Patent Publication Number: US-10777905-B2

Title: Lens with concentric hemispherical refractive structures

Description:
FIELD OF THE DISCLOSURE 
     The present disclosure is generally related to lenses and more particularly to gradient refractive index (GRIN) lenses. 
     BACKGROUND 
     Certain electronic devices communicate using electromagnetic (EM) signals. To illustrate, in some systems, data is represented using an EM signal, and the EM signal is provided from an antenna of one electronic device to an antenna of another electronic device via a communication network, such as a wireless network. 
     In some systems, an EM signal from an antenna is focused using a dish structure (e.g., a parabolic dish) or a lens. In some applications, a dish structure or a lens can be heavy and large, increasing cost of fabrication, installation, or maintenance of the dish structure or lens. In some cases, reducing the size of a dish structure or a lens also reduces the gain of the EM signal, resulting in signal quality degradation, such as by lowering a signal-to-noise ratio (SNR) of the EM signal. 
     Further, in some cases, less expensive lenses exhibit reduced focusing ability. For example, in some applications, certain ring-based lenses are associated with low focusing ability and are unable to provide a tightly focused, high-gain far-field pattern. 
     SUMMARY 
     In a particular example, a lens includes a first hemispherical refractive structure having a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure. The lens further includes a second hemispherical refractive structure having a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure. The second hemispherical refractive structure is arranged as a hemispherical shell coupled to and concentric with the first hemispherical refractive structure. The second effective refractive index is different than the first effective refractive index. 
     In another example, a method of fabricating a lens includes forming a first hemispherical refractive structure of the lens. The first hemispherical refractive structure has a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure. The method further includes forming a second hemispherical refractive structure of the lens as a hemispherical shell that is coupled to and concentric with the first hemispherical refractive structure. The second hemispherical refractive structure has a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure. The second effective refractive index is different than the first effective refractive index. 
     In another example, a method of focusing a signal using a lens includes receiving a first signal at the lens. The method further includes focusing the first signal to generate a second signal using a first hemispherical refractive structure of the lens and using a second hemispherical refractive structure of the lens. The first hemispherical refractive structure has a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure. The second hemispherical refractive structure is arranged as a hemispherical shell coupled to and concentric with the first hemispherical refractive structure. The second hemispherical refractive structure has a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure. The second effective refractive index is different than the first effective refractive index. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating certain aspects of an example of a lens. 
         FIG. 2A  is a diagram illustrating certain aspects associated with an example of the lens of  FIG. 1 . 
         FIG. 2B  is a diagram illustrating additional aspects associated with an example of the lens of  FIG. 1 . 
         FIG. 2C  is a diagram illustrating additional aspects associated with an example of the lens of  FIG. 1 . 
         FIG. 2D  is a diagram illustrating additional aspects associated with an example of the lens of  FIG. 1 . 
         FIG. 3  is a diagram of a cross-sectional view of an example of the lens of  FIG. 1 . 
         FIG. 4  is a diagram of an example of a system that includes the lens of  FIG. 1 . 
         FIG. 5  is a diagram of another example of a system that includes the lens of  FIG. 1 . 
         FIG. 6  is a flow chart of an example of a method of fabricating the lens of  FIG. 1 . 
         FIG. 7  is a flow chart of an example of a method of focusing a signal using the lens of  FIG. 1 . 
         FIG. 8  is a block diagram illustrating aspects of an example of a computing system that is configured to execute instructions to initiate or control operations of the method of  FIG. 6 , or that is configured to focus a signal by initiating or controlling operations of the method of  FIG. 7 , or both. 
