Patent Publication Number: US-6992639-B1

Title: Hybrid-mode horn antenna with selective gain

Description:
RELATED APPLICATIONS 
   The present application claims priority from U.S. Provisional Application No. 60/440,715, filed Jan. 16, 2003, entitled “Dielectric-Loaded Hybrid-Mode Horn Antenna with Selectable or High Gain and Large Bandwidth”; and from U.S. Provisional Application No. 60/480,369, filed Jun. 19, 2003, entitled “Hybrid-Mode Horn Antenna with Selective Gain”, the complete disclosures of which are incorporated herein by reference for all purposes. 

   BACKGROUND OF THE INVENTION 
   The present invention is directed generally to horn antennas, and more specifically to a new class of hybrid-mode horn antennas having selective gain. 
   Maximum directivity from a horn antenna is obtained by uniform amplitude and phase distribution over the horn aperture. Such horns are denoted as “hard” horns. They can support the transverse electromagnetic (TEM) mode, and apply to linear as well as circular polarization. They are characterized with hard boundary impedances:
 
 Z   z   =−E   z   /H   x =0 and  Z   x   =E   x   /H   z =∞,  (1)
         or soft boundary impedances:
 
 Z   z   =E   z   /H   x =∞ and  Z   x   =E   x   /H   Z =0,  (2)
   meeting the balanced hybrid condition:
 
 Z   z   Z   x =η 0   2 ,  (3)
   where η 0  is the free space wave impedance and the coordinates z and x are defined as longitudinal with and transverse to the direction of the wave, respectively.       

   Hard horns can be used in the cluster feed for multibeam reflector antennas to reduce spillover loss across the reflector edge. Such horns may also be useful in single feed reflector antennas with size limitation, and in quasi-optical amplifier arrays. 
   Two different hard horns which meet these conditions are one having longitudinal conducting strips on a dielectric wall lining, and the other having longitudinal corrugations filled with dielectric material. These horns work for various aperture sizes, and have increasing aperture efficiency for increasing size as the power in the wall area relative to the total power decreases. Dual mode and multimode horns like the Box horn can also provide high aperture efficiency, but they have a relatively narrow bandwidth, in particular for circular polarization. Higher than 100% aperture efficiency relative to the physical aperture may be achieved for endfire horns. However, these endfire horns also have a small intrinsic bandwidth and may be less mechanically robust. Linearly polarized horn antennas may exist with high aperture efficiency at the design frequency, large bandwidth and low cross-polarization. However, these as well as the other non hybrid-mode horns only work for limited aperture size, typically under 1.5 to 2λ. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention provides a new class of hybrid-mode horn antennas. The present invention facilitates the design of boundary conditions between soft and hard, supporting modes under balanced hybrid condition with uniform as well as tapered aperture distribution. In one embodiment, the horn is relatively simple mechanically, has a reasonably large bandwidth, can support linear as well as circular polarization, and can be designed for a wide range of aperture sizes. 
   In one embodiment, antennas of the present invention are dielectric-loaded circularly or linearly polarized hybrid-mode horn antennas which can be designed to a desired high directivity (gain) and low cross-polarization (axial ratio) over a wide frequency band. In one embodiment of the present invention, an antenna comprises a dielectric core inside a horn, where the core has two or more dielectric layers, and where the core is separated from the horn wall. The antenna boundary conditions facilitate a balanced hybrid-mode in the inner dielectric region with zero or negligible cross-polarization at the design frequency. With proper design, this mode can be close to a TEM mode with uniform or nearly uniform aperture distribution and consequently high gain. 
   Horn antennas of the present invention will have a wide range of uses. For example, in one embodiment the horn is used as an element in a limited scan phased array where a larger element aperture size is needed. They may provide high aperture efficiency and low grating lobes. In another embodiment, the horns are used as feed elements for reflector antennas or in quasi-optical amplifier arrays. It could be particularly useful in millimeter wave applications. Embodiments having a flat top pattern design make it a candidate earth coverage horn on-board satellites and a candidate feed for reflector antennas with enhanced directivity. 
   In one embodiment, a horn antenna of the present invention includes a conducting horn, a first dielectric layer disposed over at least a portion of the conducting horn, a second dielectric layer disposed over at least a portion of the first dielectric layer, and a third dielectric layer disposed over at least a portion of the second dielectric layer. 
   In alternative embodiments, the second dielectric layer comprises a higher dielectric constant than the third dielectric layer, and the third dielectric layer comprises a higher dielectric constant than the first dielectric layer. The first dielectric layer further may comprise a gas or air-filled gap, a vacuum region, and the like. 
   In one aspect, the conducting horn comprises an inner wall surface, and the second dielectric layer is spaced apart from the inner wall surface by a plurality of spacers. At least one of the spacers may be aligned axially or circumferentially relative to the conducting horn. 
