Patent Publication Number: US-9837693-B2

Title: Coaxial polarizer

Description:
The U.S. Government may have rights in the invention under Government Contract No. H94003-04-D-0005/7600009933 awarded by the U.S. Government to Northrop Grumman and under Government Contract No. F33657-02-D-0009/4743848 awarded by the U.S. Government to Lockheed Martin. 
    
    
     BACKGROUND 
     Circular polarization is converted from linear polarization by splitting the incoming wave into two orthogonal wave vectors that are approximately equal in amplitude and 90 degrees apart in phase. The device that converts polarization from one state to another is often called a polarizer. Such a device may take the form of a waveguide component, a flat layered material placed above an antenna aperture, or as a multiport microwave device. 
     Some waveguide polarizers are coaxial polarizers. Coaxial polarizers often have dielectric pieces attached to the outer surface of a conductive inner tube of the coaxial waveguide. These dielectric pieces are responsible for creating the 90 degree phase difference in two orthogonal output modes of equal amplitude which leads to circular polarization. In prior art coaxial polarizers, the outer surface of a conductive inner tube of the coaxial waveguide has protrusions and the dielectric pieces have mating indents, by which the dielectric pieces are attached to the protrusions of the conductive inner tube. The conductive inner tubes with protrusions require complex machining processes. Likewise, the dielectric pieces that are mated to the protrusions require complex machining processes. 
     SUMMARY 
     The present application relates to a coaxial polarizer. The coaxial polarizer includes an outer-conductive tube, an inner-conductive tube positioned within the outer-conductive tube and axially aligned with the outer-conductive tube, and two dielectric bars each having a flat-first surface. The inner-conductive tube has two shallow-cavities on opposing portions of an outer surface of the inner-conductive tube. The shallow-cavities each have at least one planar area. The at least one planar area has a cavity length parallel to a Z axis and has at least one cavity width that is perpendicular to the Z axis and perpendicular to a radial direction of the inner-conductive tube. The at least one cavity width includes a minimum width. The flat-first surface has a dielectric length parallel to the Z axis and a dielectric width perpendicular to the Z axis. The dielectric length is less than the cavity length and the dielectric width is less than the minimum width. Cross-sections of each of the two dielectric bars taken perpendicular to the Z axis have four respective surfaces in a rectangular shape. The two flat-first surfaces of the respective two dielectric bars contact at least a portion of the respective two planar areas of the two shallow-cavities. 
     The details of various embodiments of the claimed invention are set forth in the accompanying drawings and the description below. Other features and advantages will become apparent from the description, the drawings, and the claims. 
    
    
     
       DRAWINGS 
         FIG. 1  is an oblique view of one embodiment of a coaxial polarizer; 
         FIG. 2A  is an oblique view of one embodiment of the coaxial polarizer of  FIG. 1  with attached first dielectric and second dielectric; 
         FIG. 2B  is a top view of the coaxial polarizer of  FIG. 2A ; 
         FIG. 2C  is a cross section view of the coaxial polarizer of  FIG. 2A ; 
         FIG. 3  is an oblique view of one embodiment of the inner-conductive tube of the coaxial polarizer of  FIG. 1 ; 
         FIG. 4  is an expanded view of a shallow-cavity on the inner-conductive tube of  FIG. 3 ; 
         FIGS. 5A-5D  are various views of the first dielectric of  FIG. 2 ; 
         FIG. 6A  shows a TE 11  mode oriented parallel to the X axis; 
         FIG. 6B  is an end-view from the input end of a coaxial polarizer with an inner-conductive tube on which dielectric bars are positioned for right-hand-circular polarization when excited by the TE 11  mode shown in  FIG. 6A ; 
         FIG. 6C  is an end-view from the input end of a coaxial polarizer with an inner-conductive tube on which dielectric bars are positioned for left-hand-circular polarization when excited by the TE 11  mode shown in  FIG. 6A ; 
         FIG. 7  is an oblique view of one embodiment of a metal ring for use on an inner-conductive tube of a coaxial polarizer; 
         FIG. 8A  is an oblique view of an alternate embodiment of a dielectric bar for use on an inner-conductive tube of a coaxial polarizer; 
         FIG. 8B  is an oblique view of an embodiment of an inner-conductive tube with two of the dielectric bars of  FIG. 8A ; 
         FIG. 9A  is an oblique view of an alternate embodiment of a dielectric bar for use on an inner-conductive tube of a coaxial polarizer; 
         FIG. 9B  is an oblique view of an embodiment of an inner-conductive tube with two of the dielectric bars of  FIG. 9A ; 
         FIG. 10A  is an oblique view of an alternate embodiment of an inner-conductive tube; 
         FIG. 10B  is an oblique view of an alternate embodiment of the inner-conductive tube of  FIG. 10A  with a dielectric; 
         FIG. 10C  is an enlarged view of the dielectric positioned in the shallow-cavity of  FIG. 10B ; 
         FIG. 11  is an oblique view of an alternate embodiment of a dielectric bar for use on an inner-conductive tube of a coaxial polarizer; 
         FIG. 12A  is an enlarged view of one end of a shallow-cavity; 
         FIG. 12B  is an enlarged view of the edge shown in  FIG. 12A ; 
         FIG. 13  is an enlarged view of an alternate embodiment of a shallow-cavity; 
         FIG. 14  is a flow diagram of a method of making an inner-conductive tube; 
         FIG. 15  is an oblique view of an alternate embodiment of a coaxial polarizer with an inner-conductive tube and alternate dielectric bars; 
         FIG. 16  is an enlarged end view of a portion of the coaxial polarizer of  FIG. 15 ; and 
         FIG. 17  is an end view of the outer-conductive tube, the inner-conductive tube, and the dielectric bars of  FIG. 15 . 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     The coaxial polarizers described herein are single coaxial waveguide devices with one physical input port and one physical output port. The dielectric pieces are attached to the center conductor of the coaxial waveguide with ease. The machining for the center conductor in the coaxial polarizers described herein is less complex than the machining required for prior art coaxial polarizers. The dielectric pieces attached to the center conductor of the coaxial waveguide create the 90 degree phase difference in two orthogonal output modes of equal amplitude which leads to circular polarization. The dielectric pieces described herein are simpler in shape and therefore simpler to fabricate than the dielectric pieces in prior art coaxial polarizers. Likewise, the method for attaching the dielectric pieces to the center conductor is a convenient and relatively low-cost method compared to prior art methods of making coaxial polarizers. The geometry of the center conductive tube and the specific shape of the dielectric pieces are optimized and the performance, including the input return loss, of the coaxial polarizers is improved by adding a metal ring on the outer surface of the center conductor. When the diameter, length, and distance of the ring from the dielectric bars are optimized in concert with the other variables, excellent return loss and axial ratio are achieved. The steps in embodiments of the dielectric bars described herein and the impedance matching ring result in a coaxial polarizer with reduced length. The compact size of the coaxial polarizer allows antenna feeds to be small enough to meet stringent size constraints especially since other components are also required such as transitions, radiators, and filters. The configurations of dielectric bars and inner conductive tubes described herein permits a flat-first surface of the dielectric to be parallel to and attached to a planar area in a shallow-cavity on the surface of the inner conductive tube. 