     
    
    
     DETAILED DESCRIPTION 
     In a particular implementation, a lens includes concentric hemispherical (or spherical) refractive structures. In some examples, the concentric hemispherical refractive structures are manufactured using an additive manufacturing process, such as a three-dimensional (3D) printing process. By using 3D additively manufactured concentric hemispherical structures instead of certain other shapes (e.g., a ring), a gradient refractive index (GRIN) lens having a 3D gradient index profile can be manufactured relatively inexpensively. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
     In certain implementations, the lens is coupled to an antenna, a waveguide, or a horn, as illustrative examples. In some implementations, the lens is implemented in connection with a compact and lightweight antenna to replace a heavy parabolic dish antenna. Alternatively or in addition, in other examples, the lens is implemented in connection with a low profile, high-gain antenna for mobile platforms, such as cellular telephones. Alternatively or in addition, in other implementations, the lens is implemented in connection with a low-power switched beam antenna as an alternative to a phased array. Alternatively or in addition, in other examples, the lens is used to improve the gain of a horn antenna, a steerable array, or both. 
     In some examples, the lens is manufactured as a single sphere including each concentric hemispherical or spherical refractive structure (e.g., using a 3D printing process). In other examples, the lens is manufactured as two hemispheres including all concentric hemispheres to be fastened together (e.g., after the 3D printing process). In another example, refractive structures are manufactured separately and assembled (e.g., so that one of the refractive structures is concentric with another one of the refractive structures). 
     In some circumstances, a 3D printing process produces inaccurate or non-uniform infill ratios. To produce more accurate infill ratios, in some examples, hemispherical refractive structures of the lens each include a linear pattern of thin angled planes with a particular spacing. In some examples, the hemispherical refractive structures are circularly patterned (or “duplicated”) at an angle of 120 degrees. In some applications, the resulting pattern (i.e., the linear pattern of thin angled planes circularly patterned at an angle of 120 degrees) is precisely controlled for a desired infill ratio (as compared to other shapes) and is constant across multiple viewing angles. 
     Referring to  FIG. 1 , a particular illustrative example of a lens is depicted and generally designated  100 . The lens  100  is a gradient refractive index (GRIN) lens, such as a Luneburg lens or a fisheye lens, as illustrative examples. 
     The lens  100  includes multiple refractive structures. For example, in  FIG. 1 , the lens  100  includes a first hemispherical refractive structure  102  and a second hemispherical refractive structure  104 . The second hemispherical refractive structure  104  is arranged as a hemispherical shell coupled to and concentric with the first hemispherical refractive structure  102 . To further illustrate, certain illustrative aspects of the first hemispherical refractive structure  102  and the second hemispherical refractive structure  104  are described further below, such as in connection with  FIGS. 2A-2D . As an example, in some implementations, the first hemispherical refractive structure  102  and the second hemispherical refractive structure  104  have a concentric hemispherical relationship, as described further with reference to the example of  FIG. 2D . 
     In some implementations, each refractive structure of the lens  100  has a particular fill pattern that determines an effective refractive index of the refractive structure. For example, in some implementations, the first hemispherical refractive structure  102  has a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure  102 , and the second hemispherical refractive structure  104  has a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure  104 , where the second fill pattern is different from the first fill pattern. To further illustrate, in some examples, the first fill pattern includes one of a linear fill pattern  122 , a triangular fill pattern  124 , a diagonal fill pattern  126 , or a hexagonal fill pattern  128 , and the second fill pattern includes another of the linear fill pattern  122 , the triangular fill pattern  124 , the diagonal fill pattern  126 , or the hexagonal fill pattern  128 . It should be appreciated that the particular fill patterns are illustrative and that other fill patterns can be used in other implementations. 
     In a particular example, the second effective refractive index is different than (e.g., less than) the first effective refractive index (e.g., to facilitate a gradient refractive index of the lens  100 ). In one example, the first effective refractive index and the second effective refractive index define a gradient refractive index of a Luneburg lens. In another example, the first effective refractive index and the second effective refractive index define a gradient refractive index of a fisheye lens. In other examples, different effective refractive indices are selected in order to facilitate a different refractive index of the lens  100 . 
     Alternatively or in addition to use of a fill pattern to determine an effective refractive index of a refractive structure, in some implementations, a fill density is selected to determine an effective refractive index of a refractive structure. In one example, the first hemispherical refractive structure  102  has a first fill density  132 , and the second hemispherical refractive structure  104  has a second fill density  134  different than the first fill density. In the example of  FIG. 1 , the fill densities  132 ,  134  share a common fill pattern (the linear fill pattern  122 ). In other examples, the fill densities can be varied in connection with different fill patterns. 