   In one aspect, the first and second dielectric layers have a generally uniform thickness in an axial direction of the conducting horn. In another aspect, the first and/or second dielectric layer have a variable thickness in the axial direction. The horn antenna may further include a matched horn throat defined by at least a portion of the second and third dielectric layers. The horn antenna also may include an impedance matching layer near the aperture. The matching layer may be a portion of the second and/or third dielectric layers. In one aspect, the impedance matching layer is a corrugated matching layer. In another aspect, the matching layer comprises a plurality of spaced apart holes, rings, ringlets, or the like. 
   In another embodiment of the present invention, a horn antenna includes a dielectric core coupled to a conducting horn by a plurality of spacers to define a gap between the horn and core. The dielectric core includes an outer portion and an inner portion, with the outer and inner portions each including a dielectric material. The inner portion dielectric material has a different dielectric constant than the outer portion dielectric material. In one aspect, the dielectric constant of the outer portion dielectric material is greater than the dielectric constant of the inner portion dielectric material. In another aspect, the gap is at least partially filled, or completely filled with a third dielectric material having a lower dielectric constant than the dielectric constants of both the inner and outer portion dielectric materials. 
   Another embodiment of the present invention includes a reflector antenna having a reflective dish and at least one horn antenna as previously described. The horn antenna is adapted to direct a signal towards the reflective dish. In another embodiment, the present invention provides an antenna array system comprising two or more horn antennas. In still another embodiment, the present invention provides a spacecraft incorporating horn antenna(s) as described herein. The horn antenna(s) may be coupled to a spacecraft bus as needed for antenna operation. 
   The summary provides only a general outline of some embodiments according to the present invention. Many other objects, features and advantages of the present invention will become more fully apparent from the following detailed description, the appended claims and the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a simplified axial view of a hybrid-mode dielectric-loaded horn antenna according to an embodiment of the present invention; 
       FIGS. 2A and 2B  illustrate various horn cross sections for dual linear or circular polarization, and for single linear polarization, respectively; 
       FIG. 3  depicts an electromagnetic boundary model for plane wave incident field according to an embodiment of the present invention; 
       FIG. 4  graphically depicts the relation between t 2  and t 3  with ε r2  as a parameter in the dielectric horn supporting balanced hybrid modes according to an embodiment of the present invention; 
       FIG. 5  graphically depicts the relation between t 2  and ε r2  with ε r1  as a parameter in the dielectric horn supporting balanced hybrid modes based on the plane wave model according to an embodiment of the present invention; 
       FIG. 6  graphically depicts the relation between t 3  and ε r2  with ε r1  as a parameter in the dielectric horn supporting balanced hybrid modes according to an embodiment of the present invention; 
       FIG. 7  graphically depicts a total wall thickness versus ε r1  with ε r2  as a parameter in the dielectric horn under balanced hybrid condition according to an embodiment of the present invention; 
       FIG. 8  graphically depicts a boundary impedance versus t 3  with ε r1 =1.1 and ε r2 =4.0 under balanced hybrid condition in a dielectric horn according to an embodiment of the present invention; 
       FIG. 9  graphically depicts a field distribution in the wall region of a dielectric horn with ε r2 =2.0 and ε r1 =1.1, based on  FIG. 3 ; 
       FIG. 10  graphically depicts an overall aperture efficiency versus ε r2  for a dielectric horn with 3.38λ overall aperture diameter according to an embodiment of the present invention; 
       FIG. 11A  graphically depicts aperture distributions for a dielectric horn with 70 mm overall aperture diameter at 14.5 GHz, ε r1 =1.3 and ε r2 =2.5 based on the circular cylindrical model according to an embodiment of the present invention; 
       FIG. 11B  graphically depicts co- and cross-polarization radiation patterns for a dielectric horn with 70 mm overall aperture diameter at 14.5 GHz, ε r1 =1.3 and ε r2 =2.5 based on the circular cylindrical model according to an embodiment of the present invention; 
       FIG. 12  graphically depicts computed aperture efficiency and relative peak sidelobe level versus t 2  under balanced hybrid condition for the horn in  FIG. 11  at 14.5 GHz; 
       FIG. 13  graphically depicts computed aperture efficiency and relative peak cross-polarization versus frequency for a horn with 70 mm overall aperture diameter, ε r1 =1.3 and with ε r2 =2.5 and 4.0 based on the circular cylindrical model, designed for hard boundary conditions at 14.5 GHz, according to an embodiment of the present invention; 
       FIG. 14  graphically depicts computed aperture efficiency and relative peak cross-polarization versus frequency for a horn with 70 mm overall aperture diameter, ε r1 =1.3 and with ε r2= 2.5 and 4.0 based on the circular cylindrical model, designed for balanced hybrid conditions at 13.5 GHz, according to an embodiment of the present invention; 