       FIG. 1  is an oblique view of one embodiment of a coaxial polarizer  10 . The coaxial polarizer  10  has a physical input port at an input end  145  and one physical output port at an output end  146 .  FIG. 2A  is an oblique view of one embodiment of the coaxial polarizer  10  of  FIG. 1  with attached first dielectric  160 - 1  and second dielectric  160 - 2 .  FIG. 2B  is a top view of the coaxial polarizer  10  of  FIG. 2A .  FIG. 2C  is a cross section view of the coaxial polarizer  10  of  FIG. 2A .  FIG. 3  is an oblique view of one embodiment of the inner-conductive tube  130  of the coaxial polarizer  10  of  FIG. 1 .  FIG. 4  is an expanded view of a shallow-cavity  162  on the inner-conductive tube  130  of  FIG. 3 .  FIGS. 5A-5D  are various views of the first dielectric  160 - 1  of  FIGS. 2A-2C . The second dielectric  160 - 2  of  FIGS. 2A-2C  has the same shape and structure as the first dielectric  160 - 1 . The first dielectric  160 - 1  and second dielectric  160 - 2  are also referred to herein as “dielectric bar  160 - 1 ” and “dielectric bar  160 - 2 ”. 
     The coaxial polarizer  10  includes an outer-conductive tube  110  and an inner-conductive tube  130  positioned within the outer-conductive tube  110 . The inner-conductive tube  130  is axially aligned with the outer-conductive tube  110  using alignment spacers or features of the system in which the coaxial polarizer  10  is positioned. The inner-conductive tube  130  has a hollow core  131  that is bounded by the inner surface  231  of the inner-conductive tube  130 . The input end  145  of the coaxial polarizer  10  is spanned by the X-Y vectors shown in  FIG. 1 . 
     The inner-conductive tube  130  and the outer-conductive tube  110  are concentrically aligned to each other. The outer surface  230  of the inner-conductive tube  130  is radially offset from the inner surface  211  of the outer-conductive tube  110  by a distance indicted by a double-headed arrow labeled  125 . The region between the outer surface  230  of the inner-conductive tube  130  and the inner surface  211  of the outer-conductive tube  110 , which is represented generally at  111 , supports modes propagating in the Z direction from the input port at the input end  145  to the output port at the output end  146  as known to one skilled in the art. The inner-conductive tube  130  of the coaxial polarizer  10  is hollow to support a second frequency band interior to the coaxial polarizer  10 . The hollow core  131  of the inner-conductive tube  130  supports modes propagating in the Z direction from the input port at the input end  145  to the output port at the output end  146  within the hollow core  131 . In one implementation of this embodiment, the second frequency band is not required and the inner-conductive tube  130  is a solid metal cylinder. 
       FIGS. 2A-2C  shows an outline represented generally at  212  of the inner surface  211  ( FIG. 1 ) of the outer-conductive tube  110 . The outer surface  230  of inner-conductive tube  130  is visible in  FIGS. 2A-2C  through the outline  212  of the inner surface  211  ( FIG. 1 ) of the outer-conductive tube  110 . 
     The outer surface  230  of the inner-conductive tube  130  of the coaxial polarizer  10  of  FIG. 1  has been formed with shallow-cavities  162 - 1  and  162 - 2  ( FIGS. 2-4 ). The shallow-cavity  162 - 1  is also referred to herein as “first shallow-cavity  162 - 1 ”. The shallow-cavity  162 - 2  is also referred to herein as “second shallow-cavity  162 - 2 ”. The second shallow-cavity  162 - 2  is on a section of the outer surface  230  of the inner-conductive tube  130  that opposes the first shallow-cavity  162 - 1 . The shape of the shallow-cavities  162 - 1  and  162 - 2  is referred to herein as an I-shape. 
     As shown in  FIGS. 2A-2C , two dielectric bars  160 - 1  and  160 - 2  are positioned within the two opposing shallow-cavities  162 - 1  and  162 - 2 . The dielectric bar  160 - 1  is also referred to herein as “first dielectric bar  160 - 1 ”. The dielectric bar  160 - 2  is also referred to herein as “second dielectric bar  160 - 2 ”. The first shallow-cavity  162 - 1  and the second shallow-cavity  162 - 2  serve to align the respective first dielectric bar  160 - 1  and second dielectric bar  160 - 2  in two directions. The 2 dimensional alignment, which is automatically provided by the first shallow-cavity  162 - 1  and the second shallow-cavity  162 - 2 , eliminates the need for an external alignment fixture (as required in prior art systems) during assembly of the coaxial polarizer  10 . 
     A first shallow-cavity  162 - 1  is shown in  FIGS. 3 and 4 . As shown in  FIG. 4 , the first shallow-cavity  162 - 1  has a cavity length  170  parallel to a Z axis and three cavity widths  180 ,  181 , and  182  that are perpendicular to the Z axis and perpendicular to a first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . The radial direction is the direction in three dimensions (X, Y, and Z) of a radius vector. The length of the radius vector is a radius of curvature. The cavity width  180  is a minimum width  180  (i.e., a minimum-cavity width  180 ). 
     As shown in  FIG. 4 , the first-full-planar area  150  of the first shallow-cavity  162 - 1  includes a first planar area  321  in a first section  361  of the first shallow-cavity  162 - 1 . The first planar area  321  in the first section  361  has a first-cavity width  180  equal to the minimum width  180 . The planar area  321  of the first shallow-cavity  162 - 1  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130  and spans a plane X 1 ′-Z 1 ′ in the first section  361 . The first-cavity width  180  of the first planar area  321  is perpendicular to the Z 1 ′ axis and perpendicular to a first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . A first-cavity length  350  of the first planar area  321  in the first section  361  is parallel to the Z 1 ′ axis. The first planar area  321  in the first section  361  is also referred to herein as a “first-section-planar area  321 ”. 
     The first-full-planar area  150  of the first shallow-cavity  162 - 1  also includes a second planar area  322  in a second section  362  of the first shallow-cavity  162 - 1 . The second planar area  322  in the second section  362  is adjoined to and parallel to the first planar area  321  in the first section  361 . The second planar area  322  in the second section  362  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130  and spans a plane X 2 ′-Z 2 ′. The plane X 2 ′-Z 2 ′ is parallel to and overlaps with the plane X 1 ′-Z 1 ′. The second section  362  has a second-cavity width  181  that is perpendicular to the Z 2 ′ axis and perpendicular to a first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . The second-cavity width  181  is larger than the minimum width  180 . A second-cavity length of the second planar area  322  in the second section  362  is parallel to the Z 2 ′ axis. The second planar area  322  in the second section  362  is also referred to herein as a “second-section-planar area  322 ”. 
     The first-full-planar area  150  of the first shallow-cavity  162 - 1  also includes a third planar area  323  in a third section  363  of the first shallow-cavity  162 - 1 . The third planar area  323  in the third section  363  is adjoined to and parallel to the first planar area  321  in the first section  361 . The third planar area  323  in the third section  363  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130  and spans a plane X 3 ′-Z 3 ′. The plane X 3 ′-Z 3 ′ is parallel to and overlaps with the plane X 1 ′-Z 1 ′. The third section  363  has a third-cavity width  182  that is perpendicular to the Z 3 ′ axis and perpendicular to a first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . The third-cavity width  182  is larger than the minimum width  180 . The third-cavity width  182  equals the second-cavity width  181 . A third-cavity length of the third planar area  323  is parallel to the Z 3 ′ axis. The third planar area  323  in the third section  363  is also referred to herein as a “third-section-planar area  323 ”. The first-cavity length  350  of the first planar area  321 , the second-cavity length of the second planar area  322 , and the third-cavity length of the third planar area  323  are equal to the cavity length  170  of the first shallow-cavity  162 - 1 . 