     Alternatively or in addition, in some implementations, a type of material is used to determine an effective refractive index of a refractive structure. For example, in some implementations, the first hemispherical refractive structure  102  includes a first material (e.g., a first filament), and the second hemispherical refractive structure  104  includes a second material (e.g., a second filament) that is different than the first material. In some examples, the first material and the second material correspond to different 3D printer filament materials used by a 3D printer in connection with a 3D printing process. 
     In one example, fill densities of hemispherical refractive structure of the lens  100  are varied (e.g., as function of radius from the center of the lens  100 ) to achieve an effective permittivity equal to the target effective permittivity of the lens  100 . In some implementations, a weighted average is used to determine the fill density for the target effective permittivity. For example, in some implementations, a fill density f of the lens  100  is determined based on 
               f   =         ɛ   eff     -   1         ɛ   0     -   1         ,         
where ε eff  indicates the target permittivity, and where ε 0  indicates permittivity of the material of the lens  100 .
 
     To further illustrate, in some examples, the lens  100  is fabricated using an additive manufacturing process (e.g., a three-dimensional (3D) printing process) that uses, for each refractive structure of the lens  100 , a selectable fill pattern, a selectable fill density, one or more other selectable parameters, or a combination thereof. Alternatively or in addition, in some examples, the lens  100  is fabricated using a subtractive computerized manufacturing process, such as a milling process, as an illustrative example. In some examples, the lens  100  is fabricated using a combination of one or more additive computerized manufacturing processes and one or more subtractive computerized manufacturing processes, such as a combined photolithographic and etching process, as an illustrative example. 
     In some examples, each hemispherical refractive structure of the lens  100  has a thickness that is based on a wavelength (or frequency) of signals to be focused by the lens. In one example, each hemispherical refractive structure of the lens  100  has a thickness that is less than the wavelength of signals to be focused by the lens  100 . 
     One or more aspects of  FIG. 1  enable accurate focusing of signals using a relatively inexpensive lens design. For example, by using concentric hemispherical structures rather than certain other shapes (e.g., a ring), the lens  100  has a 3D gradient index profile instead of a two-dimensional (2D) gradient index profile and can be manufactured relatively inexpensively using an additive manufacturing process. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
       FIGS. 2A-2D  illustrate aspects of a hemispherical refractive structure, such as the first hemispherical refractive structure  102 , the second hemispherical refractive structure  104 , or both. It is noted that  FIGS. 2A, 2B, and 2C  are provided to facilitate conceptualization of a hemispherical refractive structure and that a hemispherical refractive structure need not be physically fabricated in accordance with  FIGS. 2A, 2B , and  2 C. To illustrate, in some examples, the aspects of  FIGS. 2A-2D  are used to generate a design of the lens  100 , and the design is used to generate instructions executable by a processor to cause a 3D printer to fabricate the lens. 
       FIG. 2A  illustrates a side view of a first plurality of plate structures  210  extending at an angle from a substrate  212 . In  FIG. 2A , the first plurality of plate structures  210  extend in a direction into or out of the page. In  FIG. 2A , a first spherical cut line  214  is shown. The first spherical cut line  214  encloses a hemispherical region to define a portion  220  of the first plurality of plate structures  210  (e.g., so that portions outside of the first spherical cut line  214  are disregarded). 
       FIG. 2B  depicts a side view of the portion  220  with portions of the first plurality of plate structures  210  that are outside the first spherical cut line  214  omitted, at  230 .  FIG. 2B  also depicts a top down view of the portion  220 , at  240 . 
     In  FIG. 2C , the portion  220  is copied and rotated (e.g., by 120 degrees) to generate a second portion  250 . A union of the portions  220 ,  250  is performed to generate a plurality of intersecting plate structures  260 .  FIG. 2C  also shows that the second portion  250  is copied and rotated (e.g., by 120 degrees) to generate a third portion  270 . A union of the third portion  270  and the plurality of intersecting plate structures  260  is performed to generate a hemispherical refractive structure, such as the first hemispherical refractive structure  102 , as an illustrative example. 
