Geometrically-independent circularly-polarized frequency reconfigurable antenna with near-zero permittivity and design method

CN122202838BActive Publication Date: 2026-08-18THE CHINESE UNIV OF HONG KONG (SHENZHEN)
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Patent Information

Application Number
CN202610579270.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2026-04-29
Publication Date
2026-08-18
Estimated Expiration
2046-04-29

AI Technical Summary

Technical Problem

[0003]现有ENZ几何无关天线仅能实现线性极化辐射,无稳定圆极化辐射通用方案;且工作频率由ENZ色散特性固定,无法在不改变几何结构的前提下实现频率调谐,难以适配多频、自适应通信场景

Benefits of technology

1)依托近零介电常数谐振腔体实现几何无关特性,腔体等面积变形后工作频率无明显偏移;

✦ Generated by Eureka AI based on patent content.

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Abstract

The application discloses a geometric-independent circular polarization frequency reconfigurable antenna with near-zero dielectric constant and a design method, and relates to the technical field of antennas.The outer conductor of a coaxial connector is connected with a near-zero dielectric constant resonant cavity in a grounded manner, and the inner conductor is connected with a dielectric-filled rectangular waveguide through a feeding probe;one end of the dielectric-filled rectangular waveguide is electrically connected with the coaxial connector, and the other end is in communication with the opening of the near-zero dielectric constant resonant cavity; a gyromagnetic material doped body is arranged in the central region inside the near-zero dielectric constant resonant cavity; a metal upper cover plate covers the top of the near-zero dielectric constant resonant cavity, and the metal upper cover plate is provided with a ring-shaped gap radiation structure; and a magnetic biasing structure is used for applying a static magnetic field along the normal direction of the near-zero dielectric constant resonant cavity to the gyromagnetic material doped body.The application realizes frequency reconfiguration through magnetic control tuning, does not need active switching devices, has high reliability, and is suitable for multiple scene communication requirements.
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Description

Technical Field

[0001] This invention relates to the field of antenna technology, and more specifically to a geometry-independent circularly polarized frequency reconfigurable antenna with near-zero dielectric constant and a design method thereof. Background Technology

[0002] The resonance condition of a traditional resonant antenna is directly related to its electrical length, and changes in geometry and shape can significantly alter the resonant frequency and radiation performance. Near-zero dielectric (ENZ) media have a real part of dielectric constant approaching zero at specific frequencies, resulting in an extremely small equivalent phase constant. This allows for a near-equal-phase distribution of the electromagnetic field within the cavity, achieving decoupling between structural geometry and operating frequency, thus forming a geometry-independent antenna.

[0003] Existing ENZ geometry-independent antennas can only achieve linear polarization radiation, lacking a universal scheme for stable circular polarization radiation. Furthermore, the operating frequency is fixed by the ENZ dispersion characteristics, making frequency tuning impossible without altering the geometry, thus hindering adaptation to multi-frequency and adaptive communication scenarios. Additionally, traditional circularly polarized antennas rely on specific geometric proportions and phase networks, making them sensitive to structural deformation and exhibiting poor environmental adaptability.

[0004] Therefore, proposing a geometry-independent circularly polarized frequency reconfigurable antenna with near-zero dielectric constant and its design method to solve the difficulties existing in the prior art is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a geometry-independent circularly polarized frequency reconfigurable antenna with near-zero dielectric constant and a design method thereof, in order to solve the technical problems existing in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant, comprising: Coaxial connector, dielectric-filled rectangular waveguide, metal top cover plate, near-zero dielectric constant resonant cavity, gyromagnetic material dopant, magnetic bias structure; The outer conductor of the coaxial connector is grounded to the near-zero dielectric constant resonant cavity, and the inner conductor is connected to the dielectric-filled rectangular waveguide through a feed probe. One end of the dielectric-filled rectangular waveguide is electrically connected to a coaxial connector, and the other end is connected to the opening of a near-zero dielectric constant resonant cavity; A gyromagnetic material dopant is placed in the central region inside a near-zero dielectric constant resonant cavity; A metal top cover is placed on top of the near-zero dielectric constant resonant cavity, and the metal top cover has an annular slit radiation structure. The magnetic bias structure is used to apply a static magnetic field along the normal of the near-zero dielectric constant resonant cavity to a gyromagnetic material dopant.

