WO2000076027A1

WO2000076027A1 - Axially symmetric gradient lenses and antenna systems employing same

Info

Publication number: WO2000076027A1
Application number: PCT/US2000/015626
Authority: WO
Inventors: Naftali Herscovici; Robert F. Williamson; Thomas Peragine
Original assignee: Spike Broadband Systems, Inc.
Priority date: 1999-06-07
Filing date: 2000-06-07
Publication date: 2000-12-14
Also published as: AU5869300A; AU5468700A; WO2000076030A1; AU5468600A; WO2000076028A1

Abstract

Axially symmetric gradient lenses, and antenna systems employing same. In one example, a lens includes an inner volume having one or more inner dielectric constants, and an enclosure having an outer surface that encloses the inner volume. The enclosure has an enclosure dielectric constant that is different from the one or more inner dielectric constants. In one aspect, the lens is constructed and arranged so as to exhibit a dielectric axial symmetry about only one axis of the lens. In another aspect, the outer surface of the lens may have a variety of non-spherical contours, including various ellipsoid contours. In yet another aspect, the lens is constructed and arranged so as to focus asymmetrical three-dimensional radiation patterns incident to the lens to one or more focal points on a single focal line around the outer surface of the enclosure. Antenna systems employing such a lens are capable of transmitting and/or receiving radiation having a variety of asymmetrical radiation patterns. In particular, a sectored antenna system employing such a lens is capable of transmitting and/or receiving a number of radiation beams throughout a 360 degree coverage area surrounding the antenna system, wherein each beam has a different respective beamwidth in azimuth and elevation.

Description

AXIALLY SYMMETRIC GRADIENT LENSES AND ANTENNA SYSTEMS

EMPLOYING SAME

Field of the Invention The present invention relates to lenses for directing, shaping, and focussing electromagnetic radiation and antenna systems employing such lenses. In particular, the invention is directed to various types of gradient lenses and antenna systems employing such lenses.

Description of the Related Art

Lenses are used to focus, direct, and/or shape electromagnetic radiation having a variety of wavelengths. A gradient lens is a type of lens that has a varying dielectric constant profile along various paths through the lens. The gradient of the lens (i.e., the varying dielectric constant profile) may be a stepped or a continuous function of distance along a particular path of travel through the lens.

A Luneberg lens is a particular type of gradient lens. Luneberg-type lenses were first proposed in the 1940's, and are discussed, for example, in the textbook "Mathematical Theory of Optics," R.K. Luneberg, University of California Press, Berkeley and Los Angeles, 1964, Library of Congress Catalog #64-19010. Conventionally, a Luneberg-type lens is in the form of a sphere of material having a dielectric constant (or index of refraction) that varies as a function of radius from the center of the sphere to an outer surface of the sphere, according to a particular mathematical relationship. An ideal Luneberg-type lens preferably has a continually varying dielectric constant as a function of radius (i.e., a continually varying gradient), but actual lenses often exhibit gradients that are a stepped function of radius due to manufacturing limitations. Luneberg-type lenses possess a unique focussing property; namely, plane waves of radiation incident upon the lens from a distant radiation source are imaged, or focussed, at a particular focal point. The incident planar waves are focussed on or near the lens surface at a focal point diametrically opposite the propagation direction of the incoming waves. Conversely, a radiation source located at a focal point on the outer surface of the lens and emitting radiation through the lens ultimately produces a plane wave of radiation propagating in a direction parallel to a diameter of the lens that includes the focal point. The gradient for an ideal Luneberg-type lens generally is given by the equation:

ε_r = 2 - ( r / R ) ² (1)

where ε_r is the dielectric constant at a given distance (r) from the sphere center, and R is the radius of the sphere. In some circumstances, it is desirable that the dielectric constant at the lens surface be equal to the surrounding medium to avoid reflections; hence, as seen from Eq. (1), £_R is equal to 1 when r = R. Additionally, it can also be seen from Eq. (1) that the ratio of the dielectric constant £_R at the center of the lens (i.e., r = 0) to that at the surface of the lens is 2 to 1.

Due to the inherent symmetry of conventional spherical Luneberg-type lenses, radiation that is transmitted through such lenses from one or more antenna feeds coupled to the lens generally has an essentially symmetric cross-sectional spatial profile as it propagates from the lens. In particular, with reference to an azimuth plane that is essentially parallel to the ground, and an elevation plane that is essentially perpendicular to the ground (and, hence, perpendicular to the azimuth plane), radiation transmitted through a conventional spherical Luneberg-type lens generally has a cross-sectional spatial profile, in a plane perpendicular to a direction of propagation, having essentially equal dimensions parallel to the azimuth and elevation planes, respectively. Similarly, radiation that is incident to a conventional spherical Luneberg-type lens and effectively focussed by the lens generally has an essentially symmetric cross-sectional spatial profile, as described above.

Summary of the Invention One embodiment of the invention is directed to a lens having at least one axis of rotation. The lens comprises an inner volume having at least one inner dielectric constant and an outer surface that encloses the inner volume, wherein the outer surface has an outer dielectric constant different from the at least one inner dielectric constant. The outer surface has a contour essentially defined by a curve that connects two points on the axis of rotation, wherein the curve is not a semicircle. The curve is rotated 360 degrees about the axis of rotation such that the rotated curve forms the contour of the outer surface, and such that any cross section of the lens in a plane orthogonal to the axis of rotation has an essentially circular shape and a center point on the axis of rotation.

In one aspect of this embodiment, the inner volume has a dielectric constant profile along a path from the axis of rotation to the outer surface that varies as a function of a distance from the axis of rotation to the outer surface.