     In some implementations, one or more aspects of a plurality of plate structures are selected in order to determine an effective refractive index associated with a hemispherical refractive structure. To illustrate, in some examples, one or more of a number of plate structures, a spacing between the plate structures, or a thickness of the plate structures are varied in order to determine an effective refractive index. 
     To illustrate,  FIG. 2D  depicts examples of the first plurality of plate structures  210  and a second plurality of plate structures  280 . In a particular example, the first hemispherical refractive structure  102  includes the first plurality of plate structures  210  (or a portion of the first plurality of plate structures, such as the portion  220 ), and the second hemispherical refractive structure  104  includes the second plurality of plate structures  280  (or a portion thereof). 
     In  FIG. 2D , the second plurality of plate structures  280  is associated with the first spherical cut line  214  and a second spherical cut line  294 . In some implementations, the first spherical cut line  214  defines a radius of the first hemispherical refractive structure  102 , and the second spherical cut line  294  defines a radius of the second hemispherical refractive structure  104 . To illustrate, in some implementations, a first radius of the first spherical cut line  214  corresponds to the radius of the first hemispherical refractive structure  102 , and a second radius of the second spherical cut line  294  corresponds to the radius of the second hemispherical refractive structure  104  (within certain manufacturing tolerances that may be associated with the particular fabrication process). A difference between the first spherical cut line  214  and the second spherical cut line  294  corresponds to a shell thickness of the second hemispherical refractive structure  104 . 
     In the example of  FIG. 2D , the spherical cut lines  214 ,  294  define concentric hemispherical structures. To illustrate, in a particular example, the first hemispherical refractive structure  102  is formed from the first plurality of plate structures  210  based on the first spherical cut line  214 , and the second hemispherical refractive structure  104  is formed from the second plurality of plate structures  280  based on the first spherical cut line  214  and the second spherical cut line  294 . 
     In one example, a first effective refractive index of the first hemispherical refractive structure  102  is based on a first spacing  216  between plate structures of the first plurality of plate structures  210 , and a second effective refractive index of the second hemispherical refractive structure  104  is based on a second spacing  282  between plate structures of the second plurality of plate structures  280 , where the second spacing  282  is different than the first spacing  216 . In the particular example of  FIG. 2D , the second spacing  282  is greater than the first spacing  216 . 
     Alternatively or in addition, in some implementations, the first effective refractive index is based on a first number of plate structures of the first plurality of plate structures  210 , and the second effective refractive index is based on a second number of plate structures of the second plurality of plate structures  280 , where the second number is different than the first number. To illustrate, in the example of  FIG. 2D , the second number of plate structures is less than the first number of plate structures. 
     Alternatively or in addition, in some implementations, the first effective refractive index is based on a first plate structure thickness  218  of the first plurality of plate structures  210 , and the second effective refractive index is based on a second plate structure thickness  284  of the second plurality of plate structures  280 , where the second plate structure thickness  284  is different than the first plate structure thickness  218 . To illustrate, in the example of  FIG. 2D , the second plate structure thickness  284  is less than the first plate structure thickness  218 . 
     Alternatively or in addition, in some implementations, the first effective refractive index is based on the first radius of the first spherical cut line  214 , and the second effective refractive index is based on the second radius of the second spherical cut line  294 , where the second radius is different than the first radius. To illustrate, in the example of  FIG. 2D , the second radius is greater than the first radius. 
     One or more aspects of  FIGS. 2A-2D  enable accurate focusing of signals using a relatively inexpensive lens design. For example, by using concentric hemispherical structures rather than certain other shapes (e.g., a ring), the lens  100  has a 3D gradient index profile instead of a two-dimensional (2D) gradient index profile and can be manufactured relatively inexpensively using an additive manufacturing process. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
       FIG. 3  illustrates a cross-sectional view of the lens  100 . In the example of  FIG. 3 , the first hemispherical refractive structure  102  is associated with a different fill density as compared to the second hemispherical refractive structure  104 . In  FIG. 3 , the first hemispherical refractive structure  102  has a first fill density that is greater than a second fill density of the second hemispherical refractive structure  104 . 
