Patent Publication Number: US-9425513-B2

Title: Lens with spatial mixed-order bandpass filter

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) AND CLAIM OF PRIORITY 
     This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Ser. No. 61/843,749 filed on Jul. 8, 2013 and entitled “SINGLE-SUBSTRATE PLANAR LENS EMPLOYING SPATIAL MIXED-ORDER BANDPASS FILTER.” The above-identified provisional patent document is hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This application relates generally to wireless communication systems and, more specifically, to the use of a lens in electromagnetic (EM) wave transmissions. 
     BACKGROUND 
     A lens is an electronic device that can focus a planar wave front of EM waves to a focal point or, conversely, collimate spherical waves emitting from a point source to plane waves. Such fundamental characteristics are widely used in various applications, such as communication, imaging, radar, and spatial power combining systems. For example, in millimeter-wave frequency bands that fifth generation (5G) communication standards may employ, lenses have been paid considerable attention as a potential solution to overcome limits in gain and beam steering capabilities of antennas operating in such frequency bands. 
     SUMMARY 
     Embodiments of this disclosure provide lenses with spatial mixed-order bandpass filters and related systems and methods. 
     In one example embodiment, an apparatus includes a plurality of layers of conductive elements and a substrate layer. A first of the layers of conductive elements has a first portion that includes conductive elements having a first structure different from a second structure of conductive elements in a second portion of the first layer. 
     In another example embodiment, a method includes transmitting electromagnetic waves through a lens. The lens includes a plurality of layers of conductive elements and a substrate layer. A first of the layers of conductive elements has a first portion that includes conductive elements having a first structure different from a second structure of conductive elements in a second portion of the first layer. 
     In yet another example embodiment, a system includes a lens, at least one antenna, and a transmitter or transceiver. The lens includes a plurality of layers of conductive elements and a substrate layer. A first of the layers of conductive elements has a first portion that includes conductive elements having a first structure different from a second structure of conductive elements in a second portion of the first layer. The at least one antenna is configured to transmit or receive electromagnetic waves through the lens. The transmitter or transceiver is configured to generate signals for wireless transmission or receive signals transmitted wirelessly via the antenna. 
     Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document. The term “couple” and its derivatives refer to any direct or indirect communication between two or more elements, whether or not those elements are in physical contact with one another. The terms “transmit,” “receive,” and “communicate,” as well as derivatives thereof, encompass both direct and indirect communication. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, means to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like. The phrase “at least one of,” when used with a list of items, means that different combinations of one or more of the listed items may be used, and only one item in the list may be needed. For example, “at least one of: A, B, and C” includes any of the following combinations: A, B, C, A and B, A and C, B and C, and A and B and C. 
     Definitions for other certain words and phrases are provided throughout this patent document. Those of ordinary skill in the art should understand that in many if not most instances, such definitions apply to prior as well as future uses of such defined words and phrases. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which like reference numerals represent like parts: 
         FIG. 1  illustrates an example wireless system in accordance with this disclosure; 
         FIG. 2  illustrates an example evolved Node B (eNB) according to this disclosure; 
         FIG. 3  illustrates an example user equipment (UE) according to this disclosure; 
         FIG. 4  illustrates an example planar frequency selective surface (FSS) lens in accordance with this disclosure; 
         FIG. 5  illustrates an exploded view of an example topology of a mixed-order bandpass FSS lens in accordance with this disclosure; 
         FIGS. 6A and 6B  illustrate perspective views of an example topology of a unit cell for a second-order bandpass FSS in accordance with this disclosure; 
         FIGS. 7A through 7C  illustrate perspective views of an example topology of a unit cell for a capacitively-loaded, first-order bandpass FSS in accordance with this disclosure; 
         FIG. 8  illustrates an example topology and equivalent circuit model of a bandpass FSS in accordance with this disclosure; 
         FIGS. 9A and 9B  illustrate equivalent circuit models for an example second-order bandpass FSS and an example capacitively-loaded, first-order bandpass FSS, respectively, of an FSS lens in accordance with this disclosure; and 
         FIGS. 10A and 10B  illustrate example magnitude and phase plots, respectively, of transmittance of a mixed-order bandpass FSS lens in accordance with this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1 through 10B , discussed below, and the various embodiments used to describe the principles of this disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of this disclosure may be implemented in any suitably-arranged system or device. 
     Various figures described below may be implemented in wireless communication systems, possibly including those that use orthogonal frequency division multiplexing (OFDM) or orthogonal frequency division multiple access (OFDMA) communication techniques. However, the descriptions of these figures are not meant to imply physical or architectural limitations in the manner in which different embodiments may be implemented. Different embodiments of this disclosure may be implemented in any suitably-arranged communication systems using any suitable communication techniques. 
