Patent Publication Number: US-11385384-B2

Title: Spoke dielectric lens

Description:
BACKGROUND 
     1. Technical Field 
     The field of the invention relates generally to antenna systems, and more specifically, to dielectric lenses for antenna systems. 
     2. Prior Art 
     Electronic devices utilize antennas to communicate using electromagnetic (EM) signals. In general, data may be represented using an EM signal, and the EM signal may be provided from an antenna of a first electronic device to an antenna of another electronic device via wireless transmission. 
     In general, for long distance communication, an EM signal from an antenna may be focused using a reflector antenna (e.g., a parabolic dish), an antenna array, or a dielectric lens antenna, such as a gradient index (GRIN) dielectric lens. Typically, a reflector antenna, antenna array, or dielectric lens antenna may be heavy and large, which may cause mobility problems and increase cost. However, reducing the size of a reflector antenna, antenna array, or a dielectric lens antenna may reduce the gain of the transmitted EM signal, which will degrade signal quality of wireless transmission. As such, there is a need for a cost-effective advanced antenna design that addresses these issues. 
     SUMMARY 
     A spoke dielectric lens is disclosed that comprises a center portion that extends along a cylinder having a central axis and a plurality of spoke portions that are attached to the center portion and extend to a spherical perimeter region in a radial direction from the center portion. The plurality of spoke portions includes at least a first monolithic spoke portion extending from the center portion to the spherical perimeter region and the center portion and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions. The center portion, the cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in a gradient index (GRIN) lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     Also disclosed is a spoke dielectric lens comprising a center portion that extends along a cylinder having a central axis and a plurality of spoke layers. Each spoke layer of the plurality of spoke layers is attached to another spoke layer of the plurality of spoke layers in a stack-up fashion along the cylinder and each spoke layer comprises a plurality of spoke portions that are attached to the cylinder and extend to a spherical perimeter region in a radial direction from the cylinder. The plurality of spoke portions includes at least a first monolithic spoke portion extending from the cylinder to the spherical perimeter region. The cylinder and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions. The cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in a GRIN lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     Other devices, apparatuses, systems, methods, features, and advantages of the invention will be or will become apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional devices, apparatuses, systems, methods, features, and advantages be included within this description, be within the scope of the invention, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The invention may be better understood by referring to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. In the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1A  is a perspective view of an example of an implementation of a spoke dielectric lens in accordance with the present disclosure. 
         FIG. 1B  is a top view of the spoke dielectric lens in accordance with the present disclosure. 
         FIG. 1C  is an expanded view of the center portion, shown in  FIGS. 1A and 1B , showing the relationship between the center portion and cylinder. 
         FIG. 1D  is a section view along a cutting plane AA′ in accordance with the present disclosure. 
         FIG. 1E  is an expanded view of a spoke portion of the spoke dielectric lens in accordance with the present disclosure. 
         FIG. 1F  is a top view showing another spoke portion adjacent to the spoke portion, shown in  FIGS. 1D and 1E , in accordance with the present disclosure. 
         FIG. 2  is a perspective view of an example of another implementation of a spoke dielectric lens in accordance with the present disclosure. 
         FIG. 3A  is a perspective view of an example of another implementation of a spoke dielectric lens in accordance with the present disclosure. 
         FIG. 3B  is a perspective exploded view of the spoke dielectric lens shown in  FIG. 3A  in accordance with the present disclosure. 
         FIG. 3C  is a perspective view of an example of an implementation of a spoke layer of the spoke dielectric lens shown in  FIGS. 3A and 3B  in accordance with the present disclosure. 
         FIG. 3D  is a top view of two adjacent spoke portions of the spoke layer shown in  FIG. 3C  in accordance with the present disclosure. 
         FIG. 4  is a perspective exploded view of an example of an implementation of another spoke dielectric lens in accordance with the present disclosure. 
         FIG. 5  is a perspective view of an example of an implementation of yet another spoke dielectric lens in accordance with the present disclosure. 
         FIG. 6A  is a perspective exploded view of the spoke dielectric lens shown in  FIG. 6  in accordance with the present disclosure. 
         FIG. 6B  is a perspective view of an example of an implementation of a spoke layer of the spoke dielectric lens shown in  FIG. 6A  in accordance with the present disclosure. 
         FIG. 7A  is a perspective view of an example of an implementation of another spoke dielectric lens in accordance with the present disclosure. 
         FIG. 7B  is a perspective exploded view of the spoke dielectric lens shown in  FIG. 7A  in accordance with the present disclosure. 
         FIG. 8  is a perspective view of a radome for use with the spoke dielectric lens shown in  FIGS. 1A-7B . 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed is a spoke dielectric lens. The spoke dielectric lens comprises a center portion that extends along a cylinder having a central axis and a plurality of spoke portions that are attached to the center portion and extend to a spherical perimeter region in a radial direction from the center portion. The plurality of spoke portions includes at least a first monolithic spoke portion extending from the center portion to the spherical perimeter region and the center portion and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions. The center portion, the cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in a gradient index (GRIN) lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     Also disclosed is a spoke dielectric lens comprising a center portion that extends along a cylinder having a central axis and a plurality of spoke layers. Each spoke layer is attached to another spoke layer of the plurality of spoke layers in a stack-up fashion along the cylinder and each spoke layer comprises a plurality of spoke portions that are attached to the cylinder and extend to a spherical perimeter region in a radial direction from the cylinder. The plurality of spoke portions includes at least a first monolithic spoke portion extending from the cylinder to the spherical perimeter region and the cylinder and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions. The cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in the GRIN lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     In this disclosure, the disclosed spoke dielectric lens may be a spherical or hemispherical GRIN dielectric lens that include, for example, a Luneburg, fisheye lens, or Maxwell fisheye lens. 