     In some examples, the lens  100  has a fill density “profile” that varies with radial distance from the center of the lens  100 . To illustrate, in some examples, fill density of the lens  100  varies according to a linear function of the radial distance from the center of the lens  100 , a quadratic function of the radial distance from the center of the lens  100 , a cubic function of the radial distance from the center of the lens  100 , a polynomial function of the radial distance from the center of the lens  100 , a spline function of the radial distance from the center of the lens  100 , an exponential function of the radial distance from the center of the lens  100 , a logarithmic function of the radial distance from the center of the lens  100 , or another function, as illustrative examples. In some applications, a particular fill density profile of the lens  100  is selected to achieve a particular gradient refractive index of the lens  100  (e.g., to achieve either a Luneburg lens gradient refractive index or a fisheye lens gradient refractive index, as illustrative examples). 
     One or more aspects of  FIG. 3  enable accurate focusing of signals using a relatively inexpensive lens. For example, by using concentric hemispherical structures rather than certain other shapes (e.g., a ring), the lens  100  has a 3D gradient index profile instead of a two-dimensional (2D) gradient index profile and can be manufactured relatively inexpensively using an additive manufacturing process. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
       FIG. 4  illustrates an example of a system  400  that includes the lens  100 . In some implementations, the lens  100  is configured to focus an electromagnetic (EM) signal received from a waveguide, to focus an EM signal to be provided to a waveguide, or a combination thereof. To illustrate, in the example of  FIG. 4 , the lens  100  is coupled to an antenna or a waveguide, such as a waveguide  416 . In the example of  FIG. 4 , the lens  100  corresponds to a Luneburg lens. 
     In one example, the lens  100  is configured to receive a first signal  414  from a source. In some examples, the lens  100  is configured to focus the first signal  414  to generate a second signal  418  (e.g., a collimated version of the first signal  414 ). In a particular example, the lens  100  is configured to focus the first signal  414  by refracting at least a first portion of the first signal  414  using the first hemispherical refractive structure  102  and by refracting at least a second portion of the first signal  414  using the second hemispherical refractive structure  104 . In some implementations, the lens  100  is configured to output the second signal  418  to the waveguide  416 . 
       FIG. 5  illustrates another example of a system  500  that includes the lens  100 . To illustrate, in the example of  FIG. 5 , the system  500  includes the lens  100 , and the lens  100  is coupled to a waveguide or an antenna, such as a radio antenna  556 . In the example of  FIG. 5 , the lens  100  corresponds to a fisheye lens. 
     In a particular example, the lens  100  is configured to receive a first signal  554  from a source. In some examples, the lens  100  is configured to focus the first signal  554  to generate a second signal  558  (e.g., a collimated version of the first signal  554 ). In a particular example, the lens  100  is configured to focus the first signal  554  by refracting at least a first portion of the first signal  554  using the first hemispherical refractive structure  102  and by refracting at least a second portion of the first signal  554  using the second hemispherical refractive structure  104 . In some implementations, the lens  100  is configured to output the second signal  558  to the radio antenna  556 . 
     It should be appreciated that the examples of  FIGS. 4 and 5  are provided for illustration and that other examples are within the scope of the disclosure. For example, although  FIG. 4  depicts a Luneburg lens implementation of the lens  100  in connection with a waveguide, in other examples, the lens  100  corresponds to a fisheye lens that is coupled to a waveguide (e.g., the waveguide  416 ). As another example, although  FIG. 5  depicts a fisheye lens implementation of the lens  100  in connection with a radio antenna, in other examples, the lens  100  corresponds to a Luneburg lens that is coupled to a radio antenna (e.g., the radio antenna  556 ). 