In another aspect of this embodiment, each circular cross section of the lens has a dielectric constant profile along a radius of the circular cross section that varies as a function of a distance from the center point to the outer surface.

In yet another aspect of this embodiment, the contour of the outer surface is an ellipsoid, such as a prolate spheroid or an oblate spheroid.

In yet another aspect of this embodiment, the lens is constructed and arranged such that at least one circular cross section of the lens defines a focal line of the lens along the outer surface of the lens.

In yet another aspect of this embodiment, the lens is constructed and arranged such that radiation incident to the lens along a plane parallel to the axis of rotation is focussed to the focal line.

Another embodiment of the invention is directed to an antenna system comprising a lens and at least one antenna feed device coupled to the lens. The lens has at least one axis of rotation and includes an inner volume having at least one inner dielectric constant and an outer surface that encloses the inner volume, wherein the outer surface has an outer dielectric constant different from the at least one inner dielectric constant. The outer surface has a contour essentially defined by a curve that connects two points on the axis of rotation, wherein the curve is not a semicircle. The curve is rotated 360 degrees about the axis of rotation such that the rotated curve forms the contour of the outer surface, and such that any cross section of the lens in a plane orthogonal to the axis of rotation has an essentially circular shape and a center point on the axis of rotation.

In various aspects of this embodiment, the antenna feed device may be constructed and arranged so as to transmit and/or receive radiation through the lens. Another embodiment of the invention is directed to a lens comprising an inner volume having at least one inner dielectric constant and an enclosure that encloses the inner volume, wherein the enclosure has an enclosure dielectric constant that is different from the at least one inner dielectric constant. The lens is constructed and arranged so as to exhibit a dielectric axial symmetry about only one axis of the lens.

Another embodiment of the invention is directed to a lens comprising an inner volume having at least one inner dielectric constant and an enclosure that encloses the inner volume, wherein the enclosure has an enclosure dielectric constant that is different from the at least one inner dielectric constant. The lens has an axis of rotation passing through the lens, a lens length along the axis of rotation, and a lens center point on the axis of rotation half-way along the lens length. The lens is constructed and arranged such that at least two paths through the lens from the center point to the outer surface have different path lengths.

Another embodiment of the invention is directed to a lens comprising an inner volume having at least one inner dielectric constant and an enclosure that encloses the inner volume, wherein the enclosure has a non-spherical contour and has an enclosure dielectric constant that is different from the at least one inner dielectric constant. Another embodiment of the invention is directed to a lens comprising an inner volume having at least one inner dielectric constant and an enclosure that encloses the inner volume, wherein the enclosure has an enclosure dielectric constant that is different from the at least one inner dielectric constant. The lens is constructed and arranged so as to focus asymmetrical three-dimensional radiation patterns incident to the lens to at least one focal point on a single focal line around an outer surface of the enclosure.

In one aspect of this embodiment, the asymmetrical three-dimensional radiation pattern has an azimuth beamwidth in an azimuth plane essentially parallel to the ground and an elevation beamwidth in an elevation plane orthogonal to the azimuth plane, wherein the azimuth beamwidth is different from the elevation beamwidth. Another embodiment of the invention is directed to a lens having a center and a non-spherical outer surface defined by a smooth surface of revolution. A geometry of the lens is defined by a three-dimensional coordinate system having an origin at the center of the lens. The lens has a plurality of dielectric constant profiles, each dielectric constant profile being defined by a dielectric constant that varies as a function of a distance from the center to the outer surface of the lens at a particular azimuth angle and a particular elevation angle in the three-dimensional coordinate system. The lens comprises a substantially solid dielectric core having a core dielectric constant and at least one substantially solid dielectric enclosure enclosing the dielectric core. The dielectric enclosure has an enclosure dielectric constant different from the core dielectric constant. The smooth surface of revolution defining the outer surface of the lens is one of a spheroid, an ellipsoid, a parabaloid, a hyperboloid, and an aspheroid.

Another embodiment of the invention is directed to a lens comprising an inner volume having at least one inner dielectric constant and an enclosure that encloses the inner volume, the enclosure having an enclosure dielectric constant that is different from the at least one inner dielectric constant. The lens has a first aperture dimension along a first axis passing through the lens and a second aperture dimension along a second axis passing through the lens, wherein the first and second axes are orthogonal and the first and second aperture dimensions are different.

Brief Description of the Drawings

The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like reference character or numeral. For purposes of clarity, not every component may be labeled in every drawing.

FIG. 1A is a diagram showing the construction and formation of a lens according to one embodiment of the invention;

FIG. IB is a diagram showing an exemplary cross-section of the lens of Fig. 1A, according to one embodiment of the invention;

FIG. 1 C is a diagram showing a perspective view of an antenna system according to an illustrative embodiment of the present invention;

FIG. ID is a diagram showing a perspective view of an antenna system according to another illustrative embodiment of the present invention; FIG. IE is a diagram showing a perspective view of an antenna system according to another illustrative embodiment of the present invention;

FIG. 2 is a top view of an azimuth cross-section of a Luneberg-type lens,; FIG. 3 is a side view of an elevation cross-section of a Luneberg-type lens; FIG. 4 is a side view of an elevation cross-section of a truncated Luneberg-type lens;

FIG. 5 is a diagram showing an elevation cross-section of a lens, according to one embodiment of the invention; FIG. 6 is a diagram showing an azimuth cross-section of the lens of FIG. 5, according to one embodiment of the invention;

FIG. 7 is a diagram showing a perspective view of a lens according to another embodiment of the invention; and FIG. 8 is a diagram showing an intersection of focal point paths of two principle planes in the antenna system of FIG. ID, according to one embodiment of the invention.