     The second shallow-cavity  162 - 2  is similar to the first shallow-cavity  162 - 1  and is also described with reference to  FIG. 4 . The numerical labels for the features in the second shallow-cavity  162 - 2  are indicated with primes. 
     The second-full-planar area  150 ′ of the second shallow-cavity  162 - 2  includes a fourth planar area  321 ′ in a fourth section  361 ′ of the second shallow-cavity  162 - 2 . The fourth planar area  321 ′ in the fourth section  361 ′ has a fourth-cavity width  180 ′ equal to a second minimum width  180 ′. The fourth planar area  321 ′ of the second shallow-cavity  162 - 2  is perpendicular to a second radial direction r 2  ( FIG. 2 ) of the inner-conductive tube  130 . As is understandable, the second radial direction r 2  and the first radial direction r 1  have equal length but opposite directions, so a plane perpendicular to one of the first or second radial direction is also perpendicular to the other. The fourth planar area  321 ′ in the fourth section  361 ′ is also referred to herein as a “fourth-section-planar area  321 ′”. 
     The second-full-planar area  150 ′ of the second shallow-cavity  162 - 2  also includes a fifth planar area  322 ′ in a fifth section  362 ′ of the second shallow-cavity  162 - 2 . The fifth planar area  322 ′ in the fifth section  362 ′ is adjoined to and parallel to the fourth planar area  321 ′ in the fourth section  361 ′. The fifth planar area  322 ′ in the fifth section  362 ′ is perpendicular to the second radial direction r 2  ( FIG. 2 ) of the inner-conductive tube  130 . The fifth section  362 ′ has a fifth-cavity width  181 ′ that is perpendicular to the Z axis and perpendicular to the second radial direction r 2  ( FIG. 2 ) of the inner-conductive tube  130 . The fifth-cavity width  181 ′ is larger than the second-minimum width  180 ′. The fifth planar area  322 ′ in the fifth section  362 ′ is also referred to herein as a “fifth-section-planar area  322 ′”. 
     The second-full-planar area  150 ′ of the second shallow-cavity  162 - 2  also includes a sixth planar area  323 ′ in a sixth section  363 ′ of the second shallow-cavity  162 - 2 . The sixth planar area  323 ′ in the sixth section  363 ′ is adjoined to and parallel to the fourth planar area  321 ′ in the fourth section  361 ′. The sixth planar area  323 ′ in the sixth section  363 ′ is perpendicular to second radial direction r 2  ( FIG. 2 ) of the inner-conductive tube  130 . The sixth section  363 ′ has a sixth-cavity width  182 ′ that is perpendicular to the Z axis and perpendicular to the second radial direction r 2  ( FIG. 2 ) of the inner-conductive tube  130 . The sixth-cavity width  182 ′ is larger than the second-minimum width  180 ′. The sixth-cavity width  182 ′ equals the fifth-cavity width  181 ′. The sixth planar area  323 ′ in the sixth section  363 ′ is also referred to herein as a “sixth-section-planar area  323 ′”. 
     In one implementation of this embodiment, the first shallow-cavity  162 - 1  and the second shallow-cavity  162 - 2  have the same dimensions. In one implementation of this embodiment, the cavity length  170  of the first shallow-cavity  162 - 1  equals the cavity length  170 ′ of the second shallow-cavity  162 - 2 . In another implementation of this embodiment, the cavity width  180  of the first shallow-cavity  162 - 1  equals the cavity width  180 ′ of the second shallow-cavity  162 - 2 . In yet another implementation of this embodiment, the first shallow-cavity  162 - 1  and the second shallow-cavity  162 - 2  have different shapes. In that case, second shallow-cavity  162 - 2  is another one of the shapes described herein. In any case, the shallow-cavities  162 - 1  and  162 - 2  each have at least one planar area that is perpendicular to a radial direction of the inner-conductive tube  130 . 
       FIG. 5A  shows an oblique view of the dielectric bars  160 - 1  and  160 - 2 .  FIG. 5B  shows a side view of the dielectric bars  160 - 1  and  160 - 2 .  FIG. 5C  shows a first cross-sectional view of the dielectric bars  160 - 1  and  160 - 2 . The plane upon which the cross-section view of  FIG. 5C  is taken is indicated by section line  5 C- 5 C in  FIG. 5B .  FIG. 5D  shows a second cross-sectional view of the dielectric bars  160 - 1  and  160 - 2 . The plane upon which the cross-section view of  FIG. 5D  is taken is indicated by section line  5 D- 5 D in  FIG. 5B . A surface  260  shown in each of the dielectric bars  160 - 1  and  160 - 2  is the surface that is attached to the shallow-cavity  162 - 1  and  162 - 2 , respectively. The surface  260  is referred to herein as the “flat-first surface  260 ”. 
     As shown in  FIG. 5B , the surface  260  has a dielectric length  270  parallel to the Z 1  axis. The dielectric length  270  ( FIG. 5B ) is less than the cavity length  170  ( FIG. 4 ). As shown in  FIGS. 5A, 5C, and 5D , the surface  260  has a dielectric width  280  parallel to the X 1  axis. The dielectric width  280  is less than the minimum width  180  ( FIG. 4 ). 
     The dielectric bars  160 - 1  and  160 - 2  each have the shape of two stepped rectangular prisms. Thus, a cross-sectional view of each of the two dielectric bars  160 - 1  and  160 - 2  taken perpendicular to the Z axis has four respective surfaces in a rectangular shape. The cross-sectional view of  FIG. 5C  shows the first surface  260  is: parallel to a second surface  261 ; perpendicular to a third surface  263 ; and perpendicular to a fourth surface  264 . The first surface  260  is offset from the second surface  261  a thickness t 1 . Each of the surfaces  260 ,  261 ,  263 , and  264  is flat. Thus, the first-cross-section shown in  FIG. 5C  has a first-rectangular shape including a width  280  that is less than the minimum width  180 . 
     A flat surface, as used herein, is not necessarily flat to known optical flatness (e.g., flatness is not based on wavelengths). As defined herein a surface is flat if there are small protrusions on the order of 10s of microns. As defined herein, surfaces are parallel to each other even if they subtend planes that intersect at an angle within a few degrees (e.g., parallelism is not based on wavelengths). 
     The cross-sectional view of  FIG. 5D  shows the first surface  260  is: parallel to a fifth surface  262 ; perpendicular to the third surface  263 ; and perpendicular to the fourth surface  264 . The first surface  260  is offset from the fifth surface  262  the thickness t 2 . The thickness t 2  is less than the thickness t 1 . Thus, the second-cross-section in  FIG. 5D  has a second-rectangular shape including the width  280  that is less than the minimum width  180 . 
