of LH metamaterials and RH materials and thus are Composite Left and Right Handed (CRLH) metamaterials. A CRLH metamaterial can behave like a LH metamaterial at low frequencies and a RH material at high frequencies. Designs and properties of various CRLH metamaterials are described in, for example, Caloz and Itoh, “Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications,” John Wiley &amp; Sons (2006). CRLH metamaterials and their applications in antennas are described by Tatsuo Itoh in “Invited paper: Prospects for Metamaterials,” Electronics Letters, Vol. 40, No. 16 (August, 2004). 
     CRLH metamaterials can be structured and engineered to exhibit electromagnetic properties that are tailored for specific applications and can be used in applications where it may be difficult, impractical or infeasible to use other materials. In addition, CRLH metamaterials may be used to develop new applications and to construct new devices that may not be possible with RH materials. 
     SUMMARY 
     Techniques and apparatus based on metamaterial structures provided for antenna and transmission line devices, including single-layer metallization and via-less metamaterial structures. 
     In one aspect, a metamaterial device includes a dielectric substrate having a first surface and a second, different surface; and a metallization layer formed on the first surface and patterned to have two or more conductive parts to form a single-layer composite left and right handed (CRLH) metamaterial structure on the first surface. 
     In another aspect, a metamaterial device includes a dielectric substrate having a first surface and a second, different surface; a first metallization layer formed on the first surface; and a second metallization layer formed on the second surface. The first and second metallization layers are patterned to have two or more conductive parts to form a composite left and right handed (CRLH) metamaterial structure that comprises a unit cell which is free of a conductive via penetrating the dielectric substrate to connect the first metallization layer and the second metallization layer. 
     In yet another aspect, a metamaterial device includes a dielectric substrate having a first surface and a second, different surface; a cell patch on the first surface; a top ground electrode spaced from the cell patch and located on the first surface; a top via line on the first surface having a first end connected to the cell patch and a second end connected to the top ground electrode; a cell launch pad formed on the second surface beneath the cell patch on the first surface and electromagnetically coupled to the cell patch through the substrate to direct a signal to or receive a signal from the cell patch without being directly connected to the cell patch through a conductive via that penetrates through the substrate; and a bottom feed line formed on the second surface and connected to the cell launch pad to direct the signal to or from cell launch pad. The cell patch, the top ground electrode, the top via line, the cell launch pad, and the bottom feed line form a composite left and right handed (CRLH) metamaterial structure. 
     These and other aspects and implementations and their variations are described in detail in the attached drawings, the detailed description and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of a 1D CRLH MTM TL based on four unit cells. 
         FIG. 2  shows an equivalent circuit of the 1D CRLH MTM TL shown in  FIG. 1   
         FIG. 3  shows another representation of the equivalent circuit of the 1D CRLH MTM TL shown in  FIG. 1 . 
         FIG. 4A  shows a two-port network matrix representation for the 1D CRLH TL equivalent circuit shown in  FIG. 2 . 
         FIG. 4B  shows another two-port network matrix representation for the 1D CRLH TL equivalent circuit shown in  FIG. 3 . 
         FIG. 5  shows an example of a 1D CRLH MTM antenna based on four unit cells. 
         FIG. 6A  shows a two-port network matrix representation for the 1D CRLH antenna equivalent circuit analogous to the TL case shown in  FIG. 4A . 
         FIG. 6B  shows another two-port network matrix representation for the 1D CRLH antenna equivalent circuit analogous to the TL case shown in  FIG. 4B . 
         FIG. 7A  shows an example of a dispersion curve for the balanced case. 
         FIG. 7B  shows an example of a dispersion curve for the unbalanced case. 
         FIG. 8  shows an example of a 1D CRLH MTM TL with a truncated ground based on four unit cells. 
         FIG. 9  shows an equivalent circuit of the 1D CRLH MTM TL with the truncated ground shown in  FIG. 8 . 
         FIG. 10  shows an example of a 1D CRLH MTM antenna with a truncated ground based on four unit cells. 
         FIG. 11  shows another example of a 1D CRLH MTM TL with a truncated ground based on four unit cells. 
         FIG. 12  shows an equivalent circuit of the 1D CRLH MTM TL with the truncated ground shown in  FIG. 11 . 
         FIGS. 13( a )-13( c )  show an example of a one-cell SLM MTM antenna structure, illustrating the 3D view, top view of the top layer and side view, respectively. 
         FIG. 14( a )  shows the simulated return loss of the one-cell SLM MTM antenna shown in  FIGS. 13( a )-13( c ) . 
         FIG. 14( b )  shows the simulated return loss of the two-cell SLM MTM antenna shown in  FIG. 14 . 
         FIG. 14( c )  shows the measured return loss of the one-cell SLM MTM antenna fabricated as shown in  FIGS. 13( a )-13( c ) . 
         FIG. 15  shows the 3D view of an example of a two-cell SLM MTM antenna. 
         FIG. 16( a )  shows the simulated input impedance of the two-cell SLM MTM antenna shown in  FIG. 15 . 
         FIG. 16( b )  shows the simulated input impedance of the two-cell SLM MTM antenna shown in  FIG. 15 . 
         FIG. 17  shows an example of a three-cell MTM TL. 
         FIG. 18  shows the simulated return loss of the three-cell MTM TL shown in  FIG. 17 . 
         FIGS. 19( a ) and 19( b )  show the electromagnetic guided wavelengths corresponding to the 1.6 GHz resonance and 1.8 GHz resonance, respectively. 
         FIGS. 20( a )-20( d )  show an example of a one-cell TLM-VL MTM antenna structure, illustrating the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. 
         FIG. 21( a )  shows a simplified equivalent circuit for a two-layer MTM structure with a via. 
         FIG. 21( b )  shows a simplified equivalent circuit for a two-layer MTM structure without a via and with a via line on the bottom layer. 
         FIG. 22( a )  shows the simulated return loss of the one-cell TLM-VL MTM antenna shown in  FIGS. 20( a )-20( d ) . 
         FIG. 22( b )  shows the simulated return loss of the one-cell TLM-VL MTM antenna shown in  FIGS. 20( a )-20( d ) , with an added via connecting the center of the cell patch and the center of the bottom truncated ground. 
         FIG. 23  shows the radiation pattern of the one-cell TLM-VL MTM antenna shown in  FIGS. 20( a )-20( d )  at 2.4 GHz. 
         FIGS. 24( a )-24( d )  show an example of a TLM-VL MTM antenna structure with a via line connected to an extended ground electrode, illustrating the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. 
         FIG. 25  shows the simulated return loss of the TLM-VL MTM antenna shown in  FIGS. 24( a )-24( d ) . 
         FIGS. 26( a ) and 26( b )  show photos of the TLM-VL MTM antenna fabricated as shown in  FIGS. 24( a )-24( d ) . 
         FIG. 27  shows the measured return loss of the TLM-VL MTM antenna shown in  FIGS. 26( a ) and 26( b ) . 
         FIGS. 28( a )-28( d )  show another example of a one-cell SLM MTM antenna structure, illustrating the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. 
         FIG. 29( a )  shows the simulated return loss of the one-cell SLM MTM antenna shown in  FIGS. 28( a )-28( d ) . 
         FIG. 29( b )  shows the simulated input impedance of the one-cell SLM MTM antenna shown in  FIGS. 28( a )-28( d ) . 
         FIGS. 30( a ) and 30( b )  show the measured efficiency of the one-cell SLM MTM antenna fabricated as shown in  FIGS. 28( a )-28( d ) , plotting the cellular band efficiency and the PCS/DCS efficiency, respectively. 
         FIG. 31  shows another example of a one-cell SLM MTM antenna structure with modifications. 
         FIGS. 32( a ) and 32( b )  show the measured efficiency of the one-cell SLM MTM antenna fabricated as shown in  FIG. 31 , plotting the cellular band efficiency and the PCS/DCS efficiency, respectively. 
         FIGS. 33( a ) and 33( b )  show the effect of an extended ground electrode on the efficiency, plotting the cellular band efficiency and the PCS/DCS efficiency, respectively, by comparing the cases with and without the extended ground electrode. 
         FIGS. 34( a )-34( d )  show another example of a TLM-VL antenna structure, illustrating the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. 
         FIG. 35( a )  shows the simulated return loss of the TLM-VL antenna shown in  FIGS. 34( a )-34( d ) . 
         FIG. 35( b )  shows the simulated input impedance of the TLM-VL antenna shown in  FIGS. 34( a )-34( d ) . 
         FIGS. 36( a )-36( d )  show an example of a semi single-layer MTM antenna structure, illustrating the 3D view, side view, top view of the top layer with the bottom layer overlaid, and the top view of the bottom layer with the top layer overlaid, respectively. 
         FIG. 37( a )  shows the simulated return loss of the semi single-layer antenna shown in  FIGS. 36( a )-36( d ) . 
         FIG. 37( b )  shows the simulated input impedance of the semi single-layer antenna shown in  FIGS. 36( a )-36( d ) . 
         FIG. 38  shows another example of a SLM MTM antenna structure, illustrating the top view of the top layer. 
         FIG. 39  shows another example of a SLM MTM antenna structure (with meander), illustrating the top view of the top layer. 
         FIG. 40  shows the simulated return losses of the SLM MTM antenna shown in  FIG. 38  and of the SLM MTM antenna (with meander) shown in  FIG. 39 . 
         FIG. 41  shows a photo of the SLM MTM antenna (with meander) fabricated as shown in  FIG. 39 . 
         FIG. 42  shows the measured return loss of the fabricated SLM MTM antenna shown in  FIG. 41 . 
         FIGS. 43( a ) and 43( b )  show the measured efficiency of the SLM MTM antenna shown in  FIG. 41 , plotting the cellular band efficiency and the PCS/DCS band efficiency, respectively. 
         FIG. 44  shows the SLM MTM antenna with meander shown in  FIG. 39  with a lumped capacitor between the launch pad and cell patch. 
         FIG. 45  shows the SLM MTM antenna with meander shown in  FIG. 39  with a lumped inductor in the shortened via line trace. 
         FIG. 46  shows the SLM MTM antenna with meander shown in  FIG. 39  with a lumped inductor in the shortened meander line trace. 
         FIG. 47  shows the simulated return losses of the SLM MTM antenna with meander for the cases with the lumped capacitor in  FIG. 44 , with the lumped inductor in  FIG. 45 , with the lumped inductor in  FIG. 46 , and without any lumped element in  FIG. 39 . 
         FIGS. 48( a )-48( f )  show an example of a three-layer M™ antenna structure with a vertical coupling, illustrating the 3D view, top view of the top layer, top view of the mid-layer, top view of the bottom layer, top view of the top and mid layers overlaid, and the side view, respectively. 
         FIG. 49( a )  shows the simulated return loss of the three-layer MTM antenna with the vertical coupling shown in  FIGS. 48( a )-48( f ) . 
         FIG. 49( b )  shows the simulated input impedance of the three-layer MTM antenna with the vertical coupling shown in  FIGS. 48( a )-48( f ) . 
         FIGS. 50( a )-50( c )  show an example of a TLM-VL MTM antenna with the vertical coupling, illustrating the 3D view, top view of the top layer and top view of the bottom layer, respectively. 
         FIG. 51( a )  shows the simulated return loss of the TLM-VL MTM antenna with the vertical coupling shown in  FIGS. 50( a )-50( c ) . 
         FIG. 51( b )  shows the simulated input impedance of the TLM-VL MTM antenna with the vertical coupling shown in  FIGS. 50( a )-50( c ) . 
     