     In  FIG. 1A , a perspective view of an example of an implementation of a spoke dielectric lens  100  is shown in accordance with the present disclosure. The spoke dielectric lens  100  includes a cylinder  102  of a center portion along a central axis  104  and a plurality of spoke portions  106  that are attached to the cylinder  102  of the center portion and extend to a spherical perimeter region  108  in a radial direction  110  from the cylinder  102  of the center portion. In this example, the plurality of spoke portions  106  includes at least a first monolithic spoke portion  112  extending from the cylinder  102  of the center portion to the spherical perimeter region  108  and the cylinder  102  of the center portion and the plurality of spoke portions  106  define a plurality of cavity regions  114  among the plurality of spoke portions  106 . As used herein, the term “monolithic” spoke portion refers to a spoke portion that includes a contiguous region including at least some material forming an approximate straight line. The center portion, the cylinder  102 , the plurality of spoke portions  106 , and the plurality of cavity regions  114  are included in a GRIN spoke dielectric lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     In this example, the central axis  104  is shown as aligned with a Z-axis while each of the spoke portions of the plurality of spoke portions  106  are shown as extending outward in the radial direction  110  along an X-axis or Y-axis normal to the central axis  104 . The spherical perimeter region  108  is located at an outer radius  116  of the spoke dielectric lens  100 , where the outer radius is at a maximum radial distance (R max ) of a radius extending from the center portion to the spherical perimeter region  108 . 
     In  FIG. 1B , a top view of the spoke dielectric lens  100  is shown in accordance with the present disclosure. In this example, the cylinder  102  is shown at the center portion  118 . In  FIG. 1C , an expanded view  120  of the center portion  118  is shown showing the relationship between the center portion  118  and cylinder  102 . In this example, the first monolithic spoke portion  112  is shown extending from the cylinder  102  to the outer radius  116  of the spherical perimeter region  108  along a radial direction in a positive direction of the X-axis. Additionally, a second monolithic spoke portion  122  is also shown extending from the cylinder  102  to the outer radius  116  of the spherical perimeter region  108  along a radial direction in the opposite (i.e., negative) direction of the X-axis. In this example, the number (N) of spoke portions in the plurality of spoke portions  106  may vary based on the design of the spoke dielectric lens  100 . The number N is related to the minimum width of the spoke portions and a frequency associated with the operation of GRIN lens. In general, the number N relates to the minimum width of the spoke portions where having more spoke portions means that the spoke portions are narrower. Generally, a larger N is beneficial, but this may be limited by the manufacturing processes. Moreover, the greater the frequency associated with the operation of GRIN lens, the higher the value of N. 
     In this example, the spoke dielectric lens  100  is shown as having a cutting plane AA′ that passes through first monolithic spoke portion  112 , second monolithic spoke portion  122 , and cylinder  102  and extends along the X and Z axes. In  FIG. 1D , a section view along a cutting plane AA′ is shown in accordance with the present disclosure. Again, the first monolithic spoke portion  112  is shown extending from the cylinder  102  to the outer radius  116  of the spherical perimeter region  108  along a radial direction in a positive direction of an X-Z plane of the X-axis and Z-axis and the second monolithic spoke portion  122  is shown extending from the cylinder  102  to the outer radius  116  of the spherical perimeter region  108  along a radial direction in the opposite direction along the X-Z plane. In this example, the first monolithic spoke portion  112  and second monolithic spoke portion  122  are generally dielectric semi-circular blades extending outward from the cylinder  102  in opposite directions. The dielectric properties, such as the dielectric constant (i.e., the relative permittivity), of both the first monolithic spoke portion  112  and second monolithic spoke portion  122  generally vary as function of a length  124  along a radius  126  from the center portion  118  to a radial distance  128  that extends outwards towards the outer radius  116 . In this example, the radial distance  128  has a component length (i.e., height (z)  130 ) projected along a length  132  of the of the cylinder  102 . 
     In  FIG. 1E , an expanded view  134  of a spoke portion  136  is shown in accordance with the present disclosure. The expanded view  134  is a top view of the spoke portion which may be, for example, a top view of the first monolithic spoke portion  112 . The spoke portion  136  may have a first width W 1  at a first distance  138  from the cylinder  102  of the center portion  118  and a second width W 2  at a second distance  140  from the cylinder  102 , where the second distance  140  is greater than the first distance  138  and the first width W 1  is different than the second width W 2 . The spoke portion  136  may also include other widths along different distances along the spoke portion  136  such as, for example, a third width W 3  at a third distance  142 . In this example, all the distances (i.e., first distance  138 , second distance  140 , and third distance  142 ) are along the radius  126  from the cylinder  102  to the outer radius  116 . In the example illustrated in  FIG. 1E , the spoke portion  136  is shown as having the second width W 2  that is greater than the first width W 1  and the spoke portion  136  having a tapered profile that increases in width as a function of distance from the cylinder  102  to the outer radius  116 . However, in another example, the spoke portion  136  may have the second width W 2  being less than the first width W 1  and the spoke portion may have a tapered profile that decreases in width as a function of distance from the cylinder  102  to the outer radius  116 . 
     Alternatively, the spoke portion  136  may further include the third width W 3  at a third distance  142  from the cylinder  102 , the third distance  142  greater than the second distance  140 , where the second width W 2  is greater than the first width W 1  and the second width W 2  is also greater than the third width W 2 . In this example, the spoke portion  136  may have a dual-tapered profile that increases in width as a function of distance from the cylinder  102  of the center portion  118  until a particular distance from the center portion  118  and then decreases in width as a function of distance from the center portion  118 . 
     Moreover as another alternative, the spoke portion  136  may have the third width W 3  at a third distance  142  from the center portion  118 , where the third distance  142  is greater than the second distance  140  and the second width W 2  is less than the first width W 1  and the second width W 2  is less than the third width W 3 . In this example, the spoke portion  136  may have a reverse dual-tapered profile that decreases in width as a function of distance from the center portion  118  until a particular distance from the center portion  118  and then increases in width as a function of distance from the center portion  118 . 
     As discussed earlier, the spoke portion  136  is constructed of a material or materials that have optional varying dielectric constant. It is appreciated by those of ordinary skill in the art that the dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space and that it is an expression of the extent to which a material concentrates electric flux such that as the dielectric constant increases, the electric flux density increases. 
     Specifically, the spoke portion  136  is constructed of a material that includes width (w), the height (z)  130 , and the length  124  along the radius (r)  126  extending from the center portion  118  to the outer radius  116 . The width w is equal to a numerical expression defined as 
     
