US 3886561 A Description (OCR text may contain errors) United States Patent us. Beyer 1 COMPENSATED ZONED DIELECTRIC LENS ANTENNA [75] Inventor: John Paul Beyer, Rockville, Md. [73] Assignee: Communications Satellite Corporation, Washington, DC. [22] Filed: Dec. 15, 1972 [21] Appl. No.: 315,693 [52] US. Cl. 343/910; 343/911 R [51] Int. Cl. H01q 15/10 [58] Field of Search 343/753-755, 343/909-911, 911 L, 785 [56] References Cited UNITED STATES PATENTS 2,978,702 4/1961 Pakan 343/909 X 2,985,880 5/1961 McMillan t 343/910 2,985,880 5/1961 McMillan 343/910 3,128,467 4/1964 Lanctot 343/785 X [451 May 27, 1975 3.256373 6/1966 Horst 343/911 R X 3,329.958 7/1967 Anderson 343/911 R X 3,430,248 2/1969 Lightbowne 343/911 R 3,465,362 9/1969 Ochiai 343/911 R Primary Examiner-Paul L. Gensler Attorney, Agent, or Firm-Sughrue, Rothwell, Mion, Zinn & Macpeak [57] ABSTRACT 5 Claims, 7 Drawing Figures Patented May 27, 1975 2 Sheets-Shut 1 Fl 0 PRIOR ART l PRIOR ART may. Patented May 27, 1975 3,886,561 2 Shuts-Sheet 2 FIG? COMPENSATED ZONED DIELECTRIC LENS ANTENNA BACKGROUND OF THE INVENTION The invention pertains to dielectric lens antennas. Dielectric lenses have been known for some time to be suitable for focusing radio waves. Such lenses operate in a similar fashion to optical lenses. Typically a radio wave emanating from a focal point with a spherical phase front passes through a properly designed dielectric lens and exits as a radio wave with a planar phase front. This focuses the radiation into a narrow beam. A side view of a typical dielectric lens and the manner in which it functions is illustrated in FIG. 1. The lens is a solid dielectric having an index of refraction 1 where 1 is usually greater than I. By way of example only, the lens geometry is a hyperbola of revolution with a planar side 14. A radio wave radiated from point source 12 has a spherical phase front, i.e., the locii of points of constant phase is a sphere. Lines 16 represent lines of constant phase. The lens effectively straightens out the phase front. The lines 18 on the output side represent the lines of constant phase. For a given frequency f,, having a free space wavelength M, the number of wavelengths between any two points separated by distance, L, will be (TI)(L)/}\, where n is the index of refraction of the medium. The dielectric lens is shaped so that the number of wavelengths between points 12 and 26 along ray path is the same as the number of wavelengths between points 12 and 28 along ray path 22. Lenses of the type described are frequency insensitive and therefore have wide band characteristics, usually a very desirable property. One of the problems with such lenses is that they are bulky and heavy relative to parabolic reflectors which would perform a similar function. The desirable characteristics of such lenses include zero aperture blockage, good scanning properties, and flexible design options. In addition, natural dielectric lenses having an index of refraction greater than unity have a natural, or built-in, aperture taper which is a powerful means of controlling sidelobe levels, and are inherently wide bandwidth. Another problem in real lenses is the inevitable presence of uncontrolled inhomogeneity in the dielectric material, which causes the phase shift through the lens to be different for rays which take different paths through the lens. This causes the phase across the planar phase front to differ from the ideal constant value, with consequent degradation of the focusing properties of the lens. One known technique for solving both the weight and inhomogeneity problem is known as zoning. This technique, simply stated, includes removing a zone or section from the lens. Referring again to FIG. I, assume a zone 30 of width, T, and having a cylindrical shape, for example, is removed from lens 10, leaving the zone filled with free space. The width, T, is selected so that the planar phase front 18 is maintained. Removal of width, T, of dielectric having index of refraction 17,, and substitution of free space having index of refraction equal to I certainly changes the number of wavelengths of fequencyf between points 12 and 28 along path 22. However, if T is selected so that the change is equal to an integral number of wavelengths, the phase along line 18 will, in the area of the zone, jump by an integral multiple of 211' radians, which is equivalent to remaining constant. Thus, T must satisfy the condition: 1),,T/M T/Ad N, where; A is the free space