    
    
     DETAILED DESCRIPTION 
     Metamaterial (MTM) structures can be used to construct antennas and other electrical components and devices, allowing for a wide range of technology advancements such as size reduction and performance improvements. The MTM antenna structures can be fabricated on various circuit platforms, including circuit boards such as a FR-4 Printed Circuit Board (PCB) or a Flexible Printed Circuit (FPC) board. Examples of other fabrication techniques include thin film fabrication techniques, system on chip (SOC) techniques, low temperature co-fired ceramic (LTCC) techniques, and monolithic microwave integrated circuit (MMIC) techniques. 
     The examples and implementations of MTM structures described in this document include Single-Layer Metallization (SLM) MTM antenna structures that place conductive components of a MTM structure, including a ground electrode, in a single conductive metallization layer formed on one side of a dielectric substrate or board, and Two-Layer Metallization Via-Less (TLM-VL) MTM antenna structures in which two conductive metallization layers on two parallel surfaces of a dielectric substrate or board are used to form a MTM structure without having a conductive via to connect one component of the MTM structure on one conductive metallization layer of the dielectric substrate or board to another component of the MTM structure on the other conductive metallization layer of the dielectric substrate or board. Such SLM MTM and TLM-VL MTM structures can be structured in various configurations and may be coupled with other MTM or non-MTM circuits and circuit elements on the circuit boards. 
     For example, such SLM MTM and TLM-VL MTM structures can be used in devices having thin substrates or materials in which via holes cannot be drilled and/or plated. For another example, such SLM and TLM-VL MTM antenna structures may be wrapped inside or around a product enclosure. Antennas based on such SLM MTM and TLM-VL MTM structures can be made conformal to the internal wall of a housing of a product, the outer surface of an antenna carrier or the contour of a device package. Examples of thin substrates or materials in which via holes cannot be drilled and/or plated include FR4 substrates with a thickness less than 10 mils, thin glass materials, Flex films, and thin-film substrates with a thickness of 3 mils-5 mils. Some of these materials can be bent easily with good manufacturability. Certain FR-4 and glass materials may require heat-bending or other techniques to achieve desired curved or bent shapes. 
     The MTM antenna structures described in this document can be configured to generate multiple frequency bands including a “low band” and a “high band.” The low band includes at least one left-handed (LH) mode resonance and the high band includes at least one right-handed (RH) mode resonance. The multi-band MTM antenna structures described in this document can be used in cell phone applications, handheld device applications (e.g., PDAs and smart phones) and other mobile device applications, in which the antenna is expected to support multiple frequency bands with adequate performance under limited space constraints. The MTM antenna designs disclosed in this document can be adapted and designed to provide one or more advantages over other antennas such as compact sizes, multiple resonances based on a single antenna solution, resonances that are stable and insensitive to shifts caused by the user interaction, and resonant frequencies that are substantially independent of the physical size. The configuration of elements in a MTM antenna structure can be structured to achieve desirable bands and bandwidths based on the single antenna solution with the CRLH properties. 
     The MTM antennas described in this document can be designed to operate in various bands, including frequency bands for cell phone and mobile device applications, WiFi applications, WiMax applications and other wireless communication applications. Examples for the frequency bands for cell phone and mobile device applications are: the cellular band (824-960 MHz) which includes two bands, CDMA and GSM bands; and the PCS/DCS band (1710-2170 MHz) which includes three bands: PCS, DCS and WCDMA bands. A quad-band antenna can be used to cover one of the CDMA and GSM bands in the cellular band and all three bands in the PCS/DCS band. A penta-band antenna can be used to cover all five bands with two in the cellular band and three in the PCS/DCS band. Examples of frequency bands for WiFi applications include two bands: one ranging from 2.4 to 2.48 GHz, and the other ranging from 5.15 GHz to 5.835 GHz. The frequency bands for WiMax applications involve three bands: 2.3-2.4 GHZ, 2.5-2.7 GHZ, and 3.5-3.8 GHz. 
     An MTM antenna or MTM transmission line (TL) is a M™ structure with one or more MTM unit cells. The equivalent circuit for each MTM unit cell includes a right-handed series inductance (LR), a right-handed shunt capacitance (CR), a left-handed series capacitance (CL), and a left-handed shunt inductance (LL). LL and CL are structured and connected to provide the left-handed properties to the unit cell. This type of CRLH TLs or antennas can be implemented by using distributed circuit elements, lumped circuit elements or a combination of both. Each unit cell is smaller than −λ/4 where λ is the wavelength of the electromagnetic signal that is transmitted in the CRLH TL or antenna. 
     A pure LH metamaterial follows the left-hand rule for the vector trio (E, H, β), and the phase velocity direction is opposite to the signal energy propagation. Both the permittivity ∈ and permeability μ of the LH material are negative. A CRLH metamaterial can exhibit both left-hand and right-hand electromagnetic modes of propagation depending on the regime or frequency of operation. Under certain circumstances, a CRLH metamaterial can exhibit a non-zero group velocity when the wavevector of a signal is zero. This situation occurs when both left-hand and right-hand modes are balanced. In an unbalanced mode, there is a bandgap in which electromagnetic wave propagation is forbidden. In the balanced case, the dispersion curve does not show any discontinuity at the transition point of the propagation constant β(ω o )=0 between the left- and right-hand modes, where the guided wavelength is infinite, i.e., λ g =2π/|β|→∞, while the group velocity is positive: 
               v   g     =         d   ⁢           ⁢   ω       d   ⁢           ⁢   β       ⁢     |     β   =   0       ⁢     &gt;   0.             
This state corresponds to the zeroth order mode m=0 in a TL implementation in the LH region. The CRHL structure supports a fine spectrum of low frequencies with the dispersion relation that follows the negative β parabolic region. This allows a physically small device to be built that is electromagnetically large with unique capabilities in manipulating and controlling near-field radiation patterns. When this TL is used as a Zeroth Order Resonator (ZOR), it allows a constant amplitude and phase resonance across the entire resonator. The ZOR mode can be used to build MTM-based power combiners and splitters or dividers, directional couplers, matching networks, and leaky wave antennas.
 
     In the case of RH TL resonators, the resonance frequency corresponds to electrical lengths θ m =β m l=mπ (m=1, 2, 3 . . . ), where l is the length of the TL. The TL length should be long to reach low and wider spectrum of resonant frequencies. The operating frequencies of a pure LH material are at low frequencies. A CRLH MTM structure is very different from an RH or LH material and can be used to reach both high and low spectral regions of the RF spectral ranges. In the CRLH case θ m =β m l=mπ, where l is the length of the CRLH TL and the parameter m=0, ±1, ±2, ±3 . . . ±∞. 
     Examples of specific MTM antenna structures are described below. Certain technical information associated with the these examples is described in U.S. patent application Ser. No. 11/741,674 entitled “Antennas, Devices, and Systems Based on Metamaterial Structures,” filed on Apr. 27, 2007, and U.S. patent application Ser. No. 11/844,982 entitled “Antennas Based on Metamaterial Structures,” filed on Aug. 24, 2007, which are incorporated by reference as part of the specification of this document. 
       FIG. 1  illustrates an example of a 1-dimensional (1D) CRLH MTM transmission line (TL) based on four unit cells. One unit cell includes a cell patch and a via, and is a building block for constructing a desired MTM structure. The illustrated TL example includes four unit cells formed in two conductive metallization layers of a substrate where four conductive cell patches are formed on the top conductive metallization layer of the substrate and the other side of the substrate has a metallization layer as the ground electrode. Four centered conductive vias are formed to penetrate through the substrate to connect the four cell patches to the ground plane, respectively. The unit cell patch on the left side is electromagnetically coupled to a first feed line and the unit cell patch on the right side is electromagnetically coupled to a second feed line. In some implementations, each unit cell patch is electromagnetically coupled to an adjacent unit cell patch without being directly in contact with the adjacent unit cell. This structure forms the MTM transmission line to receive an RF signal from one feed line and to output the RF signal at the other feed line. 
       FIG. 2  shows an equivalent network circuit of the 1D CRLH MTM TL in  FIG. 1 . The ZLin′ and ZLout′ correspond to the TL input load impedance and TL output load impedance, respectively, and are due to the TL coupling at each end. This is an example of a printed two-layer structure. LR is due to the cell patch on the dielectric substrate, and CR is due to the dielectric substrate being sandwiched between the cell patch and the ground plane. CL is due to the presence of two adjacent cell patches, and the via induces LL. 
     Each individual unit cell can have two resonances ω SE  and ω SH  corresponding to the series (SE) impedance Z and shunt (SH) admittance Y. In  FIG. 2 , the Z/2 block includes a series combination of LR/2 and 2CL, and the Y block includes a parallel combination of LL and CR. The relationships among these parameters are expressed as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         ω 
                         SH 
                       
                       = 
                       
                         1 
                         
                           
                             LL 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CR 
                           
                         
                       
                     
                     ; 
                     
                       
                         ω 
                         SE 
                       
                       = 
                       
                         1 
                         
                           
                             LL 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CL 
                           
                         
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         ω 
                         R 
                       
                       = 
                       
                         1 
                         
                           
                             LL 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CR 
                           
                         
                       
                     
                     ; 
                     
                       
                         ω 
                         L 
                       
                       = 
                       
                         1 
                         
                           
                             LL 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CL 
                           
                         
                       
                     
                     ; 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     where 
                     , 
                     
                       Z 
                       = 
                       
                         
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             LR 
                           
                           + 
                           
                             
                               1 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 CL 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             and 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Y 
                           
                         
                         = 
                         
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CR 
                           
                           + 
                           
                             
                               1 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 LL 
                               
                             
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     The two unit cells at the input/output edges in  FIG. 1  do not include CL, since CL represents the capacitance between two adjacent cell patches and is missing at these input/output edges. The absence of the CL portion at the edge unit cells prevents ω SE  frequency from resonating. Therefore, only ω SH  appears as an m=0 resonance frequency. 
     To simplify the computational analysis, a portion of the ZLin′ and ZLout′ series capacitor is included to compensate for the missing CL portion, and the remaining input and output load impedances are denoted as ZLin and ZLout, respectively, as seen in  FIG. 3 . Under this condition, all unit cells have identical parameters as represented by two series Z/2 blocks and one shunt Y block in  FIG. 3 , where the Z/2 block includes a series combination of LR/2 and 2CL, and the Y block includes a parallel combination of LL and CR. 
       FIG. 4A  and  FIG. 4B  illustrate a two-port network matrix representation for TL circuits without the load impedances as shown in  FIG. 2  and  FIG. 3 , respectively, 
       FIG. 5  illustrates an example of a 1D CRLH MTM antenna based on four unit cells. Different from the 1D CRLH MTM TL in  FIG. 1 , the antenna in  FIG. 5  couples the unit cell on the left side to a feed line to connect the antenna to a antenna circuit and the unit cell on the right side is an open circuit so that the four cells interface with the air to transmit or receive an RF signal. 
       FIG. 6A  shows a two-port network matrix representation for the antenna circuit in  FIG. 5 .  FIG. 6B  shows a two-port network matrix representation for the antenna circuit in  FIG. 5  with the modification at the edges to account for the missing CL portion to have all the unit cells identical.  FIGS. 6A and 6B  are analogous to the TL circuits shown in  FIGS. 4A and 4B , respectively. 
     In matrix notations,  FIG. 4B  represents the relationship given as below: 
                       (         Vin           Iin         )     =       (         AN       BN           CN       AN         )     ⁢     (         Vout           Iout         )         ,           Eq   .           ⁢     (   2   )                 
where AN=DN because the CRLH MTM TL circuit in  FIG. 3  is symmetric when viewed from Vin and Vout ends.
 