       FIG. 1  illustrates an example wireless network  100  according to this disclosure. The embodiment of the wireless network  100  shown in  FIG. 1  is for illustration only. Other embodiments of the wireless network  100  could be used without departing from the scope of this disclosure. 
     As shown in  FIG. 1 , the wireless network  100  includes an eNodeB (eNB)  101 , an eNB  102 , and an eNB  103 . The eNB  101  communicates with the eNB  102  and the eNB  103 . The eNB  101  also communicates with at least one Internet Protocol (IP) network  130 , such as the Internet, a proprietary IP network, or other data network. 
     The eNB  102  provides wireless broadband access to the network  130  for a first plurality of user equipments (UEs) within a coverage area  120  of the eNB  102 . The first plurality of UEs includes a UE  111 , which may be located in a small business (SB); a UE  112 , which may be located in an enterprise (E); a UE  113 , which may be located in a WiFi hotspot (HS); a UE  114 , which may be located in a first residence (R); a UE  115 , which may be located in a second residence (R); and a UE  116 , which may be a mobile device (M) like a cell phone, a wireless laptop, a wireless PDA, or the like. The eNB  103  provides wireless broadband access to the network  130  for a second plurality of UEs within a coverage area  125  of the eNB  103 . The second plurality of UEs includes the UE  115  and the UE  116 . In some embodiments, one or more of the eNBs  101 - 103  may communicate with each other and with the UEs  111 - 116  using 5G, LTE, LTE-A, WiMAX, WiFi, or other wireless communication techniques. 
     Depending on the network type, other well-known terms may be used instead of “eNodeB” or “eNB,” such as “base station” or “access point.” For the sake of convenience, the terms “eNodeB” and “eNB” are used in this patent document to refer to network infrastructure components that provide wireless access to remote terminals. Also, depending on the network type, other well-known terms may be used instead of “user equipment” or “UE,” such as “mobile station,” “subscriber station,” “remote terminal,” “wireless terminal,” or “user device.” For the sake of convenience, the terms “user equipment” and “UE” are used in this patent document to refer to remote wireless equipment that wirelessly accesses an eNB, whether the UE is a mobile device (such as a mobile telephone or smartphone) or is normally considered a stationary device (such as a desktop computer or vending machine). 
     Dotted lines show the approximate extents of the coverage areas  120  and  125 , which are shown as approximately circular for the purposes of illustration and explanation only. It should be clearly understood that the coverage areas associated with eNBs, such as the coverage areas  120  and  125 , may have other shapes, including irregular shapes, depending upon the configuration of the eNBs and variations in the radio environment associated with natural and man-made obstructions. 
     As described in more detail below, the eNBs  101 - 103  and/or the UEs  111 - 116  could include one or more mixed-order bandpass frequency selective surface (FSS) lenses. 
     Although  FIG. 1  illustrates one example of a wireless network  100 , various changes may be made to  FIG. 1 . For example, the wireless network  100  could include any number of eNBs and any number of UEs in any suitable arrangement. Also, the eNB  101  could communicate directly with any number of UEs and provide those UEs with wireless broadband access to the network  130 . Similarly, each eNB  102 - 103  could communicate directly with the network  130  and provide UEs with direct wireless broadband access to the network  130 . Further, the eNB  101 ,  102 , and/or  103  could provide access to other or additional external networks, such as external telephone networks or other types of data networks. 
       FIG. 2  illustrates an example eNB  102  according to this disclosure. The embodiment of the eNB  102  illustrated in  FIG. 2  is for illustration only, and the eNBs  101  and  103  of  FIG. 1  could have the same or similar configuration. However, eNBs come in a wide variety of configurations, and  FIG. 2  does not limit the scope of this disclosure to any particular implementation of an eNB. 
     As shown in  FIG. 2 , the eNB  102  includes multiple antennas  205   a - 205   n , multiple RF transceivers  210   a - 210   n , transmit (TX) processing circuitry  215 , and receive (RX) processing circuitry  220 . The eNB  102  also includes a controller/processor  225 , a memory  230 , and a backhaul or network interface  235 . 
     The RF transceivers  210   a - 210   n  receive from the antennas  205   a - 205   n  incoming RF signals, such as signals transmitted by UEs in the wireless network  100 . The RF transceivers  210   a - 210   n  down-convert the incoming RF signals to generate IF or baseband signals. The IF or baseband signals are sent to the RX processing circuitry  220 , which generates processed baseband signals by filtering, decoding, and/or digitizing the baseband or IF signals. The RX processing circuitry  220  transmits the processed baseband signals to the controller/processor  225  for further processing. 
