Patent Publication Number: US-9837695-B2

Title: Surface-wave waveguide with conductive sidewalls and application in antennas

Description:
FIELD 
     The present disclosure relates to waveguides and antennas, and more particularly to a surface-wave waveguide with conductive sidewalls and application of the waveguide in antennas or antenna systems. 
     BACKGROUND 
     A surface-wave (SW) media is any structure that supports a surface wave. SW mediums are a subset of a broader class of meta-materials known as artificial-impedance-surfaces or high-impedance surfaces. An SW medium may support surface waves that are polarized in either transverse electric (TE) or transverse magnetic (TM) modes. The SW index (n SW ) or the SW impedance (Z TE  and Z TM ) characterizes the SW media properties. The simplest form of an SW media is a grounded dielectric sheet. At frequencies less than about 10 or 20 Gigahertz (GHz), the grounded dielectric is not practical because it must be very thick or use a substrate with excessively high permittivity to efficiently support surface waves. An SW waveguide is an SW medium that may be formed by a strip of material including a constant SW index surrounded by an SW medium with a lower index. This structure is effectively a two-dimensional equivalent of a three-dimensional dielectric waveguide. From an optics viewpoint, the SW waveguide may be thought of as a high-index two-dimensional fiber optic transmission line surrounded by a lower index medium. The high-index and low-index regions of an SW waveguide may be realized with high and low-permittivity materials. In the case of an SW waveguide, the high-index and low-index region can be realized with metallic patches varying in size and/or shape on a dielectric substrate. SW waveguides can be used for transmitting SW power in applications, such as two-dimensional wireless power transmission for feeding structures like artificial-impedance-surface antennas (AISAs) and for controlling SW scattering. However, current SW waveguides can leak power out the sides and the AISA array elements have to be spaced more than about 1/λ (wavelength of the radiating element or antenna) apart in order to prevent grading side lobes in the radiation pattern. The wide spacing also reduces the scan angle in a direction perpendicular to a plane of the SW waveguide or measured from a plane of the waveguide. 
     SUMMARY 
     In accordance with an embodiment, a surface-wave (SW) waveguide may include a base conductive ground plane including opposite side edges and a pair of conductive side walls. One conductive side wall extends from each side edge of the conductive ground plane. The SW waveguide may also include a substrate including a dielectric material disposed on the base conductive ground plane and between the conductive side walls. The SW waveguide may additionally include an impedance sheet disposed on the substrate and between the conductive side walls. The impedance sheet may include a predetermined impedance characteristic for transmitting an electromagnetic wave. 
     In accordance with another embodiment, an antenna system may include a plurality of radiating elements configured to transmit and receive electromagnetic energy. Each of the radiating elements may include an SW waveguide. The SW waveguide may include a base conductive ground plane including opposite side edges and a pair of conductive side walls. One conductive side wall extends from each side edge of the base conductive ground plane. The SW waveguide may also include a substrate including a dielectric material disposed on the base conductive ground plane and between the conductive side walls. The SW waveguide may additionally include an impedance sheet disposed on the substrate and between the conductive side walls. The impedance sheet comprises a predetermined impedance characteristic for transmitting an electromagnetic wave. 
     In accordance with a further embodiment, a method for electronically steering an antenna system may include transmitting an electromagnetic wave along an SW waveguide. The SW waveguide may include a base conductive ground plane including opposite side edges and a pair of conductive side walls. One conductive side wall extends from each side edge of the conductive ground plane. The SW waveguide may also include a substrate comprising a dielectric material disposed on the base conductive ground plane and between the conductive side walls. The SW waveguide may additionally include an impedance sheet disposed on the substrate and between the conductive side walls. The impedance sheet may include a predetermined impedance characteristic for transmitting an electromagnetic wave and the impedance sheet may include a tunable element. The method may also include tuning the tunable element to scan a main radiation lobe of a radiation pattern generated by the antenna system over a range of angles in a direction perpendicular to a plane of the antenna system. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF DRAWINGS 
       The following detailed description of embodiments refers to the accompanying drawings, which illustrate specific embodiments of the disclosure. Other embodiments having different structures and operations do not depart from the scope of the present disclosure. 
         FIG. 1A  is a perspective view of an example of an SW waveguide including conductive side walls in accordance with an embodiment of the present disclosure. 
         FIG. 1B  is an end view of the exemplary SW waveguide of  FIG. 1A . 
         FIG. 1C  is a top view of the exemplary SW waveguide of  FIG. 1A  including an impedance sheet that can be modulated or tuned in accordance with an embodiment of the present disclosure. 
         FIG. 2  is a perspective view of an example of an SW waveguide assembly including a waveguide feed section in accordance with an embodiment of the present disclosure. 
         FIG. 3A  is a perspective view of an example of a waveguide assembly including a waveguide feed section and a coaxial feed connector integrated into the waveguide feed section in accordance with an embodiment of the present disclosure. 
         FIG. 3B  is an end view of the exemplary SW waveguide of  FIG. 3A . 
         FIG. 4A  is a top view of an example of an SW waveguide including a modulated impedance sheet and vias formed in the conductive side walls in accordance with an embodiment of the present disclosure. 