       FIG. 15A  graphically depicts computed aperture efficiency for a dielectric horn design with flat top pattern based on the circular cylindrical model with 70 mm aperture diameter at 14.5 GHz (ε r1 =1.3, ε r2 =2.5, t 2 =4.0 mm, t 3 =3.3 mm) according to an embodiment of the present invention; 
       FIG. 15B  graphically depicts computed radiation pattern for a dielectric horn design with flat top pattern based on the circular cylindrical model with 70 mm aperture diameter at 14.5 GHz (ε r1 =1.3, ε r2 =2.5, t 2 =4.0 mm, t 3 =3.3 mm) according to an embodiment of the present invention; 
       FIGS. 16–18  are simplified schematics depicting various horn antenna embodiments according to the present invention; and 
       FIG. 19  is a simplified schematic of a spacecraft according to the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In one embodiment, a new and mechanically simple dielectric loaded hybrid-mode horn is presented. In alternative embodiments of the present invention, the horn satisfies hard boundary conditions, soft boundary conditions, or boundaries between hard and soft under balanced hybrid conditions (low cross-polarization). Like other hybrid mode horns, the present design is not limited in aperture size. In some embodiments, design curves were developed based on a plane wave model, and radiation performance was computed based on a cylindrical waveguide model. In one embodiment, aperture efficiency of about ninety-four percent (94%) has been computed at the design frequency for a 3.38λ aperture with hard boundary condition and a dielectric constant of 4.0. The same horn with a dielectric constant of 2.5 can provide higher than about eighty-nine percent (89%) aperture efficiency and under −30 decibels (dB) cross-polarization over about a fifteen percent (15%) frequency range. Predicted peak sidelobes ranging from −19 to −26.5 dB at the design frequency have been obtained. In one embodiment, the horn can be designed to radiate a flat-top pattern. In a particular embodiment, the horn could be useful for millimeter wave applications and quasi-optical amplifiers. 
     FIG. 1  shows an axial cut of a dielectrically loaded horn  100  according to an embodiment of the present invention taken along an axis  200 . Horn  100  includes a conducting horn wall  110  extending from a throat region  120 . Horn wall  110  extends from throat  120  to define an aperture  180  having a diameter D. While referred to as “diameter,” it will be appreciated by those skilled in the art that horn  100  may have a variety of shapes, and that aperture  180  may be circular, elliptical, rectangular, square, or some other configuration all within the scope of the present invention. Horn  100  has anisotropic wall impedance according to (1) and (2) and can be designed to meet the balanced hybrid condition in (3) in the range from hard to soft boundary conditions. 
   The space within horn  100  is at least partially filled with a dielectric core  130 . In one embodiment, dielectric core  130  comprises an inner core portion  140  and an outer core portion  150 . In some embodiments, inner core portion  140  comprises foam, honeycomb, or the like, and outer core portion  150  comprises polystyrene, polyethylene, teflon, or the like. It will be appreciated by those skilled in the art that alternative materials also may be used within the scope of the present invention. 
   In some embodiments, dielectric core  130  is separated from wall  110  by a gap  160 . In one embodiment, gap  160  is filled or at least partially filled with air. In another embodiment, gap  160  comprises a vacuum. In one embodiment, gap  160  corresponds to a first dielectric layer. In the embodiments having gap  160 , a spacer or spacers  170  may be used to position dielectric core  130  away from horn wall  110 . Spacer(s)  170  may comprise a variety of shapes and sizes. For example, spacer(s)  170  may comprise one or more spaced rings or ring segments, or longitudinal ridges or ridge segments, running circumferentially around horn wall  110 . Spacer(s)  170  may further comprise axially aligned ridges or ridge segments. In still other embodiments, spacer(s)  170  include one or more blocks, foam pieces, honeycomb spacers, and the like. In a particular embodiment, spacer(s)  170  comprise a dielectric material with low dielectric constant. In one embodiment, the axial length of the spacers is one-quarter wavelength (¼λ) of the dielectric spacer material. 
   In another embodiment, spacer(s)  170  completely fill gap  160 . In this manner, spacer(s)  170  define a dielectric layer lining some or all of horn wall  110 , and may help to correctly position core  130 . In this embodiment, spacers  170  define a first dielectric layer, with outer core portion  150  comprising a second dielectric layer and inner core portion  140  comprising a third dielectric layer. In one embodiment, the dielectric constants of outer core portion  150  and inner core portion  140  are different. In a particular embodiment, outer portion  150  of dielectric core  130  has the highest dielectric constant, while the dielectric constant of inner portion  140  of core  130  falls between that of outer portion  150  and the dielectric material associated with gap  160 . In a particular embodiment, outer core portion  150  has a higher dielectric constant than does inner core portion  140 . In one embodiment, inner core portion  140  has a higher dielectric constant than does gap  160 . 