     The TX processing circuitry  215  receives analog or digital data (such as voice data, web data, e-mail, or interactive video game data) from the controller/processor  225 . The TX processing circuitry  215  encodes, multiplexes, and/or digitizes the outgoing baseband data to generate processed baseband or IF signals. The RF transceivers  210   a - 210   n  receive the outgoing processed baseband or IF signals from the TX processing circuitry  215  and up-converts the baseband or IF signals to RF signals that are transmitted via the antennas  205   a - 205   n.    
     The controller/processor  225  can include one or more processors or other processing devices that control the overall operation of the eNB  102 . For example, the controller/processor  225  could control the reception of forward channel signals and the transmission of reverse channel signals by the RF transceivers  210   a - 210   n , the RX processing circuitry  220 , and the TX processing circuitry  215  in accordance with well-known principles. The controller/processor  225  could support additional functions as well, such as more advanced wireless communication functions. For instance, the controller/processor  225  could support beam forming or directional routing operations in which outgoing signals from multiple antennas  205   a - 205   n  are weighted differently to effectively steer the outgoing signals in a desired direction. Any of a wide variety of other functions could be supported in the eNB  102  by the controller/processor  225 . In some embodiments, the controller/processor  225  includes at least one microprocessor or microcontroller. 
     The controller/processor  225  is also capable of executing programs and other processes resident in the memory  230 , such as a basic OS. The controller/processor  225  can move data into or out of the memory  230  as required by an executing process. 
     The controller/processor  225  is also coupled to the backhaul or network interface  235 . The backhaul or network interface  235  allows the eNB  102  to communicate with other devices or systems over a backhaul connection or over a network. The interface  235  could support communications over any suitable wired or wireless connection(s). For example, when the eNB  102  is implemented as part of a cellular communication system (such as one supporting 5G, LTE, or LTE-A), the interface  235  could allow the eNB  102  to communicate with other eNBs over a wired or wireless backhaul connection. When the eNB  102  is implemented as an access point, the interface  235  could allow the eNB  102  to communicate over a wired or wireless local area network or over a wired or wireless connection to a larger network (such as the Internet). The interface  235  includes any suitable structure supporting communications over a wired or wireless connection, such as an Ethernet or RF transceiver. 
     The memory  230  is coupled to the controller/processor  225 . Part of the memory  230  could include a RAM, and another part of the memory  230  could include a Flash memory or other ROM. 
     As described in more detail below, the eNB  102  could include one or more mixed-order bandpass FSS lenses. 
     Although  FIG. 2  illustrates one example of eNB  102 , various changes may be made to  FIG. 2 . For example, the eNB  102  could include any number of each component shown in  FIG. 2 . As a particular example, an access point could include a number of interfaces  235 , and the controller/processor  225  could support routing functions to route data between different network addresses. As another particular example, while shown as including a single instance of TX processing circuitry  215  and a single instance of RX processing circuitry  220 , the eNB  102  could include multiple instances of each (such as one per RF transceiver). Also, various components in  FIG. 2  could be combined, further subdivided, or omitted, and additional components could be added according to particular needs. 
       FIG. 3  illustrates an example UE  116  according to this disclosure. The embodiment of the UE  116  illustrated in  FIG. 3  is for illustration only, and the UEs  111 - 115  of  FIG. 1  could have the same or similar configuration. However, UEs come in a wide variety of configurations, and  FIG. 3  does not limit the scope of this disclosure to any particular implementation of a UE. 
     As shown in  FIG. 3 , the UE  116  includes an antenna  305 , a radio frequency (RF) transceiver  310 , transmit (TX) processing circuitry  315 , a microphone  320 , and receive (RX) processing circuitry  325 . The UE  116  also includes a speaker  330 , a main processor  340 , an input/output (I/O) interface (IF)  345 , a keypad  350 , a display  355 , and a memory  360 . The memory  360  includes a basic operating system (OS) program  361  and one or more applications  362 . 
     The RF transceiver  310  receives from the antenna  305  an incoming RF signal transmitted by an eNB of the network  100 . The RF transceiver  310  down-converts the incoming RF signal to generate an intermediate frequency (IF) or baseband signal. The IF or baseband signal is sent to the RX processing circuitry  325 , which generates a processed baseband signal by filtering, decoding, and/or digitizing the baseband or IF signal. The RX processing circuitry  325  transmits the processed baseband signal to the speaker  330  (such as for voice data) or to the main processor  340  for further processing (such as for web browsing data). 
     The TX processing circuitry  315  receives analog or digital voice data from the microphone  320  or other outgoing baseband data (such as web data, e-mail, or interactive video game data) from the main processor  340 . The TX processing circuitry  315  encodes, multiplexes, and/or digitizes the outgoing baseband data to generate a processed baseband or IF signal. The RF transceiver  310  receives the outgoing processed baseband or IF signal from the TX processing circuitry  315  and up-converts the baseband or IF signal to an RF signal that is transmitted via the antenna  305 . 