     In  FIGS. 6A and 6B , the parameters GR′ and GR represent a radiation resistance, and the parameters ZT′ and ZT represent a termination impedance. Each of ZT′, ZLin′ and ZLout′ includes a contribution from the additional 2CL as expressed below: 
     
       
         
           
             
               
                 
                   
                     
                       ZLin 
                       ′ 
                     
                     = 
                     
                       ZLin 
                       + 
                       
                         2 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                     
                   
                   , 
                   
                     
                       ZLout 
                       ′ 
                     
                     = 
                     
                       ZLout 
                       + 
                       
                         2 
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ZT 
                       ′ 
                     
                     = 
                     
                       ZT 
                       + 
                       
                         
                           2 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             CL 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     Since the radiation resistance GR or GR′ can be derived by either building or simulating the antenna, it may be difficult to optimize the antenna design. Therefore, it is preferable to adopt the TL approach and then simulate its corresponding antennas with various terminations ZT. The relationships in Eq. (1) are valid for the circuit in  FIG. 2  with the modified values AN′, BN′, and CN′, which reflect the missing CL portion at the two edges. 
     The frequency bands can be determined from the dispersion equation derived by letting the N CRLH cell structure resonate with not propagation phase length, where n=0, ±1, ±2, . . . ±N. Here, each of the N CRLH cells is represented by Z and Y in Eq. (1), which is different from the structure shown in  FIG. 2 , where CL is missing from end cells. Therefore, one might expect that the resonances associated with these two structures are different. However, extensive calculations show that all resonances are the same except for n=0, where both ω SE  and ω SH  resonate in the structure in  FIG. 3 , and only ω SH  resonates in the structure in  FIG. 2 . The positive phase offsets (n&gt;0) correspond to RH region resonances and the negative values (n&lt;0) are associated with LH region resonances. 
     The dispersion relation of N identical CRLH cells with the Z and Y parameters is given below: 
                   {                 N   ⁢           ⁢   β   ⁢           ⁢   p     =       cos     -   1       ⁡     (     A   N     )         ,       ⇒            A   N          ≤   1     ⇒     0   ≤   χ       =       -   ZY     ≤     4   ⁢     ∀   N                         where   ⁢           ⁢     A   N       =       1   ⁢           ⁢   at   ⁢           ⁢   even   ⁢           ⁢   resonances   ⁢        n          =                   2   ⁢   m     ∈     {     0   ,   2   ,   4   ,     …   ⁢           ⁢   2   ×     Int   ⁡     (       N   -   1     2     )           }                   and   ⁢           ⁢     A   N       =         -   1     ⁢           ⁢   at   ⁢           ⁢   odd   ⁢           ⁢   resonances   ⁢        n          =                     2   ⁢   m     +   1     ∈     {     1   ,   3   ,     …   ⁢           ⁢     (       2   ×     Int   ⁡     (     N   2     )         -   1     )         }             ,             Eq   .           ⁢     (   4   )                 
where Z and Y are given in Eq. (1), AN is derived from the linear cascade of N identical CRLH unit cells as in  FIG. 3 , and p is the cell size. Odd n=(2 m+1) and even n=2m resonances are associated with AN=−1 and AN=1, respectively. For AN′ in  FIG. 4A  and  FIG. 6A , the n=0 mode resonates at ω 0 =ω SH  only and not at both ω SE  and ω SH  due to the absence of CL at the end cells, regardless of the number of cells. Higher-order frequencies are given by the following equations for the different values of χ specified in Table 1:
 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         For 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                       &gt; 
                       0 
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         ω 
                         
                           ± 
                           n 
                         
                         2 
                       
                       = 
                       
                         
                           
                             
                               ω 
                               SH 
                               2 
                             
                             + 
                             
                               ω 
                               SE 
                               2 
                             
                             + 
                             
                               χω 
                               R 
                               2 
                             
                           
                           2 
                         
                         ± 
                         
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         SH 
                                         2 
                                       
                                       + 
                                       
                                         ω 
                                         SE 
                                         2 
                                       
                                       + 
                                       
                                         χω 
                                         R 
                                         2 
                                       
                                     
                                     2 
                                   
                                   ) 
                                 
                                 2 
                               
                               - 
                               
                                 
                                   ω 
                                   Sh 
                                   2 
                                 
                                 ⁢ 
                                 
                                   ω 
                                   SE 
                                   2 
                                 
                               
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     Table 1 provides χ values for N=1, 2, 3, and 4. It should be noted that the higher-order resonances |n|&gt;0 are the same regardless if the full CL is present at the edge cells ( FIG. 3 ) or absent ( FIG. 2 ). Furthermore, resonances close to n=0 have small χ values (near χ lower bound 0), whereas higher-order resonances tend to reach χ upper bound 4 as stated in Eq. (4). 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Resonances for N = 1, 2, 3 and 4 cells 
               
            
           
           
               
               
               
               
               
            
               
                 N\Modes 
                 |n| = 0 
                 |n| = 1 
                 |n| = 2 
                 |n| = 3 
               
               
                   
               
               
                 N = 1 
                 χ (1, 0)  = 0; ω 0  = ω SH   
                   
                   
                   
               
               
                 N = 2 
                 χ  (2, 0)  = 0; ω 0  = ω SH   
                 χ (2, 1)  = 2 
               
               
                 N = 3 
                 χ (3, 0)  = 0; ω 0  = ω SH   
                 χ (3, 1)  = 1 
                 χ (3, 2)  = 3 
               
               
                 N = 4 
                 χ (4, 0)  = 0; ω 0  = ω SH   
                 χ (4, 1)  = 2 − {square root over (2)} 
                 χ (4, 2)  = 2 
               
               
                   
               
            
           
         
       
     
     The dispersion curve β as a function of frequency w is illustrated in  FIGS. 7A and 7B  for the ω SE =ω SH  (balanced, i.e., LR CL=LL CR) and ω SE ≠ω SH  (unbalanced) cases, respectively. In the latter case, there is a frequency gap between min(ω SE ,ω SH ) and max(ω SE ,ω SH ). The limiting frequencies ω min  and ω max  values are given by the same resonance equations in Eq. (5) with χ reaching its upper bound χ=4 as stated in the following equations: 
     
       
         
           
             
               
                 
                   
                     
                       ω 
                       min 
                       2 
                     
                     = 
                     
                       
                         
                           
                             ω 
                             SH 
                             2 
                           
                           + 
                           
                             ω 
                             SE 
                             2 
                           
                           + 
                           
                             4 
                             ⁢ 
                             
                               ω 
                               R 
                               2 
                             
                           
                         
                         2 
                       
                       - 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     SH 
                                     2 
                                   
                                   + 
                                   
                                     ω 
                                     SE 
                                     2 
                                   
                                   + 
                                   
                                     4 
                                     ⁢ 
                                     
                                       ω 
                                       R 
                                       2 
                                     
                                   
                                 
                                 2 
                               
                               ) 
                             
                             2 
                           
                           - 
                           
                             
                               ω 
                               SH 
                               2 
                             
                             ⁢ 
                             
                               ω 
                               SE 
                               2 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ω 
                       max 
                       2 
                     
                     = 
                     
                       
                         
                           
                             ω 
                             SH 
                             2 
                           
                           + 
                           
                             ω 
                             SE 
                             2 
                           
                           + 
                           
                             4 
                             ⁢ 
                             
                               ω 
                               R 
                               2 
                             
                           
                         
                         2 
                       
                       - 
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       ω 
                                       SH 
                                       2 
                                     
                                     + 
                                     
                                       ω 
                                       SE 
                                       2 
                                     
                                     + 
                                     
                                       4 
                                       ⁢ 
                                       
                                         ω 
                                         R 
                                         2 
                                       
                                     
                                   
                                   2 
                                 
                                 ) 
                               
                               2 
                             
                             - 
                             
                               
                                 ω 
                                 SH 
                                 2 
                               
                               ⁢ 
                               
                                 ω 
                                 SE 
                                 2 
                               
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In addition,  FIGS. 7A and 7B  provide examples of the resonance position along the dispersion curves. In the RH region (n&gt;0) the structure size l=Np, where p is the cell size, increases with decreasing frequency. In contrast, in the LH region, lower frequencies are reached with smaller values of Np, hence size reduction. The dispersion curves provide some indication of the bandwidth around these resonances. For instance, LH resonances have the narrow bandwidth because the dispersion curves are almost flat. In the RH region, the bandwidth is wider because the dispersion curves are steeper. Thus, the first condition to obtain broadbands, 1 st  BB condition, can be expressed as follows: 
                       COND   ⁢           ⁢   1     :     ⁢     
                                     1   st     ⁢   BB   ⁢           ⁢   condition   ⁢              ⅆ   β       ⅆ   ω            res       =              -         d   ⁡     (   AN   )         d   ⁢           ⁢   ω           (     1   -     AN   2       )                res     ⁢     &lt;&lt;   1         ⁢           ⁢     
     ⁢         near   ⁢           ⁢   ω     =       ω   res     =     ω   0         ,     ω     ±   1       ,           ω     ±   2       ⁢           ⁢   …     ⁢     
     ⇒           ⁢              d   ⁢           ⁢   β       d   ⁢           ⁢   ω            res       =                  d   ⁢           ⁢   χ       d   ⁢           ⁢   ω         2   ⁢   p   ⁢       χ   ⁡     (     1   -     χ   4       )                  res     ⁢     &lt;&lt;   1             ⁢                   Eq   .           ⁢     (   7   )                     with   ⁢           ⁢   p     =         cell   ⁢           ⁢   size   ⁢           ⁢   and   ⁢       d   ⁢           ⁢   χ       d   ⁢           ⁢   ω         ⁢     |   res       =         2   ⁢     ω     ±   n           ω   R   2       ⁢     (     1   -         ω   SE   2     ⁢     ω   SH   2         ω     ±   n     4         )           ,                           
where χ is given in Eq. (4) and ω R  is defined in Eq. (1). The dispersion relation in Eq. (4) indicates that resonances occur when |AN|=1, which leads to a zero denominator in the 1 st  BB condition (COND1) of Eq. (7). As a reminder, AN is the first transmission matrix entry of the N identical unit cells ( FIG. 4B  and  FIG. 6B ). The calculation shows that COND1 is indeed independent of N and given by the second equation in Eq. (7). It is the values of the numerator and χ at resonances, which are shown in Table 1, that define the slopes of the dispersion curves, and hence possible bandwidths. Targeted structures are at most Np=λ/40 in size with the bandwidth exceeding 4%. For structures with small cell sizes p, Eq. (7) indicates that high ω R  values satisfy COND1, i.e., low CR and LR values, since for n&lt;0 resonances occur at χ values near 4 in Table 1, in other terms (1−χ/4→0).
 