     One or more aspects of  FIGS. 4 and 5  reduce cost or complexity associated with signal reception, signal transmission, or both. For example, in some implementations, the lens  100  is implemented in connection with a compact and lightweight antenna to replace a heavy parabolic dish antenna. Alternatively or in addition, in other examples, the lens  100  is implemented in connection with a low profile, high-gain antenna for mobile platforms, such as cellular telephones. Alternatively or in addition, in other implementations, the lens  100  is implemented in connection with a low-power switched beam antenna as an alternatively to a phased array. Alternatively or in addition, in other examples, the lens  100  is used to improve the gain of a horn antenna, is used in connection with a steerable array, or both. 
     Referring to  FIG. 6 , an illustrative example of a method of fabricating a lens is depicted and generally designated  600 . In some examples, the method  600  is performed to fabricate the lens  100  (e.g., a Luneburg lens or a fisheye lens, as illustrative examples). 
     The method  600  includes forming a first hemispherical refractive structure (e.g., the first hemispherical refractive structure  102 ) of a lens (e.g., the lens  100 ), at  602 . The first hemispherical refractive structure has a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure. 
     The method  600  further includes forming a second hemispherical refractive structure (e.g., the second hemispherical refractive structure  104 ) of the lens as a hemispherical shell that is coupled to and concentric with the first hemispherical refractive structure, at  604 . The second hemispherical refractive structure has a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure, and the second effective refractive index is different than (e.g., less than) the first effective refractive index. In a particular example, the first hemispherical refractive structure and the second hemispherical refractive structure are formed using an additive manufacturing process. 
     In some examples, forming the first hemispherical refractive structure includes forming a first plurality of plate structures (e.g., the first plurality of plate structures  210 ) dimensioned to provide the first effective refractive index, and forming the second hemispherical refractive structure includes forming on the first hemispherical refractive structure a second plurality of plate structures (e.g., the second plurality of plate structures  280 ) dimensioned to provide the second effective refractive index. To illustrate, in some examples, the first plurality of plate structures are dimensioned based on the first plate structure thickness  218  of  FIG. 2D , and the second plurality of plate structures are dimensioned based on the second plate structure thickness  284  of  FIG. 2D . 
     Alternatively or in addition, in some examples, forming the first hemispherical refractive structure includes forming a first plurality of plate structures (e.g., the first plurality of plate structures  210 ) having a first spacing (e.g., the first spacing  216 ) to provide the first effective refractive index. Further, in some examples, forming the second hemispherical refractive structure includes forming on the first hemispherical refractive structure a second plurality of plate structures (e.g., the second plurality of plate structures  280 ) having a second spacing (e.g., the second spacing  282 ) to provide the second effective refractive index. 
     Alternatively or in addition, in some examples, forming the first hemispherical refractive structure includes forming a first plurality of plate structures (e.g., the first plurality of plate structures  210 ) having the first fill pattern to provide the first effective refractive index, and forming the second hemispherical refractive structure includes forming on the first hemispherical refractive structure a second plurality of plate structures (e.g., the second plurality of plate structures  280 ) having the second fill pattern to provide the second effective refractive index. In a non-limiting illustrative example, the first fill pattern includes one of the linear fill pattern  122 , the triangular fill pattern  124 , the diagonal fill pattern  126 , or the hexagonal fill pattern  128 , and the second fill pattern includes another of the linear fill pattern  122 , the triangular fill pattern  124 , the diagonal fill pattern  126 , or the hexagonal fill pattern  128 . 
     Alternatively or in addition, in some examples, forming the first hemispherical refractive structure includes forming a first plurality of plate structures (e.g., the first plurality of plate structures  210 ) having a first fill density (e.g., the first fill density  132 ) to provide the first effective refractive index, and forming the second hemispherical refractive structure includes forming on the first hemispherical refractive structure a second plurality of plate structures (e.g., the second plurality of plate structures  280 ) having a second fill density (e.g., the second fill density  134 ) to provide the second effective refractive index. 
     In some implementations, the method  600  further includes attaching a first bisectional portion to a second bisectional portion to form the lens  100 . For example, after fabricating a first bisectional portion as depicted in the example of  FIG. 5 , a second bisectional portion can be attached (e.g., bonded) to the first bisectional portion to form a spherical lens (e.g., to form a Luneburg lens corresponding to the lens  100 ). Alternatively, in other implementations, the lens  100  includes a single bisectional portion, such as in a fisheye lens implementation, as an illustrative example. 