Detailed Description

Gradient lenses as discussed above and, in particular, spherical Luneberg-type lenses, conventionally are used in a variety of scientific, military, and commercial applications. In particular, Applicants have appreciated that a conventional spherical Luneberg-type lens may be suitable for wireless communication applications.

Generally, wireless communication systems transport information on data carriers that are radiated by one or more antennas (or antenna systems) into open space throughout a coverage area. Applicants have recognized that in some types of wireless communication systems, a conventional spherical Luneberg-type lens may be used with one or more antenna feed devices to form an antenna system that transmits and/or receives radiation through the lens (for purposes of the present discussion, it should be appreciated that the term "feed device" refers to a device that can transmit and/or receive radiation). Such an antenna system is capable of transmitting radiation throughout the coverage area, and also is capable of focussing radiation received by, or incident to, the antenna system (e.g., from transmitters located throughout the coverage area) to the one or more antenna feeds coupled to the lens.

In wireless communication systems, typically one or more data carriers transmitted to and/or received from some space within a coverage area constitute a wireless communication link. The geographic extent, or "range" of a given communication link in a wireless system generally may be defined by a spatial profile of the radiated data carriers.

At least one consideration in the design of a wireless communication system is the topological distribution of users; namely, the location, density, and overall distribution of users to which the wireless communication system provides communication services. In particular, throughout a given coverage area around an antenna or antenna system of a wireless communication system, a number of users may be dispersed in a variety of topological distributions. For example, in one portion of the coverage area, several users may be located together in close proximity, while in another portion of the coverage area other users may be more sparsely dispersed. Additionally, different users may be situated at different altitudes with respect to the antenna or antenna system, and at different distances along the ground from the antenna or antenna system.

The spatial profiles of radiation transmitted from an antenna or antenna system generally are based in part on the construction and arrangement of the antenna or antenna system. For example, as discussed above, an antenna system employing a conventional spherical Luneberg-type lens typically provides for transmission and reception of radiation having an essentially symmetrical radiation pattern, due to the spherical symmetry of the lens.

Applicants have recognized that while conventional spherical Luneberg-type lenses indeed may be useful for a wide variety of wireless communication system applications, the symmetrical geometry of the lens may provide for a limited range of possible spatial profiles for transmitted and received radiation in a wireless communication system. The essentially symmetrical spatial profile of radiation associated with such an antenna system in turn may limit the possible topological distributions of users throughout the coverage area to which the system can practically and reliably provide communication services.

In view of the foregoing, Applicants have recognized that a wireless communication system having an antenna or antenna system with the capability of radiating data carriers with a variety of diverse spatial profiles may be useful for accommodating a variety of topological distributions of users located at various heights and distances from the antenna or antenna system. In particular, Applicants have recognized that antenna systems that are constructed and arranged so as to transmit and receive radiation having an asymmetrical cross-sectional spatial profile would facilitate the implementation of a wireless communication system capable of accommodating a wide variety of topological distributions of users. It should be appreciated that the foregoing discussion regarding wireless communication system applications for an antenna system having the capability of transmitting and receiving asymmetrical radiation patterns is provided for purposes of illustration only, and that such antenna systems are not limited to this particular application. Additionally, it should be appreciated that the foregoing discussion is not intended to be limiting with respect to potential applications of various gradient lenses according to the invention, as discussed further below.

One example of an antenna system capable of transmitting and/or receiving radiation having an asymmetric spatial profile is given by a spherical Luneberg-type lens, to which is coupled one or more asymmetric feed devices. As discussed above, the symmetry of a spherical Luneberg-type lens results in an almost symmetrical radiation pattern in an azimuth plane and an elevation plane when the shape of a feed device coupled to the lens is symmetrical. However, altering an aspect ratio of the feed device changes the resultant radiation pattern. For example, increasing a dimension of the feed device along a direction perpendicular to the azimuth plane narrows the resultant radiation pattern in the elevation plane. Similarly, increasing a dimension of the feed device along a direction parallel to the azimuth plane narrows the resultant radiation pattern in the azimuth plane. In contrast, decreasing a dimension of the feed device in a direction parallel to a plane widens the resultant radiation pattern in that plane.

A typical relationship between antenna aperture size and a spatial profile (herein after "beamwidth") of a radiation pattern in a particular plane is given by:

λ

WB (2)

A

where W_B is the beamwidth of the radiation pattern in the particular plane, A is the size of the antenna aperture (e.g., the dimension of a feed device in the plane), and λ is the radiation wavelength (given by the speed of light c divided by a frequency /of the radiation). The factor A: is a constant associated with different radiation patterns. From the above relationship, as discussed above, it may be appreciated that increasing the aperture size A results in a smaller (or "narrower") beamwidth wg.

If the lens-based antenna system providing for asymmetrical radiation profiles, as described above, is used in an application that requires multi-directional coverage, numerous feed devices may be coupled to and distributed around the lens. In such an antenna system, increasing one or more physical dimensions of one or more of the feed devices to achieve asymmetrical beamwidths may not be possible due to size constraints of the lens. In view of the foregoing, one embodiment of the present invention is directed to a lens having one or more of a particular shape, particular dimensions, and/or particular dielectric profiles, so as to facilitate the shaping, directing, and/or focusing of asymmetrical radiation profiles that travel through the lens. In one aspect of this embodiment, the lens is an axially symmetric gradient lens. In another embodiment, an antenna system including an axially symmetric gradient lens is provided, which antenna system has the capability of transmitting and/or receiving asymmetric radiation profiles.