     As previously indicated, once the dispersion curve slopes have steep values, then the next step is to identify suitable matching. Ideal matching impedances have fixed values and may not require large matching network footprints. Here, the word “matching impedance” refers to a feed line and termination in the case of a single side feed such as in antennas. To analyze an input/output matching network, Zin and Zout can be computed for the TL circuit in  FIG. 4B . Since the network in  FIG. 3  is symmetric, it is straightforward to demonstrate that Zin=Zout. It can be demonstrated that Zin is independent of N as indicated in the equation below: 
                       Zin   2     =       BN   CN     =       BI     C   ⁢           ⁢   1       =       Z   Y     ⁢     (     1   -     χ   4       )             ,           Eq   .           ⁢     (   8   )                 
which has only positive real values. One reason that B1/C1 is greater than zero is due to the condition of |AN|≦1 in Eq. (4), which leads to the following impedance condition:
 
0 ≦−ZY=χ≦ 4.
 
The 2 nd  broadband (BB) condition is for Zin to slightly vary with frequency near resonances in order to maintain constant matching. Remember that the real input impedance Zin′ includes a contribution from the CL series capacitance as stated in Eq. (3). The 2 nd  BB condition is given below:
 
     
       
         
           
             
               
                 
                   
                     COND 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   : 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       2 
                       ed 
                     
                     ⁢ 
                     BB 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     condition 
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     near 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     resonances 
                   
                   , 
                   
                     
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Zin 
                       
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                       
                     
                     ⁢ 
                     
                       | 
                       
                         near 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         res 
                       
                     
                     ⁢ 
                     
                       &lt;&lt; 
                       1. 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     Different from the transmission line example in  FIG. 2  and  FIG. 3 , antenna designs have an open-ended side with an infinite impedance which poorly matches the structure edge impedance. The capacitance termination is given by the equation below: 
                       Z   T     =     AN   CN       ,           Eq   .           ⁢     (   10   )                 
which depends on N and is purely imaginary. Since LH resonances are typically narrower than RH resonances, selected matching values are closer to the ones derived in the n&lt;0 region than the n&gt;0 region.
 
     One method to increase the bandwidth of LH resonances is to reduce the shunt capacitor CR. This reduction can lead to higher ω R  values of steeper dispersion curves as explained in Eq. (7). There are various methods of decreasing CR, including but not limited to: 1) increasing substrate thickness, 2) reducing the cell patch area, 3) reducing the ground area under the top cell patch, resulting in a “truncated ground,” or combinations of the above techniques. 
     The MTM TL and antenna structures in  FIGS. 1 and 5  use a conductive layer to cover the entire bottom surface of the substrate as the full ground electrode. A truncated ground electrode that has been patterned to expose one or more portions of the substrate surface can be used to reduce the area of the ground electrode to less than that of the full substrate surface. This can increase the resonant bandwidth and tune the resonant frequency. Two examples of a truncated ground structure are discussed with reference to  FIGS. 8 and 11 , where the amount of the ground electrode in the area in the footprint of a cell patch on the ground electrode side of the substrate has been reduced, and a remaining strip line (via line) is used to connect the via of the cell patch to a main ground electrode outside the footprint of the cell patch. This truncated ground approach may be implemented in various configurations to achieve broadband resonances. 
       FIG. 8  illustrates one example of a truncated ground electrode for a four-cell MTM transmission line where the ground electrode has a dimension that is less than the cell patch along one direction underneath the cell patch. The ground conductive layer includes a via line that is connected to the vias and passes through underneath the cell patches. The via line has a width that is less than a dimension of the cell path of each unit cell. The use of a truncated ground may be a preferred choice over other methods in implementations of commercial devices where the substrate thickness cannot be increased or the cell patch area cannot be reduced because of the associated decrease in antenna efficiencies. When the ground is truncated, another inductor Lp ( FIG. 9 ) is introduced by the metallization strip (via line) that connects the vias to the main ground as illustrated in  FIG. 8 .  FIG. 10  shows a four-cell antenna counterpart with the truncated ground analogous to the TL structure in  FIG. 8 . 
       FIG. 11  illustrates another example of a MTM antenna having a truncated ground structure. In this example, the ground conductive layer includes via lines and a main ground that is formed outside the footprint of the cell patches. Each via line is connected to the main ground at a first distal end and is connected to the via at a second distal end. The via line has a width that is less than a dimension of the cell path of each unit cell. 
     The equations for the truncated ground structure can be derived. In the truncated ground examples, the shunt capacitance CR becomes small, and the resonances follow the same equations as in Eqs. (1), (5) and (6) and Table 1. Two approaches are presented.  FIGS. 8 and 9  represent the first approach, Approach 1, wherein the resonances are the same as in Eqs. (1), (5) and (6) and Table 1 after replacing LR by (LR+Lp). For |n|≠0, each mode has two resonances corresponding to (1) ω±n for LR being replaced by (LR+Lp) and (2) ω±n for LR being replaced by (LR+Lp/N) where N is the number of unit cells. Under this Approach 1, the impedance equation becomes: 
                       Zin   2     =       BN   CN     =         B   ⁢           ⁢   1       C   ⁢           ⁢   1       =       Z   Y     ⁢     (     1   -       χ   +     χ   P       4       )     ⁢       (     1   -   χ   -     χ   P       )       (     1   -   χ   -       χ   P     /   N       )               ,     
     ⁢       where   ⁢           ⁢   χ     =         -   YZ     ⁢           ⁢   and   ⁢           ⁢   χ     =     -     YZ   P           ,           Eq   .           ⁢     (   11   )                 
where Zp=jωLp and Z, Y are defined in Eq. (2). The impedance equation in Eq. (11) provides that the two resonances ω and ω′ have low and high impedances, respectively. Thus, it is easy to tune near the ω resonance in most cases.
 
     The second approach, Approach 2, is illustrated in  FIGS. 11 and 12  and the resonances are the same as in Eqs. (1), (5), and (6) and Table 1 after replacing LL by (LL+Lp). In the second approach, the combined shunt inductor (LL+Lp) increases while the shunt capacitor CR decreases, which leads to lower LH frequencies. 
     The above exemplary MTM structures are formed on two metallization layers and one of the two metallization layers is used as the ground electrode and is connected to the other metallization layer through a conductive via. Such two-layer CRLH MTM TLs and antennas with a via can be constructed with a full ground electrode as shown in  FIGS. 1 and 5  or a truncated ground electrode as shown in  FIGS. 8 and 10 . 
     SLM and TLM-VL MTM structures described here simplify the above two-layer-via design by either reducing the two-layer design into a single metallization layer design or by providing a two-layer design without the interconnecting vias. SLM and TLM-VL MTM structures may be used to reduce device cost and simplify manufacturing. Specific examples and implementations of such SLM MTM structures and TLM-VL MTM structures are described below. 
     A SLM MTM structure, despite its simpler structure, can be implemented to perform functions of a two-layer CRLH MTM structure with a via connected to a truncated ground. In a two-layer CRLH MTM structure with a via connecting the two metallization layers, the shunt capacitance CR is induced in the dielectric material between the cell patch on the top layer and the ground metallization on the bottom layer and the value of CR tends to be small with the truncated ground electrode in comparison with a design that has a full ground electrode. 
     A SLM MTM structure can be formed in a single conductive layer to have various circuit components and the ground electrode. In one implementation, a SLM MTM structure includes a dielectric substrate having a first substrate surface and an opposite substrate surface, a metallization layer formed on the first substrate surface and patterned to have two or more metallization parts to form a single-layer metamaterial structure within the metallization layer without a conductive via penetrating the dielectric substrate. The metallization parts in the metallization layer include a first metal patch as a unit cell patch of the SLM MTM structure, a second metal patch as a ground electrode for the unit cell and spatially separated from the unit cell patch, a via metal line that interconnects the ground electrode and the unit cell patch, a signal feed line that electromagnetically coupled to the unit cell patch without being directly in contact with the unit cell patch. 
     Therefore, there is no dielectric material vertically sandwiched between two metallization parts in this SLM MTM structure. As a result, the shunt capacitance CR of the SLM MTM structure is negligibly small with a proper design. A small shunt capacitance can still be induced between the cell patch and the ground electrode, both of which are in the single metallization layer. The shunt inductance LL in the SLM MTM structure is negligible due to the absence of the via penetrating the substrate, but the inductance Lp can be relatively large due to the via metal line in the metallization layer connected to the ground electrode. 
       FIGS. 13( a )-13( c )  show an example of a one-cell SLM MTM antenna, showing the 3D view, top view of the top layer and side view, respectively. This one-cell SLM MTM antenna is formed on a substrate  1301 . A top metallization layer is formed on the top surface of the substrate  1301  and is patterned to form components of the SLM cell and the ground electrode for the SLM cell. 
     More specifically, the top metallization layer is patterned into various metal parts: a top ground electrode  1324 , a metal patch  1308  as a cell patch which is spaced from the top ground electrode  1324 , a launch pad  1304  separate from the cell patch  1308  by a coupling gap  1328 , and a via line  1312  that interconnects the top ground electrode  1324  and the cell patch  1308 . A feed line  1316  is formed in the top metallization layer and is connected to the launch pad  1304  to direct a signal to or receive a signal from the cell patch  1308 . This single metallization layer design eliminates the need for a truncated ground formed on the bottom surface of the substrate  1301  and a conductive via that penetrates through the substrate  1301  to connect the cell patch  1308  and the truncated ground. 
     In the illustrated example, the bottom surface of the substrate  1301  has a bottom metallization layer that is not used to construct a component of the SLM MTM structure. This bottom metallization layer is patterned to form a bottom ground electrode  1325  that occupies a portion of the substrate  1301  while exposing another portion of the bottom surface of the substrate  1301 . The cell patch  1308  of the SLM MTM structure formed in the top metallization layer is located above the portion of the bottom surface that is free of the bottom metallization and is not above the bottom ground electrode  1325  to eliminate or minimize the shunt capacitance associated with the cell patch  1308 . The top ground electrode  1324  is formed above the bottom ground electrode  1325  so that a co-planer waveguide (CPW) feed  1320  can be formed in the top electrode ground  1324 . This CPW feed  1320  is connected to the feed line  1316  to direct a signal to or receive a signal from the cell patch  1308 . Therefore, in this particular example, the CPW ground is formed by top and bottom ground planes or electrodes  1324  and  1325  and the bottom ground electrode  1325  is provided to achieve the CPW design for the feed line. In other implementations where the above particular CPW design is not used, the bottom ground electrode  1325  can be eliminated. For example, the antenna formed by the SLM MTM structure can be fed with a CPW line that does not require a bottom ground electrode  1325  and is supported by the top ground electrode  1324  only, or a probed patch, or a cable connector. 
     To a certain extent, the present SLM MTM antenna can be viewed as a MTM structure in which the via and via line in a two-layer MTM antenna are replaced with a via line located on the top metallization layer. The position and length of the via line  1312  can be designed to produce desired impedance matching conditions and to produce desired one or more frequency bands. 
     Notably, in this one-cell SLM MTM antenna structure, the portion of the bottom surface of the substrate  1301  underneath the cell patch  1308  is free of a metal part and there is no truncated ground or metallization areas directly below the cell patch  1308  on the bottom layer of the substrate  1301 . The feed line  1316  delivers power of an electromagnetic signal from the CPW feed  1320  to the launch pad  1304 , which capacitively couples the electromagnetic signal to the cell patch  1308  through a coupling gap  1328 . The dimension of the gap  1328  can be set based on the design, such as a few mils in one implementation. The cell patch  1308  is connected to the ground electrode  1324  through the via line  1312 . The SLM MTM antenna equivalent circuit is similar to the equivalent circuit for the two-layer CRLH MTM antenna with a via connected to a truncated ground, analyzed in the previous sections, except that the shunt capacitance CR and the shunt inductor LL are negligible but Lp is large in the SLM MTM antenna. 
     Table 2 is a summary for the elements of the one-cell SLM antenna structure shown in  FIGS. 13( a ), 13( b ) and 13( c ) . 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Parameter 
                 Description 
                 Location 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Antenna 
                 Each antenna element comprises an SLM Cell 
                   
               
               
                 Element 
                 connected to the CPW Feed 1320 through a 
               
               
                   
                 Launch Pad 1304 and a Feed Line 1316. 
               