     The main processor  340  can include one or more processors or other processing devices and execute the basic OS program  361  stored in the memory  360  in order to control the overall operation of the UE  116 . For example, the main processor  340  could control the reception of forward channel signals and the transmission of reverse channel signals by the RF transceiver  310 , the RX processing circuitry  325 , and the TX processing circuitry  315  in accordance with well-known principles. In some embodiments, the main processor  340  includes at least one microprocessor or microcontroller. 
     The main processor  340  is also capable of executing other processes and programs resident in the memory  360 . The main processor  340  can move data into or out of the memory  360  as required by an executing process. In some embodiments, the main processor  340  is configured to execute the applications  362  based on the OS program  361  or in response to signals received from eNBs or an operator. The main processor  340  is also coupled to the I/O interface  345 , which provides the UE  116  with the ability to connect to other devices, such as laptop computers and handheld computers. The I/O interface  345  is the communication path between these accessories and the main processor  340 . 
     The main processor  340  is also coupled to the keypad  350  and the display  355 . The operator of the UE  116  can use the keypad  350  to enter data into the UE  116 . The display  355  may be a liquid crystal display or other display capable of rendering text and/or at least limited graphics, such as from web sites. 
     The memory  360  is coupled to the main processor  340 . Part of the memory  360  could include a random access memory (RAM), and another part of the memory  360  could include a Flash memory or other read-only memory (ROM). 
     As described in more detail below, the UE  116  could include one or more mixed-order bandpass FSS lenses. 
     Although  FIG. 3  illustrates one example of UE  116 , various changes may be made to  FIG. 3 . For example, various components in  FIG. 3  could be combined, further subdivided, or omitted, and additional components could be added according to particular needs. As a particular example, the main processor  340  could be divided into multiple processors, such as one or more central processing units (CPUs) and one or more graphics processing units (GPUs). Also, while  FIG. 3  illustrates the UE  116  configured as a mobile telephone or smartphone, UEs could be configured to operate as other types of mobile or stationary devices. 
     Embodiments of this disclosure recognize and take into account the fact that lenses may provide several significant improvements to antennas used in communication systems, including microwave and millimeter wave (MMW) communication systems. These improvements can include increased antenna directivity for specific point-to-point communications and improved link availability; increased antenna gains for better signal-to-noise ratios, data capacities, and link reliabilities; reduced antenna side-lobes for more effective use of antenna radiation patterns and for less interference from other radios; and reduced antenna losses for lower system power consumptions. Lenses provide these improvements while maintaining the capability of antenna pattern beam steering, which is useful in many microwave and MMW communication systems. Further, these enhancements can be realized using only passive structures to avoid the complexity and energy losses associated with approaches where active devices are used for such improvements. 
     Embodiments of this disclosure also recognize and take into account the fact that phase shifts realized by a frequency selective surface (FSS) can be used to design planar lenses. In these lenses, a wide range of phase shifts may be covered by tuning high-order bandpass FSSs. For example, cascading multiple first-order FSSs with a spacing of a quarter wavelength between each panel can increase the overall thickness of the FSS and enhance the sensitivity of the frequency response to the angle and polarization of incidence of EM waves. Advances in FSS technology also enable the synthesis of low-profile high-order bandpass FSSs that are composed entirely of non-resonant periodic structures. One type of FSS uses a pair of inductive and capacitive layers to increase one or more orders of the bandpass response. However, this stacked topology with multiple bonding layers constitutes a bottleneck for commercial MMW applications due to its high cost and to performance degradations caused by multiple bonding layers. 
     Embodiments of this disclosure further recognize and take into account the fact that certain planar lens technologies for microwave or MMW systems have critical drawbacks, which hamper their practical applications. These drawbacks can include the following:
         bulk and size—to obtain phase changes for collimation or focusing, fully dielectric lenses are thick, bulky, and heavy; and   complexity—construction that involves multiple metal and dielectric layers, alternating metal layers of different and complicated layout designs, and bonding layers between dielectric layers having dielectric and electrical properties inconsistent with other dielectric layers increase cost, weight, and insertion losses of planar lenses.       

     Additionally, shortcomings in certain high-order bandpass FSS lenses may include the following:
         high fabrication costs due to a large number of substrate, metal, and bonding layers;   high ohmic losses due to a large number of metallic traces;   high dielectric losses due to a large number of substrate and bonding layers; and   poor fabrication tolerances due to mismatches in material properties between bonding layers and dielectric layers.       