An axially symmetric gradient lens according to one embodiment of the invention has dielectric constant profiles (i.e., gradients) that vary through the lens, in a manner similar to that of a conventional spherical Luneberg-type lens. In one aspect of this embodiment, however, an axially symmetric gradient lens according to the invention is not spherically shaped, unlike a conventional spherical Luneberg-type lens. As discussed above, a conventional spherical Luneberg-type lens focuses plane waves of radiation incident upon the lens from a distant radiation source to a particular focal point. In particular, two perpendicular planar waves incident from any direction may be focused by a conventional spherical Luneberg-type lens; thus, such a lens has focal points over the entire outer surface of the lens.

In contrast, an axially symmetric gradient lens, according to one embodiment of the invention, has focal points at particular locations around the lens or along a particular path circumscribing the lens. For example, in one aspect, an axially symmetric gradient lens according to one embodiment of the invention has circular cross-sections orthogonal to an axis of rotation through the lens, and has one circular circumscribed path of focal points on the outer surface of the lens.

In another aspect, examples of different lens shapes suitable for purposes of the invention according to various embodiments include, but are not limited to, generally spheroid shapes, including various ellipsoids such as a prolate spheroid shape or an oblate spheroid, a parabaloid shape, a hyperboloid shape or an aspheroid shape.

Following below are more detailed descriptions of various concepts related to, and embodiments of, axially symmetric gradient lenses according to the present invention. It should be appreciated that various aspects of the invention as discussed above and outlined further below may be implemented in any of numerous ways, as the invention is not limited to any particular manner of implementation. Examples of specific implementations are provided for illustrative purposes only. Fig. 1A is a diagram illustrating the construction and formation of a lens according to one embodiment of the invention. Fig. 1 A shows that the lens 600 has at least one axis of rotation 508, shown for example in Fig. 1 A as a vertical z-axis of a three dimensional coordinate system. The lens 600 includes an inner volume 500 having at least one inner dielectric constant 502 (εj). According to various embodiments, the inner volume 500 may be substantially or partially solid. The lens 600 also includes an outer surface 504 that encloses the inner volume 500. The outer surface 504 of the lens 600 in Fig. 1 A is represented as a dashed line to the left of the axis 508 and a solid line to the right of the axis 508, as discussed further below. In the lens 600 of Fig. 1 A, the outer surface 504 has an outer dielectric constant 505 (ε_out) different from the inner dielectric constant 502.

In the embodiment of Fig. 1 A, the outer surface 504 of the lens 600 has a contour essentially defined by a curve 506 (shown as a solid line) that connects two points 510 and 512 on the axis of rotation 508. For purposes of the present discussion, a curve is defined as any arbitrarily shaped continuous line that connects the two points 510 and 512, or any series of line segments connected to one another which provide a path between the two points 510 and 512. Any curve 506 that is not a semicircle (i.e., a half- circle) is suitable for this embodiment of the invention. According to the present embodiment, to form the contour of the outer surface 504 of the lens 600, the curve 506 is rotated 360 degrees about the axis of rotation 508 such that the rotated curve forms the contour of the outer surface (including both the dashed and solid lines).

As a result of the foregoing procedure, it should be appreciated that any cross section of the lens in a plane orthogonal to the axis of rotation 508 (i.e., any cross section of the lens parallel to the x-y plane in Fig. 1 A) has an essentially circular shape and a center point on the at least one axis of rotation. Additionally, it should be appreciated that the particular shapes or contours of the inner volume and the outer surface shown in Fig. 1 A are for purposes of illustration only, and that the invention is not limited in this respect, as a number of different shapes or contours are possible according to various embodiments. In particular, according to one embodiment of the invention discussed further below, the curve 506 may represent at least a portion of an ellipse, and the resulting contour of the outer surface 504 may be an ellipsoid, such as a prolate spheroid or an oblate spheroid, for example. According to one aspect of the embodiment shown in Fig. 1 A, the inner volume 500 may have a dielectric constant profile along a path 516 from the axis of rotation 508 to the outer surface 504, that varies as a function of a distance from axis of rotation to the outer surface. While Fig. 1 A shows only one such path 516 for purposes of illustration, it should be appreciated that a variety of different paths from the axis 508 to the outer surface 504 are possible in the lens 600, and that such paths may have varying dielectric constant profiles as a function of a distance along the path. In another aspect, one or more such dielectric constant profiles may vary as essentially continuous functions or, alternatively, step-wise functions of a distance from the at least one axis of rotation to the outer surface, as discussed further below. Accordingly, it should be appreciated that the inner dielectric constant 502 shown for purposes of illustration in Fig. 1 A may in some cases represent a number of different dielectric constants or a varying dielectric constant as a function of position in the lens from the axis 508.

Fig. IB is a diagram showing an example of one circular cross-section 518 of a lens similar to the lens of Fig. 1 A, wherein the cross-section 518 is taken perpendicular to the axis of rotation 508 (i.e., parallel to the x-y plane shown in Fig. 1 A). In particular, the circular cross-section 518 shown in Fig. IB is taken along the x-y plane shown in Fig. 1 A, such that the center point of the cross section is given by the point 514. According to one embodiment of the invention, as exemplified by the cross-section 518 of Fig. IB, each cross-section of the lens has a dielectric constant profile along a radius 520 of the cross-section that varies as a function of a distance from the center point (i.e., the point 514 in Fig. IB) to the outer surface 504. According to one aspect of this embodiment, the dielectric constant profile along the radius 520 may vary as an essentially continuous function of the distance from the center point of the cross-section to the outer surface. Alternatively, as shown in Fig. IB, the dielectric constant profile along the radius 520 may vary as an essentially stepwise function of the distance from the center point of the cross-section to the outer surface.