         FIG. 4B  is a side view of the exemplary SW waveguide of  FIG. 4A . 
         FIG. 5A  is a perspective view of an example of an SW waveguide including conductive side walls and a center conductor in accordance with an embodiment of the present disclosure. 
         FIG. 5B  is an end view of the exemplary SW waveguide of  FIG. 5A . 
         FIG. 6  is a block schematic diagram of an example of an antenna system in accordance with an embodiment of the present disclosure. 
         FIG. 7  is a schematic diagram of an example of an antenna system including SW waveguides with conductive side walls in accordance with an embodiment of the present disclosure. 
         FIG. 8  is an example of a method of operation of an antenna system including surface waveguides with conductive sides in accordance with an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description of embodiments refers to the accompanying drawings, which illustrate specific embodiments of the disclosure. Other embodiments having different structures and operations do not depart from the scope of the present disclosure. Like reference numerals may refer to the same element or component in the different drawings. 
     In accordance with an exemplary embodiment, an SW waveguide includes side walls that confine a surface-wave propagating along the waveguide to remain within a well-defined channel. The side walls of the SW waveguide do not allow surface-wave power to leak out the sides of the waveguide. The side walls also permit the SW waveguide to be made narrower than previous SW waveguides without side walls. Narrower waveguides are advantageous for use with SW waveguide artificial-impedance-surface antenna (AISA) arrays where the AISA array elements have to be spaced closer than ½λ apart in order to prevent grating side lobes in the radiation pattern of the antenna. Where λ is the wavelength of the radiating elements of the AISA array. A narrow SW waveguide in an AISA array that prevents grating side lobes allows the antenna to be scanned to much higher scan angles because the radiation pattern from a narrower SW AISA extends farther to each side of the antenna. 
     The exemplary embodiments described herein enable the design of antennas, for example satellite communications antennas (SATCOM) and other antennas, that are electronically-steerable AISAs. The AISAs do not have side lobes and include a higher scan angle than other AISAs that cannot be spaced closer than ½λ. The exemplary SW waveguide AISA embodiments described herein may be made with a width less than about ½λ or narrower. The ½λ spacing or less between the antenna array elements eliminates side grating lobes. As the width gets smaller, the SW waveguide radiation pattern broadens out in the direction of its width. This facilitates scanning to high angles relative to the SW waveguide axis or plane defined the radiating surface of the SW waveguide. 
       FIG. 1A  is a perspective view of an example of an SW waveguide  100  including conductive side walls  102  and  104  (as best shown in  FIG. 1B  and  FIG. 1C ) in accordance with an embodiment of the present disclosure.  FIG. 1B  is an end view of the exemplary SW waveguide  100  of  FIG. 1A  and  FIG. 1C  is top view of the exemplary SW waveguide  100  of  FIG. 1A  including an example of an impedance sheet  106  that can be modulated or tuned in accordance with another embodiment of the present disclosure. 
     The SW waveguide  100  may include a base conductive ground plane  108  as best shown in  FIG. 1B . The base conductive ground plane  108  may include opposite side edges  110  and  112 . The base conductive ground plane  108  may be any conductive material capable of conducting electrical or magnetic energy. The conductive ground plane  108  may also be a semiconductor material in another exemplary embodiment. The pair of conductive side walls  102  and  104  may respectively extend from each side edge  110  and  112  of the conductive ground plane  108 . The conductive side walls  102  and  104  may be any conductive material capable of conducting electrical and magnetic energy. The conductive side walls  102  and  104  may also be a semiconductor material in another exemplary embodiment. 
     A substrate  114  may be disposed on the base conductive ground plane  108  and between the conductive side walls  102  and  104 . The substrate  114  may be a dielectric material. The substrate material can be any plastic, glass or electronic substrate such as those used by printed circuit board fabricators. In another embodiment, the substrate  114  may include or may be replaced by an air core. The air core replacing the substrate  114  will reduce SW propagation loss that may be caused by radio frequency (RF) losses in the substrate  114 . 
     An impedance sheet  106  may be disposed on the substrate  114  and between the conductive side walls  102  and  104 . The impedance sheet  106  may include a predetermined impedance characteristic for transmitting an electromagnetic wave. One method of producing an impedance sheet is to print conductive patches and/or form other components, such as for example, variable reactive components as described herein on top of the substrate  114 . In an embodiment, the predetermined impedance characteristic of the impedance sheet  106  may have constant impedance across a surface of the substrate  114  or length and width of the impedance sheet  106 . In another embodiment, the predetermined impedance characteristic of the impedance sheet  106  may vary across the sheet  106 , such as along at least a length or longest dimension of the impedance sheet  106 . 
     As described in more detail herein, the impedance sheet  106  may be formed with different elements or impedance elements  107 , such as radiating elements and tunable elements that permit the impedance sheet  106  to be modulated. In an AISA, the impedance or elements  107  of the impedance sheet  106  may be periodically modulated to produce radiation from a surface electromagnetic wave propagating along the SW waveguide  100 . The impedance elements  107  of the impedance sheet  106  may be fixed or may be tunable through application of a voltage to variable reactive elements built into the impedance sheet  106 . Examples of such impedance sheets are described in U.S. patent application Ser. No. 13/934,553, filed Jul. 3, 2014 and which is assigned to the same assignee as the present application and is incorporated herein by reference. 