     In one implementation of this embodiment, the first dielectric  160 - 1  and the second dielectric  160 - 2  have the same shape. In another implementation of this embodiment, the first dielectric  160 - 1  and the second dielectric  160 - 2  have different shapes. In that case, second dielectric  160 - 2  has the shape of any of the other dielectric shapes described herein. In any case, the first dielectric  160 - 1  and second dielectric  160 - 2  each have a flat-first surface  260  that is rectangular in shape. The first dielectric  160 - 1  and the second dielectric  160 - 2  are placed into the respective minimally oversized shallow-cavities  162 - 1  and  162 - 2 . As shown in  FIG. 2 , the two flat-first surfaces  260 - 1  and  260 - 2  of the respective two dielectric bars  160 - 1  and  160 - 2  contact at least a portion of the respective planar areas of the two shallow-cavities  162 - 1  and  162 - 2 . 
     In one implementation of this embodiment, the shallow-cavities  162 - 1  and  162 - 2  are machined on the outer surface  230  of the inner-conductive tube  130 , and the first dielectric  160 - 1  and the second dielectric  160 - 2  are held in place within the shallow-cavities  162 - 1  and  162 - 2  with industrial adhesive. When the first dielectric  160 - 1  and the second dielectric  160 - 2  are attached to the inner-conductive tube  130  and enclosed in the outer-conductive tube  110 , they do not touch the inner surface  211  ( FIG. 1 ) of the outer-conductive tube  110 . 
     The capital letter I-shape of the shallow-cavities  162 - 1  and  162 - 2  shown in  FIGS. 2-4  prevents interior radii in the corners that would interfere with the respective exterior corners of the dielectric bars  160 - 1  and  160 - 2 . To accomplish this during machining, the end-mill bit is allowed to “run off” of the part to create the top and bottom portions of the capital letter I. Four distinct shallow sides, which do not extend beyond the original diameter of the inner-conductive tube, remain for the purpose of locating the dielectric bars  160 - 1  and  160 - 2  in the respective shallow-cavities  162 - 1  and  162 - 2  during assembly of the coaxial polarizer  10 . However, due to part tolerances, the shallow-cavities  162 - 1  and  162 - 2  are intentionally designed to be oversized (i.e., larger than the dielectric bars  160 - 1  and  160 - 2  to be attached). In this way, the shallow-cavities  162 - 1  and  162 - 2  are not designed to captivate the dielectric bars  160 - 1  and  160 - 2  in a snap-fit. Instead shallow-cavities  162 - 1  and  162 - 2  are guides to align the dielectric bars  160 - 1  and  160 - 2  in two directions (the X and Z directions) without an external alignment fixture. The dielectric bars  160 - 1  and  160 - 2  are glued into the shallow-cavities  162 - 1  and  162 - 2  during assembly. It is important that the wall thickness of the hollow inner-conductive tube  130  is thick enough so the bottom floor (e.g., the planar area including sections  361 - 363 ) of the shallow-cavities  162 - 1  and  162 - 2  does not penetrate through to the interior surface of the circular waveguide  131 . 
       FIG. 6A  shows a TE 11  mode oriented parallel to the X axis.  FIG. 6B  is an end-view from the input end  145  of a coaxial polarizer  10  with an inner-conductive tube  130  on which dielectric bars  160 - 1  and  160 - 2  are positioned for right-hand-circular polarization when excited by the TE 11  mode shown in  FIG. 6A .  FIG. 6C  is an end-view from the input end  145  of a coaxial polarizer  10  with an inner-conductive tube  130  on which dielectric bars  160 - 1  and  160 - 2  are positioned for left-hand-circular polarization when excited by the TE 11  mode shown in  FIG. 6A . 
     As shown in  FIG. 6A , the input electric field of the input electromagnetic wave that is incident upon the coaxial polarizer  10  is a horizontally polarized (e.g., parallel to the X axis) TE 11  mode. By positioning the dielectric bars  160 - 1  and  160 - 2  at a 45 degree orientation with respect to the input TE 11  mode (e.g., with respect to the X axis) the electromagnetic wave output from the output end  146  ( FIG. 1 ) of the coaxial polarizer  10  ( FIG. 1 ) is either right hand circularly polarized or left hand circularly polarized. 
     As shown in  FIGS. 6A-6C , the inner surface  211  ( FIG. 1 ) of the outer-conductive tube  110  is represented generally at  212 . As shown in  FIGS. 6B and 6C , the dielectric bars  160 - 1  and  160 - 2  are separated from the inner surface  211  ( FIG. 1 ) of the outer-conductive tube  110  by the gaps represented generally at  166 - 1  and  166 - 2 , respectively. 
     As shown in  FIG. 6B , a line  195  taken perpendicular to the flat surface  261 - 1  of dielectric bar  160 - 1  that intersects the center of the inner-conductive tube  130  is at 45 degrees with respect to the positive X axis (+X) in the quadrant of the dielectric bar  160 - 1 . Since the dielectric bar  160 - 2  is on the outer surface  230  of the inner-conductive tube  130  opposing the dielectric bar  160 - 1 , the line  195  is also perpendicular to the flat surface  261 - 1  of dielectric bar  160 - 2 . Thus, the line  195  in the quadrant of the dielectric bar  160 - 2  is at 45 degrees with respect to the negative X axis (−X). This configuration of the dielectric bars  160 - 1  and  160 - 2  with reference to input horizontal TE 11  mode ( FIG. 6A ) results in the electromagnetic wave output from the output end  146  ( FIG. 1 ) of the coaxial polarizer  10  ( FIG. 1 ) being right hand circularly polarized. 
     As shown in  FIG. 6C , the orientation of the dielectric bars  160 - 1  and  160 - 2 , with respect to the X axis, is rotated by 90 degrees from the orientation of the dielectric bars  160 - 1  and  160 - 2  in  FIG. 6B . As shown in  FIG. 6C , a line  196  taken perpendicular to the flat surface  261 - 1  of dielectric bar  160 - 1  that intersects the center of the inner-conductive tube  130  is at 45 degrees with respect to the negative X axis (−X) in the quadrant of the dielectric bar  160 - 1 . Since the dielectric bar  160 - 2  is on the outer surface  230  of the inner-conductive tube  130  opposing the dielectric bar  160 - 1 , the line  196  is also perpendicular to the flat surface  261 - 2  of dielectric bar  160 - 2 . Thus, the line  196  in the quadrant of the dielectric bar  160 - 2  is at 45 degrees with respect to the positive X axis (+X). This configuration of the dielectric bars  160 - 1  and  160 - 2  with reference to the input horizontal TE 11  mode ( FIG. 6A ) results in the electromagnetic wave output from the output end  146  ( FIG. 1 ) of the coaxial polarizer  10  ( FIG. 1 ) being left hand circularly polarized. 
       FIG. 7  is an oblique view of one embodiment of a metal ring  190  for use on an inner-conductive tube  130  of a coaxial polarizer  10  ( FIG. 1 ). The metal ring  190  is manufactured as part of the inner-conductive tube  130 . The metal ring  190  encircles the outer surface  230  of the inner-conductive tube  130 . The metal ring  190  is offset, along the Z axis, from the shallow-cavities  162 - 1  and  162 - 2  and thus is also offset from the dielectric bars  160 - 1  and  160 - 2  when they are positioned in the respective shallow-cavities  162 - 1  and  162 - 2 . 
       FIG. 8A  is an oblique view of an alternate embodiment of a dielectric  161  for use on an inner-conductive tube  171  of a coaxial polarizer  10 . The dielectric bar  161  has a length L 1 . The dielectric bar  161  includes a central portion represented generally at  135  having a thickness t 3 . The dielectric bar  161  includes side portions represented generally at  136  and  137  having a thickness t 4 . The thickness t 3  is greater than the thickness t 4 . Thus, the dielectric bar  161  has the shape of three stepped rectangular prisms. 