As illustrated in Fig. IB, according to one embodiment of the invention a lens similar to that shown in Fig. IB may be constructed and arranged such that the inner volume 500 has a number of different dielectric constants. In particular, the lens may be constructed and arranged such that the inner volume includes one or more dielectric shells 522A-522C enclosing a dielectric core 524, and disposed between the dielectric core and the outer surface, wherein each shell has a different dielectric constant. While Fig. IB shows three dielectric shells, it should be appreciated that the invention is not limited in this respect, as any number of dielectric shells may be employed in a lens according to various embodiments. Each of the dielectric shells may be contiguous with another of the dielectric shells, for example, or alternatively, in one embodiment, a small air gap may separate each of the dielectric shells.

As shown in Fig. IB, the dielectric shells discussed above appear in each circular cross-section of the lens as concentric bands of dielectric material, wherein each band has a different dielectric constant. According to one embodiment of the invention, the lens is constructed and arranged such that for at least one circular cross section of the lens, at least two bands have a different dimension along a radius of the circular cross section. For example, Fig. IB illustrates the respective dimensions 526A-526C for the concentric bands corresponding to the dielectric shells 522A-522C. According to this embodiment, at least two of the dimensions 526A-526C may be different. According to yet another embodiment, for a first circular cross section of the lens similar to the cross- section shown in Fig. IB, each concentric band has a respective first dimension along a radius of the first circular cross section, and for at least one other circular cross section of the lens, each concentric band has a respective second dimension along a radius of the other circular cross section, wherein each respective second dimension is different from each respective first dimension. According to one embodiment of the invention, a lens is provided with an outer surface having an essentially spheroid contour. A spheroid is a surface of revolution obtained by rotating an ellipse around one of its axes. Rotating an ellipse around its minor axis results in an oblate spheroid, whereas rotating an ellipse around its major axis results in a prolate spheroid. If the ellipse to be rotated is a circle, the resulting spheroid is a sphere. The Cartesian equation for a spheroid is:

2 2 2

A a ^A c -i (3)

where a and c are constants. If a > c, the surface of revolution is an oblate spheroid. If a< c, the surface of revolution is a prolate spheroid.

A spheroidal lens according to one embodiment of the invention has a theoretically infinite number of focal points present within a circle of focal points on the outer surface of the lens (i.e., a focal line circumscribing the lens). This characteristic allows one to place as many antenna feed devices as practically possible around the focal line of the lens to obtain a corresponding number of radiation beams. According to one aspect, using a non-spherical lens to shape the radiation beams rather than using asymmetric feed devices to shape beams, as discussed above, antenna systems according to the invention may employ physically smaller antenna feed devices, therefore permitting the placement of a greater number of antenna feed devices around the lens than would be possible with a conventional spherical lens.

Fig. IC illustrates one embodiment of the present invention, wherein an antenna system 1 includes an oblate spheroid lens 2. In this embodiment, cross-sections of the lens 2 perpendicular to the X-Y plane of lens 2 are shaped as ellipses, whereas cross- sections of the lens 2 parallel to the X-Y plane are shaped as circles, essentially as illustrated in Fig. IB. As discussed above, it should be appreciated that the invention is not limited to the particular lens shape shown in Fig. IC, as the perimeter shape of a cross-section of the lens 2 perpendicular to the X-Y plane may be any of a variety of shapes.

According to one aspect of this embodiment, the lens 2 of Fig. IC is a gradient lens, in that it has one or more dielectric constant profiles that each vary as a function of a distance through the lens according to a particular mathematical relationship. For example, in one aspect of this embodiment, the lens 2 may be a Luneberg-type lens, wherein a ratio of the dielectric constant at an innermost portion of the lens 2 to a dielectric constant near the outer surface of the lens is approximately 2 to 1.

In the embodiment shown in Fig. IC, a plurality of feed devices 5 are provided along a focal point circle 7 that circumscribes an outer surface 4 of the lens 2. The feed devices 5 may be coupled to the lens 2 in a variety of manners, as the invention is not limited to any particular manner of coupling. The focal point circle 7 includes a theoretically infinite number of focal points along a circle formed by the cross-section of a plane parallel to the X-Y plane with the lens 2. As discussed above, the overall shape (i.e., contour of the outer surface of the lens) and/or arrangement of the lens 2 may be varied such that the focal point circle 7 is present at a different position and/or orientation with respect to the coordinate system shown in Fig. IC.

In the exemplary antenna system shown in Fig. 1 C, the feed devices 5 may have symmetric apertures or asymmetric apertures, depending on the desired spatial profile of radiation transmitted and/or received by the antenna system 1. Additionally, the feed devices 5 may be distributed around the lens 2 in a variety of manners to transmit radiation to and/or receive radiation from particular portions of a radiation coverage area. For example, the feed devices 5 may be distributed uniformly around the lens 2 to provide an essentially omni-directional radiation pattern having a number of beams each corresponding to a particular feed device 5. In such an embodiment, the feed devices 5 may be positioned at essentially regular intervals around all or a portion of the focal point circle 7. Alternatively, the feed devices 5 may be distributed around the lens 2 in a non-uniform manner. According to one aspect of the embodiment shown in Fig. IC, a difference between a first dimension 3 A of the lens 2 in an azimuth plane given by the x-y plane shown in Fig. IC, and a second dimension 3B of the lens 2 along an axis of rotation (i.e., the z-axis 508) may allow asymmetric radiation patterns to be radiated without requiring the use of asymmetric feed devices. In particular, the dimensions 3 A and 3B shown in Fig. IC may be considered to be apertures of the antenna system 1 (in azimuth and elevation directions, respectively), such that different azimuth and elevation beamwidths according to Eq. (2) above may be realized by virtue of the different dimensions of the lens 2.