               
                 Feed Line 
                 Connects the Launch Pad 1304 with the CPW 
                 Top Layer 
               
               
                   
                 Feed 1320. 
               
               
                 Launch Pad 
                 Rectangular shape that connects a Cell Patch 
                 Top Layer 
               
               
                   
                 1308 to the Feed Line 1316. There is a 
               
               
                   
                 Coupling Gap 1328 between the Launch Pad 
               
               
                   
                 1304 and Cell Patch 1308. 
               
            
           
           
               
               
               
               
            
               
                 SLM Cell 
                 Cell Patch 
                 Rectangular shape 
                 Top Layer 
               
               
                   
                 Via Line 
                 Line that connects the Cell Patch 
                 Top Layer 
               
               
                   
                   
                 1308 with the top ground 
               
               
                   
                   
                 electrode 1324 
               
               
                   
               
            
           
         
       
     
     The one-cell SLM antenna structure shown in  FIGS. 13( a ), 13( b ) and 13( c )  can be implemented for various applications. For example, design parameters associated with the SLM MTM antenna specifically for WiFi applications can be selected as follows: the substrate  1332  is 20 mm wide and 0.787 mm thick; the material is FR4 with a dielectric constant of 4.4; the feed line  1316  is 0.4 mm wide; the gap between the launch pad  1304  and the edge of the ground electrode  1324  is 2.5 mm; the launch pad  1304  has 3.5 mm in width and 2 mm in length; the cell patch  1308  is 8 mm long and 5 mm wide and is located at 0.1 mm away from the launch pad  1304 ; and the portion of the via line  1312  that connects to the cell patch  1308  is 2 mm offset from the middle length of the cell. 
     The analyses for two-layer MTM structures are described in the previous sections. Similar analyses can be carried out for the case of a truncated ground with a negligible shunt capacitance CR for the one-cell (N=1) SLM MTM antenna. This exemplary antenna with the above parameter values has two frequency bands as illustrated in the simulated return loss in  FIG. 14( a )  and the measured return loss in  FIG. 14( b ) . The lowest band has LH contributions and is centered at 2.45 GHz. This band has a bandwidth of about 100 MHz at −10 dB as shown in  FIG. 14( a ) . The 50-Ω matching occurs at the high-frequency edge of the LH band as illustrated in  FIG. 14( c ) , which shows the simulated input impedance. 
     The above one-cell SLM MTM antenna formed in the single-layer metamaterial structure can be used to construct SLM MTM antennas with two or more electromagnetically coupled cells. Such a SLM MTM antenna includes at least a first cell metal patch formed at a first location on a first substrate surface of a substrate and a second cell metal patch formed at a second location on the first substrate surface, a ground electrode formed at a third location on the first substrate surface that is spaced from the first and second locations as the ground for the first and second cell metal patches, and at least one feed line formed on the first substrate surface and electromagnetically coupled to one of the first and second cell metal patches. For each cell metal patch, a via line is formed on the first substrate surface to include a first end that is connected to the ground electrode and a second end that is connected to the cell metal patch. On the second substrate surface on the opposite side of the first substrate surface, no metal part is formed at a location corresponding to a cell metal patch on the first substrate surface. 
       FIG. 15  illustrates an example of a two-cell SLM MTM antenna, which is similar in structure to the previous one-cell SLM MTM antenna in  FIG. 13( a ) , except that the top ground electrode is extended to the front of the two cell patches  1508 - 1  and  1508 - 2  to connect the two cell patches  1508 - 1  and  1508 - 2  by two separate via lines  1512 - 1  and  1512 - 2  to the top ground electrode. Similar to  FIG. 13( a ) , the bottom surface of the substrate for the two-cell SLM MTM antenna in  FIG. 15  has a bottom metallization layer that is patterned to form a bottom ground electrode which forms the CPW ground with the top ground electrode  1524  and is not used to construct a component of the SLM MTM structure. This bottom metallization layer is patterned with the bottom ground electrode to occupy a portion of the bottom surface of the substrate while exposing another portion of the bottom surface of the substrate. The top ground electrode  1524  and the two SLM cells  1508 - 1  and  1508 - 2  are formed on the top surface of the substrate. The unit cell patches  1508 - 1  and  1508 - 2  in the top metallization layer are located above the portion of the bottom surface that is free of the bottom metallization to eliminate or minimize the shunt capacitance associated with the unit cell patches  1508 - 1  and  1508 - 2 . The bottom ground electrode and the top ground electrode  1524  are used to form the CPW ground to support the CPW feed  1520 . In other implementations where the above particular CPW design that requires the bottom ground electrode is not used, the bottom metallization layer can be eliminated and a CPW line that does not require a bottom ground plane, or a probed patch, or a cable connector can be used to supply signals to or receive signals from the two-cell antenna. 
     Specifically, the cell patch 1 ( 1508 - 1 ) and cell patch 2 ( 1508 - 2 ) of two-cell SLM antenna are located to be next to each other and are separated by a coupling gap 2 ( 1528 - 2 ) to provide electromagnetic coupling therebetween. A launch pad  1504  in the top metallization layer couples the electromagnetic signal to or from the cell patch 1 ( 1508 - 1 ) through a coupling gap 1 ( 1528 - 1 ). A feed line  1516  formed in the top metallization layer connects a grounded CPW feed  1520 , a metal strip that is separated from the ground electrode  1524  by a narrow gap, with the launch pad  1504 . The top ground electrode  1524  has a extended portion or protrusion  1536  located in front of the two cell patches  1508 - 1  and  1508 - 2 . This configuration enables two via lines  1512 - 1  and  1512 - 2  connecting the two cell patches  1508 - 1  and  1508 - 2  to the top ground electrode to be substantially equal in length. 
     The analyses for two-layer MTM structures are described in the previous sections. Similar analyses can be carried out for the case of a truncated ground with a negligible shunt capacitance CR for the two-cell (N=2) SLM MTM antenna. The simulated return loss for the two-cell SLM MTM antenna is shown in  FIG. 16( a ) . The comparison of the return losses between the one-cell design in  FIG. 13( a )  and two-cell designs in  FIG. 15  shows that the lowest and narrow resonance of the two-cell SLM MTM antenna in  FIG. 16( a )  corresponds to higher-order LH modes. The simulated input impedance is shown in  FIG. 16( b ) . 
       FIG. 17  shows an example of three-cell transmission line (TL) in a SLM MTM configuration where only the top metallization layer pattern is shown. The values of the electromagnetic guided wavelengths corresponding to two different resonances in the low frequency region of this TL confirm that the low frequency resonances are indeed in the LH region. This TL structure comprises three cell patches  1728 - 1 ,  1728 - 2  and  1728 - 3  placed in a row with a coupling gap between two adjacent cell patches to provide electromagnetic coupling without direct contact. The cell patches  1728 - 1 ,  1728 - 2  and  1728 - 3  are connected to the ground electrode  1724  through three via lines  1712 - 1 ,  1712 - 2  and  1712 - 3 , respectively. Two feed lines  1716 - 1  and  1716 - 2  are electromagnetically coupled two end cell patches  1708 - 1  and  1708 - 3  as the input and output of the TL. Two CPW feeds  1720 - 1  and  1720 - 2  are connected to the feed lines  1716 - 1  and  1716 - 2 , respectively to deliver some signal power to both ends of the three-cell series, respectively. The rest of the signal power is radiated. The first cell patch  1708 - 1  is capacitively coupled over a coupling gap 1 ( 1728 - 1 ) to a launch pad 1 ( 1704 - 1 ), which is coupled to the CPW feed 1 ( 1720 - 1 ) through the feed line 1 ( 1716 - 1 ). The second cell patch 2 ( 1708 - 2 ) is capacitively coupled to the first cell patch 1 ( 1708 - 1 ) over a coupling gap  1728 - 2 , and the third cell patch  1708 - 3  is capacitively coupled to the second cell patch  1708 - 2  over a coupling gap  1728 - 3 . The other end of the third cell patch  1708 - 3  is coupled to the CPW feed 2 ( 1720 - 2 ) through a launch pad 2 ( 1704 - 2 ) and the feed line 2  1716 - 2 , with a coupling gap 4 ( 1728 - 4 ) between the launch pad 2 ( 1704 - 2 ) and the third cell patch ( 1708 - 3 ). 
     The design parameters are chosen to generate the 1.6 GHz and 1.8 GHz resonances in the simulated return loss as shown in  FIG. 18 . The electromagnetic guided wavelengths corresponding to these two resonances are depicted in  FIGS. 19( a ) and 19( b ) , respectively. In the conventional non-MTM right-hand (RH) RF circuits, the guided wavelength increases as the frequency decreases, thereby making RH RF structures larger for lower frequencies. On the other hand, in the left-hand (LH) MTM RF circuits, the guided wavelength decreases as the frequency decreases. Thus,  FIGS. 19( a ) and 19( b )  confirm that these low resonances are indeed in the LH region. 
     In addition to SLM MTM structures, TLM-VL MTM structures also simplify the structure of a two-layer CRLH MTM antenna with a via connected to a bottom truncated ground by eliminating the via as a via-less (VL) MTM structure. Such a TLM-VL MTM structure can include a dielectric substrate having a first substrate surface and an opposite substrate surface, and a first metallization layer formed on the first substrate surface and patterned to comprise a ground electrode part and a cell metal patch that are spaced from each other. A feed line is formed on the first substrate surface and is electromagnetically coupled to one end of the cell metal patch. This TLM-VL MTM structure includes a second metallization layer formed on the second substrate surface and patterned to include a metal patch located underneath the cell metal patch without being connected to the cell metal patch by a conductive via that penetrates through the dielectric substrate. The metal patch underneath the top cell metal patch can be a truncated ground. When properly configured, such a TLM-VL MTM structure can be operated to achieve the functions of a two-layer CRLH MTM antenna with a via connected to a truncated ground. Different from a SLM MTM structure, a TLM-VL MTM structure exhibits a small but finite shunt capacitance CR between a cell patch on one metallization layer and a second metallization layer due to the dielectric material sandwiched between the cell patch on the top layer and the truncated ground on the bottom layer. The inductance of the inductor Lp associated with the metal via line is relatively large, and the via line is in series with the shunt capacitor CR. The shunt inductance LL in the TLM-VL MTM is negligible due to the absence of the via. LH resonances can be excited in the frequency region below the minimum of [ω sh =1/√(LL CR), ω se =1/√(LR CL)], where LL is defined as (LL+Lp) as in the Approach 2 above. 
     An example of a one-cell TLM-VL antenna is depicted in  FIGS. 20( a )-20( d ) , showing the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. This one-cell TLM-VL antenna structure includes components in top and bottom metallization layers. Referring to  FIG. 20( c ) , the components in the top metallization layer include a top ground electrode  2024 , a CPW feed  2020  formed in a gap in the top ground electrode  2024 , a launch pad  2004 , a feed line  2016  connecting the CPW feed  2020  and the launch pad  2004 , and a cell patch  2008  spaced from the launch pad  2004  by a coupling gap  2028 . The bottom metallization layer is patterned to form the bottom ground electrode  2025  underneath the top ground electrode  2024 , a bottom truncated ground  2036  underneath the cell patch  2008  and a via line  2012  connecting the bottom truncated ground  2036  and the bottom ground electrode  2025 . The feed line  2016  in this example is connected to the CPW feed  2020  that requires a bottom ground plane. Thus, the CPW ground comprises both top and bottom ground electrodes  2024  and  2025  in this example. In other implementations, the antenna can be fed with a conventional CPW line that does not require a bottom ground, with a probed patch, or simply with a cable connector or a microstrip TL. Different from the via-less (VL) design in the SLM MTM structures, a bottom truncated ground  2036  that corresponds to the cell patch on the top surface of the substrate is formed on the bottom surface of the substrate to create a resonating structure. The signal is coupled through the dielectric material between the cell patch  2008  and the bottom truncated ground  2036 . The launch pad  2004  couples the electromagnetic signal to the cell patch  2008  through a coupling gap  2028 . The dimension of the gap  2008  can be a few mils. Because of the presence of the bottom truncated ground  2036  underneath the cell patch  2008 , a shunt capacitor CR is effectuated between the cell patch  2008  and the bottom truncated ground  2036 . The via line  2012  that connects the bottom truncated ground  2036  with the bottom ground electrode  2025  induces an inductance (Lp) that is in series with the shunt capacitor CR as shown in  FIG. 21( b ) . In this example, the shunt inductor LL is negligible because no vias is involved in the structure. In  FIG. 21( b ) , the notation LL represents LL+Lp as in the Approach 2. In a two-layer MTM structure with a via, CR is in parallel with LL, which is induced by the via, as explained in the previous sections with reference to  FIGS. 2, 3, 9 and 12 . The simplified equivalent circuit is reproduced for the latter case in  FIG. 21( a )  for comparison. 
     For the TLM-VL antenna structure in  FIGS. 20( a )-20( d ) , because LL (i.e., Lp) is large and CR is finite, the frequency 
               ω   sh     =     1         L   L     ⁢     C   R                 
is always less than
 