       FIG. 8B  is an oblique view of an embodiment of an inner-conductive tube  171  with two of the dielectric bars  161 - 1  and  161 - 2  of  FIG. 8A . As shown in  FIG. 8B , the section  245  of the inner-conductive tube  171  at the input end  145  has a diameter D 1  that is larger than the diameter D 2  of the inner-conductive tube  171  at the output end  146 . The section  246  of the inner-conductive tube  171  between the section  245  and the metal ring  190  has a diameter that is smaller than the diameter D 1 . As shown in  FIG. 8B , the dielectric bars  161 - 1  and  161 - 2  of  FIG. 8A  are positioned in and attached to the shallow-cavities (not labeled in  FIG. 8B ) of the inner-conductive tube  171 . 
       FIG. 9A  is an oblique view of an alternate embodiment of a dielectric bar  162  for use on an inner-conductive tube  172  of a coaxial polarizer  10 . The dielectric bar  162  is a rectangular prism having a single thickness t 5  along the length of L 1  of the dielectric bar  162 .  FIG. 9B  is an oblique view of an embodiment of an inner-conductive tube  172  with two of the dielectric bars  162 - 1  and  162 - 2  of  FIG. 9A . As shown in  FIG. 9B , the dielectric bars  162 - 1  and  162 - 2  of  FIG. 9A  are positioned in and attached to the shallow-cavities (not labeled in  FIG. 9B ) of the inner-conductive tube  171 . As shown in  FIG. 9B , the inner-conductive tube  172  includes a metal ring  190 . 
     In one implementation of this embodiment, the dielectric bars  162 - 1  and  162 - 2  of  FIG. 9A  are attached to the inner-conductive tube  130  of  FIG. 3 . In another implementation of this embodiment, the dielectric bars  162 - 1  and  162 - 2  of  FIG. 9A  are attached to the inner-conductive tube  171  of  FIG. 8B . In yet another implementation of this embodiment, the dielectric bars  161 - 1  and  161 - 2  of  FIG. 8A  are attached to the inner-conductive tube  172  of  FIG. 9B . 
       FIG. 10A  is an oblique view of an alternate embodiment of an inner-conductive tube  135 . In this embodiment, the planar area of the shallow-cavity  163  includes a single planar area ( 159 ) that is rectangular in shape. Due to the machining process, the rectangular shaped shallow-cavity  163  has rounded corners represented generally at  164 .  FIG. 10  B is an oblique view of an alternate embodiment of the inner-conductive tube  135  with a dielectric bar  166 - 1 . A second dielectric bar on the opposing side of the inner-conductive tube  135  is not visible, but that second dielectric bar has the same structure and function as the dielectric bar  166 - 1 .  FIG. 10C  is an enlarged view of the dielectric bar  166 - 1  positioned in and attached to the shallow-cavity  163  of  FIG. 10A . 
     The dielectric bar  166  differs from the dielectric bar  160 - 1  shown in  FIG. 5A , in that the dielectric bar  166  has chamfered-edges represented generally at  167  ( FIG. 10C ) on the edges that are perpendicular to the flat-first surface  260  ( FIGS. 5B-5C ) of the dielectric bar  166 - 1 . The chamfered-edges  167  are also referred to herein as “vertical-corner edges  167 ”. The chamfered-edges  167  are proximal to a respective rounded corner  164  when the flat-first surface  260  of the dielectric bar  166 - 1  contacts at least a portion of the planar area of the shallow-cavity  163 . As shown in  FIG. 10C , the dielectric bar  166  is slightly smaller in dimension than the rectangular shaped shallow-cavity  163 . The width  180  of the rectangular shaped shallow-cavity  163  is larger by ΔW than the width of the dielectric bar  166 . 
       FIG. 11  is an oblique view of an alternate embodiment of a dielectric bar  168  for use on an inner-conductive tube  130  of a coaxial polarizer  10 .  FIG. 12A  is an enlarged view of one end of a shallow-cavity  165 . The shallow-cavity  165  has the I-beam shape of the shallow-cavity  162  ( FIGS. 3 and 4 ).  FIG. 12A  shows the shallow-cavity  165  has the second planar area  322  in the second section  362  that is adjoined to and parallel to the first planar area  321  in the first section  361 . The second planar area  322  has an edge  410  along the X 2 ′ axis.  FIG. 12B  is an enlarged view of the edge  410  shown in  FIG. 12A . As is clearly shown in  FIG. 12B , the edge  410  is not formed as a right angle corner but is formed with a chamfered corner. This chamfering of the edge  410  is due to practical machining considerations with end-mills, which are worn down with use. The wear of the end-mills cause chamfers or radii in the interior corners of the milled surface. The dielectric bar  168  shown in  FIG. 11  has chamfered corners  169  at the edges of the flat-first surface  260  that are perpendicular to the dielectric length L 1  of the dielectric bar  168 . The chamfered corners  169  allow for the dielectric bar  168  to be almost as long as the shallow-cavity  165  and to be positioned in the shallow-cavity  362  without hitting the chamfered edge  410 . If a dielectric bar does not have a chamfered corners, the dielectric bar is shortened in length (along the Z direction) so the flat-first surface  260  of the dielectric bar does not sit on the chamfered edge  410 . If an edge of the flat-first surface  260  of a dielectric bar were to sit on the chamfered edge  410  ( FIGS. 12A and 12B ), the flat-first surface  260  ( FIGS. 5B-5D ) would not be parallel to the second planar area  322  in the second section  362  of the shallow-cavity  165  ( FIG. 12A ). 
       FIG. 13  is an enlarged view of an alternate embodiment of a shallow-cavity  460 . The shallow-cavity  460  is designed to avoid problems due to the chamfering of the edge  410  shown in  FIGS. 12A and 12B . The shallow-cavity  460  includes: a first-planar area  461  that spans a first plane X 1 ″-Z 1 ″ in the first section  361 ; a second-planar area  462  that spans a second plane X 2 ″-Z 2 ″ in the second section  362 ; and a third planar area  463  that spans a third plane X 3 ″-Z 3 ″ in the third section  363 . The second plane X 2 ″-Z 2 ″ is offset by −Δr in a negative radial direction (e.g., in the −Y 2 ″ direction) from the first plane X 1 ″-Z 1 ″. The third plane X 3 ″-Z 3 ″ is offset by −Δr in the negative radial direction (e.g., in the −Y 3 ″ direction) from the first plane X 1 ″-Z 1 ″. In one implementation of this embodiment, the third plane X 3 ″-Z 3 ″ and the second plane X 2 ″-Z 2 ″ span a common plane. 
     The first-section-planar area  461  that spans the first plane X 1 ″-Z 1 ″ has a first-cavity width  180  equal to the first-minimum width  180 . The first-section-planar area  461  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . 