In Fig. IC, a support 10 for the antenna system 1 is illustrated in phantom. It should be appreciated that the invention is not limited by the particular construction and configuration of a lens or antenna system support structure shown in Fig. 1 C, and that a variety of support mechanisms are suitable for purposes of the invention.

Fig. ID shows another embodiment of the invention, wherein an antenna system 1 includes a prolate spheroid lens 2. In this embodiment, similar to the oblate spheroid shaped lens 2 of Fig. IB, cross-sections of the lens 2 perpendicular to the X-Y plane of lens 2 are shaped as ellipses, whereas cross-sections of the lens 2 parallel to the X-Y plane are shaped as circles. In the embodiment shown in Fig. ID, however, the dimension 3 A of the lens 2 in the azimuth (X-Y) plane is smaller than the dimension 3B of the lens along the Z-axis. Fig. IE shows another embodiment of the invention, in which a prolate spheroid lens 2 for use in an antenna system similar to that shown in Fig. ID is constructed and arranged in a different orientation than the lens 2 of Fig. ID. In this embodiment, cross- sections perpendicular to the azimuth (X-Y) plane of the lens 2 in the azimuth (X-Y) plane are shaped as circles, as shown in Fig. IE, whereas cross-sections of the lens 2 parallel to the azimuth plane are shaped as ellipses. In a similar manner, according to another embodiment of the invention, the oblate spheroid lens 2 of Fig. IC may be rotated 90 degrees about the Y-axis. According to one aspect, lenses according to various embodiments of the present invention generally may be more efficient lens than, for example, a conventional spherical Luneberg-type lens, for purposes of directing, shaping, and/or focusing asymmetric radiation profiles, as illustrated in Figs. 2-6. For purposes of comparison between conventional spherical Luneberg-type lenses and lenses according to various embodiments of the invention, Fig. 2 shows a cross-section 22 of a conventional spherical Luneberg-type lens 20, wherein the cross-section 22 is parallel to an azimuth plane. Fig. 3 is a diagram similar to that of Fig. 2 of a conventional lens 20, showing an exemplary elevation plane 24 of the lens 20. Fig. 4 is a diagram similar to that of Fig. 3, showing a truncated elevation plane 26 that serves as a model for a lens according to one embodiment of the invention. Finally, Figs. 5 and 6 illustrate an exemplary elevation plane 28 and an exemplary azimuth plane 30, respectively, of a lens according to one embodiment of the invention, similar to that of the lens used in the example of the antenna system shown in Fig. IC.

With reference again to Fig. IC, for purposes of the present discussion, the X-Y plane serves as an azimuth plane and any plane orthogonal to the X-Y plane serves as an elevation plane. A spheroid-shaped lens 2, similar to that shown in Fig. IC, according to one embodiment of the invention, that is irradiated by a feed device 5 having a relatively larger dimension parallel to the elevation plane (i.e., to produce a relatively narrower radiation spatial profile parallel to the elevation plane), and a relatively smaller dimension parallel to the azimuth plane (i.e., to produce a relatively wider spatial profile parallel to an azimuth plane) provides a higher percentage of the lens volume for shaping, directing, and focusing radiation than does, for example, a conventional spheroidally-shaped Luneberg-type lens with an asymmetrical feed device.

For example, as shown in Fig. 2, a conventional spherical-type lens 20 is shown irradiated by a feed device having a relatively small dimension parallel to the azimuth plane, thereby generating a wider radiation profile parallel to the azimuth plane 22 shown in Fig. 2. In this example, a substantial portion of an azimuth cross-section of the lens 20 is used, as shown in Fig. 2 by a shaded region 9 of the lens 2, to shape the radiation profile parallel to the azimuth plane.

Fig. 3 shows an example of an elevation plane 24 of the lens 20 shown in Fig. 2. As can be seen in Fig. 3, the radiation from the feed device intercepts less of the elevation plane 24 of the lens than is intercepted by the azimuth plane 22 of the lens 20 shown in Fig. 2. Accordingly, in Fig. 3, two portions 25 A and 25B of the elevation plane 24 of the lens remains "unused" (i.e., does not function to shape the radiation). These unused portions 25 A and 25B of the lens volume may represent an inefficiency of the lens in terms of, for example, size, weight, and cost Fig. 4 is a diagram similar to Fig. 3 showing a truncated elevation plane 26 that may be used as an illustrative model for a lens according to one embodiment of the invention. While the effect of the truncated elevation plane 26 generally may increase the efficiency of the lens with respect to the volume of the lens that is used for shaping the radiation, such a truncation may adversely affect the performance of the lens (e.g., with respect to electrical characteristics of resulting radiation profiles) in some circumstances.