   In a particular embodiment, gap  160  is a generally uniform gap having a thickness t 3  and extending from about throat region  120  to aperture  180 . In one embodiment, outer portion  150  of core  130  has a generally uniform thickness t 2 . Gap thickness t 3  and outer core portion thickness t 2  depends on the frequency as shown, for example, in  FIG. 4 . In some embodiments, such as is shown in  FIG. 1 , the cross sectional area of inner portion  140  increases with increased distance from throat region  120 . In a particular embodiment, thickness t 3  and/or thickness t 2  vary between the horn throat and aperture. In other words, t 2  or t 3  vary as a function of the distance along axis  200  from the throat  120  to aperture  180 . One or both thicknesses t 2 , t 3  may be greater near throat  120  than near aperture  180 , or may be less near throat  120  than near aperture  180 . An example of such an embodiment is shown in  FIG. 17 , in which horn antenna  250  includes outer core portion  150  having variable thickness t 2 . 
   In one embodiment, throat region  120  of horn  100  is matched to convert the incident field into a field with approximately the same cross-sectional distribution as is required in aperture  180 . This may be accomplished, for example, by the physical arrangement of inner core portion  140  and outer core portion  150  depicted in  FIG. 1 . In this manner, the desired mode for horn  100  is excited. Further, this arrangement helps to reduce return loss or the reflection of energy in the throat. 
   Horn  100  may further include one or more matching layers  190  between dielectric and free space in aperture  180 . Matching layers  190  may comprise, for example, one or more dielectric materials coupled to core portion(s)  140  and/or  150  near aperture  180 . In one embodiment, matching layer  190  has a dielectric constant between the dielectric constant of core portion(s)  140 ,  150  to which it is coupled, and the dielectric constant of the ambient air or vacuum. In a particular embodiment, matching layer  190  includes a plurality of spaced apart rings or holes. The spaced apart rings or holes (not shown) may have a variety of shapes and may be formed in symmetrical or non-symmetrical patterns. In one embodiment, the holes are formed in the aperture portion of core portions  140  and/or  150  to create a matching layer portion of core  130 . In one embodiment, the holes and/or rings are formed to have depth of about one-quarter wavelength (¼λ) of the dielectric material in which they are formed. In a particular embodiment, outer portion  150  includes a corrugated matching layer (not shown) at aperture  180 . 
   Horns  100  of the present invention can have different cross sections, including circular, rectangular, elliptical, or the like for circular or linear polarization ( FIG. 2A ). In one embodiment, a rectangular cross section for linear polarization and maximum gain is used ( FIG. 2B ). Horn  100  may also be implemented as a profiled horn for reduced size. Since the central region can be designed with low dielectric constant or permittivity, minimal or reduced overall RF loss can be achieved. 
   Plane Wave Horn Model 
     FIG. 3  shows the model for a plane wave incidence on the boundary. By expressing the electric and magnetic fields in the three regions, and forcing continuous tangential fields and continuous tangential propagation constant across the two boundaries, the following transverse electric (TE) and transverse magnetic (TM) boundary impedances can be derived at y=t 2 +t 3 : 
                 Z   TE     =       Z   x     =       -       E   x       H   z         =       -   j     ⁢           ⁢     η   0     ⁢       k   0       k   y2       ⁢           k   y3     ⁢     T   2       +       k   y2     ⁢     T   3             k   y3     -       k   y2     ⁢     T   2     ⁢     T   3                   ,           (   4   )                   Z   TM     =       Z   z     =         E   z       H   x       =       -   j     ⁢           ⁢     η   0     ⁢       k   y2         k   0     ⁢     ɛ   r2         ⁢           ɛ   r3     ⁢     k   y2     ⁢     T   2       +       ɛ   r2     ⁢     k   y3     ⁢     T   3               ɛ   r3     ⁢     k   y2       -       ɛ   r2     ⁢     k   y3     ⁢     T   2     ⁢     T   3                   ,           (   5   )                       where η 0  is the free space wave impedance, k 0 =2π/λ 0  is the free space wave number and λ 0  is the free space wavelength. The orientation of the coordinate system as well as the relative permittivities ε r1 , ε r2  and ε r3  are defined in  FIG. 3 , T q =tan(k yq t q ), q=2 or 3, and the wave numbers are: 
               k   y2     =       k   0     ⁢           ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1           ⁢     ⟶       θ   1     →     90   ⁢   °         ⁢     k   0       ⁢         ɛ   r2     -     ɛ   r1                   (   6   )                 k   y3     =       k   0     ⁢           ɛ   r3     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1           ⁢     ⟶       θ   1     →     90   ⁢   °         ⁢     k   0       ⁢         ɛ   r3     -     ɛ   r1                   (   7   )             
   where the angle of incidence θ 1  are defined in  FIG. 3 . Gracing incidence or θ 1 =90° is approximately achieved when the waveguide is operated well above cut-off, which occurs in the aperture of the horn.       