     Accordingly, various embodiments of this disclosure provide low-cost, low-profile planar lenses. The lenses of this disclosure can be used in various ways, such as for gain/pattern enhancements of radiating elements (such as antennas) operating in wireless communication platforms like UEs and eNBs. Moreover, various embodiments of this disclosure provide thinner configurations of planar lenses to cover elements with a reduced loading complexity. Further, the lenses of various embodiments of this disclosure may enhance system gains at RF front ends without using active devices and thus improve signal-to-noise ratios (SNRs). In addition, the increase in the power level of a received signal may allow for a reduction of power consumption in the overall system and more reliable wireless connections. 
     In various embodiments of this disclosure, planar lenses employ a mixed-order bandpass filter response, which may allow for a reduction in the number of substrates and metal layers in the lenses while maintaining phase shift targets. In some embodiments, the planar lenses of the present disclosure employ a single-substrate spatial mixed-order bandpass filter including one dielectric substrate and two metal layers. This approach allows for the reduction in the number of substrate and metal layers while maintaining desired goals for phase shift. For example, some conventional lenses employ a third-order bandpass filter response, four substrates, five metal layers, and three bonding layers (where both inductive and capacitive layers are used). However, to achieve a comparable or larger amount of phase shift, the single-substrate spatial mixed-order bandpass lens of the present disclosure uses one substrate and two metal layers and may not require bonding layers. 
       FIG. 4  illustrates an example planar FSS lens  400  in accordance with this disclosure. In this illustrative example, a phase shift is realized by the phase response of an FSS of the lens  400 . An aperture of the lens  400  is split into multiple different zones (such as Zone1, Zone2, . . . , ZoneN). As depicted in  FIG. 4 , rays passing through the different zones of the FSS experience different amounts of phase shift. More specifically, the phase shift experienced by rays passing through the lens  400  decreases the further the rays are from the center of the lens  400 , so there are higher phase shifts near the center of the lens  400  and lower phase shifts near the edges of the lens  400 . 
     It may be necessary or desirable to reduce the focal length f of the lens  400  for compact wireless devices having small form factor demands, such as UEs. Reducing the focal length can involve maximizing the difference in phase shifts across the lens  400  (where Δφ diff =|φ 1 −φ N |). The value of Δφ diff  is determined by the tunable range of the phase shift of FSS elements within the pass band of the FSS. The lens  400  may acquire the tunable range by modifying the sizes of the FSS elements slightly according to the number of zones. 
     Other design parameters for the lens  400  include the size of the lens aperture (AP), the thickness (t) of the lens  400 , and the size of FSS unit cells. As the aperture size increases, the focusing gain increases, but the focal length f also increases when Δφ diff  is fixed. The lens thickness is related to the sensitivity of the lens  400  to the angle of incidence of EM waves. In addition, smaller FSS unit cells lead to finer focusing resolutions of the lens  400  but can require better tolerances of a fabrication process. The aforementioned design parameters in the lens  400  may be determined by considering the tradeoffs among performance, size, and fabrication conditions. 
       FIG. 5  illustrates an exploded view of an example topology of a mixed-order bandpass FSS lens  500  in accordance with this disclosure. In this illustrative example, the lens  500  includes a substrate layer  505  and two conductive element layers  510  and  515 . As is described in greater detail below, the lens  500  is mixed-order in that the lens  500  includes a capacitively-loaded first-order bandpass FSS portion  520  and a second-order bandpass FSS portion  525 . Portion  530  of layer  510  is enlarged to illustrate details of the patterns of conductive elements present in layer  510 , which is described in greater detail below. 
       FIGS. 6A and 6B  illustrate perspective views of an example topology of a unit cell  600  for a second-order bandpass FSS in accordance with this disclosure. In this illustrative embodiment, the unit cell  600  is an example of a unit cell present within a cross section of the second-order bandpass FSS portion  525  of the lens  500  in  FIG. 5 . In  FIG. 6A , the unit cell  600  is depicted in a side view, with a portion  605  of the substrate layer  505  present in the unit cell  600  depicted as being transparent so that the structure of a conductive element  610  in the conductive element layer  510  is viewable. In  FIG. 6B , the unit cell  600  is depicted in a top and/or bottom view, with the structure of the conductive element  610  and/or a conductive element  615  distinguished from the underlying portion  605  of the substrate layer  505 . 
     The unit cell  600  is a second-order bandpass FSS. For example, the combination of a dielectric in the substrate portion  605  and metal in the conductive elements  610  and  615  provides a bandpass filter response for EM waves that propagate through the unit cell  600 . Each side of the unit cell  600  provides a single-order bandpass FSS such that the unit cell  600  is a second-order bandpass FSS. Several such unit cells  600  form the second-order bandpass FSS portion  525  of the lens  500 . For instance, the outer portions of the lens  500  may employ the second-order bandpass FSS. Different amounts of phase shifts and tuning of phase shifts may be obtainable by varying properties of the unit cell  600 . These properties include, for example, the size of the conductive elements  610 / 615  in the conductive element layers  510 / 515 , the thickness of the conductive elements  610 / 615  in the conductive element layers  510 / 515 , g 1  (the size(s) of the gap between adjacent conductive elements  610 / 615  in a conductive element layer  510 / 515 ), g 2  (the size(s) of the gaps within the conductive elements  610 / 615 ), L (the length between gaps on opposite ends of the conductive element), w (the width between gaps on the same end of the conductive element), and/or other properties of the structure of the conductive elements  610 / 615  in the unit cell  600 . 