In view of the foregoing, as described above in connection with Figs. 1 A- ID, a lens according to one embodiment of the invention may be constructed so as to have asymmetrical dimensions parallel to two orthogonal planes (e.g., different azimuth and elevation dimensions). For example, Fig. 5 shows an example of an elevation plane 23 of a lens according to the invention as shown in Fig. IC, whereas Fig. 6 shows an example of an azimuth plane 30 of the same lens. In the example shown in Figs. 5 and 6, a radiation pattern similar to that produced by the lens shown in Figs. 2 and 3 may be produced, but with a lens of lesser volume. Fig. 7 is a diagram illustrating yet another embodiment of the invention, where a top portion 12 and a bottom portion 13 of a lens 50 are not similar in shape. In the illustrated embodiment of Fig. 7, the lens 50 has circular cross-sections perpendicular to the Z-axis 508, as in the embodiments discussed above in connection with Figs. 1A-1D. While not shown explicitly in Fig. 7, the lens 50 may be used in antenna systems having one or more feed devices coupled to the lens, as shown for example in Figs. IC and ID. It should be appreciated that the particular shape of the lens 50 shown in Fig. 7 is chosen for purposes of illustration only, a variety of shapes and/or outer surface contours of the lens 50 are possible according to various embodiments of the invention. In particular, according to one embodiment, the lens 50 may be constructed and arranged to have a particular shape and/or outer surface contour that facilitates focussing of radiation around a particular focal line circumscribing an outer surface of the lens, as discussed further below in connection with Fig. 8. Fig. 8 is a diagram showing a diagram of a lens according to one embodiment of the invention for purposes of illustrating concepts related to focal lines of the lens. In Fig. 8, an elevation focal line 27 and an azimuth focal line 28 circumscribe the lens 2 proximate to an outer surface of the lens 2. Also shown are two points 29 where the focal paths intersect. In the example of Fig. 8, the focal line 28 forms a circular path circumscribing the lens in the azimuth (i.e., X-Y) plane, whereas in an elevation plane (i.e., X-Z, Y-Z, or any plane perpendicular to the azimuth plane) the focal line 27 forms an ellipse. It is possible to form a lens wherein the two focal point paths 27 and 28 do not intersect. Accordingly, in one embodiment of the invention, the lens is constructed and arranged such that radiation incident to the lens 2 parallel to the azimuth plane, as well as radiation incident to the lens 2 perpendicular to the azimuth plane, is focussed along the focal line 28. According to one aspect, to have both focal lines 27 and 28 intersect proximate to the lens outer surface, a particular contour or shape of the lens may be selected (e.g., as shown in Fig. 7), and/or the dielectric constant profiles along paths with different angles of elevation (φ) may be defined by different functions of distance along those paths (e.g., as shown in Fig. 8).

Lenses according to various embodiments of the invention as discussed above may be fabricated by any of a number of appropriate methods. For example, one fabrication method may utilize a series of pre-fabricated shells made of a variety of dielectric materials (e.g., foamed plastic, various polymers, etc.) that are assembled in a particular manner. For example, each shell may be formed in a shape corresponding to approximately half of the lens, and has a particular dielectric constant in a range of from approximately 2 for the innermost shell to 1 for the outermost shell. A lens according to the invention may be assembled by placing, one inside another, successively smaller shells as respective "bottom halves" of the lens, and then successively attaching respective "top halves" of the lens to the bottom halves, proceeding from the smallest shell to the largest. The resulting lens essentially is a series of shells, wherein one shell is contained within another. In one embodiment, successive hemispheroid shells may be assembled in the manner described above, wherein each shell of the spheroid may or may not have a uniform thickness, or the same thickness. In particular, by varying the respective thicknesses and/or uniformity of each shell of the lens, and/or selecting particular dielectric constants for the shells, the lens can be constructed such that one circular cross section of the lens defines a focal line of the lens along the outer surface of the lens, and such that radiation incident to the lens having an asymmetric cross-sectional profile along two orthogonal axes is focussed to the focal line.

Having thus described at least one illustrative embodiment of the invention, various alterations, modifications and improvements will readily occur to those skilled in the art. Such alterations, modifications and improvements are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description is by way of example only and is not intended as limiting.

What is claimed is:

1. A lens having at least one axis of rotation, the lens comprising: an inner volume having at least one inner dielectric constant; and an outer surface that encloses the inner volume, the outer surface having an outer dielectric constant different from the at least one inner dielectric constant, the outer surface having a contour essentially defined by a curve that connects two points on the at least one axis of rotation, wherein the curve is not a semicircle, the curve being rotated 360 degrees about the at least one axis of rotation such that the rotated curve forms the contour of the outer surface, and such that any cross section of the lens in a plane orthogonal to the at least one axis of rotation has an essentially circular shape and a center point on the at least one axis of rotation.

2. The lens of claim 1, wherein the inner volume has a dielectric constant profile along a path from the at least one axis of rotation to the outer surface that varies as a function of a distance from the at least one axis of rotation to the outer surface.

3. The lens of claim 1, wherein the inner volume has a dielectric constant profile along a path from the at least one axis of rotation to the outer surface that varies as an essentially continuous function of a distance from the at least one axis of rotation to the outer surface.

4. The lens of claim 1 , wherein each circular cross section of the lens has a dielectric constant profile along a radius of the circular cross section that varies as a function of a distance from the center point to the outer surface.

5. The lens of claim 1, wherein each circular cross section of the lens has a dielectric constant profile along a radius of the circular cross section that varies as an essentially continuous function of a distance from the center point to the outer surface.

6. The lens of claim 1 , wherein the lens is constructed and arranged such that the inner volume has a plurality of inner dielectric constants, each inner dielectric

Claims

constant of the plurality of inner dielectric constants being different from another inner dielectric constant of the plurality of inner dielectric constants, each inner dielectric constant being different from the outer dielectric constant.

i 7. The lens of claim 1, wherein the inner volume is substantially solid.

8. The lens of claim 7, wherein the inner volume includes a dielectric core having a first inner dielectric constant, the at least one axis of rotation passing through dielectric core.

9. The lens of claim 8, wherein the inner volume includes at least one dielectric shell enclosing the dielectric core and disposed between the dielectric core and the outer surface, the at least one dielectric shell having a second inner dielectric constant different than the first inner dielectric constant.

10. The lens of claim 1, wherein the inner volume is at least partially solid.

11. The lens of claim 10, wherein the inner volume includes at least one dielectric material separated from the outer surface by an air gap.