     The second-section-planar area  462  that spans the second plane X 2 ″-Z 2 ″ has a second-cavity width  181 . The second-section-planar area  462  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . The third-section-planar area  463  that spans the second plane X 3 ″-Z 3 ″ has a third-cavity width  182 . The third-section-planar area  463  is perpendicular to the first radial direction r 1  ( FIG. 2 ) of the inner-conductive tube  130 . The second-section-planar area  462  and the third-section-planar area  463  are offset from each other in the Z direction by a length  350  of the first-section-planar area  461 , and wherein the second-cavity width  181  and third-cavity width  182  are larger than the first-minimum width  180 . The embodiments of shallow-cavity  165  and  460  shown in  FIGS. 12A and 13  provide a precise alignment in the Z-direction of a dielectric bar inserted into the shallow-cavity  165  or  460 . These embodiments of shallow-cavity  165  and  460  are used for parts requiring very tight tolerances. 
     The coaxial polarizer is designed using a full-wave electromagnetic field solver software package such as ANSYS HFSS, commercially available from ANSYS, Inc., or CST Microwave Studio, commercially available from CST Computer Simulation Technology AB. The coaxial polarizer of this application is useful in dual-frequency concentric antenna feeds. The space  125  must be large enough so that the first frequency band is above the TE 11  cutoff frequency for the coaxial waveguide and, hence, electromagnetic waves within this first intended frequency band will propagate in the coaxial waveguide. The circular waveguide diameter must be chosen to be large enough so that the second frequency band is above the TE 11  cutoff frequency and, hence, electromagnetic waves within this second intended frequency will propagate in the circular waveguide. The outer tube diameter must be small enough to meet the space constraints of the system in which it is being installed. Additionally, the inner tube wall thickness must be of sufficient size to allow room for the shallow cavities for a chosen dielectric bar width which is also a key parameter in the design. The inner and outer conductor tube diameters and the inner tube wall thickness are typically chosen in advance of computer optimization runs based on the constraints above. Then, the width of the dielectric bars  161 - 1  and  161 - 2  and the lengths and thicknesses of the various sections of the dielectric bars are adjusted to optimize the performance of the coaxial polarizer in the first frequency band. Specifically, the goal of the computer controlled optimizer is to find the dielectric bar geometry which minimizes the axial ratio of the polarizer such that the resulting electromagnetic field polarization at the output of the polarizer is circular. Additionally, in some embodiments, the return loss of the input electromagnetic wave may be optimized through adjustment of the geometry and the location of the conductive ring  190  ( FIG. 7 ). In other embodiments, the return loss of the input electromagnetic wave may be optimized through adjustment of the geometry and the location of the quarter-wave-transformer  246  ( FIG. 8B ). 
     In one embodiment of the inner-conductive tube  171  shown in  FIG. 8B , the diameter of the inner conductor at the input end  145  and the diameter of the inner conductor at the output end  146  are different. This feature is useful in designs where a radiator section connected to the output port has a different inner conductor diameter than the rectangular-waveguide-to-coaxial-waveguide transition section connected to the input port. In this embodiment, the section with the metal ring  190  also has a larger diameter than the section  246 . The section  246  of reduced diameter is a quarter-wave-transformer  246  designed to achieve a low return loss for the input wave. With the quarter-wave-transformer  246 , the return loss is optimized. The dielectric bars  161 - 1  and  161 - 2  have a length L 1 . The overall length of the coaxial polarizer including the quarter-wave-transformer  246  is length L 2 . 
       FIG. 14  is a flow diagram of a method  1400  of making an inner-conductive tube  130 . Method  1400  is applicable to a coaxial polarizer formed from any combination of the embodiments of shallow cavities and dielectric bars described in  FIGS. 1-13 . 
     At block  1402 , a first shallow-cavity  162  having at least one first-planar area is machined on an outer-curved surface of a cylindrical piece aligned to an axial direction. As defined herein, a cylindrical piece is either a solid metal cylinder or a metal cylindrical tube. In one implementation of this embodiment, machining is done on a solid metal cylinder and the piece is later machined to bore a hole axially into the solid metal cylinder to form a metal cylindrical tube. In another implementation of this embodiment, the machining is done on a solid metal cylinder and the piece is used for a single frequency band coaxial polarizer. 
     At block  1404 , a second shallow-cavity  162  having at least one second-planar area  162 - 2  is machined on the outer-curved surface of the cylindrical piece, wherein the first-planar area opposes the second planar area. 
     In one implementation of this embodiment, the processes at block  1402  and  1404  are performed as follows. A first-planar area is machined in a first section  361  of the first shallow-cavity  162 . Then a second-planar area is machined in a second section  362  of the first shallow-cavity  162 . Then a third-planar area is machined in a third section  363  of the first shallow-cavity  162 . The first-planar area has a length parallel to the axial direction and a width equal to a minimum width. The second-planar area has a second width greater than the minimum width  180 . The second-planar area adjoins the first-planar area at a first end of first-planar area. The third-planar area has a third width greater than the minimum width  180 . The third-planar area adjoins the first-planar area at a second end of first-planar area. 
     In another implementation of this embodiment, the processes at block  1402  and  1404  are performed as follows. A first-planar area is machined in a first section  361  of the first region parallel to the axial direction for an extent equal to a cavity length  140 . A second-planar area is machined in a second section  362  of the first shallow-cavity  162 . A third-planar area is machined in a third section  363  of the first shallow-cavity  162 . The second-planar area has a second length perpendicular to the axial direction. The second-planar area is offset in a negative radial direction from the first-planar area. The third-planar area has a third length perpendicular to the axial direction. The third planar area is offset in a negative radial direction from the first-planar area. 
     In yet another implementation of this embodiment, first and second rectangular planar surfaces are machined in opposing first and second sections to have a length larger than the length of the dielectric bars. In one embodiment of this case, the vertical-corner edges of the dielectric bars that are parallel to the radial direction of the cylindrical piece, when installed, are chamfered. In another embodiment of this case, dielectric bar has chamfered corners at the edges of the flat-first surface that are perpendicular to the dielectric bar length. In yet another embodiment of this case, the dielectric bars have chamfered vertical-corner edges and chamfered corners at the edges of the flat-first surface that are perpendicular to the dielectric bar length. 
     Block  1406  is optional. At block  1406 , a metal ring  190  is positioned over the outer surface  230  of the cylindrical tube. The metal ring  190  is offset, along the Z axis, from the first shallow-cavity  162  and the second shallow-cavity  162 . In one implementation of this embodiment, the metal ring  190  is formed by machining the outer surface  131  of the inner-conductive tube  130 . In another implementation of this embodiment, the metal ring  190  is formed as a separate piece from the inner-conductive tube  130  and is then positioned on the outer surface  131  of the inner-conductive tube  130 . 
     At block  1408 , a flat surface of a first dielectric bar is attached to the at least one planar area of the first shallow-cavity. In one implementation of this embodiment, the flat surface of a first dielectric  160 - 1  is positioned inside the first shallow-cavity  162 - 1  and then the flat surface of the first dielectric  160 - 1  is glued to the at least one planar area of the first shallow-cavity  162 . In this manner, a flat-first surface of first dielectric  160 - 1  is parallel to and attached to a planar area in a first shallow-cavity  162 - 1  on the surface of the inner conductive tube  130 . 
     At block  1410 , a flat surface of a second dielectric bar is attached to the at least one planar area of the second shallow-cavity. In one implementation of this embodiment, the flat surface of a second dielectric  160 - 2  is positioned inside the second shallow-cavity  162  and the flat surface of the second dielectric  160 - 2  is glued to the at least one planar area of the second shallow-cavity  162 . In this manner, a flat-first surface of second dielectric  160 - 2  is parallel to and attached to a planar area in a second shallow-cavity  162 - 2  on the surface of the inner conductive tube  130 . 