       
         
           
             
               
                 2 
                 ⁢ 
                 π 
                 ⁢ 
                 
                   r 
                   ⁡ 
                   
                     ( 
                     
                       
                         z 
                         2 
                       
                       + 
                       
                         r 
                         2 
                       
                       - 
                       
                         R 
                         max 
                         2 
                       
                     
                     ) 
                   
                 
               
               
                 N 
                 ⁢ 
                 
                   
                     R 
                     max 
                     2 
                   
                   ⁡ 
                   
                     ( 
                     
                       
                         ɛ 
                         rel 
                       
                       - 
                       1 
                     
                     ) 
                   
                 
               
             
             . 
           
         
       
     
     In this expression, R max  is equal to the outer radius  116  of the GRIN lens at the spherical perimeter region  108 , N is equal to a number of spoke portions (such as spoke portion  136 ) in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities. 
     In this example and as discussed earlier, the height z  130  is equal to the component length of the radius r  126  from the center portion  118  projected along the central axis  104 . The number of spoke portions N is related to a frequency of operation associated with the GRIN lens. Moreover, in this example, the plurality of relative permittivities include a continuous range of relative permittivities. 
     In  FIG. 1F , another spoke portion  144  is shown adjacent to the first spoke portion  136  in accordance with the present disclosure. In this example, similar to the first spoke portion  136 , the second spoke portion  144  may have a first width W 4  at the first distance  138  from the cylinder  102  of the center portion  118  and a second width W 5  at the second distance  140  from the cylinder  102 , where the second distance  140  is greater than the first distance  138  and the first width W 4  is different than the second width W 5 . The second spoke portion  144  may also include other widths along different distances along the second spoke portion  144  such as, for example, a third width (not shown) at the third distance  142 . 
     In this example, the first spoke portion  136  and the second spoke portion  144  are approximately adjacent to each other and define, in combination with the cylinder  102  and the spherical perimeter region  108  at the outer radius  116  a cavity region  146  between the first spoke portion  136  and second spoke portion  144  that extends from the cylinder  102  to the spherical perimeter region  108 . The cavity region  146  has a first width W 1C  at the first distance  138  from the center portion  118  and a second width W 2C  at the second distance  140  from the center portion  118 , where the first width W 1C  is different than the second width W 2C . 
     Similar to the first spoke portion  136 , the second spoke portion  144  and cavity region  146  may have tapered profiles. Specifically, the cavity region  146  may have a tapered profile that increases in width as a function of distance from the center portion  118 , where the second width W 2C  is greater than the first width W 1C . Alternatively, the cavity region  146  may have a tapered profile that decreases in width as a function of distance from the center portion  118 , where the second width W 2C  is less than the first width W 1C . 
     In these examples, the cavity region  146  may be empty (i.e., air or vacuum gap) or filled with a dielectric material that is different than the dielectric material of the first spoke portion  136  and second spoke portion  144 , where dielectric material of the cavity region  146  has a different dielectric constant then the material utilized to construct the first spoke portion  136  and second spoke portion  144 . It is appreciated by those of ordinary skill in the art that the dielectric constant is the ratio of the permittivity of a material/substance to the permittivity of free space and that it is an expression of the extent to which a material concentrates electric flux such that as the dielectric constant increases, the electric flux density increases. 
     In general, the cylinder  102  of the center portion  118  and plurality of spoke portions  106  define the plurality of cavity regions  114  among the plurality of spoke portions  106 . Additionally, one or more of the plurality of cavity regions  114  may be filled with or may include a material, such as a second material (e.g., a plastic or another material) that is different than a first material included in the plurality of spoke portions  106 . The second material may have a different dielectric constant than the first material. Moreover, the cylinder  102  may be constructed of a material that has a dielectric constant that is greater than dielectric constants associated with the plurality of spoke portions  106 . 
     In general, the cylinder  102  and plurality of spoke portions  106  may be constructed of materials that include, for example, a thermoset plastic, a polycarbonate, a cross-linked polystyrene copolymer, and Polytetrafluoroethylene (“PTFE”). As such, example materials include REXOLITE® and TEFLON®. REXOLITE® 1422 is manufactured by C-Lec Plastics, Inc. of Philadelphia, Pa. TEFLON® is available from The Chemours Company of Wilmington, Del. In this example, the spoke dielectric lens  100  may be formed by injection molding or some other process (e.g. 3-D printing or additive manufacturing). In this example, the spoke dielectric lens  100  may optionally include a radome (shown in  FIG. 8  as radome  800 ) disposed adjacent to the spherical perimeter region  108  of the spoke dielectric lens  100 . 
     As described earlier, the spoke dielectric lens  100  has a plurality of relative permittivities constants that are based on a radial distance  128  from the center portion  118  (e.g., where each radius  126  of the spoke dielectric lens  100  is associated with a particular relative permittivity). As used herein, a relative permittivity refers to an average relative permittivity associated with a portion of the spoke dielectric lens  100 , where the average relative permittivity is affected by the relative permittivities of other portions of the spoke dielectric lens  100 . For example, a relative permittivity may be determined using a weighted average that weights other relative permittivities based on proximity to a given portion of the spoke dielectric lens  100 . In a particular example, a relative permittivity is affected by a relative permittivity of one or more materials used to fabricate the spoke dielectric lens  100  and by a relative permittivity of the plurality of cavity regions  114  of the spoke dielectric lens  100  (which may be approximately equal to one). 
     Specifically, the spoke portions of the plurality of spoke portions  106  have a tapered profile, where a width of a spoke portion varies based on radial distance  128  from the center portion  118  to form the tapered profile. As a result, in this example, the plurality of relative permittivities includes a continuous range of relative permittivities based on tapered profiles of the plurality of spoke portions  106 . Moreover, a “smooth” tapering of the plurality of spoke portions  106  may result in “smooth” transitions of relative permittivities of the spoke dielectric lens  100  (e.g., instead of discontinuous or stepwise changes in relative permittivities). 
     In this example, a number of spoke portions N included in the spoke dielectric lens  100  is related to a frequency associated with the spoke dielectric lens  100 . For example, the number of spoke portions N may be selected based on a particular frequency or frequency range of operation that is to be provided to the spoke dielectric lens  100 . In general, the spoke dielectric lens  100  is configured to focus (e.g., collimate) an EM signal that is to be transmitted or received by the spoke dielectric lens  100 . When integrated into GRIN lens, the GRIN lens is configured to focus EM radiation to transmit or to receive a far-field high-gain signal. In this example, the GRIN lens may be integrated into an antenna having a radome and configured to transmit or receive an EM signal through the GRIN lens. 
     In general, the spoke dielectric lens  100  is a Luneburg lens, however, the spoke dielectric lens  100  may also be configured as a Maxwell fisheye lens. In the case of a Luneburg lens, the spoke dielectric lens  100  is configured as a spherically symmetric GRIN lens with varying refractive index which decreases radially from the center portion  118  to the spherical perimeter region  108  according to the relationship 
     
       
         
           
             
               n 
               = 
               
                 
                   
                     ɛ 
                     rel 
                   
                 
                 = 
                 
                   
                     2 
                     - 
                     
                       
                         ( 
                         
                           r 
                           
                             R 
                             max 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
             
             , 
           
         
       
     
     where n is the refractive index, r is the radius  126 , R max  is the outer radius  116  of the GRIN lens at the spherical perimeter region  108  and ε rel  is a relative permittivity of the plurality of relative permittivities of the GRIN lens. In this example, the Luneburg lens focuses collimated EM radiation incident on the surface of spherical perimeter region  108  to a point on the opposite surface. 
     If the spoke dielectric lens  100  is configured as a Maxwell&#39;s fisheye lens, the spoke dielectric lens  100  will be a spherically symmetric GRIN lens with a varying reflective index that decreases radially from the center portion  118  to the spherical perimeter region  108  according to the relationship 
     