   By inserting (4) and (5) into (3), the following design condition is obtained for the support of modes under balanced hybrid conditions in the central (interior) horn region: 
               R   =           Z   TE     ⁢     Z   TM         η   1       =         -       ɛ   r1       ɛ   r2         ⁢           k   y3     ⁢     T   2       +       k   y2     ⁢     T   3             k   y3     -       k   y2     ⁢     T   2     ⁢     T   3           ⁢           ɛ   r3     ⁢     k   y2     ⁢     T   2       +       ɛ   r2     ⁢     k   y3     ⁢     T   3               ɛ   r3     ⁢     k   y2       -       ɛ   r2     ⁢     k   y3     ⁢     T   2     ⁢     T   3             =   1         ,           (   8   )             
         where η 1  is the wave impedance in the central horn region. Although there are solutions to (8) for real T 3 , it can be shown that when hard boundary conditions from (1) are applied to (4) and (5), a solution is obtained only when T 3  is imaginary. Consequently, solutions with evanescent fields in the outer region are being sought, such that
 
 k   y3   =jk′   y3   =jk   0 √{square root over (ε r1  sin 2 θ 1 −ε r3 )} and  T   3   =jTH   3   =j  tan  h ( k′   y3   t   3 ).
       

   This is achieved for gracing incidence if ε r1 &gt;ε r3 . Thus the following expression for supporting balanced hybrid modes in the central horn region can be derived: 
               t   2     =         λ   0       2   ⁢   π   ⁢         ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1               ⁢         -   B     ±         B   2     -     4   ⁢   A   ⁢           ⁢   C             2   ⁢   A                 (   9   )             
 
where 
                   A   =         ɛ   r1     ⁢     ɛ   r3       -       ɛ   r2   2     ⁢     TH   3   2                     B   =         ɛ   r3     ⁡     (       ɛ   r1     -     ɛ   r2       )       ⁢     (         k   y2       k   y3   ′       -         ɛ   r2       ɛ   r3       ⁢       k   y3   ′       k   y2           )     ⁢     TH   3                   C   =         ɛ   r2     ⁡     (       ɛ   r3     -       ɛ   r1     ⁢     TH   3   2         )       .                   (   10   )             
 
   The thickness t 3  of the outer region has its minimum value when the square root expression in the numerator of (9) is zero. The special cases T 2 =0 and T 2 =∞ result in the following design condition when applied to (8): 
                 t   3     =           λ   0       4   ⁢   π   ⁢           ɛ   r1     ⁢     sin   2     ⁢     θ   1       -     ɛ   r3             ⁢     ln   ⁡     (       1   +         ɛ   r3     /     ɛ   r1             1   -         ɛ   r3     /     ɛ   r1             )       ⁢           ⁢   for   ⁢           ⁢     T   2       =   0       ,           (   11   )                 t   3     =           λ   0       4   ⁢   π   ⁢           ɛ   r1     ⁢     sin   2     ⁢     θ   1       -     ɛ   r3             ⁢     ln   ⁡     (       1   +           ɛ   r1     ⁢     ɛ   r3         /     ɛ   r2           1   -           ɛ   r1     ⁢     ɛ   r3         /     ɛ   r2           )       ⁢           ⁢   for   ⁢           ⁢     T   2       =     ∞   .               (   12   )             
 
   If ε r1 =ε r2  both cases above results in the same solution, and similar or identical to a single dielectric soft horn solution. 