     In another embodiment, the impedance sheet  106  may include an array of metallic patches  116  similar to that shown in  FIG. 1C  or similar to the embodiment described with reference to  FIG. 4A  herein. In the exemplary embodiment illustrated in  FIG. 1C , the impedance sheet  106  may include a plurality of metallic patches  116  disposed adjacent one another at a predetermined distance “D”. A tunable impedance element  118  or variable reactive element may be electrically connected between adjacent metal patches  116 . Examples of the tunable impedance element  118  or variable reactive element may include, but is not necessarily limited to a varactor, a liquid crystal element, a tunable material element comprising barium strontium nitrate or other tunable impedance element capable of modulating or tuning the impedance sheet  106  to provide the performance characteristics described herein, such as for example steering a main lobe or beam of a radiation pattern of an AISA. As described in more detail herein the tunable impedance element  118  may be configured to be tuned by a voltage being connected to at least one of the adjacent metallic patches  116  or by electric field or magnetic field being coupled to the tunable impedance element  118 . The metallic patches  116  may be uniform and may have the same length and width dimensions and may be uniformly spaced from one another. In another embodiment, the metallic patches  116  may be different sizes and may have different shapes depending on what performance characteristics may be desired. The metallic patches  116  or radiating elements may also be at a varying spacing form one another. For example, the spacing between the metallic patches  116  may alternate between a long and short spacing. 
     The SW waveguide  100  including side walls  102  and  104  guides a surface wave  120  along a confined path or SW channel defined by the impedance sheet  106  between the side walls  102  and  104 . As previously described, the side walls  102  and  104  prevent RF power from leaking from the impedance sheet  106  or channel. The surface wave  120  may be excited and coupled to external RF transmission lines by one of various exemplary arrangements. Referring also to  FIG. 2  and  FIGS. 3A and 3B , these figures illustrate examples of mechanisms for coupling to and exciting a surface wave on an SW waveguide similar to waveguide  100 .  FIG. 2  is a perspective view of an example of an SW waveguide assembly  200  including a waveguide feed section  202  in accordance with an embodiment of the present disclosure. The SW waveguide assembly  200  in  FIG. 2  may include a waveguide similar to the SW waveguide  100  in  FIGS. 1A-1C . In the exemplary embodiment in  FIG. 2 , the SW waveguide  100  may be terminated by a waveguide feed section  202 . The waveguide feed section  202  may be a rectangular waveguide section  202  as illustrated in  FIG. 2 . The waveguide feed section  202  includes a first end  204  that has a shape and size that corresponds to a shape and size of an end of the SW waveguide  100  to matingly contact the end of the SW waveguide  100 . The waveguide feed section  202  may be formed by top and bottom conductive walls  206  and  208  and side conductive walls  210  and  212 . The top conductive wall  206  of the waveguide feed section  202  may correspond to and contact or join the impedance sheet  106 . The bottom conductive wall  208  may correspond to and may contact or join the base conductive ground plane  108 . The side conductive wall  210  may correspond to and may contact or join the conductive side wall  102  of the waveguide  100  and the side conductive wall  212  of the waveguide feed section  202  may correspond to and may contact or join the conductive side wall  112  of the SW waveguide  100 . A waveguide aperture  214  is at an opposite end or second end of the waveguide feed section  202  from the first end  204  of the waveguide feed section  202  that interfaces with or joins the SW waveguide  100 . The first end  204  defines a feed of the waveguide feed section  202  where an electromagnetic wave is transmitted from the waveguide feed section  202  to the SW waveguide  100 . The waveguide feed section  202  may be connected to standard waveguide feed components in any of a number of arrangement. For example, the width and height of the waveguide feed section  202  may be tapered from the SW waveguide  100  dimensions to the dimensions of a standard waveguide section. 
       FIG. 3A  is a perspective view of an example of an SW waveguide assembly  300  including a waveguide feed section  302  and a coaxial connector  304  integrated into the waveguide feed section  302  in accordance with an embodiment of the present disclosure.  FIG. 3B  is an end view of the exemplary SW waveguide assembly  300  of  FIG. 3A . The SW waveguide assembly  300  in  FIG. 3A  may include a waveguide similar to the SW waveguide  100  in  FIGS. 1A-1C . In the exemplary embodiment in  FIG. 3A , the SW waveguide  100  may be terminated by a waveguide feed section  302 . The waveguide feed section  302  may be similar to the waveguide feed section  202  in  FIG. 2 . However, the waveguide feed section  302  is terminated by a conductive end cap  306  rather than an aperture  214 . A coaxial feed connector  304  is integrated into the waveguide feed section  302 . A center conductor  308  in the coaxial connector  304  is used to excite surface waves in the SW waveguide  100  in response to an electromagnetic signal being transmitted by a coaxial transmission line (not shown in  FIGS. 3A and 3B ) connected to the coaxial connector  304 , or a surface wave signal may be extracted by the center conductor  308  in response to an electromagnetic signal being received by elements  107  of the SW waveguide  100  as described herein. While the coaxial connector  304  is shown in the exemplary embodiment in  FIGS. 3A and 3B  as entering a bottom conductive wall of the waveguide feed section  302 , the coaxial connector  304  may also enter the waveguide feed section  302  through any of the other walls or through the end cap  306 . 