12. The lens of claim 11 , wherein the inner volume includes a plurality of dielectric shells.

13. The lens of claim 1, wherein the curve is at least a portion of an ellipse.

14. The lens of claim 13, wherein the contour of the outer surface is essentially a prolate spheroid.

15. The lens of claim 13, wherein the contour of the outer surface is essentially an oblate spheroid.

16. The lens of claim 1, wherein the lens is constructed and arranged such that each circular cross section of the lens includes a plurality of concentric bands of dielectric material, each band of the plurality of concentric bands having a different inner dielectric constant.

17. The lens of claim 16, wherein for at least one circular cross section of the lens, at least two bands of the plurality of concentric bands have a different dimension along a radius of the circular cross section.

18. The lens of claim 16, wherein: for a first circular cross section of the lens, each concentric band of the plurality of concentric bands has a respective first dimension along a radius of the first circular cross section; and for at least one other circular cross section of the lens, each concentric band of the plurality of concentric bands has a respective second dimension along a radius of the at least one other circular cross section, wherein each respective second dimension is different from each respective first dimension.

19. The lens of claim 1, wherein the lens is constructed and arranged such that at least one circular cross section of the lens defines a focal line of the lens along the outer surface of the lens.

20. The lens of claim 19, wherein the lens is constructed and arranged such that radiation incident to the lens along a plane parallel to the at least one axis of rotation is focussed to the focal line.

21. An antenna system, comprising: a lens having at least one axis of rotation, the lens including: an inner volume having at least one inner dielectric constant; and an outer surface that encloses the inner volume, the outer surface having an outer dielectric constant different from the at least one inner dielectric constant, the outer surface having a contour essentially defined by a curve that connects two points on the at least one axis of rotation, wherein the curve is not a semicircle, the curve being rotated 360 degrees about the at least one axis of rotation such that the rotated curve forms the contour of the outer surface, and such that any cross section of the lens in a plane orthogonal to the at least one axis of rotation has an essentially circular shape and a center point on the at least one axis of rotation; and at least one antenna feed device coupled to the lens.

22. The antenna system of claim 21, wherein the at least one antenna feed device is constructed and arranged so as to transmit radiation.

23. The antenna system of claim 21, wherein the at least one antenna feed device is constructed and arranged so as to receive radiation.

24. The antenna system of claim 21 , wherein the at least one antenna feed device is constructed and arranged so as to transmit and receive radiation.

25. The antenna system of claim 21 , wherein the lens is constructed and arranged such that at least one circular cross section of the lens defines a focal line of the lens along the outer surface of the lens.

26. The antenna system of claim 25, wherein the at least one antenna feed device is coupled to the lens proximate to the focal line.

27. The antenna system of claim 26, wherein: the at least one antenna feed device includes a plurality of antenna feed devices; and each antenna feed device of the plurality of antenna feed devices is coupled to the lens proximate to the focal line.

28. The lens of claim 26, wherein the lens is constructed and arranged such that radiation incident to the lens along a plane parallel to the at least one axis of rotation is focussed to the focal line.

29. A lens comprising: an inner volume having at least one inner dielectric constant; and an enclosure that encloses the inner volume, the enclosure having an enclosure dielectric constant that is different from the at least one inner dielectric constant, wherein the lens is constructed and arranged so as to exhibit a dielectric axial symmetry about only one axis of the lens.

30. A lens comprising: an inner volume having at least one inner dielectric constant; and an enclosure that encloses the inner volume, the enclosure having an enclosure dielectric constant that is different from the at least one inner dielectric constant, wherein the lens has an axis of rotation passing through the lens, a lens length along the axis of rotation, and a lens center point on the axis of rotation half-way along the lens length, and wherein at least two paths through the lens from the center point to the outer surface have different path lengths.

31. A lens comprising: an inner volume having at least one inner dielectric constant; and an enclosure that encloses the inner volume, the enclosure having a non-spherical contour and having an enclosure dielectric constant that is different from the at least one inner dielectric constant.

32. A lens comprising: an inner volume having at least one inner dielectric constant; and an enclosure that encloses the inner volume, the enclosure having an enclosure dielectric constant that is different from the at least one inner dielectric constant, wherein the lens is constructed and arranged so as to focus asymmetrical three- dimensional radiation patterns incident to the lens to at least one focal point on a single focal line around an outer surface of the enclosure.

33. The lens of claim 32, wherein the asymmetrical three-dimensional radiation pattern has an azimuth beamwidth in an azimuth plane essentially parallel to the ground and an elevation beamwidth in an elevation plane orthogonal to the azimuth plane, and wherein the azimuth beamwidth is different from the elevation beamwidth.

34. A lens having a center and a non-spherical outer surface defined by a smooth surface of revolution, a geometry of the lens being defined by a three-dimensional coordinate system having an origin at the center of the lens, the lens having a plurality of dielectric constant profiles, each dielectric constant profile being defined by a dielectric constant that varies as a function of a distance from the center to the outer surface of the lens at a particular azimuth angle and a particular elevation angle in the three-dimensional coordinate system, the lens comprising: a substantially solid dielectric core having a core dielectric constant; and at least one substantially solid dielectric enclosure enclosing the dielectric core, the at least one dielectric enclosure having an enclosure dielectric constant different from the core dielectric constant, wherein the smooth surface of revolution is one of a spheroid, an ellipsoid, a parabaloid, a hyperboloid, and an aspheroid.

35. A lens comprising: an inner volume having at least one inner dielectric constant; and an enclosure that encloses the inner volume, the enclosure having an enclosure dielectric constant that is different from the at least one inner dielectric constant, wherein the lens has a first aperture dimension along a first axis passing through the lens and a second aperture dimension along a second axis passing through the lens, the first and second axes being orthogonal and the first and second aperture dimensions being different.

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