wavelength at the design frequency; n is the index of refraction of the dielectric lens, and N is an integer. It will be recognized that T/Ad is the number of wavelengths of design frequency f in a width T of free space, and n T/Ad is the number of wavelengths of design frequency f in a length T of dielectric 17 Put in words, equation (l) says that the phase of ray 22 at any point on the output side of lens 10 will be changed by an integral number of wavelengths, N, due to removing a width, T, of the dielectric. Further zoning can be accomplished using the same constraints. An example of multiple zones is shown in FIG. 2. While zoning is useful to solve the problems of weight and inhomogeneity it results in a lens which is highly frequency sensitive. The width, T, is selected based on the design frequency f,,. At frequencies other than f,, or integral multiples thereof, the wavelength difference caused by the removal of the zone is no longer an integral number. Consequently, the phase at point 28 will differ from that at point 26, resulting in loss of focus, deterioration of the beam, and a decrease in gain. It is also known in the art to provide artificial lenses instead of dielectric lenses for use as the focusing means. Typically, an artificial lens consists of parallel conductive slats separated by free space or other dielectric, or consists of horizontal and vertical conductive slats, forming an egg-crate arrangement, also separated by free space or other dielectric. One advantage of such artificial dielectric lenses over natural dielectric lenses is that they weigh a lot less. Additionally, they typically can be made to be more homogenous than some conventional natural dielectrics which are presently used for lens antennas. A problem with artificial dielectric lenses is that they are also highly frequency sensitive. Unlike natural dielectrics, the apparent index of refraction of an artificial dielectric is frequency dependent and can be expressed as: no l L'VI where, 11,, is the apparent index of refraction; A is the free space wavelength of any frequency of interest; and A is twice the slat-to-slat spacing. As will be appreciated by examining equation (2), the apparent index of refraction is less than unity. Also the artificial lens has a minimum cut-off frequency, f} l/k For any frequency less than f A becomes greater than h and 1 becomes an imaginary number. SUMMARY OF THE INVENTION Although both zoned natural dielectric lenses and artificial dielectric lenses are frequency sensitive, it has been discovered by applicant that the creation of a zone in a natural dielectric lens and the filling of that zone with an artificial dielectric results in a lens which has wider bandwidth properties than an equivalent natural dielectric lens with simple (uncompensated) zoning, weighs less than the unzoned natural dielectric lens, and is less sensitive to inhomogeneities in the dielectric. The width, T, of the zone is selected so that the number of wavelengths of the design frequency through a width, T, of the artificial dielectric differs by an integral number from the number of wavelengths of the design frequency through a width, T, of the natural dielectric. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a cross-sectional side view of a prior art zoned natural dielectric lens. FIG. 2 is a cross-sectional side view of a prior art natural dielectric lens having multiple zones. FIG. 3 is a cross-sectional side view of a preferred embodiment of the present invention. FIGS. 4 and 5 are, respectively, a cross-sectional side view and a perspective view of a lens constructed according to the teachings of this invention and having quarter wave matching sections. FIG. 6 is a perspective view of a cylindrically shaped lens constructed in accordance with the teachings of the present invention. FIG. 7 is a cross-sectional side view of an embodiment of the invention having multiple zones. DETAILED DESCRIPTION OF THE DRAWINGS FIGS. 1 and 2 have already been described in the background section above. FIG. 3 shows a natural dielectric lens 34 having a zone 44 of cylindrical shape and a depth or width, T. Point 32 represents the radiation of a radio wave, lines 38, 40 and 42 represent ray paths of the radio wave from point 32 through lens 34, and line 36 represents a line of constant phase. Assuming initially that lens 34 is not zoned, the phase from of the radiated wave which passes through the lens will be planar on the output side of lens 