       FIG. 4A  is a top view of an example of an SW waveguide  400  including a modulated impedance sheet  402  and vias  404  (as best shown in  FIG. 4B ) formed in the conductive side walls  405  in accordance with an embodiment of the present disclosure. Other exemplary embodiments may have only the modulated impedance sheet  402  or only the vias  404 .  FIG. 4B  is a side view of the exemplary SW waveguide  400  of  FIG. 4A . The SW waveguide  400  may be similar to the SW waveguide  100  of  FIG. 1  except the impedance sheet  106  in  FIG. 1  may be realized by the impedance sheet  402  that includes an array of conductive patches  406  on top of the substrate  114 . The conductive side walls  102  and  104  in  FIG. 1  may be replaced by conductive vias  404  that are electrically connected through the dielectric substrate  114  from the base conductive ground plane  108  to a metallic strip  408  that may connect an opposite end or top of the vias  404  to each other on each side of the SW waveguide  400  as shown in  FIG. 4A . The SW waveguide  400  including the vias  404  may define a substrate integrated waveguide (SIW) with a top conductor replaced by a patterned metal representing the impedance sheet  402 . The exemplary embodiment in  FIGS. 4A and 4B  may also be terminated by a waveguide feed section  410  including an integrated coaxial connector  412  that may be similar to the waveguide feed section  302  with integrated coaxial connector  304 . The waveguide assembly  400  could also be terminated by a waveguide feed section  410  similar to waveguide feed section  202  in  FIG. 2  or by some other mechanism for propagating a surface wave in the waveguide assembly  400 . The waveguide feed section  410  may also include conductive vias  414  (best shown in  FIG. 4B ) that electrically connect between a bottom wall  416  and an upper wall  418  of the waveguide feed section  410 . 
     The SW impedance (Z SW ) and the corresponding SW index (n SW ) for the exemplary SW waveguides described herein may be determined by the geometric dimensions of the SW waveguides, the impedance of the impedance sheet (Z sheet ), and the dielectric properties by solving the walled-SW waveguide transverse-resonance method (TRM) equation (equation 1) for n SW : 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Where k 0  is the wavenumber of free-space radiation with the same frequency as the surface wave. Z 0 , Z sub  and Z sheet  are the impedance of free space, the dielectric substrate and the impedance sheet respectively. n sub  and d are the refractive index and thickness of the dielectric substrate, respectively. w is the width of the SW waveguide. When the impedance sheet is realized as an array of conductive patches, Z sheet  is determined from the patch geometry and the substrate properties. 
       FIG. 5A  is a perspective view of an example of an SW waveguide  500  including conductive side walls  102  and  104  and a center conductor  506  in accordance with an embodiment of the present disclosure.  FIG. 5B  is an end view of the exemplary SW waveguide  500  of  FIG. 5A . The SW waveguide  500  may be similar to the SW waveguide  100  in  FIGS. 1A and 1B  except including the center conductor  506  embedded within the dielectric substrate  114 . The center conductor  506  may extend substantially the entire length of the SW waveguide  500  or only partially the length of the waveguide  500 . The center conductor  506  may have a substantially rectangular cross-section as shown in the exemplary embodiment in  FIGS. 5A and 5B . In other embodiments, the center conductor  506  may have another cross-section, such as for example, square, round or some other shape. The center conductor  506  may be fed by a coaxial connector  508  shown by broken lines in  FIGS. 5A and 5B  or by another suitable arrangement. The center conductor  506  allows the SW waveguide  500  to be narrower than other waveguides without a center conductor because the SW waveguide  500  with the center conductor  506  does not have a low frequency cutoff. As previously discussed, narrower SW waveguides are advantageous for antenna arrays of SW waveguide AISAs because the waveguides can be spaced less than about ½λ apart. Adjacent SW waveguides may also share a common side wall in AISAs. 
       FIG. 6  is a block schematic diagram of an example of an antenna system  600  in accordance with an embodiment of the present disclosure. The antenna system  600  may include antenna  602 , a voltage controller  604 , a phase shifter  606 , and a radio frequency module  608 . The antenna  602  may be an artificial impedance surface antenna (AISA)  610  in this illustrative example. 
     The antenna  602  may be configured to transmit and/or a receive radiation pattern  612 . Further, the antenna  602  may be configured to electronically control the radiation pattern  612 , such as the direction of scan or angle of a main lobe of the radiation pattern  612 . When the antenna  602  is used for transmitting, radiation pattern  612  may be the strength of the radio waves transmitted from the antenna  602  as a function of direction. Radiation pattern  612  may be referred to as a transmitting pattern when antenna  602  is used for transmitting. When antenna  602  is used for receiving, radiation pattern  612  may be the sensitivity of antenna  602  to radio waves as a function of direction. Radiation pattern  612  may be referred to as a receiving pattern when the antenna  602  is used for receiving. The transmitting pattern and receiving pattern of antenna  602  may be identical. Consequently, the transmitting pattern and receiving pattern of the antenna  602  may be simply referred to as radiation pattern  612 . 