[0007] Optionally, the gyromagnetic material dopant is a yttrium iron garnet disc.

[0008] Optionally, the interior of the dielectric-filled rectangular waveguide is filled with F4BM220 dielectric material with a relative permittivity of 2.2.

[0009] Optionally, the annular slit radiation structure can be an open annular slit, a segmented annular slit, or a double-opening annular slit.

[0010] Optionally, the magnetic bias structure can be a permanent magnet, an electromagnetic coil, or an integrated planar coil.

[0011] A design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant, comprising the following steps: S1. Determine the target operating frequency of the antenna; S2. Based on the equivalent ENZ effect of the cutoff waveguide, design a near-zero dielectric constant resonant cavity to match the target operating frequency; S3. Place a gyromagnetic material dopant in the central region of the near-zero dielectric constant resonant cavity, build a magnetic bias structure and apply a static magnetic field to construct a geometry-independent ENZ vortex cavity. S4. Extract the definite vortex modes of the ENZ vortex cavity through intrinsic mode analysis; S5. Determine the dimensions of the annular slit radiation structure of the metal top cover plate and complete the coupling matching from the vortex mode to the free space circularly polarized wave. S6. Complete the feed design and impedance matching of the coaxial connector and dielectric-filled rectangular waveguide, and test the antenna reflection coefficient; S7. Adjust the static magnetic field strength output by the magnetic bias structure, change the equivalent permeability tensor of the gyromagnetic material dopant, control the antenna operating frequency, and realize magnetically reconfigurable frequency control. S8. Keeping the effective area or equivalent volume of the near-zero dielectric constant resonant cavity unchanged, deform the shape of the near-zero dielectric constant resonant cavity with equal area to verify the antenna geometry-independent characteristics. S9. If the antenna's circular polarization performance, frequency reconfigurability performance, impedance matching performance, or geometry independence characteristics do not meet the standards, iterate and optimize according to the priority of circular polarization performance, frequency reconfigurability performance, impedance matching performance, and geometry independence characteristics, and return to S3; if all meet the standards, the design is complete.

[0012] Optionally, a static magnetic field in S3 is applied along the normal of the near-zero dielectric constant resonant cavity.

[0013] Optionally, the antenna operating frequency can be continuously adjusted or switched in stages by adjusting the static magnetic field strength in S7.

[0014] Optionally, in S7, the direction of the antenna's circular polarization can be changed by altering the direction of the static magnetic field.