34. It is assumed, of course, that the lens geometry is designed in accordance with known techniques to provide a planar phase front. The number of wavelengths along edge rays 38 and 42 and center ray 40 between points 32 and line 36 will be the same. Since only the relative phase is important it can be assumed that the phase (1: at line 36 is zero for each of the rays. If the zone has a width, T, and is filled with an artificial dielectric, the ray 40 will still have a phase of zero at line 36 provided the substitution of the artificial dielectric changes the number of wavelengths along path 40 by an integral number. To maintain the planar phase front, T, must satisfy the equation: n T/Ad n T/Ad Integral Number N, where: M is the free space wavelength of design frequency f1; 11,, is the index of refraction of the natural dielectric 34', and 1 is the apparent index of refraction of the artificial dielectric 44 at the design frequency. Solving equation (3) for the width, T, gives: T N dl'no ,11 From equation (2), the apparent index of refraction 1 at the design frequency is given by: m (id/W1. By setting, T, in accordance with equation (4) the phase front of the output wave will be maintained, provided the frequency of the wave is f If the frequency changes to f, 1],, the change in the number of wavelengths along the center ray due to the substitution of the artificial dielectric will be: electric 44 at frequency f,. In this case, 11 is given by: "a l/ C) The phase error, Adz, at frequency f,, given in number of wavelengths, will be the difference between D and the nearest integral number. This may be expressed as: A4) N (1),,T/A, T/A Substituting for T in equation (8) results in: d N d/ l)(no 10 141 no) I It will be noted that when f f,,, A, will equal A 1 will equal n and the phase error will be zero. Also as A, increases, the term (A /A becomes smaller, and the term (1 n l'n 1; becomes larger. As )t, decreases, the opposite takes place. Thus, the two terms tend to offset each other for variations of A, from A and the phase error remains close to zero over a certain bandwidth. A specific example will now be given to demonstrate the bandwidth properties of the invention. Consider a natural dielectric plano-hyperbolic lens as shown in FIG. 3 made of dielectric material with a refractive index 1 1.25. Consider further that a zoning cavity is cut to the plane surface and then filled with an eggcrate artificial dielectric. Assume that operation is desired over a 0.5 gigahertz band centered at 3.95 Gl-Iz. The outer limits of the band are 3.7 GHz and 4.2 GI-Iz. Assume further that the artificial dielectric is made to have an apparent index of refraction of 0.8 at the band center. This is done by substituting for 1 and A in equation (5), solving for k and setting the slat-to-slat spacing at )t l2. The width of the zone, in accordance with equation (4) will be: T Ari/L25 0.8 z 6.65 inches. It will be noted that in the above equation, N is set at unity. The zone is thus referred to as a one wavelength zone. With the materials and the zone width selected as described, the phase error at the design frequency, 3.95 Gl-lz, will be zero. In accordance with equations (7) and (9), the phase error at the low end of the band is; A l 1.25 0.768/1.2S 0.8)(3.7/3.95)=0.003 wavelengths. This is a negligible phase error. At the high frequency end of the band, the phase error is, Adi l 1.25 0.826/l.25 0.8)(4.2/3.95)=0.0028 wavelengths. This is also negligible. Note that, over the same band, a lens with a simple (uncompensated) one wavelength zone would have had a phase error of -0.063 wavelengths at both 3.7 GH: and at 4.2 GHZ. Thus, compensation of the zone has reduced the error by a factor of more than times. The excellent compensation obtained for a one wavelength zone in the above example in this case only 6.65 inches deep suggests that equally good results would be otained for deeper cavities. Thus, a four wavelength cavity (N 4) would have phase error at the band-edges of N(0.003) =0.0l 2, and N(0.0028)==0.012. This means that a large fraction of the dielectric material might be removed, without serious loss in bandwidth, by stacking zone cavities as illustrated in FIG. 7 and filling the cavities with artificial dielectric. One problem, not mentioned above, is that of providing a good match at a dielectric interface to reduce power reflection. This problem and its solution is not limited to the subject invention but applies to prior art