       
         
           
             
               
                 ɛ 
                 rel 
               
               = 
               
                 
                   ɛ 
                   0 
                 
                 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           ( 
                           
                             r 
                             
                               R 
                               max 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     ) 
                   
                   2 
                 
               
             
             , 
           
         
       
     
     where ε 0  is the permittivity at the center portion  118 , r is the radius  126 , R max  is the outer radius  116  of the GRIN lens at the spherical perimeter region  108  and ε rel  is a relative permittivity of the plurality of relative permittivities of the GRIN lens. In this example, the Maxwell&#39;s Fisheye lens focuses each point on the surface of spherical perimeter region  108  to a point on the opposite side of the surface of spherical perimeter region  108 . By cutting the spoke dielectric lens  100  (that is configured as a Maxwell Fisheye lens) in half into a hemisphere, the hemispherical fisheye lens would focus collimate EM radiation incident on the flat surface of hemisphere to a point on the opposite spherical surface of the spherical perimeter region  108 . 
     In the case that the spoke dielectric lens  100  is configured as a Maxwell fisheye lens, the relationship for determining the width w of the spoke portion  136  is different than previously described. The relationship for the width w of the spoke portion  136  for a Maxwell fisheye lens is 
     
       
         
           
             w 
             = 
             
               
                 
                   2 
                   ⁢ 
                   π 
                   ⁢ 
                   
                     r 
                     ⁡ 
                     
                       ( 
                       
                         
                           z 
                           4 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             
                               z 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   r 
                                   2 
                                 
                                 + 
                                 
                                   R 
                                   max 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           r 
                           4 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             r 
                             2 
                           
                           ⁢ 
                           
                             R 
                             max 
                             2 
                           
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 ɛ 
                                 rel 
                               
                               - 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           
                             R 
                             max 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
                 
                   
                     N 
                     ⁡ 
                     
                       ( 
                       
                         
                           ɛ 
                           rel 
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           z 
                           2 
                         
                         + 
                         
                           r 
                           2 
                         
                         - 
                         
                           R 
                           max 
                           2 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               . 
             
           
         
       
     