     Radiation pattern  612  may include main lobe  616  and one or more side lobes. Main lobe  616  may be the lobe at the direction in which antenna  602  is being directed. When antenna  602  is used for transmitting, main lobe  616  is located at the direction in which antenna  602  transmits the strongest radio waves to form a radio frequency beam. When antenna  602  is used for transmitting, main lobe  616  may also be referred to as the primary gain lobe of radiation pattern  612 . When antenna  602  is used for receiving, main lobe  616  is located at the direction in which antenna  602  is most sensitive to incoming radio waves. 
     In this illustrative example, antenna  602  is configured to electronically steer main lobe  616  of radiation pattern  612  in a desired direction  614 . The main lobe  616  of radiation pattern  612  may be electronically steered by controlling phi steering angle  618  and theta steering angle  620  at which main lobe  616  is directed. Phi steering angle  618  and theta steering angle  620  are spherical coordinates. When antenna  602  is operating in an X-Y plane, phi steering angle  618  is the angle of main lobe  616  in the X-Y plane relative to the X-axis. Further, theta steering angle  620  is the angle of main lobe  616  relative to a Z-axis that is orthogonal to the X-Y plane. 
     Antenna  602  may operate in the X-Y plane by having an array of radiating elements  622  that lie in the X-Y plane. As used herein, an “array” of items may include one or more items arranged in rows and/or columns. In this illustrative example, the array of radiating elements  622  may be a single radiating element or a plurality of radiating elements. In one illustrative example, each radiating element in the array of radiating elements  622  may take the form of an artificial impedance surface, surface wave waveguide structure. The SW waveguide structure may be similar to one of those previously described with conductive side walls. 
     Radiating element  623  may be an example of one radiating element in the array of radiating elements  622 . Radiating element  623  may be configured to emit radiation that contributes to radiation pattern  612 . 
     As depicted, radiating element  623  may be implemented using a dielectric substrate  624 . Radiating element  623  may include one or more surface wave channels that are formed on the dielectric substrate  624 . For example, radiating element  623  may include a surface wave channel  625 . Surface wave channel  625  may be configured to constrain the path of surface waves propagated along dielectric substrate  624 , and surface wave channel  625  in particular. The surface wave channel  625  may be defined by an impedance sheet, such as the impedance sheet  106  disposed on the dielectric substrate  114  and between the two conductive side walls  102  and  104  in the exemplary SW waveguide  100  described with reference to  FIGS. 1A-1C . 
     In one illustrative example, the array of radiating elements  622  may be positioned substantially parallel to the X-axis and arranged and spaced along the Y-axis. Further, when more than one surface wave channel is formed on a dielectric substrate, these surface wave channels may be formed substantially parallel to the X-axis and arranged and spaced along the Y-axis. 
     In this illustrative example, impedance elements and tunable elements located on a dielectric substrate may be used to form each surface wave channel of a radiating element in the array of radiating elements  622 . For example, surface wave channel  625  may be comprised of a plurality of impedance elements  626  and a plurality of tunable elements  628  located on the surface of the dielectric substrate  624  similar to that previously described with reference to  FIG. 1C . Together, the plurality of impedance elements  626 , plurality of tunable elements  628 , and dielectric substrate  624  form an artificial impedance surface from which radiation or electromagnetic signals may be transmitted or likewise received by the impedance sheet or SW channel  625 . 
     An impedance element of the plurality of impedance elements  626  may be implemented in a number of different ways. In one illustrative example, an impedance element may be implemented as a resonating element. In one illustrative example, an impedance element may be implemented as an element comprised of a conductive material. The conductive material may be, for example, without limitation, a metallic material. Depending on the implementation, an impedance element may be implemented as a metallic strip, a patch of conductive paint, a metallic mesh material, a metallic film, a deposit of a metallic substrate, or some other type of conductive element. In some cases, an impedance element may be implemented as a resonant structure such as, for example, a split-ring resonator (SRR), an electrically-coupled resonator (ECR), a structure comprised of one or more metamaterials, or some other type of structure or element. 
     Each one of plurality of tunable elements  628  may be an element that can be controlled, or tuned, to change an angle of the one or more surface waves being propagated along radiating element  623 . In this illustrative example, each of the plurality of tunable elements  628  may be an element having a capacitance that can be varied based on the voltage applied to the tunable element. 
     In one illustrative example, a plurality of impedance elements  626  may take the form of a plurality of metallic strips  632  and a plurality of tunable elements  628  may take the form of a plurality of varactors  634 . Each of plurality of varactors  634  may be a semiconductor element diode that has a capacitance dependent on the voltage applied to the semiconductor element diode. 
     In one illustrative example, the plurality of metallic strips  632  may be arranged in a row that extends along the X-axis. For example, the plurality of metallic strips  132  may be periodically distributed on the dielectric substrate  624  along the X-axis. The plurality of varactors  634  may be electrically connected to the plurality of metallic strips  632  on the surface of dielectric substrate  624 . In particular, at least one varactor of the plurality of varactors  634  may be positioned between each adjacent pair of metallic strips of the plurality of metallic strips  632 . Further, the plurality of varactors  634  may be aligned such that all of the varactor connections on each metallic strip have the same polarity. 