   The condition for ideally soft and hard boundaries can be derived by applying (4) and (5) to (1) for hard boundary condition, and to equation (2) for soft boundary condition. Both these boundary conditions result in the same expression for t 3 , but different t 2  according to: 
                 t   3     =         λ   0       4   ⁢   π   ⁢           ɛ   r1     ⁢     sin   2     ⁢     θ   1       -     ɛ   r3             ⁢     ln   ⁡     (       1   +         ɛ   r3     /     ɛ   r2             1   -         ɛ   r3     /     ɛ   r2             )           ,     soft   ⁢           ⁢   and   ⁢           ⁢   hard   ⁢           ⁢   boundaries     ,           (   13   )                   t   2     =         λ   0       2   ⁢   π   ⁢         ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1               ⁡     [         tan     -   1       ⁢           ɛ   r3     ⁡     (       ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1         )           ɛ   r2     ⁡     (         ɛ   r1     ⁢     sin   2     ⁢     θ   1       -     ɛ   r3       )             +   π     ]         ,     soft   ⁢           ⁢   boundary     ,           (   14   )                   t   2     =         λ   0       2   ⁢   π   ⁢         ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1               ⁢     tan     -   1       ⁢           ɛ   r2     ⁡     (         ɛ   r1     ⁢     sin   2     ⁢     θ   1       -     ɛ   r3       )           ɛ   r3     ⁡     (       ɛ   r2     -       ɛ   r1     ⁢     sin   2     ⁢     θ   1         )               ,     hard   ⁢           ⁢     boundary   .               (   15   )             
 
   Based on  FIG. 3 , the following pertinent plane wave electric field components can be derived for regions  2  and  3 : 
                 E   x2   TE     =           k   y3   ′     ⁢     sin   ⁡     [       k   y2     ⁡     (     y   -     t   3       )       ]         +       k   y2     ⁢     cos   ⁡     [       k   y2     ⁡     (     y   -     t   3       )       ]       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )                 k   y3   ′     ⁢     sin   ⁡     (       k   y2     ⁢     t   2       )         +       k   y2     ⁢     cos   ⁡     (       k   y2     ⁢     t   2       )       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )               ,           (   16   )                   E   x3   TE     =           k   y2       k   y3   ′             k   y3   ′     ⁢     sin   ⁡     (       k   y2     ⁢     t   2       )         +       k   y2     ⁢     cos   ⁡     (       k   y2     ⁢     t   2       )       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )             ⁢       cosh   ⁡     (       k   y3   ′     ⁢   y     )         cosh   ⁡     (       k   y3   ′     ⁢     t   3       )             ,           (   17   )                   E   y2   TM     =       η   0     ⁢         ɛ   r1         ɛ   r2       ⁢           k   y3   ′     ⁢     cos   ⁡     [       k   y2     ⁡     (     y   -     t   3       )       ]         +       k   y3   ′     ⁢       ɛ   r2       ɛ   r3       ⁢     sin   ⁡     [       k   y2     ⁡     (     y   -     t   3       )       ]       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )                 k   y2     ⁢     cos   ⁡     (       k   y2     ⁢     t   2       )         +       k   y3   ′     ⁢       ɛ   r2       ɛ   r3       ⁢     sin   ⁡     (       k   y2     ⁢     t   2       )       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )                 ,           (   18   )                 E   y3   TM     =     j   ⁢           ɛ   r1       ɛ   r3       ⁢     k   y2             k   y2     ⁢     cos   ⁡     (       k   y2     ⁢     t   2       )         +       k   y3   ′     ⁢       ɛ   2       ɛ   3       ⁢     sin   ⁡     (       k   y2     ⁢     t   2       )       ⁢     tanh   ⁡     (       k   y3   ′     ⁢     t   3       )             ⁢         cosh   ⁡     (       k   y3   ′     ⁢   y     )         cosh   ⁡     (       k   y3   ′     ⁢     t   3       )         .               (   19   )             
 
   Circular Cylindrical Horn Model 
   A computer program was developed to predict the propagation constant and field distribution inside a circular cylindrical waveguide symmetrically filled with three dielectric materials as shown in  FIG. 1 . The method is similar to one used for two dielectric materials. Expressions for the electric and magnetic field components in the three regions were first established. The tangential components of the field as well as the wave numbers were forced to be continuous across the boundaries, resulting in a linear matrix equation including an eight by eight (8×8) matrix. The propagation constant was found by iteratively solving for the determinant of this matrix, while the constants of the field components were found by solving the linear matrix equation through matrix inversion. Finally, the radiation pattern was computed based on the Kirchhoff-Huygen radiation integral. 
   Computed Results—Plane Wave Model Analysis 
   In all the cases analyzed below it is assumed that ε r3 =1.0 (air gap  160  in outer region) and that θ 1 =90° (gracing incidence). In  FIG. 4 , solutions to the balanced hybrid equation (8) given in (9) and (10) are illustrated for ε r1 =1.1 and for different values of ε r2  between 2.0 and 6.0. It can be seen that there are two solutions to t 2  for a given t 3  above a certain minimum value. Also, the special solutions to the soft and hard cases in (13) to (15) are marked. The type of waveguide solution corresponding to the different sections of each curve can be studied by the cylindrical waveguide model and will be discussed below. 
     FIG. 5  shows the relation between t 2  and ε r2  with ε r1  as a parameter based on (14) and (15) for soft and hard boundary conditions. It can be seen that t 2  decreases with decreasing ε r1  and with increasing ε r2 .  FIG. 6  shows the relation between t 3  and ε r2  with ε r1  as a parameter for soft and hard boundaries based on (13). As stated under (13) the curves for hard and soft boundaries are identical. Here t 3  decreases with increasing ε r1  and with increasing ε r2 . 