               ω   se     =       1         L   R     ⁢     C   L           .           
The LH resonances occur below the minimum of ω sh  and ω se . The effective permittivity and permeability are given by the following equations respectively:
 
             ɛ   =       -       (       ω   sh   2     -     ω   2       )         L   L     ⁡     (       ω   2     ⁢     ω   sh   2       )           &lt;   0                 μ   =       -       L   R     (         ω   se   2     -     ω   2         ω   2       )       &lt;   0.           
The resonances are derived in a similar way as explained for a two-layer MTM structure with a via, except for the modification explained above and illustrated in  FIGS. 21( a ) and 21( b ) .
 
     The design parameters for the one-cell TLM-VL antenna shown in  FIGS. 20( a )-20( d )  are determined to produce a resonance at 2.4 GHz, which is broad as can be seen from the simulated return loss in  FIG. 22( a ) . To verify that the resonance is indeed triggered by an LH mode, a via is added to connect the center of the cell patch  2008  and the center of the bottom truncated ground  2036 . This procedure is used to determine the location of the lowest LH mode corresponding to the antenna structure with the added via. The antenna with the via does have an LH resonance near 2.4 GHz, as evidenced in  FIG. 22( b ) . In addition,  FIG. 22( a )  shows that, due to the presence of an RH mode near 3.6 GHz, a broadband covering both the WiFi and WiMax bands is achievable using this TLM-VL MTM antenna structure.  FIG. 23  shows the radiation pattern of the one-cell TLM-VL antenna in  FIGS. 20( a )-20( d )  at 2.4 GHz. The pattern is substantially omnidirectional in the X-Z plane since the antenna shape is symmetric with respect to the Y-axis. 
       FIGS. 24( a )-24( d )  illustrate an example of a TLM-VL MTM antenna with a via line  2412  connected to a bottom extended ground electrode  2440  while other elements of this structure in the top metallization layer are similar to those in  FIGS. 20( a )-20( d ) . Referring to  FIG. 24( d ) , the bottom metallization layer is patterned to form the bottom ground electrode  2025  with two integral extended ground parts  2440 . In the illustrated example, the extended ground electrode part  2440  are symmetric extensions on both sides of the bottom truncated ground  2036  and the via line  2412  connects one extended part  2440  to the bottom truncated ground  2036 . Other designs of the bottom ground electrode extensions are also possible. 
       FIG. 25  shows the simulated return loss and the broadband resonance similar to the result in  FIG. 22( a )   for  a device without the extended ground electrode. Different from the TLM-VL MTM antenna in  FIGS. 20( a )-20( d ) , the lowest LH resonance here is generated around 1.3 GHZ, and two RH resonances are generated near 2.8 GHz and 3.8 GHz. The high RH resonances together produce a broadband covering the WiFi and WiMax bands, and the lowest LH resonance can be used to cover a GPS band, for example. 
       FIGS. 26( a ) and 26( b )  show photos of a TLM-VL antenna fabricated based on the design in  FIGS. 24( a )-24( d )  with the extended ground electrode  2440 . The return loss measured for this antenna is depicted in  FIG. 27 , showing similar trends as the simulation result in  FIG. 25 . 
       FIGS. 28( a )-28( d )  provide another example of a one-cell SLM MTM antenna, showing the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. This antenna is specifically designed to produce quad-band resonances for quad-band cell phone applications and is formed by using two top and bottom metallization layers formed on two surfaces of the substrate  2832 . The antenna is formed in the top metallization layer that is patterned to form various components. 
     Referring to  FIG. 28( c ) , the top metallization layer is patterned to include a top ground electrode  2824 , a CPW feed  2820  formed in a gap within the top ground electrode  2824 , a feed line  2816  connected to the CPW feed  2820 , a launch pad  2804  connected to the feed line  2816 , a cell patch  2808  spaced from the launch pad by a coupling gap  2828 , and a via line  2812  that connects the cell patch  2808  to the top ground electrode  2824 . The antenna is fed by a grounded CPW feed  2820  which can be configured to have a characteristic impedance of 50Ω. The feed line  2816  connects the CPW feed  2820  to the launch pad  2804 . The locations of a PCB hole  2840  and a PCB component  2844  are indicated in  FIGS. 28( a )-28( d )  for reference. 
     Referring to  FIG. 28( d ) , the bottom metallization layer is patterned to include the bottom ground electrode  2825 , a tuning metal stub  2836  extended from the bottom ground electrode  2825  and one or more PCB board components  2844 . The pattern of the bottom metallization layer provides a metal free region underneath the cell patch  2808 . 
     In this example the feed line  2816  is 0.5 mm×14 mm. The launch pad  2804  is 0.5 mm×10 mm in total. The cell patch  2808  is capacitively coupled to the launch pad  2804  through a coupling gap  2828  of 0.1 mm (4 mil). The cell patch  2804  is 4 mm×20 mm with a cutout at one corner. The cell patch  2808  is shorted to the ground electrode  2824  through the via line  2812 . The via line width is 0.3 mm (12 mil) and its length is 27 mm in total with two bends. The shape of the ground electrode  2824  is optimized and includes the tuning stub  2836  for better matching in both the cellular band (890-960 MHz) and the PCS/DCS band (1700-2170 MHz). The antenna covers an area of 17 mm×24 mm. Generally, the matching at high frequencies can be improved by bringing the top ground electrode  2824  closer to the launch pad  2804 . On the other hand, in this example, the ground is added near the launch pad on the bottom layer, as indicated as the tuning stub  2836 . Its size is 2.7 mm×17 mm. The substrate is a standard FR4 material with a dielectric constant of 4.4. 
     The HFSS EM simulation software is used to simulate the antenna performance. In addition, some samples are fabricated and characterized by measurements. The simulated return loss is shown in  FIG. 29( a ) , which indicates good matching in both cellular and PCS/DCS bands. Four representative points in this figure are: point 1=(0.94 GHz, −2.94 dB), point 2=(1.02 GHz, −6.21 dB), point 3=(1.75 GHz, −7.02 dB) and point 4=(2.20 GHz, −5.15 dB). The simulated input impedance is plotted in  FIG. 29( b ) . 
     The efficiency measured for the fabricated antenna is plotted in  FIGS. 30( a ) and 30( b ) , which correspond to the cellular band efficiency and the PCS/DCS band efficiency, respectively. The antenna is highly efficient peaking at 52% in the cellular band and 78% in the PCS/DCS band. 
     Cell phones and handheld devices tend to be compact and thus may have complex electromagnetic properties, making the antenna integration difficult. Some antenna modifications can be made in the present implementation to enable stable operation of the antenna inside the device. 
       FIG. 31  shows an exemplary modified SLM MTM antenna structure based on the SLM MTM antenna in  FIGS. 28( a )-28( d ) . The top metallization layer is patterned to include the top ground electrode  2824 , the CPW feed  2820 , the feed line  3116 , the extended launch pad  3152 , the cell patch  3108  and the extended cell patch  3148 , and the via line  3112  connecting the cell patch  3108  to the top ground electrode  2824 . The first modification is to increase the size of the launch pad to provide the extended launch pad  3152  to improve the capacitive component of the antenna impedance. This makes the loop larger in the Smith Chart, deliberately mismatching the antenna in free space. When the antenna is integrated in the device, the loop shrinks due to the loading of components around it. Thus, this scheme makes the antenna better matched when integrated. The second modification is to add an L shaped extended cell patch  3148  to the cell patch  3108 . This increases the capacitive coupling between the cell patch  3108  and the extended cell patch  3152  due to the increased length of the coupling gap  3128 , thereby decreasing the resonant frequency of the low band. 
     Another tuning parameter in the device in  FIG. 31  is the point of contact  3114  between the via line  3112  and the top ground electrode  3124  on the top metallization layer. This contact point  3114  can be moved closer to the feed line  3116  to improve matching in the low band while increasing mismatching in the high band. The opposite effect is seen when the contact point  3114  is moved away from the feed line  3116 . The locations of a PCB hole  3140  and a PCB component  3144  in the bottom metallization layer are indicated in  FIG. 31  for reference. 
     The antenna with the above modifications was fabricated. The measured efficiency of the antenna is shown in  FIGS. 32( a ) and 32( b ) . The antenna is highly efficient peaking at 51% in the cellular band and 74% in the PCS/DCS band. To analyze the effect of reducing the clearance around the antenna, the ground electrode in  FIG. 31  is extended to below the antenna cell and on the side.  FIGS. 33( a ) and 33( b )  summarize the effect on efficiencies, for the cellular band and the PCS/DCS band, respectively. It can be seen from these figures that the antenna performance is affected by the ground extension. 
       FIGS. 34( a )-34( d )  shows an example of a quad-band TLM-VL MTM antenna for cell phone applications, showing the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. This TLM-VL MTM antenna includes a launch pad  3404  and a cell patch  3408  on the top layer without having a via line connecting the cell patch  3408  to the top ground electrode  3424 . On the bottom metallization layer, this TLM-VL MTM antenna includes a bottom truncated ground  3436  and a via line  3412  that connects the bottom truncated ground  3436  to the bottom ground electrode  3425 . The antenna is fed by a grounded CPW feed  3420  formed in the top ground electrode  3424  and a feed line  3416  connecting the CPW feed  3420  to the launch pad  3404 . The feed may be configured to have a characteristic impedance of 50Ω. The locations of a PCB hole  3440  and a PCB component  3444  are also indicated in the figures for reference. 
     In one implementation of this design, the feed line  3416  is comprised of two sections for matching purposes. The first section is 1.2 mm×17.3 mm and the second section is 0.7 mm×5.23 mm. The L-shaped launch pad  3404  is used to provide sufficient coupling to the cell patch  3408  and better impedance matching. One arm of the L-shaped launch pad  3404  is 1 mm×5.6 mm and the other arm is 0.4 mm×3.1 mm. The cell patch  3408  is capacitively coupled to the launch pad  3404  with gaps of 0.4 mm in the longer arm and 0.2 mm in the shorter arm. The cell patch  3408  is 5.4 mm×15 mm, and the bottom truncated ground  3436  is 5.4 mm×10.9 mm. The shunt capacitor CR is induced because of the presence of the bottom truncated ground  3436  underneath the cell patch  3408 . The via line  3412  that connects the bottom truncated ground  3436  with the bottom ground electrode  3425  induces an inductance (Lp) that is in series with CR as shown in  FIG. 21( b ) . The shunt inductor LL is negligible because of no vias involved in the structure. In  FIG. 21( b ) , the notation LL represents LL+Lp as in the Analysis 2. The via line dimension is 0.3 mm×40.9 mm. The via line route is optimized to match both the cellular band (824-960 MHz) and PCS/DCS band (1700-2170 MHz). The antenna covers the area of 15.9 mm×22 mm. The substrate is an FR4 material with a dielectric constant of 4.4. 
     Table 3 provides a summary of the elements of the TLM-VL antenna structure in this example. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Parameter 
                 Description 
                 Location 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Antenna 
                 Each antenna element comprises a cell 
                   