[0015] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a geometry-independent circularly polarized frequency reconfigurable antenna with near-zero dielectric constant and a design method, the beneficial effects of which are: 1) Relying on a near-zero dielectric constant resonant cavity, geometric independence is achieved, and the operating frequency does not shift significantly after the cavity is deformed to the same area; 2) The combination of gyromagnetic material and annular gap provides a stable output of circularly polarized waves with a defined rotation direction, and the axial ratio meets engineering requirements; 3) Magnetic control tuning enables frequency reconfiguration without the need for active switching devices, resulting in high reliability and adaptability to various communication scenarios. 4) By introducing controllable non-reciprocity, a stable and definite vortex mode with a defined direction is obtained from the mechanism and circular polarization radiation is achieved. Stable circular polarization can be achieved while maintaining adaptability to shape changes. At the same time, by using magnetic field tuning to change the equivalent dispersion, frequency tuning can be achieved without loading active switching devices. Frequency reconfigurability can be achieved without changing the shape geometry, reducing dependence on loading active devices, improving reliability and maintaining a geometry-independent core. It is suitable for constrained installation space and multi-form packaging scenarios. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 A structural diagram of a geometry-independent circularly polarized frequency reconfigurable antenna with near-zero dielectric constant provided by the present invention; Figure 2 A phase distribution diagram of the magnetic field at half height of the cavity provided for this invention; Figure 3 The radiation pattern of the ENZ antenna provided by this invention; Figure 4 Axis ratio diagram of the operating frequency of the ENZ antenna provided by this invention; Figure 5 The reflection coefficient curves of the antenna under different magnetic field strengths are provided for the present invention. Figure 6 Top views of cavities of different shapes that maintain a constant cavity area, provided by the present invention; Figure 7 Reflection coefficient curves of cavities with different shapes provided by the present invention; Among them, 1-coaxial connector, 2-dielectric-filled rectangular waveguide, 3-annular slit radiation structure, 4-metal top cover plate, 5-near-zero dielectric constant resonant cavity, and 6-ferromagnetic material dopant. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] See Figure 1 As shown, this invention discloses a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant, comprising: 1. Coaxial connector; 2. Dielectric-filled rectangular waveguide; 3. Metal top cover plate; 4. Near-zero dielectric constant resonant cavity; 5. Gyromagnetic material dopant; 6. Magnetic bias structure. The outer conductor of coaxial connector 1 is grounded to the near-zero dielectric constant resonant cavity 5, and the inner conductor is connected to the dielectric-filled rectangular waveguide 2 through a feed probe. One end of the dielectric-filled rectangular waveguide 2 is electrically connected to the coaxial connector 1, and the other end is connected to the opening of the near-zero dielectric constant resonant cavity 5; A gyromagnetic material dopant 6 is placed in the central region inside the near-zero dielectric constant resonant cavity 5; A metal top cover plate 4 covers the top of the near-zero dielectric constant resonant cavity 5, and the metal top cover plate 4 has an annular slit radiation structure 3. The magnetic bias structure is used to apply a static magnetic field along the normal direction of the near-zero dielectric constant resonant cavity 5 to the gyromagnetic material dopant 6.

[0020] Specifically, coaxial connector 1 serves as the RF input terminal of the antenna. Located on the side of the structure, it is used to feed external RF signals into the antenna system. The metal top cover plate 4 and the near-zero dielectric constant resonant cavity 5 together form the upper metal boundary, which together with the annular slit radiation structure 3 constitutes the radiator; The near-zero dielectric constant resonant cavity 5, a gray block structure (including the cavity opening), is the core functional module of the antenna; its structure is realized by the near-zero dielectric constant resonant cavity 5 operating at the cutoff frequency. It provides a near-zero equivalent dielectric constant (ENZ) condition within the operating frequency band, making the electromagnetic field distribution within the cavity approximately uniform.

[0021] Furthermore, the gyromagnetic material dopant 6 is a yttrium iron garnet disc.

[0022] Specifically, the yttrium iron garnet (YIG) gyromagnetic material dopant 6 exhibits gyromagnetic non-reciprocal characteristics under the action of an external static magnetic field, breaking the time reversal symmetry; an ENZ vortex cavity with a definite rotation direction is constructed in the near-zero dielectric constant resonant cavity 5, providing the basic conditions for circularly polarized radiation; at the same time, by changing the strength of the external magnetic field, it can be used to realize the reconfigurable magnetic control frequency within a certain bandwidth range.

[0023] YIG can be replaced with other ferrite / magneto-optical materials, as long as they can provide an tunable anisotropic permeability tensor and produce non-reciprocity under a magnetic field.

[0024] Furthermore, the interior of the dielectric-filled rectangular waveguide 2 is filled with F4BM220 dielectric material with a relative permittivity of 2.2.