   The total “wall” thickness t 2 +t 3  versus ε r1  with ε r2  as a parameter is illustrated in  FIG. 7  for soft and hard boundary conditions. Higher value of ε r2  reduces the thickness of the wall, which is expected to result in higher aperture efficiency at the design frequency. Also, there is a minimum wall thickness for a given ε r2  vs. ε r2 , occurring at increasing ε r1  when ε r2  increases. In comparison, the wall thickness of a single dielectric hard horn with dielectric constant of ε r  is t=¼√{square root over (ε r −1)}), which is slightly less than t 2 +t 3  of the horn above for a given ε r2 =ε r . 
     FIG. 8  illustrates the boundary impedances versus t 3  on the inner boundary for ε r1  =1.1 and ε r2 =4.0 under balanced hybrid condition. For hard and soft boundary conditions the impedance is either zero or infinite as discussed above. It can be seen that the boundary impedance can be designed for any positive or negative value between 0 and infinity for a given combination of t 2  and t 3 , where each point along the curve meets the balanced hybrid condition. In  FIG. 8 , the symbols “+’ and “−” refer to the upper and lower part of the curve, respectively, in  FIG. 4  with ε r2 =4.0. 
     FIG. 9  shows the computed linear field distribution in regions  2  and  3  for both polarizations transverse to the direction of propagation (z) where the field strength in the central region  1  is unity. The distributions are computed based on the field expressions in (16) to (19). Although the fields are evanescent in region  3 , the component normal to the boundary is still only 70% of the field strength in the central region, while the component parallel to the boundary drops to zero at the outer wall. In region  2 , the normal component is discontinuous and lower than in the two surrounding regions. High field strength in the wall region is advantageous for aperture efficiency, but degrades radiated cross-polarization since the field is not balanced. 
     FIG. 10  shows aperture efficiency versus ε r2  for a dielectric horn with ε r2  as a parameter. It is assumed that the linear field distribution in  FIG. 9  is applied to a waveguide with circular symmetry and 3.38λ overall diameter. The overall aperture efficiency is computed from power integration over the aperture fields given in (16) to (19). As indicated earlier, the efficiency increases with increasing ε r2 . Also, when ε r1  increases the efficiency increases until it saturates around ε r1 =1.3−1.5, depending on the value of ε r2 . Since in one embodiment a low dielectric constant is desired in the central region, ε r2 ≈1.3 in a particular embodiment where high aperture efficiency is desired. Increasing ε r2  increases the efficiency, but is expected to decrease the bandwidth. For larger apertures the aperture efficiency will increase. 
   Computed Results—Circular Cylindrical Model Analysis 
   In this section, the results are based on computations based on the circular cylindrical model. In all embodiments, the horn diameter is 70 mm or 3.38λ at 14.5 GHz, ε r1 =1.3, and uniform phase is assumed over the aperture (ideal cylindrical aperture model).  FIG. 11A  shows aperture distributions for six different designs between ideally hard and approximately soft for a horn at 14.5 GHz and ε r2 ≈2.5, while  FIG. 11B  shows the corresponding radiation patterns. The hard boundary aperture efficiency of 92.3% is only 0.5% lower than the efficiency computed by the plane wave model in  FIG. 10 .  FIG. 12  presents curves for aperture efficiency and relative peak sidelobe level versus t 2  for the same case. These curves can be used to trade horn efficiency against sidelobe level. A similar set of trade curves can be generated for horn efficiency or sidelobe level versus beamwidth. The examples shown in  FIGS. 11 and 12  can be found along the section of the curve with ε r2 =2.5 in  FIG. 4  on the right side of the hard boundary mark. 
     FIG. 13  shows aperture efficiency and relative peak cross-polarization versus the frequency with ε r2 =2.5 and 4.0. In one embodiment, the horn is designed with hard boundary condition at 14.5 GHz. Beyond this frequency the waveguide supports surface waves, indicated on the curve in  FIG. 4  to the left of the hard boundary mark.  FIG. 14  presents corresponding results for a horn with the same dielectric materials, designed for balanced hybrid condition at 13.5 GHz. It shows that the embodiment where ε r2 =2.5 yields larger bandwidth compared to the embodiment where ε r2 =4.0. Slightly above the center frequency cross-polarization contributions from the core region and the wall region add up destructively to generate relative peak cross-polarization below −40 dB. The design results in a worst-case cross-polarization below −26.5 dB and aperture efficiency higher than 87.5 dB over the frequency band 11.7 to 14.5 GHz, while cross-polarization under −30 dB and aperture efficiency over about 89% has been achieved over about a 15% bandwidth. 