               
               
                 Element 
                 connected to the 50 Ω CPW Feed 3420 via 
               
               
                   
                 a Launch Pad 3404 and a Feed Line 3416. 
               
               
                   
                 Both Launch Pad 3404 and Feed Line 3416 
               
               
                   
                 are located on the top layer of 
               
               
                   
                 Substrate 3432. 
               
               
                 Feed Line 
                 Connects the Launch Pad 3404 with the 
                 Top Layer 
               
               
                   
                 50 Ω CPW Feed 3420. 
               
               
                 Launch 
                 L-shape that couples a Cell Patch 3408 
                 Top Layer 
               
               
                 Pad 
                 to the Feed Line 3416. There is a 
               
               
                   
                 Coupling Gap 3428 between the 
               
               
                   
                 Launch Pad 3404 and the Cell Patch 3408. 
               
            
           
           
               
               
               
               
            
               
                 Cell 
                 Top Cell 
                 Rectangular shape 
                 Top Layer 
               
               
                   
                 Patch 
               
               
                   
                 Bottom 
                 Rectangular shape 
                 Bottom 
               
               
                   
                 Truncated 
                   
                 Layer 
               
               
                   
                 ground 
               
               
                   
                 Via Line 
                 Connects the Bottom 
                 Bottom 
               
               
                   
                   
                 truncated ground 3436 
                 Layer 
               
               
                   
                   
                 with the bottom ground 
               
               
                   
                   
                 electrode 3425. 
               
               
                   
               
            
           
         
       
     
     The HFSS EM simulation software is used to simulate the antenna performance. The simulated return loss is shown in  FIG. 35( a )  and shows good matching in both cellular and PCS/DCS bands. The simulated input impedance is shown in  FIG. 35( b ) . 
     In the above MTM structure examples, each unit cell has a single cell patch that is located at one location. In some implementations, a cell patch may include at least two metal patches located at different locations that are interconnected to effectuate an “extended” cell patch. 
       FIGS. 36( a )-36( d )  show an example of a penta-band MTM antenna with a semi single-layer structure, showing the 3D view, side view, top view of the top layer and top view of the bottom layer, respectively. In this design, a cell includes two metal patches that are respectively formed in the top and bottom metallization layers and are connected by conductive vias. Of the two metal patches, the cell patch  3608  in the top layer is larger in size than the extended cell patch  3644  in the bottom layer and thus is the main cell patch. The extended cell patch  3644  in the bottom layer is not connected to a ground electrode. A via line  3612  is formed in the top layer, the same layer of the cell patch  3608 , to connect the cell patch  3608  to the top ground electrode  3624 . As such, the top ground electrode  3624  is the ground electrode for the cell patch  3608 . Therefore, this device does not have a bottom truncated ground for the cell in the bottom layer. For this reason, this design is a “semi single-layer structure.” 
     More specifically, this MTM antenna has a launch pad  3604  with an added meander line  3652  and a cell patch  3608 , all of which are on the top layer. The cell patch  3608  is extended to an a cell patch extension  3644  in the bottom layer by using one or more vias  3648  to connect the cell patch  3608  on the top and the cell patch extension  3644  on the bottom. The launch pad  3604  may also be extended to an a launch pad extension  3636  in the bottom layer by using one or more vias  3640  to connect the launch pad  3604  on the top and the launch pad extension  3636  on the bottom. The launch pad extension  3636  on the bottom layer can also be referred to as an extended launch pad  3636 , and the cell patch extension  3644  on the bottom layer can also be referred to as an extended cell patch  3644 . The respective vias are referred to as launch pad connecting vias  3640  and cell connecting vias  3648  in the figures. Such extensions can be made to comply with the space requirements while maintaining a certain performance level. 
       FIG. 36( c )  shows the bottom layer that is overlaid with the top layer.  FIG. 36( d )  show the top layer that is overlaid with the bottom layer. 
     The antenna is fed by a grounded CPW feed  3620  with a characteristic impedance of 50Ω. The feed line  3616  connects the CPW feed  3620  to the launch pad  3604 , which has the added meander line  3652 . The cell patch  3608  has a polygonal shape, and capacitively coupled to the launch pad  3604  through a coupling gap  3628 . The cell patch  3608  is shorted to the top ground electrode  3624  on the top layer through the via line  3612 . The via line route is optimized for matching. The substrate  3632  can be made of a suitable dielectric material, e.g., an FR4 material with a dielectric constant of 4.4. 
     Table 4 provides a summary of the elements of the semi single-layer penta-band MTM antenna structure in this example. 
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Parameter 
                 Description 
                 Location 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Antenna 
                 Each antenna element comprises a cell 
                   
               
               
                 Element 
                 connected to the 50 Ω CPW Feed 3620 via 
               
               
                   
                 a Launch Pad 3604 and a Feed Line 3616. 
               
               
                   
                 Both Launch Pad 3604 and Feed Line 3616 
               
               
                   
                 are located on the top layer of 
               
               
                   
                 Substrate 3632. 
               
               
                 Feed Line 
                 Connects the Launch Pad 3604 with the 
                 Top Layer 
               
               
                   
                 50 Ω CPW Feed 3620. 
               
               
                 Launch Pad 
                 Rectangular shaped and is coupled to a 
                 Top Layer 
               
               
                   
                 Cell Patch 3608 through a Coupling Gap 
               
               
                   
                 3628. A Meander Line 3652 is attached to 
               
               
                   
                 the Launch Pad 3604. 
               
               
                 Meander 
                 Added to the Launch Pad 3604. 
               
               
                 Line 
               
               
                 Extended 
                 A rectangular shaped patch that is an 
                 Bottom 
               
               
                 Launch Pad 
                 extension of the Launch Pad 3604. 
                 Layer 
               
               
                 Launch Pad 
                 Vias connecting the Launch Pad 3604 on 
               
               
                 Connecting 
                 the top layer with the Extended Launch 
               
               
                 Vias 
                 Pad 3636 on the bottom layer. 
               
            
           
           
               
               
               
               
            
               
                 Cell 
                 Cell Patch 
                 Polygonal shape 
                 Top Layer 
               
               
                   
                 Extended 
                 A rectangular shaped patch 
                 Bottom 
               
               
                   
                 Cell Patch 
                 that is an extension of the 
                 Layer 
               
               
                   
                   
                 Cell Patch 3608. 
               
               
                   
                 Via Line 
                 Line that connects the Cell 
                 Top Layer 
               
               
                   
                   
                 Patch with the top ground 
               
               
                   
                   
                 electrode 3624. 
               
               
                   
                 Cell 
                 Vias connecting the Cell 
               
               
                   
                 Connecting 
                 Patch 3608 on the top layer 
               
               
                   
                 Vias 
                 with the Extended Cell Patch 
               
               
                   
                   
                 3644 on the bottom layer. 
               
               
                   
               
            
           
         
       
     
     The HFSS EM simulation software is used to simulate the antenna performance. The simulated return loss is shown in  FIG. 37( a ) , and the simulated input impedance is shown in  FIG. 37( b ) . As evidenced by these figures, the LH resonance appears at about 800 MHZ in this example. 
     Penta-band MTM antennas can be constructed based on a single layer. One example of a SLM penta-band MTM antenna is shown in  FIG. 38 , which shows the top view of the top layer. The CPW feed and CPW ground are omitted in this figure. 
     Examples for various parameters in one exemplary implementation are provided below. The launch pad  3804  is rectangular shaped with dimensions of 10.5 mm×0.5 mm. The feed line  3816  delivers power from the CPW feed to the launch pad  3804 , and is 10 mm×0.5 mm. The launch pad  3804  couples capacitively to the cell patch  3808 , which is 32 mm×3.5 mm. The coupling gap  3828  is 0.25 mm in width. There are two cutouts at the corners of the cell patch  3808 . The first cutout is near the launch pad with dimensions of 10.5 mm×0.75 mm. The second cutout is at the top corner of the cell patch  3808  with dimensions of 4.35 mm×0.75 mm. The second cutout is not critical to the performance but is shaped to meet the board outline of a product for the present application. The via line  3812  connects the cell patch  3808  to the CPW ground. The width of the via line  3812  is 0.5 mm. The total length of the via line is 45.9 mm. The via line has seven segments of lengths 0.4 mm, 23 mm, 3.25 mm, 8 mm, 1.5 mm, 8 mm and 1.75 mm, respectively, starting from the cell patch  3808  to the CPW ground. 
     The routing of the via line  3812  is shown in  FIG. 38 . In one implementation, the via line  3812  terminates on the CPW ground at 1 mm away from the feed line  3816 . 
       FIG. 39  shows another example of a SLM penta-band antenna. Only the top view of the top layer is presented and the CPW feed and CPW ground are omitted in this figure. A meander line  3952  is attached to the launch pad  3904 . The total length of the meander is 84.8 mm in this example. The remaining structure can be identical to the one shown in  FIG. 38 . 
     The SLM penta-band antenna shown in  FIG. 38  (without the meander line) creates two distinct bands, as evidenced by the simulated return loss indicated by the line with cross points in  FIG. 40 . The low band has a sufficient bandwidth to meet quad-band cell phone applications but is too narrow to meet the requirement for penta-band cell phone applications. The SLM penta-band antenna with the meander line  3952 , shown in  FIG. 39 , can be used to increase the bandwidth. The length of the meander line  3952  is adjusted to create a resonance at a frequency higher than, but close to the LH resonance. The resulting bandwidth of the two modes is sufficient to cover the low band ranging from 824 MHz to 960 MHz, as can be seen from the simulated return loss indicated by the line with open squares in  FIG. 40 . While in this particular example the meander line  3952  is used to create the additional mode in the low band, it can be used to increase the high band as well if needed, but with a shorter meander line length. Furthermore, it possible to use a spiral, multi-layer meander line or a combination of these to introduce an additional mode. 
     Table 5 provides a summary of the elements of the SLM penta-band MTM antenna structure with a meander line. 
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 Parameter 
                 Description 
                 Location 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 Antenna 
                 Each antenna element comprises a cell 
                   
               
               
                 Element 
                 connected to the 50 Ω CPW Feed via a 
               
               
                   
                 Launch Pad 3904 and Feed Line 3916. 
               