     The dielectric substrate  624 , plurality of impedance elements  626 , and plurality of tunable elements  628  may be configured with respect to a selected design configuration  636  for the surface wave channel  625 , and radiating element  623  in particular. Depending on the implementation, each radiating element in the array of radiating elements  622  may have a same or different selected design configuration. 
     As depicted, selected design configuration  636  may include a number of design parameters such as, but not limited to, impedance element width  638 , impedance element spacing  640 , tunable element spacing  642 , and substrate thickness  644 . Impedance element width  638  may be the width of an impedance element in the plurality of impedance elements  626 . Impedance element width  638  may be selected to be the same or different for each of plurality of impedance elements  626 , depending on the implementation. 
     Impedance element spacing  640  may be the spacing of the plurality of impedance elements  626  with respect to the X-axis. Tunable element spacing  642  may be the spacing of the plurality of tunable elements  628  with respect to the X-axis. Further, substrate thickness  644  may be the thickness of the dielectric substrate  624  on which a particular waveguide is implemented. 
     The values for the different parameters in the selected design configuration  636  may be selected based on, for example, without limitation, the radiation frequency at which antenna  602  is configured to operate. Other considerations include, for example, the desired impedance modulations for antenna  602 . 
     Voltages may be applied to the plurality of tunable elements  628  by applying voltages to the plurality of impedance elements  626  because the plurality of impedance elements  626  may be electrically connected to the plurality of tunable elements  628 . In particular, the voltages applied to the plurality of impedance elements  626 , and thereby the plurality of tunable elements  628 , may change the capacitance of the plurality of tunable elements  628 . Changing the capacitance of the plurality of tunable elements  628  may, in turn, change the surface impedance of the antenna  602 . Changing the surface impedance of the antenna  602  changes the radiation pattern  612  produced. 
     In other words, by controlling the voltages applied to the plurality of impedance elements  626 , the capacitances of the plurality of tunable elements  628  may be varied. Varying the capacitances of the plurality of tunable elements  628  may vary, or modulate, the capacitive coupling and impedance between the plurality of impedance elements  626 . Varying, or modulating, the capacitive coupling and impedance between the plurality of impedance elements  626  may change the theta steering angle  620  of the antenna  602 . 
     The voltages may be applied to the plurality of impedance elements  626  using voltage controller  604 . Voltage controller  604  may include a number of voltage sources  646 , number of grounds  648 , number of voltage lines  650 , and/or some other type of component. In some cases, voltage controller  604  may be referred to as a voltage control network. 
     A voltage source in the number of voltage sources  646  may take the form of, for example, without limitation, a digital to analog converter (DAC), a variable voltage source, or some other type of voltage source. The grounds  648  may be used to ground at least a portion of the plurality of impedance elements  626 . The voltage lines  650  may be used to transmit voltage from the respective voltage sources  646  and/or grounds  648  to the plurality of impedance elements  626 . 
     In one illustrative example, each of the plurality of impedance elements  626  may receive voltage from one of the number of voltage sources  646 . In another illustrative example, a portion of the plurality of impedance elements  626  may receive voltage from the number of voltage sources  646  through a corresponding portion of the number of voltage lines  650 , while another portion of the plurality of impedance elements  626  may be electrically connected to respective ones of the number of grounds  648  through a corresponding portion of the number of voltage lines  650 . 
     In some cases, the controller  651  may be used to control the number of voltage sources  646 . Controller  651  may be considered part of or separate from antenna system  600 , depending on the implementation. Controller  651  may be implemented using a microprocessor, an integrated circuit, a computer, a central processing unit, a plurality of computers in communication with each other, or some other type of computer or processor. 
     Surface waves  652  propagated along the array of radiating elements  622  may be coupled to a number of transmission lines  656  by a plurality of surface wave feeds  630  located on the dielectric substrate  624 . A surface wave feed of the plurality of surface wave feeds  630  may be any device that is capable of converting a surface wave into a radio frequency signal and/or a radio frequency signal into a surface wave. In one illustrative example, a surface wave feed of the plurality of surface wave feeds  630  is located at the end of each waveguide in the array of radiating elements  622  on dielectric substrate  624 . Similar to that previously described, the surface wave feeds  630  may be a waveguide feed section similar to waveguide feed sections  202  and  302  in  FIGS. 2 and 3A  respectively. 
     For example, when antenna  602  is in a receiving mode, the one or more surface waves propagating along radiating element  623  may be received at a corresponding surface wave feed of the plurality of surface wave feeds  630  and converted into a corresponding radio frequency signal  654 . Radio frequency signal  654  may be sent to the radio frequency module  608  over one or more transmission lines  656 . Radio frequency module  608  may then function as a receiver and process radio frequency signal  654  accordingly. 
     Depending on the implementation, radio frequency module  608  may function as a transmitter, a receiver, or a combination of the two. In some illustrative examples, radio frequency module  608  may be referred to as transmit/receive module  658  or transceiver. 
     In some cases, radio frequency signal  654  may pass through the phase shifter  606  prior to being sent to radio frequency module  608 . Phase shifter  606  may include any number of phase shifters, power dividers, transmission lines, and/or other components configured to shift the phase of radio frequency signal  654 . In some cases, phase shifter  606  may be referred to as a phase-shifting network. 