     Note that the structure of the conductive elements  610  and  615  shown in  FIGS. 6A and 6B  is for the purpose of illustrating one example of a second-order bandpass FSS. Other suitable structure shapes may be utilized (such as rectangles, triangles, and ellipses). Additionally, any number of different sizes, positions, and number of gaps within the conductive elements  610 / 615  may be suitably employed in accordance with the principles of the present disclosure. 
       FIGS. 7A through 7C  illustrate perspective views of an example topology of a unit cell  700  for a capacitively-loaded, first-order bandpass FSS in accordance with this disclosure. In this illustrative embodiment, the unit cell  700  is an example of a unit cell present within a cross section of the capacitively-loaded, first-order bandpass FSS portion  520  of the lens  500  in  FIG. 5 . 
     In  FIG. 7A , the unit cell  700  is depicted in a side view, with a portion  705  of the substrate layer  505  present in the unit cell  700  depicted as transparent so that the structure of conductive elements  710  in the conductive element layer  510  is viewable. In  FIG. 7B , the unit cell  700  is depicted from one side  720  (such as a top and/or bottom view), with the structure of the conductive elements  710  distinguished from the underlying portion  705  of the substrate layer  505 . In  FIG. 7C , the unit cell  700  is depicted from the other side  725  (such as a bottom and/or top side), with the structure of conductive elements  715  again distinguished from the underlying portion  705  of the substrate layer  505 . In various embodiments, the conductive elements  710 / 715  have the same structure as the conductive elements  610 / 615  in the unit cell  600 . 
     The unit cell  700  is a capacitively-loaded, first-order bandpass FSS. For example, the combination of a dielectric in the substrate portion  705  and metal in the conductive elements  710  provides a capacitive filter response for EM waves that propagate through the side  720  of the unit cell  700 . For example, the structure of the conductive elements may have a patch structure, such as a rectangular shape, which provides the capacitive filter response for EM waves that propagate through the side  720  of the unit cell  700 . Similarly, as discussed above with regard to  FIGS. 6A and 6B , the combination of the dielectric in the substrate portion  705  and metal in the conductive elements  715  provides a bandpass filter response for EM waves that propagate through the side  725  of the unit cell  700 . Thus, the unit cell  700  is a first-order bandpass FSS that is “capacitively loaded.” 
     Several such unit cells  700  form the capacitively-loaded, first-order bandpass FSS portion  520  of the lens  500 . For instance, the inner portions of the lens  500  may employ the capacitively-loaded, first-order bandpass FSS. Different amounts of phase shifts and tuning of phase shifts may be obtainable by varying properties of the unit cell  700 . As discussed above with regard to  FIGS. 6A and 6B , these properties include, for example, size, thickness, g 1 , g 2 , L, w, and/or other properties of the structure of the conductive elements  710 / 715  in the unit cell  700 . Additionally, the side  720  includes the property g 3 , which refers to the size(s) of the gap between adjacent conductive elements  710  in the side  720  and/or in the portion  525  of the layer  510  of the lens  500 . 
     Note that the illustrations of the unit cells  600  and  700  are examples only and for the purpose of showing the structure and arrangement of individual conductive elements within their respective layers. As illustrated in  FIG. 5 , the lens  500  includes multiple unit cells, and the substrate layer  505  is substantially contiguous or unbroken across the multiple unit cells. 
       FIG. 8  illustrates an example topology and equivalent circuit model of a bandpass FSS  800  in accordance with this disclosure. In this illustrative example, the FSS  800  may be a portion of either side of the lens  500  having a bandpass filter metal layer structure, such as the layer  515  or the portions of the layer  510  in the second-order portion  525 . As shown in  FIG. 8 , the combination of the dielectric in the substrate layer  505  and the metal in the conductive element layer(s)  510  and/or  515  provides a bandpass filter response for EM waves that propagate through the bandpass FSS  800 . A circuit model  805  illustrates a shunt resonator including a shunt inductor and shunt capacitor realized on a single surface including conductive elements and dielectric gaps. 