     Thus, the various embodiments of the coaxial polarizers formed from the inner conductive tubes shown in  FIGS. 1, 2, 3, 4, 6B, 6C, 8B, 9B, 10B, 10C, 12, and 13  and the dielectric bars shown in  FIGS. 2, 5A-5D, 6B, 6C, 8A, 8B, 9A, 10B, 10C, and 11  do not require any protrusions on the outer surface of the conductive inner tube to which the dielectric bars are mated in a snap-fit fashion. Rather, the at least one flat surface of the dielectric bar is guided into a shallow cavity and attached to a flat surface of the shallow cavity. These conductive tubes and the dielectric bars are formed without complex machining processes, thus they are low cost and easy to assemble. 
       FIG. 15  is an oblique view of an outer surface  930  of an alternate embodiment of a coaxial polarizer with an inner-conductive tube  830  and alternate dielectric bars  862 - 1  and  862 - 2 .  FIG. 15  shows an outline  812  of the inner surface  211  of the outer-conductive tube  110  ( FIGS. 1 and 16 ), which is not shown in  FIG. 15  in order for the dielectric bars  862 - 1  and  862 - 2  to be visible. Only the outer surface  930  of inner-conductive tube  830  is visible in  FIG. 15 .  FIG. 16  is an enlarged end view of a portion of the coaxial polarizer  18  of  FIG. 15 .  FIG. 17  is an end view of the outer-conductive tube  110 , the inner-conductive tube  830 , and the dielectric bars  862 - 1  and  862 - 2  of  FIG. 15 . The coaxial polarizer  18  differs from the coaxial polarizer  10  in that there is no planar surface on the outer surface  930  of inner-conductive tube  830  and the dielectric bars  862 - 1  and  862 - 2  have curved surfaces which are attached to the curved outer surface  930  of inner-conductive tube  830 . 
     The coaxial polarizer  18  includes an outer-conductive tube  110  (of which only a portion is visible in  FIG. 16 ), an inner-conductive tube  830  positioned within the outer-conductive tube  110  and axially aligned with the outer-conductive tube  110 , a first dielectric  862 - 1  positioned on the curved outer surface  930  of the inner-conductive tube  830 , and a second dielectric  862 - 2  positioned on the curved outer surface  930  of the inner-conductive tube  830  opposing the first dielectric  862 - 1 . 
     The inner-conductive tube  830  has an axial dimension parallel to a Z axis and an outer surface  930  ( FIG. 16 ) with a radius of curvature r 1  ( FIG. 16 ). The outer-conductive tube  110  has an axial dimension parallel to a Z axis and an inner surface  211  ( FIG. 16 ) with a radius of curvature r 2  ( FIG. 16 ). The difference between the radius of curvature r 2  and the radius of curvature r 1  is greater than the maximum thickness of the first dielectric  862 - 1  and the maximum thickness of the second dielectric  862 - 2 . In one implementation of this embodiment, the maximum thickness of the first dielectric  862 - 1  and the second dielectric  862 - 2  are the same. A gap represented generally at  905  ( FIG. 16 ) is between the top surface  910  of the first dielectric  862 - 1  and the inner surface  211  of the outer-conductive tube  110 . The gap  905  has a thickness Δr gap . 
     As shown in  FIG. 17 , the first dielectric  862 - 1  includes a curved first surface  912 - 1 , an opposing curved second surface  911 - 1 , an opposing curved third surface  910 - 1 , a fourth surface  913 - 1 , and a fifth surface  914 - 1 . The fourth surface  913 - 1  is parallel to the radial direction r 1  oriented by the angle φ 1 . The fifth surface  914 - 1  is parallel to the radial direction r 2  oriented by the angle φ 2 . As shown in  FIG. 16 , the first curved surface  912  is offset by the thickness t6 from the second curved surface  911  and the first curved surface  912  is offset by the thickness t 7  from the third curved surface  910 . 
     As shown in  FIG. 17 , the second dielectric  862 - 2  includes a curved sixth surface  912 - 2 , an opposing curved seventh surface  911 - 2 , an opposing curved eighth surface  910 - 2 , a ninth surface  913 - 2 , and a tenth surface  914 - 2 . The ninth surface  913 - 2  is parallel to the radial direction r 3  oriented by the angle φ 3 . The tenth surface  914 - 2  is parallel to the radial direction r 4  oriented by the angle φ 4 . In one implementation of this embodiment, angle φ 1  equals angle φ 2 , equals angle θ 3 , and also equals angle θ 4 . 
     The coaxial polarizer  18  can be arranged with reference to an input electromagnetic wave to output either right hand or left hand polarization as described above with reference to the coaxial polarizer  10 . As is understandable to one skilled in the art, the various embodiments of shallow cavities on the outer surface of the inner-conductive tube and the various embodiments of dielectric bars can be used in any desired combination to provide many different configurations of the coaxial polarizers. 
     Example Embodiments 
     Example 1 includes a coaxial polarizer comprising: an outer-conductive tube; an inner-conductive tube positioned within the outer-conductive tube and axially aligned with the outer-conductive tube, the inner-conductive tube having two shallow-cavities on opposing portions of an outer surface of the inner-conductive tube, the shallow-cavities each having at least one planar area, the at least one planar area having a cavity length parallel to a Z axis and having at least one cavity width that is perpendicular to the Z axis and perpendicular to a radial direction of the inner-conductive tube, the at least one cavity width including a minimum width; and two dielectric bars each having a flat-first surface, the flat-first surface having a dielectric length parallel to the Z axis and a dielectric width perpendicular to the Z axis, the dielectric length being less than the cavity length and the dielectric width being less than the minimum width, wherein cross-sections of each of the two dielectric bars taken perpendicular to the Z axis have four respective surfaces in a rectangular shape, and wherein the two flat-first surfaces of the respective two dielectric bars contact at least a portion of the respective two planar areas of the two shallow-cavities. 
     Example 2 includes the coaxial polarizer of Example 1, further comprising: a metal ring encircling the outer surface of the inner-conductive tube, the ring being offset, along the Z axis, from the shallow-cavities. 
     Example 3 includes the coaxial polarizer of any of Examples 1-2, wherein the two opposing planar areas of the respective two shallow-cavities comprises: a first planar area in a first section having a first-cavity width equal to the minimum width, first-cavity width being perpendicular to the Z axis and perpendicular to a radial direction of the inner-conductive tube; a second planar area in a second section adjoined to the first section and having a second-cavity width perpendicular to the Z axis and perpendicular to the radial direction of the inner-conductive tube; and a third planar area in a third section adjoined to the first section having a third-cavity width perpendicular to the Z axis and perpendicular to the radial direction of the inner-conductive tube, wherein the second section and the third section are offset from each other by a length of the first section, and wherein the second-cavity width and the third-cavity width are larger than the minimum width. 
     Example 4 includes the coaxial polarizer of Example 3, wherein the at least one planar area of at least one of the opposing two shallow-cavities comprises: a first-planar area that spans a first plane in the first section; a second-planar area that spans a second plane in the second section, the second plane being offset in a negative radial direction from the first plane; and a third planar area that spans a third plane in the third section, the third plane being offset in the negative radial direction from the first plane. 