     In this expression, z is the height  130 , r is the length  124  along the radius extending from the center portion  118 , R max  is equal to the outer radius  116  of the GRIN lens at the spherical perimeter region  108 , N is equal to a number of spoke portions (such as spoke portion  136 ) in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities. 
     In these examples, each spoke portion of the plurality of spoke portions  106  may be designed to have a spoke width w that varies with height z  130  so as to provide a continuous effective permittivity variation on a plane, with only step-wise permittivity variation along a vertical axis (i.e., the central axis  104 ). Alternatively, each spoke portion may be designed with a twist, similar to a fan blade, to increase uniformity of the spoke portion placement around the spherical (or hemispherical) spherical perimeter region  108 . 
     The spoke dielectric lens  100  may be fabricated using an additive computerized manufacturing process, such as a three-dimensional (3D) printing process or a sintering process. Alternatively, or in addition, the spoke dielectric lens  100  may be fabricated using a subtractive computerized manufacturing process, such as a milling process. In a particular example, the spoke dielectric lens  100  is fabricated using a combination of one or more additive computerized manufacturing processes and one or more additive and one or more subtractive computerized manufacturing processes, such as a combined photolithographic and etching process, as an illustrative example. The spoke dielectric lens  100  may be manufactured using a single material or using multiple materials (e.g., using a primary material and one or more dopant materials). 
     Turning to  FIG. 2 , a perspective view of an example of another implementation of a spoke dielectric lens  200  is shown in accordance with the present disclosure. Similar to the spoke dielectric lens  100  shown in  FIGS. 1A-1F , the spoke dielectric lens  200  includes a cylinder  202  of a center portion along the central axis  104  and a plurality of spoke portions  204  that are attached to the cylinder  202  of the center portion and extend to a spherical perimeter region  206  in a radial direction from the cylinder  202  of the center portion. In this example, the plurality of spoke portions  204  includes at least a first monolithic spoke portion  208  extending from the cylinder  102  of the center portion to the spherical perimeter region  206  and the cylinder  202  of the center portion and the plurality of spoke portions  204  define a plurality of cavity regions  210  among the plurality of spoke portions  204 . The center portion, the cylinder  202 , the plurality of spoke portions  204 , and the plurality of cavity regions  210  are included in a GRIN lens having a plurality of relative permittivities that are based on a radial distance from the center portion. The difference in this example is that the spoke dielectric lens  200  is a hemisphere spoke dielectric lens  200  instead of a full spherical spoke dielectric lens  100  as shown and described in  FIGS. 1A-1F . 
     In  FIG. 3A , a perspective view of an example of another implementation of a spoke dielectric lens  300  is shown in accordance with the present disclosure. Instead of utilizing a plurality of spoke portions  106  that extend the full height z  130  of the cylinder along the central axis  104  as shown and described in  FIGS. 1A-2 , the spoke dielectric lens  300  is instead constructed by utilizing a plurality of spoke layers  302  that are stacked up in a stack-up direction  304  to form the spoke dielectric lens  300 . The spoke dielectric lens  300  comprises a center portion  306  that extends along a cylinder having a central axis  308  and the plurality of spoke layers  302 . In this example, each spoke layer of the plurality of spoke layers  302  is attached to another spoke layer of the plurality of spoke layers  302  in a stack-up fashion along the cylinder in the stack-up direction  304  along the central axis  308 . Each spoke layer comprises a plurality of spoke portions  310  that are attached to the cylinder and extend to a spherical perimeter region  312  in a radial direction  314  from the cylinder. The plurality of spoke portions  310  includes at least a first monolithic spoke portion extending from the cylinder to the spherical perimeter region  312  and the cylinder and the plurality of spoke portions  310  define a plurality of cavity regions  316  among the plurality of spoke portions  310 . In this example, the cylinder, the plurality of spoke portions  310 , and the plurality of cavity regions  316  are included in a GRIN lens having a plurality of relative permittivities that are based on a radial distance from the center portion  306 . 
     In this example, it is appreciated that while only four (4) spoke layers are shown of the plurality of spoke layers  302 , the entire spoke dielectric lens  300  is constructed of a potentially large number of spoke layers. In this example, only four spoke layers are shown for purpose of ease of illustration and it is not meant to limit the number of spoke layers in the plurality of spoke layers  302 . 
     In  FIG. 3B , a perspective exploded view of the spoke dielectric lens  300  is shown in accordance with the present disclosure. In this example the spoke dielectric lens  300  is shown to be constructed from a plurality of spoke layers  302  that include, for example a first spoke layer  318 , second spoke layer  320 , third spoke layer  322 , fourth spoke layer  324 , and fifth spoke layer  326 . Again, in this example, it is appreciated that while only five (5) spoke layers are shown of the plurality of spoke layers  302 , the entire spoke dielectric lens  300  is constructed of a potentially large number of spoke layers and the five spoke layers are shown for purpose of ease of illustration. In this example, the third spoke layer  322  is the middle and largest spoke layer of the plurality of spoke layers  302 . The third spoke layer  322  has the largest radius extending from the cylinder  328  of the center portion  306  to the outer radius of the spherical perimeter region  312 . Second spoke layer  320  has a smaller radius than the third spoke layer  322  and the first spoke layer  318  has a smaller radius than the second spoke layer  320 . Similarly, the fourth spoke layer  324  has a smaller radius than the third spoke layer  322  and the fifth spoke layer  326  has a smaller radius than the fourth spoke layer  324 . 
     In general, the spoke dielectric lens  300  may be fabricated using an additive computerized manufacturing process, such as a 3D printing process or a sintering process. Alternatively, or in addition, the spoke dielectric lens  300  may be fabricated using a subtractive computerized manufacturing process, such as a milling process. In a particular example, the spoke dielectric lens  300  is fabricated using a combination of one or more additive computerized manufacturing processes and one or more additive and one or more subtractive computerized manufacturing processes, such as a combined photolithographic and etching process, as an illustrative example. The spoke dielectric lens  300  may be manufactured using a single material or using multiple materials (e.g., using a primary material and one or more dopant materials). 
     In  FIG. 3C , a perspective view of an example of an implementation of a spoke layer  330  of the spoke dielectric lens  300  is shown in accordance with the present disclosure. In this example, the cylinder  332  is shown in relation to the center portion  306 , plurality of spoke portions  310 , and plurality of cavity regions  316 . The spoke layer  330  has a height z  334  and when attached to the other spoke layers of the plurality of spoke layers  302 , the cylinder  332  and the cylinders of the other spoke layers forms a combined cylinder that runs an entire diameter of spoke dielectric lens  300  along the central axis  308  in the Z-axis. In this example, the spoke layer  330  is shown to include a first spoke portion  336  and second spoke portion  338  of the plurality of spoke portions  310  and a cavity region  340  of the plurality of cavity regions  316 . 
     In  FIG. 3D , an expanded view  342  of two adjacent spoke portions (i.e., the first spoke portion  336  and second spoke portion  338 ) of the spoke layer  330  is shown in accordance with the present disclosure. The expanded view  134  is a top view of the spoke layer  330 . The first spoke portion  336  and second spoke portion  338  are a first and second monolithic spoke portions. 
     In this example, the first spoke portion  336  may have a first width W 1A  at a first distance  344  from the cylinder  328  of the center portion  306  and a second width W 2A  at a second distance  346  from the cylinder  328 , where the second distance  346  is greater than the first distance  344  and the first width W 1A  is different than the second width W 2A . The first spoke portion  336  may also include other widths along different distances along the first spoke portion  336  such as, for example, a third width at a third distance. In this example, all the distances (i.e., first distance  344 , second distance  346 , and third distance) are along a radius from the cylinder  328  to the outer radius  348  at the spherical perimeter region  312 . In this example, the first spoke portion  336  is shown as having the second width W 2A  that is greater than the first width W 1A  and the first spoke portion  336  having a tapered profile that increases in width as a function of distance from the cylinder  328  to the outer radius  348 . However, in another example, the first spoke portion  336  may have the second width W 2A  being less than the first width W 1A  and the first spoke portion  336  may have a tapered profile that decreases in width as a function of distance from the cylinder  328  to the outer radius  348 . Similarly, the second spoke portion  338  is shown as having the second width W 5A  that is greater than the first width W 4A  and the second spoke portion  338  having a tapered profile that increases in width as a function of distance from the cylinder  328  to the outer radius  348 . However, in another example, the second spoke portion  338  may have the second width W 5A  being less than the first width W 4A  and the second spoke portion  338  may have a tapered profile that decreases in width as a function of distance from the cylinder  328  to the outer radius  348 . 
     Moreover, in this example, the second spoke portion  338  may have a first width W 4A  at the first distance  344  from the cylinder  328  of the center portion  306  and a second width W 5A  at the second distance  346  from the cylinder  328 , where the second distance  346  is greater than the first distance  344  and the first width W 4A  is different than the second width W 5A . The second spoke portion  338  may also include other widths along different distances along the second spoke portion  338  such as, for example, a third width (not shown) at the third distance. 
     Furthermore, in this example, the first spoke portion  336  and the second spoke portion  338  are approximately adjacent to each other and define, in combination with the cylinder  328  and the spherical perimeter region  312  at the outer radius  348  the cavity region  340  between the first spoke portion  336  and second spoke portion  338  that extends from the cylinder  328  to the spherical perimeter region  312 . The cavity region  340  has a first width W 1CA  at the first distance  344  from the center portion  306  and a second width W 2CA  at the second distance  346  from the center portion  306 , where the first width W 1CA  is different than the second width W 2CA . 
     Similar to the first spoke portion  336 , the second spoke portion  338  and the cavity region  340  may have tapered profiles. Specifically, the cavity region  340  may have a tapered profile that increases in width as a function of distance from the center portion  306 , where the second width W 2CA  is greater than the first width W 1CA . Alternatively, the cavity region  340  may have a tapered profile that decreases in width as a function of distance from the center portion  306 , where the second width W 2CA  is less than the first width W 1CA . 
     As discussed previously, a spoke portion of the plurality of spoke portions  310  (e.g., first spoke portion  336  or second spoke portion  338 ) is constructed of a material that includes width (w), a height z  334  of the spoke layer  330 , and the length along the radius (r) extending from the center portion  306  to the outer radius  348 . The width w is equal to a numerical expression defined as 
     
       
         
           
             
               
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     In this expression, R max  is equal to the outer radius  348  of the spoke layer  330  at the spherical perimeter region  108 , N is equal to a number of spoke portions (such as spoke portion  336  or  338 ) in the plurality of spoke portions  310 , and ε rel  a relative permittivity of the plurality of relative permittivities. 
     Again, in the case that the spoke dielectric lens  300  is configured as a Maxwell fisheye lens, the relationship for determining the width w of the spoke portion is different than previously described. The relationship for the width w of the spoke portion for a Maxwell fisheye lens is 
     
       
         