     When antenna  602  is in a transmitting mode, radio frequency signal  654  may be sent from radio frequency module  608  to antenna  602  over the transmission lines  156 . In particular, radio frequency signal  654  may be received at one of the plurality of surface wave feeds  630  and converted into one or more surface waves that are then propagated along a corresponding waveguide in the array of radiating elements  622 . 
     In this illustrative example, the relative phase difference between the plurality of surface wave feeds  630  may be changed to change a phi steering angle  618  of the radiation pattern  612  that is transmitted or received. Thus, by controlling the relative phase difference between the plurality of surface wave feeds  630  and controlling the voltages applied to the tunable elements of each waveguide in array of radiating elements  622 , the phi steering angle  618  and theta steering angle  620 , respectively, may be controlled. In other words, antenna  602  may be electronically steered in two dimensions. The phi steering angle may be defined as controlling the angular direction of a main beam of the radiation pattern of the antenna  602  in a plane corresponding to the plane of the antenna  602  or in an X-Y coordinate plane. The theta steering angle may be defined as controlling the angular direction of the main beam of the radiation pattern in a direction perpendicular to the plane of the antenna  602  or in an X-Z coordinate plane. 
     Depending on the implementation, radiating element  623  may be configured to emit linearly polarized radiation or circularly polarized radiation. When configured to emit linearly polarized radiation, the plurality of metallic strips used for each surface wave channel on radiating element  623  may be angled in the same direction relative to the X-axis along which the plurality of metallic strips are distributed. Typically, only a single surface wave channel is needed for each radiating element  623 . 
     However, when radiating element  623  is configured for producing circularly polarized radiation, surface wave channel  625  may be a first surface wave channel and a second surface wave channel  645  may also be present in radiating element  623 . Surface wave channel  625  and second surface wave channel  645  may be about 90 degrees out of phase from each other. The interaction between the radiation from these two coupled surface wave channels makes it possible to create circularly polarized radiation. 
     The plurality of impedance elements  626  that form surface wave channel  625  may be a first plurality of impedance elements that radiate with a polarization at an angle to the polarization of the surface wave electric field. A second plurality of impedance elements that form a second surface wave channel  645  may radiate with a polarization at an angle offset about 90 degrees as compared to surface wave channel  625 . 
     For example, each impedance element in the first plurality of impedance elements of surface wave channel  625  may have a tensor impedance with a principal angle that is angled at a first angle relative to an X-axis of radiating element  623 . Further, each impedance element in the second plurality of impedance elements of the second surface wave channel  645  may have a tensor impedance that is angled at a second angle relative to the X-axis of the corresponding radiating element. The difference between the first angle and the second angle may be about 90 degrees. 
     The capacitance between the first plurality of impedance elements may be controlled using plurality of tunable elements  628 , which may be a first plurality of tunable elements. The capacitance between the second plurality of impedance elements may be controlled using a second plurality of tunable elements. 
     As a more specific example, the plurality of metallic strips  632  on surface wave channel  625  may be angled at about positive 45 degrees with respect to the X-axis along which plurality of metallic strips  632  is distributed. However, the plurality of metallic strips used for second surface wave channel  645  may be angled at about negative 45 degrees with respect to the X-axis along which the plurality of metallic strips is distributed. This variation in tilt angle produces radiation of different linear polarizations, that when combined with a 90 degree phase shift, may produce circularly polarized radiation. 
     The illustration of antenna system  600  in  FIG. 1  is not meant to imply physical or architectural limitations to the manner in which an illustrative embodiment may be implemented. Other components in addition to or in place of the ones illustrated may be used. Some components may be optional. Also, the blocks are presented to illustrate some functional components. One or more of these blocks may be combined, divided, or combined and divided into different blocks when implemented in an illustrative embodiment. 
     For example, in other illustrative examples, phase shifter  606  may not be included in antenna system  600 . Instead, the transmission lines  656  may be used to couple the plurality of surface wave feeds  630  to a number of power dividers and/or other types of components, and these different components to radio frequency module  608 . In some examples, the transmission lines  656  may directly couple the plurality of surface wave feeds  630  to the radio frequency module  608 . 
     In some illustrative examples, a tunable element of the plurality of tunable elements  628  may be implemented as a pocket of variable material embedded in dielectric substrate  124 . As used herein, a “variable material” may be any material having a permittivity that may be varied. The permittivity of the variable material may be varied to change, for example, the capacitance between two impedance elements between which the variable material is located. The variable material may be a voltage-variable material or any electrically variable material, such as, for example, without limitation, a liquid crystal material or barium strontium titanate (BST). 
     In other illustrative examples, a tunable element of the plurality of tunable elements  628  may be part of a corresponding impedance element of the plurality of impedance elements  626 . For example, a resonant structure having a tunable element may be used. The resonant structure may be, for example, without limitation, a split-ring resonator, an electrically-coupled resonator, or some other type of resonant structure. 