[0025] Specifically, the dielectric-filled rectangular waveguide 2 efficiently delivers radio frequency energy to the near-zero dielectric constant resonant cavity 5. One end of the dielectric-filled rectangular waveguide 2 is electrically connected to the coaxial connector 1, and the other end is connected to the opening of the near-zero dielectric constant resonant cavity 5, thus coupling near-field energy to the near-zero dielectric constant resonant cavity 5.

[0026] Furthermore, the annular slit radiation structure 3 can be an open annular slit, a segmented annular slit, or a double-opening annular slit.

[0027] Specifically, the annular slit radiation structure 3 serves as a coupling channel between the vortex cavity and free space radiation: it converts the vortex and angular momentum modes with definite rotation direction formed in the ENZ+YIG cavity into a free space radiation field, forming a highly efficient circularly polarized radiator.

[0028] Furthermore, the magnetic bias structure can be a permanent magnet, an electromagnetic coil, or an integrated planar coil.

[0029] and Figure 1 Corresponding to the aforementioned structure, this invention also discloses a design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant, used for... Figure 1 The specific implementation of the structure includes the following steps: S1. Determine the target operating frequency of the antenna; S2. Based on the equivalent ENZ effect of the cutoff waveguide, a near-zero dielectric constant resonant cavity 5 is designed to match the target operating frequency; S3. Place a gyromagnetic material dopant 6 in the central region of the near-zero dielectric constant resonant cavity 5, build a magnetic bias structure and apply a static magnetic field to construct a geometry-independent ENZ vortex cavity. S4. Extract the definite vortex modes of the ENZ vortex cavity through intrinsic mode analysis; S5. Determine the dimensions of the annular slit radiation structure 3 of the metal top cover plate 4, and complete the coupling matching from the vortex mode to the free space circularly polarized wave. S6. Complete the feed design and impedance matching of coaxial connector 1 and dielectric-filled rectangular waveguide 2, and test the antenna reflection coefficient; S7. Adjust the static magnetic field strength output by the magnetic bias structure, change the equivalent permeability tensor of the gyromagnetic material dopant 6, regulate the antenna operating frequency, and realize magnetically reconfigurable frequency control. S8. Keeping the effective area or equivalent volume of the near-zero dielectric constant resonant cavity 5 unchanged, deform the shape of the near-zero dielectric constant resonant cavity 5 with equal area to verify the antenna geometry-independent characteristics. S9. If the antenna's circular polarization performance, frequency reconfigurability performance, impedance matching performance, or geometry independence characteristics do not meet the standards, iterate and optimize according to the priority of circular polarization performance, frequency reconfigurability performance, impedance matching performance, and geometry independence characteristics, and return to S3; if all meet the standards, the design is complete.

[0030] Furthermore, a static magnetic field is applied in S3 along the normal direction of the near-zero dielectric constant resonant cavity 5.

[0031] Furthermore, in S7, the antenna operating frequency can be continuously adjusted or switched in stages by adjusting the static magnetic field strength.

[0032] Furthermore, in S7, the direction of the antenna's circular polarization is changed by altering the direction of the static magnetic field.

[0033] like Figure 2 As shown, this is the half-height plane of the cavity (i.e., along the cavity height direction) of the antenna of the present invention at the operating frequency. The diagram shows the phase distribution of the magnetic field at a cross-section. The color scale on the right side of the diagram represents the phase angle, ranging from 0° to 360°; different colors correspond to different phase values. Figure 2 It can be seen that inside the near-zero dielectric constant resonant cavity 5 ( Figure 2 The magnetic field phase in the square region exhibits a characteristic of continuous rotational change with azimuth: the phase gradually changes along the circumferential direction from a certain direction, achieving a complete coverage from 0° to 360°, and a distinct phase singularity appears near the center of the cavity. This phenomenon indicates that a vortex mode with a definite rotational direction (a mode carrying an angular phase gradient) has formed inside the cavity, that is, the magnetic field phase rotates monotonically along the circumferential direction, reflecting the characteristics of the vortex cavity constructed by breaking the time reversal symmetry using a gyromagnetic material (such as YIG) in this invention.