           
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     In this expression, z is the height  334 , r is the length along the radius extending from the center portion  306 , R max  is equal to the outer radius  348  of the spoke layer  330  at the spherical perimeter region  312 , N is equal to a number of spoke portions in the plurality of spoke portions  310 , and ε rel  a relative permittivity of the plurality of relative permittivities. 
     Turning to  FIG. 4 , a perspective exploded view of an example of an implementation of another spoke dielectric lens  400  is shown in accordance with the present disclosure. Similar to the spoke dielectric lens  300  shown in  FIGS. 3A-3D , the spoke dielectric lens  400  includes a combined cylinder  328  of a center portion  306  along the central axis  308  and a plurality of spoke layers  402  that are attached to the cylinder  328  and extend to the spherical perimeter region  312  in the radial direction  314  from the cylinder  328 . The difference in this example is that the spoke dielectric lens  400  is a hemisphere spoke dielectric lens  400  instead of a full spherical spoke dielectric lens  300  as shown and described in  FIGS. 3A-3D . 
     In this example the spoke dielectric lens  400  is shown to be constructed from a plurality of spoke layers  402  that include, for example the first spoke layer  318 , second spoke layer  320 , and the third spoke layer  322 . In this example, the third spoke layer  322  is the middle and largest spoke layer of the plurality of spoke layers  302 . The third spoke layer  322  has the largest radius extending from the cylinder  328  of the center portion  306  to the outer radius of the spherical perimeter region  312 . Second spoke layer  320  has a smaller radius than the third spoke layer  322  and the first spoke layer  318  has a smaller radius than the second spoke layer  320 . The first, second, and third spoke layers  318 ,  320 , and  322  are stacked-up along the stack-up direction  404 . 
     In general, the spoke dielectric lens  400  may be fabricated using an additive computerized manufacturing process, such as a 3D printing process or a sintering process. Alternatively, or in addition, the spoke dielectric lens  400  may be fabricated using a subtractive computerized manufacturing process, such as a milling process. In a particular example, the spoke dielectric lens  400  is fabricated using a combination of one or more additive computerized manufacturing processes and one or more additive and one or more subtractive computerized manufacturing processes, such as a combined photolithographic and etching process, as an illustrative example. The spoke dielectric lens  400  may be manufactured using a single material or using multiple materials (e.g., using a primary material and one or more dopant materials). 
     In  FIG. 5 , a perspective view of an example of an implementation of yet another spoke dielectric lens  500  is shown in accordance with the present disclosure. In this example, each spoke portion of the plurality of spoke portions  502  is designed with a twist, similar to a fan blade, to increase uniformity of the spoke portion placement around the spherical perimeter region  504 . Similar to the previous examples, the spoke dielectric lens  500  is oriented about a center portion  506  around a central axis  508 . 
     In this example, the spoke dielectric lens  500  is constructed by utilizing a plurality of spoke layers  510  that are stacked up in a stack-up direction  512  to form the spoke dielectric lens  500 . The spoke dielectric lens  500  comprises the center portion  506  that extends along a cylinder along the central axis  508  and the plurality of spoke layers  510 . 
     In this example, each spoke layer of the plurality of spoke layers  510  is attached to another spoke layer of the plurality of spoke layers  510  in a stack-up fashion along the cylinder in the stack-up direction  512  along the central axis  508  along the Z-axis. Each spoke layer comprises spoke portions of the plurality of spoke portions  502  that are attached to the cylinder and extend to the spherical perimeter region  504  in a radial direction  514  from the cylinder. The plurality of spoke portions  502  includes at least a first monolithic spoke portion extending from the cylinder to the spherical perimeter region  504  and the cylinder and the plurality of spoke portions  502  define a plurality of cavity regions among the plurality of spoke portions  502 . In this example, the cylinder, the plurality of spoke portions  502 , and the plurality of cavity regions are included in a GRIN lens having a plurality of relative permittivities that are based on a radial distance from the center portion  506 . 
     In this example, it is again appreciated that while only four (4) spoke layers are shown of the plurality of spoke layers  510 , the entire spoke dielectric lens  500  is constructed of a potentially large number of spoke layers. In this example, only four spoke layers are shown for purpose of ease of illustration and it is not meant to limit the number of spoke layers in the plurality of spoke layers  510 . 
     In  FIG. 6A , a perspective exploded view of the spoke dielectric lens  500  is shown in accordance with the present disclosure. In this example the spoke dielectric lens  500  is shown to be constructed from a plurality of spoke layers  510  that include, for example a first spoke layer  518 , second spoke layer  520 , third spoke layer  522 , fourth spoke layer  524 , and fifth spoke layer  526 . Again, in this example, it is appreciated that while only five (5) spoke layers are shown of the plurality of spoke layers  510 , the entire spoke dielectric lens  500  is constructed of a potentially large number of spoke layers and the five spoke layers are shown for purpose of ease of illustration. In this example, the third spoke layer  522  is the middle and largest spoke layer of the plurality of spoke layers  510 . The third spoke layer  522  has the largest radius extending from the cylinder  528  of the center portion  506  to the outer radius of the spherical perimeter region  504 . The second spoke layer  520  has a smaller radius than the third spoke layer  522  and the first spoke layer  518  has a smaller radius than the second spoke layer  520 . Similarly, the fourth spoke layer  524  has a smaller radius than the third spoke layer  522  and the fifth spoke layer  526  has a smaller radius than the fourth spoke layer  524 . 
     In general, the spoke dielectric lens  500  may be fabricated using an additive computerized manufacturing process, such as a 3D printing process or a sintering process. Alternatively, or in addition, the spoke dielectric lens  500  may be fabricated using a subtractive computerized manufacturing process, such as a milling process. In a particular example, the spoke dielectric lens  500  is fabricated using a combination of one or more additive computerized manufacturing processes and one or more additive and one or more subtractive computerized manufacturing processes, such as a combined photolithographic and etching process, as an illustrative example. The spoke dielectric lens  500  may be manufactured using a single material or using multiple materials (e.g., using a primary material and one or more dopant materials). 
     In  FIG. 6B , a perspective view of an example of an implementation of a spoke layer  600  of the spoke dielectric lens  500  is shown in accordance with the present disclosure. In this example, the cylinder  528  is shown in relation to the center portion  506 , plurality of spoke portions  502 , and plurality of cavity regions  602 . The spoke layer  600  has a height z  604  and when attached to the other spoke layers of the plurality of spoke layers  510 , the cylinder  528  and the cylinders of the other spoke layers forms a combined cylinder that runs an entire diameter of the spoke dielectric lens  500  along the central axis  508  in the Z-axis. In this example, the spoke layer  600  is shown to include a first spoke portion  606  and second spoke portion  608  of the plurality of spoke portions  502  and a cavity region  610  of the plurality of cavity regions  602 . 
     In this example, each of the spoke portions of the plurality of spoke portions  502  are shown as having a twist, similar to a fan blade, to increase the uniformity of the spoke portion placement around the spherical perimeter region  504 . 
     Turning to  FIG. 7A , a perspective view of an example of an implementation of another spoke dielectric lens  700  is shown in accordance with the present disclosure. The spoke dielectric lens  700  is a hemisphere spoke dielectric lens  700  instead of a full spherical spoke dielectric lens  600  as shown and described in  FIGS. 5-6B . In  FIG. 7B , a perspective exploded view of the spoke dielectric lens  700  is shown in accordance with the present disclosure. In this example, the plurality of spoke layers  510  are stacked up in the stack-up direction  512  along the central axis  508  that is along the Z-axis from a bottom spoke layer  702  to a top spoke layer  704 , where the bottom spoke layer  702  has the largest radius to the spherical perimeter region  504  and the top spoke layer  704  has the smallest radius to the spherical perimeter region  504 . 
     Turning to  FIG. 8 , a perspective view of a radome  800  is shown for use with the spoke dielectric lens shown in  FIGS. 1A-8B . 
     It will be understood that various aspects or details of the disclosure may be changed without departing from the scope of the disclosure. It is not exhaustive and does not limit the claimed disclosures to the precise form disclosed. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation. Modifications and variations are possible in light of the above description or may be acquired from practicing the disclosure. The claims and their equivalents define the scope of the disclosure. Moreover, although the techniques have been described in language specific to structural features and/or methodological acts, it is to be understood that the appended claims are not necessarily limited to the features or acts described. Rather, the features and acts are described as example implementations of such techniques. 
     Further, the disclosure comprises embodiments according to the following clauses. 
     Clause 1. A dielectric lens comprising: a center portion that extends along a cylinder having a central axis; and a plurality of spoke portions that are attached to the center portion and extend to a spherical perimeter region in a radial direction from the center portion, wherein the plurality of spoke portions includes at least a first monolithic spoke portion extending from the center portion to the spherical perimeter region, wherein the center portion and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions, and wherein the center portion, the cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in a gradient index (GRIN) lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     Clause 2. The dielectric lens of clause 1, wherein the dielectric lens is a Luneburg lens, each spoke portion of the plurality of spoke portions is constructed of a material that includes a width, a height (z), and a length along a radius (r) extending from the center portion, the width is equal to a numerical expression defined as 
                 2   ⁢   π   ⁢     r   ⁡     (       z   2     +     r   2     -     R   max   2       )           N   ⁢       R   max   2     ⁡     (       ɛ   rel     -   1     )           ,         
and
 