     One or more aspects of  FIG. 6  enable inexpensive fabrication of certain lenses. For example, by using concentric hemispherical structures rather than certain other shapes (e.g., a ring), the lens  100  has a 3D gradient index profile instead of a two-dimensional (2D) gradient index profile and can be manufactured relatively inexpensively using an additive manufacturing process. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
     Referring to  FIG. 7 , a method of focusing a signal using a lens is depicted and generally designated  700 . In a particular example, the method  700  is performed to operate the lens  100  (e.g., a Luneburg lens or a fisheye lens, as illustrative examples). 
     The method  700  includes receiving a first signal at a lens, at  702 . To illustrate, in some implementations, the lens  100  receives the first signal  414 . In another example, the lens  100  receives the first signal  554 . 
     The method  700  further includes focusing the first signal to generate a second signal, at  704 . The first signal is focused using a first hemispherical refractive structure (e.g., the first hemispherical refractive structure  102 ) of the lens and using a second hemispherical refractive structure (e.g., the second hemispherical refractive structure  104 ) of the lens. The first hemispherical refractive structure has a first effective refractive index based on a first fill pattern of the first hemispherical refractive structure. The second hemispherical refractive structure is arranged as a hemispherical shell coupled to and concentric with the first hemispherical refractive structure. The second hemispherical refractive structure has a second effective refractive index based on a second fill pattern of the second hemispherical refractive structure, and the second effective refractive index is different than (e.g., less than) the first effective refractive index. 
     In one example, the method  700  further includes outputting the second signal to a waveguide. To illustrate, in some implementations, the lens  100  outputs the second signal  418  to the waveguide  416 . In another example, the method  700  further includes outputting the second signal to radio antenna. To illustrate, in some implementations, the lens  100  outputs the second signal  558  to the radio antenna  556 . In other implementations, the second signal is output to free space. 
     One or more aspects of  FIG. 7  enable enhanced focusing of signals. For example, by using concentric hemispherical structures rather than certain other shapes (e.g., a ring), the lens  100  has a 3D gradient index profile instead of a two-dimensional (2D) gradient index profile. In some applications, the 3D gradient index profile increases focusing power as compared to a 2D gradient index profile, achieving a tightly focused, high-gain far-field pattern in a compact, lightweight, and easy-to-manufacture package. 
       FIG. 8  is an illustration of a block diagram of a computing environment  800  including a computing device  810  (e.g., a general-purpose computing device) configured to support embodiments of computer-implemented methods and computer-executable program instructions (or code) according to the present disclosure. In some examples, the computing device  810 , or portions thereof, execute instructions to initiate, perform, or control operations described herein. 
     The computing device  810  includes a processor  852 . The processor  852  is configured to communicate with a memory  814  (e.g., a system memory), one or more storage devices  840 , one or more input/output interfaces  850 , a communications interface  826 , or a combination thereof. 
     Depending on the particular implementation, the memory  814  includes volatile memory devices (e.g., random access memory (RAM) devices), nonvolatile memory devices (e.g., read-only memory (ROM) devices, programmable read-only memory, or flash memory), one or more other memory devices, or a combination thereof. In  FIG. 8 , the memory  814  stores an operating system  832 , which can include a basic input/output system for booting the computing device  810  as well as a full operating system to enable the computing device  810  to interact with users, other programs, and other devices. The particular example of  FIG. 8  also depicts that the memory  814  stores one or more applications  834  executable by the processor  852 . In some examples, the one or more applications  834  include instructions executable by the processor  852  to transmit signals between components of the computing device  810 , such as the memory  814 , the one or more storage devices  840 , the one or more input/output interfaces  850 , the communications interface  826 , or a combination thereof. 