[0034] like Figure 3 The image shows the circular polarization radiation pattern of the ENZ geometry-independent circularly polarized antenna of this invention at the operating frequency. Figure 3It is evident that near the main radiation direction (main lobe direction), the left-hand circular polarization component is significantly higher than the right-hand circular polarization component, and maintains its dominance over a large angular range. This indicates that the antenna can generate circularly polarized radiation dominated by left-hand circular polarization at its operating frequency. Simultaneously, the right-hand circular polarization component is effectively suppressed in the main radiation direction, demonstrating that the antenna possesses good polarization purity and left-hand circular polarization radiation characteristics.

[0035] like Figure 4 The figure shows the polar coordinate curve of the axial ratio (AR) of the ENZ antenna of this invention at the operating frequency as a function of angle, with the radial coordinate representing the axial ratio (dB). The axial ratio is used to measure the degree of circular polarization: the closer the AR is to 0dB, the more ideal the circular polarization; in engineering, AR ≤ 3dB is usually used as the criterion for circular polarization. Figure 3 As can be seen, within the angular range near the main radiation direction, the axial ratio curve satisfies or approaches the 3dB threshold (and achieves a lower axial ratio near the main lobe), indicating that the antenna has good circular polarization radiation characteristics at the operating frequency. This further confirms that the antenna of the present invention achieves stable circular polarization radiation at the target operating frequency, and has a clear circular polarization direction and good polarization purity.

[0036] like Figure 5 As shown, the antenna of the present invention is subjected to different applied static magnetic field strengths. Reflection coefficient under certain conditions Curve showing variation with frequency. Figure 5 Comparative results of multiple sets of magnetic field strengths are presented. Figure 5 As can be seen from this, with the increase of the applied static magnetic field strength The change in frequency indicates that the antenna's resonant point shifts continuously and in stages along the frequency axis, demonstrating that the antenna's operating frequency can be effectively controlled by a magnetic field, achieving reconfigurable magnetically controlled frequency. Simultaneously, at each magnetic field operating point, the resonant notch filter generally achieves an engineering-usable matching level (within...). The matching criteria indicate that the present invention can still maintain good impedance matching performance during frequency tuning.

[0037] like Figure 6 The diagram shown is a top view of the near-zero dielectric constant resonant cavity 5 of the present invention under the condition of keeping the effective area (or equivalent volume) of the cavity unchanged. Figure 6 Various external structures, such as circular cavity, triangular cavity, hexagonal cavity, and irregular (maple leaf) cavity, are presented, while maintaining the consistent arrangement of the feeding structure and the radiation structure.

[0038] like Figure 7 As shown, in Figure 6 The reflection coefficient of the antenna of the present invention is shown under various cavity shapes. A comparison curve showing how frequency changes. Legends correspond to various cavity shapes, including circular, triangular, hexagonal, and irregular shapes. Figure 7 It can be seen that, under the condition of keeping the effective area (or equivalent volume) of the cavity consistent and other key parameters basically the same, cavities with different shapes... The curves highly overlap or show only a minimal offset near the resonant frequency. This indicates that the operating frequency and matching characteristics of the antenna of this invention are insensitive to changes in the cavity shape, verifying the core characteristic of the ENZ geometry-independent antenna of this invention: its operating frequency is mainly determined by the dispersion characteristics of the ENZ equivalent parameters, rather than by the specific geometry of the cavity. Therefore, even if the cavity shape varies arbitrarily within a large range, this invention can still achieve similar operating results, providing good adaptability for the antenna in different installation spaces, packaging forms, and complex environments.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Regarding the methods disclosed in the embodiments, since they correspond to the structures disclosed in the embodiments, the descriptions are relatively simple; relevant details can be found in the method section.