wherein R max  is equal to an outer radius of the GRIN lens at the spherical perimeter region, N is equal to a number of spoke portions in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities.
 
     Clause 3. The dielectric lens of clause 2, wherein z is equal to a component length of r from the center portion projected along the central axis. 
     Clause 4. The dielectric lens of clause 2, wherein N is related to a frequency associated with the GRIN lens. 
     Clause 5. The dielectric lens of clause 2, wherein the plurality of relative permittivities include a continuous range of relative permittivities. 
     Clause 6. The dielectric lens of clause 1, wherein the first monolithic spoke portion has a first width at a first distance from the center portion and a second width at a second distance from the center portion, wherein the second distance is greater than the first distance, and wherein the first width is different than the second width. 
     Clause 7. The dielectric lens of clause 6, wherein the second width is greater than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that increases in width as a function of distance from the center portion. 
     Clause 8. The dielectric lens of clause 6, wherein the second width is less than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that decreases in width as a function of distance from the center portion. 
     Clause 9. The dielectric lens of clause 6, wherein the first monolithic spoke portion further has a third width at a third distance from the center portion, the third distance greater than the second distance, wherein the second width is greater than the first width and is greater than the third width, and wherein the first monolithic spoke portion has a dual-tapered profile that increases in width as a function of distance from the center portion until a particular distance from the center portion and then decreases in width as a function of distance from the center portion. 
     Clause 10. The dielectric lens of clause 6, wherein the first monolithic spoke portion further has a third width at a third distance from the center portion, the third distance greater than the second distance, wherein the second width is less than the first width and is less than the third width, and wherein the first monolithic spoke portion has a reverse dual-tapered profile that decreases in width as a function of distance from the center portion until a particular distance from the center portion and then increases in width as a function of distance from the center portion. 
     Clause 11. The dielectric lens of clause 1, wherein the plurality of cavity regions includes at least a first monolithic cavity region extending from the center portion to the spherical perimeter region, wherein the first monolithic cavity region has a first width at a first distance from the center portion and a second width at a second distance from the center portion, the second distance greater than the first distance, and wherein the first width is different than the second width. 
     Clause 12. The dielectric lens of clause 11, wherein the second width is greater than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that increases in width as a function of distance from the center portion. 
     Clause 13. The dielectric lens of clause 11, wherein the second width is less than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that decreases in width as a function of distance from the center portion. 
     Clause 14. The dielectric lens of clause 1, wherein the GRIN lens is further configured to focus electromagnetic radiation to transmit or to receive a far-field high-gain signal. 
     Clause 15. The dielectric lens of clause 1, further comprising an antenna configured to transmit or to receive an electromagnetic signal through the GRIN lens. 
     Clause 16. The dielectric lens of clause 1, wherein the spherical perimeter region is a hemisphere. 
     Clause 17. The dielectric lens of clause 1, wherein the spherical perimeter region is a sphere. 
     Clause 18. The dielectric lens of clause 1, wherein the dielectric lens is a Maxwell fisheye lens. 
     Clause 19. The dielectric lens of clause 18, wherein each spoke portion of the plurality of spoke portions is constructed of a material that includes a width, a height (z), and a length along a radius (r) extending from the center portion, wherein the width is equal to a numerical expression defined as 
                 2   ⁢   π   ⁢     r   ⁡     (       z   4     +     2   ⁢       z   2     ⁡     (       r   2     +     R   max   2       )         +     r   4     +     2   ⁢     r   2     ⁢     R   max   2       -       (       ɛ   rel     -   1     )     ⁢     R   max   2         )             N   ⁡     (       ɛ   rel     -   1     )       ⁢       (       z   2     +     r   2     -     R   max   2       )     2         ,         
wherein R max  is equal to an outer radius of the GRIN lens at the spherical perimeter region, N is equal to a number of spoke portions in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities.
 