       FIGS. 9A and 9B  illustrate equivalent circuit models for an example second-order bandpass FSS and an example capacitively-loaded, first-order bandpass FSS, respectively, of an FSS lens in accordance with this disclosure. In this illustrative example, a circuit model  900  shows the circuit equivalence of the phase shift obtained by EM waves that propagate through the second-order bandpass FSS bandpass portions of an FSS lens, such as the portion  525  in the lens  500 . As depicted, the model  900  includes two bandpass filter responses (a capacitor in parallel with an inductor). A circuit model  905  shows the circuit equivalence of the phase shift obtained by EM waves that propagate through a capacitively-loaded, first-order bandpass FSS, such as the portion  520  in the lens  500 . As depicted, the model  905  includes one bandpass filter response (a capacitor in parallel with an inductor) on one side, with the other side having a capacitive filter response. The circuit models  900  and  905  are for the purpose of illustrating an equivalent or approximate representation of the phase shift properties of the different portions of the FSS lens  500 . 
     The capacitive loading in the capacitively-loaded first-order bandpass FSS lowers the overall phase shift values for the portion  520  of the FSS lens  500  at the operating frequency of the lens  500 . The capacitive loading can allow the portion  520  of the FSS lens  500  to cover a new tunable range of phase shifts that may not be covered by a bandpass-only spatial FSS. For example, the tunable range of phase shifts for different-order bandpass spatial FSSs may overlap. As a result, a mixed-order bandpass-only FSS may not provide additional tunable ranges of phase shifts beyond that of the highest order in the bandpass FSS. For instance, the tunable range of phase shifts for first- and second-order bandpass FSSs may be encompassed within the tunable range of phase shifts for a third-order bandpass FSS. On the other hand, the capacitive loading of the portion  520  of the FSS lens  500  modifies the slope of the lower cutoff frequency response, which moves the tunable range of phase shifts for the capacitively-loaded, first-order FSS portion  520  of the FSS lens  500  to cover a range that may not be covered by the second-order bandpass FSS portion  525  of the FSS lens  500 . 
     Combining the capacitively-loaded, first-order bandpass FSS portion  520  with the second-order bandpass FSS portion  525  to form a mixed-order bandpass FSS lens  500  provides enhancements in the tunable range of phase shifts of the FSS lens structure without increasing the order of the filter response. In other words, the capacitively-loaded first- and second-order FSS lens of the present disclosure may provide a tunable range of phase shifts comparable to that of a third-order bandpass filter, which is unexpected for bandpass filters. In addition, the use of a single substrate, while providing a comparable tunable range of phase shifts as a third-order bandpass FSS lens (which may need multiple substrates and bonding layers), provides several advantages as described herein. 
       FIGS. 10A and 10B  illustrate example magnitude and phase plots, respectively, of transmittance of a mixed-order bandpass FSS lens in accordance with this disclosure.  FIG. 10A  illustrates a plot  1000  of the magnitude response of different portions of the FSS lens  500 .  FIG. 10B  illustrates a plot  1005  of the frequency response of different portions of the FSS lens  500 . As illustrated, the phase response for the first-order portions of the FSS lens  500  does not overlap the phase response for the second-order portions of the FSS lens  500 . As a result, a tunable range  1010  of the mixed-order FSS lens  500  is increased. In this example, the tunable range  1010  of the FSS lens  500  may be about 200°. This tunable range may be greater than some third-order bandpass FSS lenses, which may employ much larger numbers of metal, substrate, and/or bonding layers. Accordingly, the mixed-order bandpass FSS lens  500  can achieve desired goals of attaining suitable phase shift tunable ranges while reducing the size, thickness, and/or machining limitations of existing lenses. 
     In particular embodiments, the lens  500  can represent a single-substrate mixed-order bandpass FSS lens designed for a 28.2 GHz operating frequency with a unit cell size of 2.7 mm, and the dielectric constant and thickness of the substrates (Rogers 3003) are 3 mm and 0.5 mm, respectively. In these embodiments, the lens  500  provides sub-wavelength filtering. For example, the size or lateral dimension of the conductive elements and the overall thickness of the lens may be less than a wavelength of the operating frequency designed for spatial phase shifting by the lens  500 . 
     To achieve different steps of phase shift, design parameters (such as g 1 , g 2 , g 3 , w, and L) are appropriately tuned for the second-order and capacitively-loaded first-order bandpass portions. Values for the design parameters of the FSS lens  500  for the 28.2 GHz design example are listed in the legend for the plots  1000  and  1005 . The values and dimensions described above are examples only and are not limitations on different dimensions that may be utilized in accordance with embodiments of this disclosure. For example, the sizes, number, and/or gaps of the conductive elements in any of the layers may be increased or decreased based on various factors, such as phase shifts, lens thicknesses, and/or machining tolerances. 