               
                   
                 Both Launch Pad 3904 and Feed Line 3916 
               
               
                   
                 are located on the top of substrate. 
               
               
                 Feed Line 
                 Connects the Launch Pad 3904 with the 
                 Top Layer 
               
               
                   
                 50 Ω CPW Feed. 
               
               
                 Launch 
                 Rectangular shaped and is coupled to a 
                 Top Layer 
               
               
                 Pad 
                 Cell Patch 3908 through a Coupling Gap 
               
               
                   
                 3928. A Meander Line 3952 is attached 
               
               
                   
                 to the Launch Pad 3904. 
               
               
                 Meander 
                 Added to the Launch Pad 3904. 
                 Top layer 
               
               
                 Line 
               
            
           
           
               
               
               
               
            
               
                 Cell 
                 Cell 
                 Polygonal shape 
                 Top Layer 
               
               
                   
                 Patch 
               
               
                   
                 Via Line 
                 Connects the Cell Patch 3908 
                 Top Layer 
               
               
                   
                   
                 with the top ground electrode. 
               
               
                   
               
            
           
         
       
     
       FIG. 41  shows a photo of the antenna prototype of the SLM penta-band MTM antenna with a meander line in  FIG. 39 , fabricated based on a 1 mm FR-4 board.  FIG. 42  shows the measured return loss of the prototype. This antenna has a −6 dB return loss with the bandwidth of 240 MHz (760 MHz-1000 MHz) in the low band and 600 MHz bandwidth in the high band. 
     The measured efficiency is shown in  FIGS. 43( a ) and 43( b )  for the low band and high band, respectively. The peak efficiency in the low-band is 66%, and a near constant 60% efficiency is achieved in the high band. 
     In many practical situations there are space constraints that require a certain routing of traces in the antenna structure. The antenna can be further compacted by using lumped circuit elements, such as capacitors or inductors, to augment the inductance and capacitance involved in the structure.  FIGS. 44, 45 and 46  show such design examples where the SLM penta-band MTM antenna with a meander line in  FIG. 39  is used. 
     In  FIG. 44 , the capacitance between the launch pad  3904  and the cell patch  3908  is enhanced by using a lumped capacitor  4410 . In this example, the gap between the launch pad  3904  and cell patch  3908  is increased from 0.25 mm to 0.4 mm, and the reduced capacitance is compensated for by the added lumped capacitance of 0.3 pF. Instead of increasing the gap, the length of the gap can be reduced and the reduced capacitance can be compensated for by the added lumped capacitance. 
     In  FIG. 45 , a lumped inductor  4510  is added to the via line trace. The length of the via line  3912  is reduced by 24 mm, but the reduced inductance due to the shortened via line  3912  is compensated for by the added lumped inductance of 10 nH. 
     In  FIG. 46 , a lumped inductor  4610  is added and the length of the meander line  3952  is reduced. In this example, the inductor  4610  is coupled at the junction of the meander line  3952  and the launch pad  3904 . By adding an inductance of 23 nH using the lumped inductor  4610 , the printed meander line  3952  required to obtain the low resonance same as the one shown in  FIG. 40  is now reduced from 84.8 mm to 45.7 mm. 
     Since lumped elements do not radiate, the lumped elements can be located at locations where there is little radiation to minimize the impact on the radiation efficiency of the antenna. For example, it is possible to obtain the same resonance with the meander line by adding the inductor  4610  at the beginning or end of the meander line. However, adding the inductor  4610  at the end of the meander line may significantly reduce the radiation efficiency because the end of the meander line has the highest radiation. It should be noted that these lumped element techniques can be combined to achieve further miniaturization. 
       FIG. 47  shows the simulation results for the SLM penta-band MTM antenna loaded with the lumped elements described above. As evidenced in this figure, the bands and bandwidths similar to those in  FIG. 40  can be obtained with the loading techniques described above. 
     In the SLM or TLM-VL MTM antenna examples described so far, the coupling structure for capacitive coupling between the launch pad and cell patch is implemented in a planar fashion, that is, both the launch pad and cell patch are located on the same layer and thus the coupling gap between the two is formed in the same plane. However, the coupling gap can be formed vertically, that is, the launch pad and cell patch can be located on two different layers, thereby forming a vertical, non-planar coupling gap in between. 
     An example of a three-layer MTM antenna with the vertical coupling between a cell patch and a launch pad at different layers is illustrated in  FIGS. 48( a )-48( f ) , showing the 3D view, top view of the top layer, top view of the mid-layer, top view of the bottom layer, top view of the top and mid layers overlaid, and the side view, respectively. As shown in  FIG. 48( f ) , this three-layer MTM structure comprises a top substrate  4832  and a bottom substrate  4833  that are stacked over each other to provide three metallization layers, the top layer on the top surface of the top substrate  4832 , the middle layer between the two substrates  4832  and  4833 , and the bottom layer on the bottom surface of the substrate  4833 . In one implementation, the middle layer may 30 mil (0.76 mm) and the bottom layer is 1 mm. This keeps the overall thickness of 1 mm same as a two-layer structure. 
     The top layer includes a feed line  4816  that connects a CPW feed  4820  to a launch pad  4804 . The CPW feed  4829  can be formed in a CPW structure that has a top ground electrode  4824  and a bottom ground electrode  4825 . Both the feed line  4816  and launch pad  4804  have a rectangular shape with dimensions of 6.7 mm×0.3 mm and 18 mm×0.5 mm, respectively. The mid layer includes an L-shaped cell patch  4808  which may, in one implementation, have one section with dimensions of 6.477 mm×18.4 mm and the other section with dimensions of 6.0 mm×6.9 mm. A vertical coupling gap  4852  is formed between the launch pad  4804  on the top layer and the cell patch  4808  on the mid layer. A via  4840  is formed in the bottom substrate to couple the cell patch  4808  on the mid layer to a via line  4812  on the bottom layer through a via pad  4844 . The via line  4812  on the bottom layer is shorted to the bottom ground electrode  4825  with two bends, as can be seen from  FIG. 48( d ) . 
     The simulated return loss of the three-layer MTM antenna with the vertical coupling is plotted in  FIG. 49( a ) , which shows two bands at −6 dB return loss: the low band at 0.925-0.99 GHz and the high-band at 1.48-2.36 GHz. 
     The simulated input impedance of the three-layer M™ antenna with the vertical coupling is plotted in  FIG. 49( b ) . Generally, a perfect 50Ω matching corresponds to Real(Zin)=50Ω and Imaginary(Zin)=0 within the operating frequency band, and implies good transfer of energy between the CPW feed and antenna.  FIG. 49( b )  shows that a good matching occurs near 950 MHZ in the low band (LH mode) and near 1.8 GHz in the high band (RH mode). 
     The three-layer MTM antenna with the vertical coupling described above can be modified to include only two layers without vias. An example of such a TLM-VL MTM antenna with the vertical coupling is illustrated in  FIGS. 50( a )-50( c ) , showing the 3D view, top view of the top layer and top view of the bottom layer, respectively. This TLM-VL MTM antenna includes a launch pad  5004  on the top layer and a cell patch  5008  on the bottom layer. A feed line  5016  connects the launch pad  5004  to the CPW feed  5020  formed in the top ground electrode  5024  on the top layer. The vertical coupling gap  5052  is formed between the launch pad  5004  on the top layer and the cell patch  5008  on the bottom layer. Different from the three-layer counterpart, this TLM-VL MTM antenna has a via line  5012  on the same bottom layer as the cell patch  5008  and directly connects the cell patch  5008  to the bottom ground electrode  5025 . 
     The simulated return loss of the TLM-VL MTM antenna with the vertical coupling is plotted in  FIG. 51( a ) , which shows low and high bands. The bandwidth of the high band is narrower than that for the three-layer counterpart, as can be seen upon comparing  FIG. 49( a )  and  FIG. 51( a ) . 
     The simulated input impedance of the TLM-VL MTM antenna with the vertical coupling is plotted in  FIG. 51( b ) , which shows that a good matching occurs near 950 MHZ in the low band (LH mode) but not in the high band (RH mode). 
     Based on the above examples, various CRLH MTM structures can be constructed. One example is a metamaterial device that includes a dielectric substrate having a first surface and a second, different surface; and a composite left and right handed (CRLH) metamaterial structure formed on the substrate. This structure includes a ground electrode on the first surface; a cell patch on the first surface and spaced from the ground electrode; a via line coupling the cell patch with the ground electrode; and a feed line on the first surface and electromagnetically coupled to the cell patch through a gap to direct a signal to or from the cell patch. In one configuration, this structure also includes a cell patch extension formed on the second surface and a conductive via penetrating the substrate to connect the cell patch on the first surface to the cell patch extension on the second surface. In another configuration, this structure can further include a launch pad formed on the first surface and positioned between the feed line and the cell patch. The launch patch is spaced from and electromagnetically coupled to the cell patch and connected to the feed line. A launch pad extension is formed on the second surface and a conductive via that penetrates the substrate to connect the launch pad on the first surface to the launch pad extension on the second surface. 
     Another example for a metamaterial device is a CRLH MTM structure formed on a dielectric substrate having a first surface and a second, different surface. This MTM structure includes a cell patch on the first surface; a top ground electrode spaced from the cell patch and located on the first surface; a top via line on the first surface having a first end connected to the cell patch and a second end connected to the top ground electrode; and a bottom cell ground electrode formed on the second surface beneath the cell patch on the first surface. The bottom cell ground electrode is not directly connected to the cell patch through a conductive via that penetrates through the substrate. This MTM structure also includes a bottom ground electrode formed on the second surface spaced from the bottom cell ground electrode; a bottom via line on the second surface having a first end connected to the bottom cell ground electrode and a second end connected to the bottom ground electrode; a launch pad on the first surface spaced from the cell patch by a gap to electromagnetically coupled to the cell patch; and a feed line connected to the launch pad to direct a signal to or from the cell patch. The second surface is free of a metallization area underneath the cell patch on the first surface. 
     While this specification contains many specifics, these should not be construed as limitations on the scope of an invention or of what may be claimed, but rather as descriptions of features specific to particular embodiments of the invention. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or a variation of a subcombination. 
     Only a few implementations are disclosed. However, it is understood that variations and enhancements may be made.