[0040] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A geometric-independent circularly-polarized frequency reconfigurable antenna with near-zero permittivity, characterized in that, include: Coaxial connector, dielectric-filled rectangular waveguide, metal top cover plate, near-zero dielectric constant resonant cavity, gyromagnetic material dopant, magnetic bias structure; The outer conductor of the coaxial connector is grounded to the near-zero dielectric constant resonant cavity, and the inner conductor is connected to the dielectric-filled rectangular waveguide through a feed probe. One end of the dielectric-filled rectangular waveguide is electrically connected to a coaxial connector, and the other end is connected to the opening of a near-zero dielectric constant resonant cavity; A gyromagnetic material dopant is placed in the central region inside a near-zero dielectric constant resonant cavity; A metal top cover is placed on top of the near-zero dielectric constant resonant cavity, and the metal top cover has an annular slit radiation structure. The magnetic bias structure is used to apply a static magnetic field along the normal of the near-zero dielectric constant resonant cavity to a gyromagnetic material dopant.

2. The dielectrically almost zero-geometrically reconfigurable circularly polarized frequency antenna according to claim 1, wherein, The gyromagnetic material dopant is a yttrium iron garnet disc.

3. The dielectrically almost zero-geometrically reconfigurable circularly polarized frequency antenna according to claim 1, wherein, The interior of the dielectric-filled rectangular waveguide is filled with F4BM220 dielectric material with a relative permittivity of 2.

2.

4. The near-zero dielectric constant, geometrically independent circularly polarized frequency reconfigurable antenna according to claim 1, characterized in that, The annular slit radiation structure can be an open annular slit, a segmented annular slit, or a double-opening annular slit.

5. A geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant according to claim 1, characterized in that, The magnetic bias structure is a permanent magnet, an electromagnetic coil, or an integrated planar coil.

6. A design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant, characterized in that... The application of a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant as described in any one of claims 1-5 includes the following steps: S1. Determine the target operating frequency of the antenna; S2. Based on the equivalent ENZ effect of the cutoff waveguide, design a near-zero dielectric constant resonant cavity to match the target operating frequency; S3. Place a gyromagnetic material dopant in the central region of the near-zero dielectric constant resonant cavity, build a magnetic bias structure and apply a static magnetic field to construct a geometry-independent ENZ vortex cavity. S4. Extract the definite vortex modes of the ENZ vortex cavity through intrinsic mode analysis; S5. Determine the dimensions of the annular slit radiation structure of the metal top cover plate and complete the coupling matching from the vortex mode to the free space circularly polarized wave. S6. Complete the feed design and impedance matching of the coaxial connector and dielectric-filled rectangular waveguide, and test the antenna reflection coefficient; S7. Adjust the static magnetic field strength output by the magnetic bias structure, change the equivalent permeability tensor of the gyromagnetic material dopant, control the antenna operating frequency, and realize magnetically reconfigurable frequency control. S8. Keeping the effective area or equivalent volume of the near-zero dielectric constant resonant cavity unchanged, deform the shape of the near-zero dielectric constant resonant cavity with equal area to verify the antenna geometry-independent characteristics. S9. If the antenna's circular polarization performance, frequency reconfigurability performance, impedance matching performance, or geometry independence characteristics do not meet the standards, iterate and optimize according to the priority of circular polarization performance, frequency reconfigurability performance, impedance matching performance, and geometry independence characteristics, and return to S3; if all meet the standards, the design is complete.

7. The design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant according to claim 6, characterized in that, In S3, a static magnetic field is applied along the normal direction of the near-zero dielectric constant resonant cavity.

8. The design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant according to claim 6, characterized in that, In S7, the antenna operating frequency can be continuously adjusted or switched in stages by adjusting the static magnetic field strength.

9. The design method for a geometry-independent circularly polarized frequency-reconfigurable antenna with near-zero dielectric constant according to claim 6, characterized in that, In S7, the direction of the antenna's circular polarization is changed by altering the direction of the static magnetic field.

Citation Information

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