     The mixed-order bandpass FSS lens  500  of the present disclosure may utilize fewer metal and dielectric layers than that of existing planar lenses while providing comparable or better ranges of spatial phase shifts. First-order capacitively-loaded elements may be placed in the center of the FSS lens  500 , while second-order elements may be placed around the outside of the lens. The higher absolute phase delay of the first-order capacitively-loaded elements is utilized in the central portion of the lens  500  to provide a larger phase delay for collimation or focusing EM waves near the center of the lens. The second-order elements towards the outer region of the lens  500  provide less absolute phase delay but contribute to a wider range of phase delay for tuning the collimation or focusing of the planar lens  500 . 
     Depending on the implementation, advantages of using the mixed-order bandpass FSS lens of this disclosure may include:
         lower fabrication costs due to a single substrate layer;   lower fabrication costs due to the removal of the need for bonding layers;   lower dielectric losses due to smaller numbers of substrate and bonding layers; and   lower ohmic losses due to smaller numbers of metal or conductive layers.       

     In various embodiments, the FSS lenses can enhance coverage of a beam steering angle. For example, an FSS lens may include spatial phase shifters that cause waves propagating through the lens to be focused in any desired angle. In other embodiments, the FSS lenses may be utilized for beam broadening. This beam broadening can provide different levels of beam widths in different angles of radiation, which can enable multi-functional wireless communications (such as antenna diversity). 
     While various embodiments above describe FSS lenses as being used in conjunction with a patch array antenna, the FSS lenses of this disclosure can be used with any type or shape of antennas, such as horn antennas, monopole antennas, dipole antennas, and slot antennas. Additionally, while the shape of the FSS lens is illustrated in some of the figures as being flat, the FSS lens may be a curved, non-flat, and/or conformal lens. Also, while the use of metal for the conductive elements has been described, the conductive elements could be fabricated from other conductive material(s). Moreover, while the shape of the conductive elements is illustrated in some of the figures as being rectangular or square, the conductive elements may have other shapes. For example, the conductive elements may be hexagons, ellipses, circles, octagons, shapes with curved as well as straight edges, etc. In addition, the FSS lenses of this disclosure can be designed and fabricated for applications involving nearly any RF frequency range, from a few megahertz to multiple hundreds of gigahertz (such as 1 MHz to 300 GHz). Finally, the planar lenses of this disclosure can be fabricated and integrated with various platforms without strict fabrication process requirements. For instance, patterns in the planar lenses of this disclosure may only be two dimensional without requiring vertical structures. 
     Embodiments of this disclosure provide several significant improvements to antennas for wireless communication systems and other applications. For example, the FSS lenses of this disclosure can provide increased antenna gains and directivities, reduced antenna pattern side-lobes, and reduced antenna losses. These technical improvements provide a host of commercial and market advantages to any products and systems using such lenses. For instance, the FSS lenses of this disclosure can provide higher data throughputs or higher data capacities. The higher antenna gains of antennas with lenses produce higher signal-to-noise ratio values, and higher signal-to-noise ratio values provide higher data throughputs and higher data capacities. 
     As another example, the FSS lenses of this disclosure can provide better connection availabilities and better connection establishments. The FSS lenses can provide higher gains and stronger signals, and stronger signal levels between eNBs and UEs (or between other devices) provide more dependable initial establishment of connection between the devices. The FSS lenses of this disclosure can also provide more reliable wireless connections due to higher directivities and higher interference suppressions of antennas with lenses. Higher directivities of beam steering provide alignment of antenna patterns with communication paths or channels. Higher directivities and lower side-lobes also reduce the level of undesired signals intercepted along a desired communication path. The FSS lenses of this disclosure can further provide lower densities of eNBs with a greater range of UEs. The higher antenna gains allow UEs to operate farther from their eNBs with comparable transmitter powers, allowing fewer eNBs within a given area. 
     As yet another example, the FSS lenses of this disclosure can provide longer battery life for mobile or consumer products. The enhanced gain of a mobile antenna allows a reduction in transmitter power for comparable signal level. The improved gain of an eNB antenna provides a reduction in the power required for the receiver at a UE. The enhanced gain can reduce the electrical power consumed in the UE&#39;s electronics and allow longer operations between battery recharge cycles. The FSS lenses of this disclosure can also provide smaller products or products with more features and functions. The enhanced antenna directivities or gains provided allow the area used by the antenna to be reduced. The extra area may be re-allocated for components needed for other system functions or features, or the extra area may be used to reduce the overall size and volume of a UE or eNB. 
     Embodiments of this disclosure also provide several design and construction advantages. For example, the FSS lenses of this disclosure may reduce the number of both metal and dielectric layers used, which can simplify lens design and construction; reduce the lens cost, thickness (size), and weight; and reduce or eliminate extraneous materials in lens construction that may degrade performance. 
     Although this disclosure has been described with an example embodiment, various changes and modifications may be suggested to one skilled in the art. It is intended that this disclosure encompass such changes and modifications as fall within the scope of the appended claims.