       FIG. 7  is a schematic diagram of an example of an antenna system  700  including an array of SW waveguides  702   a - 702   n  with conductive side walls  704  in accordance with an embodiment of the present disclosure. The antenna system  700  may be used for the antenna system  600  of  FIG. 6 . The array of SW waveguides  702   a - 702   n  may form an AISA  706 . The SW waveguides  702   a - 702   n  may be similar to any of the SW waveguides with conductive side walls described herein or other SW waveguide assembly that include conductive side walls. Accordingly, the SW waveguides  702   a - 702   n  may be similar to the SW waveguide  100  described with reference to  FIGS. 1A-1C , SW waveguide  200  in  FIG. 2 , SW waveguide  300  in  FIG. 3A , SW waveguide  400  in  FIGS. 4A-4B , SW waveguide  500  in  FIGS. 5A-5B  or other SW waveguide including conductive side walls similar to that described herein. As depicted in  FIG. 7 , the adjacent SW waveguides  702   a - 702   n  may share a common side wall  704  that permits the adjacent SW waveguides  702   a - 702   n  to be spaced less than about ½λ apart in an array of SW AISAs. In another embodiment, the side walls  704  of adjacent SW waveguides  702   a - 704   n  may abut one another rather than share a common side wall. 
     In the exemplary embodiment illustrated in  FIG. 7 , the SW waveguides  702   a - 704   n  may each include a impedance sheet  708  similar to the impedance sheet  106  described with reference to  FIG. 1C . However, other impedance sheets similar to those described herein or other configurations may also be used depending upon the particular performance and radiation pattern characteristics desired. In the exemplary embodiment of  FIG. 7 , the impedance sheet  708  may include a plurality of metallic patches  710 . The metallic patches  710  may also be referred to as radiating elements. The metallic patches  710  may be spaced from one another at a uniform distance or may be spaced according to a particular pattern, such as alternating wide and narrow spacing. The metallic patches  710  may also be the same width or may have different widths, such as for example alternating wide and narrow widths. At least one tunable element  712  or variable reactive element may be electrically connected between adjacent metallic patches  710 . Examples of the tunable element  712  or variable reactive element may include, but is not necessarily limited to a varactor, a liquid crystal element, a tunable material element comprising barium strontium nitrate or other tunable impedance element capable of modulating or tuning the impedance sheet  708  to provide certain performance characteristics, such as those described herein, for example, steering a main lobe or beam of a radiation pattern of the SW AISA  706 . As described in more detail herein the tunable element  712  may be configured to be tuned by a voltage being connected to at least one of the adjacent metallic patches  710  or by electric field or magnetic field being coupled to the tunable element  712 . 
     The antenna system  700  may also include a controller  714  and voltage controller  716  configured to control a voltage or voltages applied to the tunable elements  712  and/or metallic patches  710  for controlling operation and steering of the SW AISA  706 . The controller  714  may be similar to the controller  651  described with reference to  FIG. 6  and the voltage controller  716  may be similar to voltage controller  604 . The voltage controller  716  may include a digital-to-analog converter  718 . 
     The antenna system  700  may also include a radio frequency (RF) transceiver  720  that may be coupled to the SW AISA  706  by a plurality of transmission lines  722  and a phase shifter  724 . The RF transceiver  720  may be similar to the RF module  608  of  FIG. 6  and the phase shifter  724  may be similar to the phase shifter  606  in  FIG. 6 . The RF transceiver  720  may transmit and receive electromagnetic or RF signals to and from the SW AISA  706  via the transmission lines  722  and phase shifter  724  similar to that described with respect to the exemplary embodiment of  FIG. 6 . 
       FIG. 8  is an example of a method  800  of operation of an antenna system including SW waveguides with conductive sides in accordance with an embodiment of the present disclosure. The method  800  may be embodied in and performed by the system  600  of  FIG. 6 or 700  of  FIG. 7 . In block  802 , an electromagnetic signal may be transmitted along an SW waveguide of an AISA array. The SW waveguide may include a tunable impedance sheet disposed between conductive side walls similar to that described herein. The tunable impedance sheet may include a plurality of electromagnetic radiating elements and tunable elements associated with the radiating elements. 
     In block  804 , a radiation pattern may be generated by the SW AISA in response to the electromagnetic signal. 
     In block  806 , the tunable elements of the impedance sheet may be electronically tuned to scan or steer a main radiation lobe of the radiation pattern over a range of angles in a direction perpendicular to a plane of the antenna (theta direction). A control voltage may be applied to the tunable element associated with each radiating element to scan or steer the antenna. 
     In block  808 , the main lobe may be electronically steered in a plane of the SW AISA (phi direction) by controlling a relative phase difference between a plurality of SW feeds of the SW AISA. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of embodiments of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to embodiments of the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of embodiments of the invention. The embodiment was chosen and described in order to best explain the principles of embodiments of the invention and the practical application, and to enable others of ordinary skill in the art to understand embodiments of the invention for various embodiments with various modifications as are suited to the particular use contemplated. 
     Although specific embodiments have been illustrated and described herein, those of ordinary skill in the art appreciate that any arrangement which is calculated to achieve the same purpose may be substituted for the specific embodiments shown and that embodiments of the invention have other applications in other environments. This application is intended to cover any adaptations or variations of the present invention. The following claims are in no way intended to limit the scope of embodiments of the invention to the specific embodiments described herein.