dielectric lenses as well. As is well known, the amount of a wave which is reflected at a dielectric interface, e.g., interface between lens and free space, varies directly with the ratio of the indices of refraction of the two mediums, e.g., lens and free space. A standard technique is to provide a quarter wave matching section between the two mediums. The optimum matching section has an index of refraction 1 V m 1 where 17 and 17, are the respective indices of refraction of the two interfacing mediums, and has a depth equal to 17, lt /4, where M is the free-space wavelength at the design frequency. ln a typical prior art lens, such as shown in FIG. 1, quarter wave matching sections are typically provided at both free space-lens interfaces. The same would be the case for the subject invention except that an additional quarter wave matching section could, and prefer ably should, be provided at the interface between the natural dielectric and the artificial dielectric. A lens in accordance with the present invention provided with quarter wave matching sections 50 at every interface is illustrated in FIG. 4. It should be noted that quarter wave matching sections are not necessary for the subject invention to be operable. However, such sections will improve the lens power transmission property. It turns out that the optimum parameters for a lens constructed in accordance with the teaching of this invention are: 1;, n l, where; n is the index of refraction of the natural dielectric; and n is the apparent index of refraction of the artificial dielectric at the design frequency. This optimum condition is unrelated to the matching problem, but it enables a simple expedient from a construction standpoint. The index of refraction of the optimum quarter wave section at the natural-artificial interface is that of free space. Consequently, a good matching section is provided by a free space region of depth h /4. Although the embodiment of the invention described thus far includes a lens having an overall planohyperbolic geometry, it will be appreciated by one of ordinary skill in the art that the subject invention is not limited to any particular overall shape of the lens. As a further example, FIG. 6 illustrates a cylindrical lens, constructed in accordance with the teachings of this invention. The natural dielectric is shown at 60 and the artificial dielectric at 62. This particular shaped lens is suitable for radiation emanating along a focal line rather than from a focal point. What is claimed is: l. A dielectric lens for radio wave antennas, said lens being formed of a solid natural dielectric material having a zone cut-out therefrom and filled with an artificial dielectric material constructed of parallel metal conductive slats and having an apparent index of refraction n at any frequency f defined by: A is the free space wavelength of frequency f; and A is twice the slat-to-slat spacing of said artificial dielectric. 2. A dielectric lens as claimed in claim 1 wherein said zone has a depth, T, which satisfies the equation: where; N is an integral number; A is the free space wavelength of a design frequency; n is the index of refraction of said natural dielectric material; and 11 is the apparent index of refraction of said artificial dielectric at said design frequency. 3. A dielectric lens as claimed in claim 2 wherein n," m 4. A dielectric lens as claimed in claim 2 having stacked zones filled with said artificial dielectric material. 5. A dielectric lens for radio wave antennas, said lens being formed of a solid natural dielectric material having a zone cut-out therefrom and filled with an artificial dielectric material constructed of parallel metal conductive slats and having an apparent index of refraction 11,, at any frequency f defined by: "a1 (klktazlliza where; A is the free space wavelength of frequency f; and h is twice the slat-to-slat spacing of said artificial dielectric; said zone having a depth T, which satisfies the equation: T N Milne im where; N is an integral number; A is the free space wavelength of a design frequency; 1 is the index of refraction of said natural dielectric material; 1 is the apparent index of refraction of said artificial dielectric at said design frequency; wherein, 1 1 1; and, a quarter wave matching section of free space be tween the interface formed by said natural dielectric material and said artificial dielectric material. Patent Citations
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