     Clause 20. The dielectric lens of clause 19, wherein z is equal to a component length of r from the center portion projected along the central axis and wherein N is related to a frequency associated with the GRIN lens. 
     Clause 21. The dielectric lens of clause 1, wherein the spherical perimeter region is a sphere. 
     Clause 22. The dielectric lens of clause 1, wherein the at least first monolithic spoke portion extends along a spoke axis from the center portion that is normal to the central axis and twists along the spoke axis. 
     Clause 23. The dielectric lens of clause 1, wherein the dielectric lens is manufactured utilizing a three-dimensional printing method. 
     Clause 24. A dielectric lens comprising: a center portion that extends along a cylinder having a central axis; and a plurality of spoke layers wherein each spoke layer of the plurality of spoke layers is attached to another spoke layer of the plurality of spoke layers in a stack-up fashion along the cylinder and each spoke layer comprises: a plurality of spoke portions that are attached to the cylinder and extend to a spherical perimeter region in a radial direction from the cylinder, wherein the plurality of spoke portions includes at least a first monolithic spoke portion extending from the cylinder to the spherical perimeter region, wherein the cylinder and the plurality of spoke portions define a plurality of cavity regions among the plurality of spoke portions, and wherein the cylinder, the plurality of spoke portions, and the plurality of cavity regions are included in a gradient index (GRIN) lens having a plurality of relative permittivities that are based on a radial distance from the center portion. 
     Clause 25. The dielectric lens of clause 24, wherein the dielectric lens is a Luneburg lens, each spoke portion of the plurality of spoke portions is constructed of a material that includes a width, a height (z), and a length along a radius (r) extending from the cylinder, the width is equal to a numerical expression defined as 
                 2   ⁢   π   ⁢     r   ⁡     (       z   2     +     r   2     -     R   max   2       )           N   ⁢       R   max   2     ⁡     (       ɛ   rel     -   1     )           ,         
and
 
wherein R max  is equal to an outer radius of the GRIN lens at the spherical perimeter region, N is equal to a number of spoke portions in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities.
 
     Clause 26. The dielectric lens of clause 25, wherein z is equal to a height of a spoke layer of the plurality of spoke layers. 
     Clause 27. The dielectric lens of clause 25, wherein N is related to a frequency associated with the GRIN lens. 
     Clause 28. The dielectric lens of clause 25, wherein the plurality of relative permittivities include a continuous range of relative permittivities. 
     Clause 29. The dielectric lens of clause 24, wherein the first monolithic spoke portion has a first width at a first distance from the cylinder and a second width at a second distance from the cylinder, the second distance greater than the first distance, and wherein the first width is different than the second width. 
     Clause 30. The dielectric lens of clause 29, wherein the second width is greater than the first width, and wherein the at least first monolithic spoke portion has a tapered profile that increases in width as a function of distance from the cylinder. 
     Clause 31. The dielectric lens of clause 29, wherein the second width is less than the first width, and wherein the at least first monolithic spoke portion has a tapered profile that decreases in width as a function of distance from the cylinder. 
     Clause 32. The dielectric lens of clause 29, wherein the first monolithic spoke portion further has a third width at a third distance from the cylinder, the third distance greater than the second distance, wherein the second width is greater than the first width and is greater than the third width, and wherein the first monolithic spoke portion has a dual-tapered profile that increases in width as a function of distance from the cylinder until a particular distance from the cylinder and then decreases in width as a function of distance from the cylinder. 
     Clause 33. The dielectric lens of clause 29, wherein the first monolithic spoke portion further has a third width at a third distance from the cylinder, the third distance greater than the second distance, wherein the second width is less than the first width and is less than the third width, and wherein the first monolithic spoke portion has a reverse dual-tapered profile that decreases in width as a function of distance from the cylinder until a particular distance from the cylinder and then increases in width as a function of distance from the cylinder. 
     Clause 34. The dielectric lens of clause 24, wherein the plurality of cavity regions includes at least a first monolithic cavity region extending from the cylinder to the spherical perimeter region, wherein the first monolithic cavity region has a first width at a first distance from the cylinder and a second width at a second distance from the cylinder, the second distance greater than the first distance, and wherein the first width is different than the second width. 
     Clause 35. The dielectric lens of clause 34, wherein the second width is greater than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that increases in width as a function of distance from the cylinder. 
     Clause 36. The dielectric lens of clause 34, wherein the second width is less than the first width, and wherein the at least first monolithic spoke portion of the plurality of spoke portions has a tapered profile that decreases in width as a function of distance from the cylinder. 
     Clause 37. The dielectric lens of clause 24, wherein the GRIN lens is further configured to focus electromagnetic radiation to transmit or to receive a far-field high-gain signal. 
     Clause 38. The dielectric lens of clause 24, further comprising an antenna configured to transmit or to receive an electromagnetic signal through the GRIN lens. 
     Clause 39. The dielectric lens of clause 24, wherein the spherical perimeter region is a hemisphere. 
     Clause 40. The dielectric lens of clause 24, wherein the spherical perimeter region is a sphere. 
     Clause 41. The dielectric lens of clause 24, wherein the dielectric lens is a Maxwell fisheye lens. 
     Clause 42. The dielectric lens of clause 41, wherein each spoke portion of the plurality of spoke portions is constructed of a material that includes a width, a height (z), and a length along a radius (r) extending from the cylinder, wherein the width is equal to a numerical expression defined as 
                 2   ⁢   π   ⁢     r   ⁡     (       z   4     +     2   ⁢       z   2     ⁡     (       r   2     +     R   max   2       )         +     r   4     +     2   ⁢     r   2     ⁢     R   max   2       -       (       ɛ   rel     -   1     )     ⁢     R   max   2         )             N   ⁡     (       ɛ   rel     -   1     )       ⁢       (       z   2     +     r   2     -     R   max   2       )     2         ,         
wherein R max  is equal to an outer radius of the GRIN lens at the spherical perimeter region, N is equal to a number of spoke portions in the plurality of spoke portions, and ε rel  is a relative permittivity of the plurality of relative permittivities.
 
     Clause 43. The dielectric lens of clause 42, wherein z is equal to a component length of r from the center portion projected along the central axis and wherein N is related to a frequency associated with the GRIN lens. 
     Clause 44. The dielectric lens of clause 24, wherein the at least first monolithic spoke portion extends along a spoke axis from the cylinder that is normal to the central axis and twists along the spoke axis. 
     Clause 45. The dielectric lens of clause 24, wherein the dielectric lens is manufactured utilizing a three-dimensional printing method. 
     To the extent that terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements. Moreover, conditional language such as, among others, “can,” “could,” “might” or “may,” unless specifically stated otherwise, are understood within the context to present that certain examples include, while other examples do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that certain features, elements and/or steps are in any way required for one or more examples or that one or more examples necessarily include logic for deciding, with or without user input or prompting, whether certain features, elements and/or steps are included or are to be performed in any particular example. Conjunctive language such as the phrase “at least one of X, Y or Z,” unless specifically stated otherwise, is to be understood to present that an item, term, etc. may be either X, Y, or Z, or a combination thereof.