     In certain implementations, the memory  814  further stores hemispherical refractive structure fabrication instructions  836  executable by the processor  852  to initiate or control operations of the method  600  of  FIG. 6 . To illustrate, in some implementations, the computing device  810  includes or is in communication with a manufacturing device, such as a three-dimensional (3D) printer device  890 . In some examples, the hemispherical refractive structure fabrication instructions  836  are executable by the processor  852  to cause the 3D printer device  890  to fabricate the lens  100 . 
     In some implementations, one or more storage devices  840  include nonvolatile storage devices, such as magnetic disks, optical disks, or flash memory devices. In some examples, the one or more storage devices  840  include removable memory devices, non-removable memory devices or both. In some cases, the one or more storage devices  840  are configured to store an operating system, images of operating systems, applications, and program data. In a particular example, the memory  814 , the one or more storage devices  840 , or both, include tangible computer-readable media. 
     In the example of  FIG. 8 , the processor  852  is configured to communicate with the one or more input/output interfaces  850  to enable the computing device  810  to communicate with one or more input/output devices  870  to facilitate user interaction. In some implementations, the one or more input/output interfaces  850  include serial interfaces (e.g., universal serial bus (USB) interfaces or Institute of Electrical and Electronics Engineers (IEEE) 1394 interfaces), parallel interfaces, display adapters, audio adapters, one or more other interfaces, or a combination thereof. In some examples, the one or more input/output devices  870  include keyboards, pointing devices, displays, speakers, microphones, touch screens, one or more other devices, or a combination thereof. In some examples, the processor  852  is configured to detect interaction events based on user input received via the one or more input/output interfaces  850 . Additionally, in some implementations, the processor  852  is configured to send a display to a display device via the one or more input/output interfaces  850 . In some implementations, the one or more input/output devices  870  include the 3D printer device  890 . 
     In a particular example, the processor  852  is configured to communicate with (or send signals to) one or more devices  880  using the communications interface  826 . In some implementations, the communications interface  826  includes one or more wired interfaces (e.g., Ethernet interfaces), one or more wireless interfaces that comply with an IEEE 802.11 communication protocol, one or more other wireless interfaces, one or more optical interfaces, or one or more other network interfaces, or a combination thereof. In some examples, the one or more devices  880  include host computers, servers, workstations, one or more other computing devices, or a combination thereof. 
     In some implementations, the computing device  810  is configured to communicate with the one or more devices  880  using the system  400 . To illustrate, in some examples, the communications interface  826  includes an EM interface configured to communicate with the one or more devices  880  using an EM network that includes the system  400 . Alternatively or in addition, in some implementations, the computing device  810  is configured to communicate with the one or more devices  880  using the system  500 . To illustrate, in some examples, the communications interface  826  includes a radio interface configured to communicate with the one or more devices  880  using a radio network that includes the system  500 . 
     The illustrations of the examples described herein are intended to provide a general understanding of the structure of the various implementations. The illustrations are not intended to serve as a complete description of all of the elements and features of apparatus and systems that utilize the structures or methods described herein. Many other implementations may be apparent to those of skill in the art upon reviewing the disclosure. Other implementations may be utilized and derived from the disclosure, such that structural and logical substitutions and changes may be made without departing from the scope of the disclosure. For example, method operations may be performed in a different order than shown in the figures or one or more method operations may be omitted. Accordingly, the disclosure and the figures are to be regarded as illustrative rather than restrictive. 
     Moreover, although specific examples have been illustrated and described herein, it should be appreciated that any subsequent arrangement designed to achieve the same or similar results may be substituted for the specific implementations shown. This disclosure is intended to cover any and all subsequent adaptations or variations of various implementations. Combinations of the above implementations, and other implementations not specifically described herein, will be apparent to those of skill in the art upon reviewing the description. 
     The Abstract of the Disclosure is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, various features may be grouped together or described in a single implementation for the purpose of streamlining the disclosure. Examples described above illustrate, but do not limit, the disclosure. It should also be understood that numerous modifications and variations are possible in accordance with the principles of the present disclosure. As the following claims reflect, the claimed subject matter may be directed to less than all of the features of any of the disclosed examples. Accordingly, the scope of the disclosure is defined by the following claims and their equivalents.