     Example 5 includes the coaxial polarizer of any of Examples 1-4, wherein at least one of the two dielectric bars has at least one chamfered corner at at least one of the edges of the flat-first surface perpendicular to the dielectric length. 
     Example 6 includes the coaxial polarizer of any of Examples 1-5, wherein the at least one planar area of the respective two shallow-cavities include a single planar area that is rectangular in shape. 
     Example 7 includes the coaxial polarizer of Example 6, wherein the rectangular shape of the at least one planar area includes rounded corners, wherein each of the two dielectric bars further comprises: at least one chamfered-edge perpendicular to the flat-first surface, wherein at least one chamfered-edge is proximal to a respective at least one rounded corner when the flat-first surface of the dielectric bar contacts the at least a portion of the planar area of the shallow-cavity. 
     Example 8 includes the coaxial polarizer of any of Examples 1-7, wherein the cross-sections of each of the two dielectric bars taken perpendicular to the Z axis include: a first-cross-section having a first-rectangular shape including a width that is less than the minimum width, and wherein a second-cross-section having a second-rectangular shape including a width that is less than the minimum width. 
     Example 9 includes an inner-conductive tube for use in a coaxial polarizer, comprising: a first shallow-cavity on an outer surface of the inner-conductive tube, wherein the first shallow-cavity has a first-full-planar area, the first-planar area having a first-cavity length parallel to a Z axis and having at least one first-cavity width perpendicular to the Z axis and perpendicular to a first radial direction of the inner-conductive tube, the at least one first-cavity width including a first-minimum width; and a second shallow-cavity on the outer surface of the inner-conductive tube, the second shallow-cavity opposing the first shallow-cavity and having a second-full-planar area, the second-full-planar area having a second-cavity length parallel to the Z axis and having at least one second-cavity width perpendicular to the Z axis and perpendicular to a second radial direction of the inner-conductive tube, the at least one second-cavity width including a second-minimum width. 
     Example 10 includes the inner-conductive tube of Example 9, further comprising: a metal ring encircling the outer surface of the inner-conductive tube, the ring being offset, along the Z axis, from the first shallow-cavity and the second shallow-cavity. 
     Example 11 includes the inner-conductive tube of any of Examples 9-10, wherein the first-cavity length equals the second-cavity length and the at least one first-cavity width equals the at least one second-cavity width. 
     Example 12 includes the inner-conductive tube of any of Examples 9-11, wherein the first-full-planar area of the first shallow-cavity comprises: a first planar area in a first section having a first-cavity width equal to the first-minimum width, and first-cavity width being perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube; a second planar area in a second section adjoined to the first section and having a second-cavity width perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube; and a third planar area in a third section adjoined to the first section having a third-cavity width perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube, wherein the second section and the third section are offset from each other by a length of the first section, and wherein the second-cavity width and third-cavity width are larger than the first-minimum width. 
     Example 13 includes the inner-conductive tube of Example 12, wherein the second-full-planar area of the second shallow-cavity comprises: a fourth planar area in a fourth section having the fourth-cavity width equal to the second-minimum width, the fourth-cavity width being perpendicular to the Z axis and perpendicular to the second radial direction of the inner-conductive tube; a fifth planar area in a fifth section adjoined to the fourth section having a fifth-cavity width perpendicular to the Z axis and perpendicular to the second radial direction of the inner-conductive tube; and a sixth planar area in a sixth section adjoined to the fourth section having a sixth cavity width perpendicular to the Z axis, wherein the fifth section and the sixth section are offset from each other by a length of the fourth section, and wherein the fifth-cavity width and sixth-cavity width are larger than the second-minimum width. 
     Example 14 includes the inner-conductive tube of any of Examples 9-13, wherein at least one of the first shallow-cavity and the second shallow-cavity comprises: a first-section-planar area that spans a first plane, the first-section-planar area having the first-cavity width equal to the first-minimum width, the first-cavity width being perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube; a second-section-planar area that spans a second plane adjoining the first plane, the second-section-planar area having a third-cavity width perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube, the second plane being offset in a negative radial direction from the first plane; and a third-section-planar area that spans a third plane adjoining the first plane, the third-section-planar area having a fourth-cavity width perpendicular to the Z axis and perpendicular to the first radial direction of the inner-conductive tube, the third plane being offset in the negative radial direction from the first plane, wherein the second-section-planar area and the third-section-planar area are offset from each other by a length of the first-section-planar area, and wherein the third-cavity width and the fourth-cavity width are larger than the first-minimum width. 
     Example 15 includes the inner-conductive tube of any of Examples 9-14, wherein at least one of the first-full-planar area of the first shallow-cavity and the second-full-planar area of the second shallow-cavity is rectangular in shape. 
     Example 16 includes a method of making an inner-conductive tube, the method comprising: machining a first shallow-cavity having at least one first-planar area on an outer-curved surface of a cylindrical piece aligned to an axial direction; and machining a second shallow-cavity having at least one second-planar area on an outer-curved surface of the cylindrical piece, wherein the first-planar area opposes the second planar area. 
     Example 17 includes the method of Example 16, wherein machining the first shallow-cavity having the at least one first-planar area on the first region of the outer surface of the cylindrical tube comprises: machining a first-planar area in a first section of the first shallow-cavity, the first-planar area having a length parallel to the axial direction and a first width perpendicular to the axial direction; machining a second-planar area in a second section of the first shallow-cavity, the second-planar area having a second width perpendicular to the axial direction and the second-planar area adjoining the first-planar area at a first end of first-planar area; and machining a third-planar area in a third section of the first shallow-cavity, the third-planar area having a third width perpendicular to the axial direction and the third-planar area adjoining the first-planar area at a second end of first-planar area. 
     Example 18 includes the method of any of Examples 16-17, wherein machining the first shallow-cavity having the at least one first-planar area on the first region of the outer surface of the cylindrical tube comprises: machining a first-planar area in a first section of the first, the first-planar area having a length parallel to the axial direction and a first width perpendicular to the axial direction; machining a second-planar area in a second section of the first shallow-cavity, the second-planar area having a second width perpendicular to the axial direction, wherein second-planar area is offset in a negative radial direction from the first-planar area; and machining a third-planar area in a third section of the first shallow-cavity, third-planar area having a third width perpendicular to the axial direction, wherein the third planar area is offset in a negative radial direction from the first-planar area. 
     Example 19 includes the method of any of Examples 16-18, further comprising: positioning a metal ring over the outer surface of the cylindrical tube, wherein the ring is offset, along the Z axis, from the first shallow-cavity and the second shallow-cavity. 
     Example 20 includes the method of any of Examples 16-19, further comprising: attaching a flat surface of a first dielectric bar to the at least one planar area of the first shallow-cavity; and attaching a flat surface of a second dielectric bar to the at least one planar area of the second shallow-cavity. 
     A number of embodiments of the invention defined by the following claims have been described. Nevertheless, it will be understood that various modifications to the described embodiments may be made without departing from the spirit and scope of the claimed invention. For example, although the technique for machining an inner-conductive core of a coaxial polarizer is described above, the technique for forming the shallow cavities on the outer surface of the inner-conductive core can include other processes including heating the metal and impressing the shallow cavities on the outer surface of the inner-conductive core or other types of molding or shaping metal. Accordingly, other embodiments are within the scope of the following claims.