     FIG. 15  shows aperture distribution and radiation pattern for a dielectric-loaded horn designed to generate a broad pattern. In this embodiment the fields in the wall region (regions  2  and  3  in  FIG. 3 ) have been utilized constructively to produce a J 1 (x)/x-type distribution which radiates an approximately flat top pattern. Such feed horns can be used as reflector feeds for optimal antenna efficiency. They can alternatively be implemented as dual hybrid-mode corrugated horns or hybrid-mode horns with a dielectric phase-correcting lens in the aperture. Solutions to flat top patterns can be found along the section of the curve in  FIG. 4  to the left of the soft boundary mark. 
     FIG. 16  depicts an alternative horn antenna embodiment according to the present invention. More specifically,  FIG. 16  depicts an array of horn antennas  300  according to the present invention. Horn antennas  300  may comprise one or more different horn antenna embodiments disclosed or discussed herein, including without limitation horn antenna  100  depicted in  FIG. 1 , and horn antenna  250  depicted in  FIG. 17 . 
     FIG. 18  depicts a simplified overall view of a horn antenna  400  according to an embodiment of the present invention. Horn  400  components and their materials may be similar or identical to those discussed in conjunction with earlier figures, including  FIG. 1 . As shown in  FIG. 18 , horn antenna  400  includes a horn wall  410  coupled to a flange  420 . Flange  420  may be used, for example, to couple horn antenna  400  to a desired structure, spacecraft, or the like. Horn  400  further includes an inner core portion  460 , which is disposed within an outer core portion  430 . Outer core portion  430  may further include, or be coupled to a plurality of spacers  440 . Spacers  440  are disposed between the inner surface of horn wall  410  and the outer surface of outer core portion  430 , to help provide the proper alignment and positioning of the two relative to one another. As shown in  FIG. 18 , a matching layer  470  is coupled to inner core portion  460 . Outer core portion  430 , in one embodiment, includes a corrugated edge  450  to operate as a matching layer for outer core portion  430 . 
     FIG. 19  depicts a simplified schematic of a spacecraft  500  having one or more horn antennas  100  according to the present invention. Again, horn antenna  100  associated with spacecraft  500  may include one or more embodiments of horn antennas discussed herein. 
   The present invention provides a new class of hybrid mode horn antennas which can be designed for a specific gain or sidelobe requirement and low cross-polarization. In one embodiment, the horn consists of a conical metal horn with a dual dielectric core, separated from the horn wall by a thin air-gap and/or low-dielectric material. In one embodiment, the central conical core is implemented with low dielectric, ensuring low dielectric loss, or with solid, low loss dielectric to allow for millimeter wave implementation. Cross-polarization is expected to be low since the horn supports modes under balanced hybrid condition inside the central core, although contribution to cross-polarization from the wall region may degrade the cross-polarization performance somewhat. A plane wave model was developed to derive design expressions and generate parametric design curves for the horn. Also, a circular cylindrical waveguide model was developed to analyze the radiation performance of the horn. 
   In one embodiment, predicted aperture efficiency over about 94% and relative peak cross-polarization under −37 dB was predicted at center frequency for a 3.38λ hard horn with a dielectric constant of 4.0. Cross-polarization under −40 dB has been predicted slightly off center frequency. Similarly, predicted aperture efficiency over about 89% and relative peak cross-polarization under −30 dB was predicted over the frequency band 12.5 to 14.5 GHz for the same aperture size. In one embodiment, the same horn is designed with aperture efficiency ranging from about 92% to about 78% and corresponding relative peak sidelobes between −19 to −26.5 dB at the design frequency, and with cross-polarization under −36 dB over the range. In one embodiment, the horn is used to generate a flat top pattern over a ±30° field-of-view and with −30 dB relative peak cross-polarization. 
   In one embodiment, the new horn is mechanically simple relative to other known hard horn antennas. According to the present invention, the horn can be used as an element in a limited scan array where a larger aperture size is needed. It can also be used in applications where gain and sidelobes could be traded for optimal antenna performance, e.g. as feeds for reflector antennas or in quasi-optical amplifier arrays. The horns of the present invention are particularly useful in millimeter wave applications in an embodiment. Finally, the flat top pattern design makes it a candidate earth coverage horn on-board satellites and a candidate feed for reflector antennas with enhanced directivity. 
   Notwithstanding the above description, it should be recognized that many other functions, methods, and combinations thereof are possible in accordance with the invention. Thus, although the invention is described with reference to specific ents and figures thereof, the embodiments and figures are merely illustrative, and ting of the invention. Rather, the scope of the invention is to be determined solely by the appended claims.