Artificial surface plasmon full-space beam scanning leaky-wave antenna
By designing an antenna structure that includes a dielectric substrate, a balun structure, and metal stubs, a full-space scanning leaky-wave antenna with an artificial surface plasmon polariton beam scanning system was achieved. This solves the problems of limited beam scanning range and large bandwidth occupation in existing technologies, and has the advantages of high efficiency and high gain. It is suitable for wireless communication such as automotive radar.
Patent Information
- Application Number
- CN202310862986.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-13
- Publication Date
- 2026-01-30
- Estimated Expiration
- 2043-07-13
AI Technical Summary
Existing leaky wave antennas based on artificial surface plasmons have limited beam scanning range, making it difficult to achieve full-space scanning, and traditional periodic microstrip leaky wave antennas require a large operating bandwidth.
Design an antenna structure comprising a dielectric substrate, a balun structure, an artificial surface plasmon stripe group, and metal stubs. A 180° phase difference current is achieved through the balun structure. Combined with the artificial surface plasmon transition section and the radiation section, the harmonics are modulated using a dipole array and metal stubs to achieve full-space beam scanning.
It achieves full-space scanning of the main beam from back-firing to end-firing, and features high radiation efficiency, high directivity, high gain, small bandwidth occupation, and small overall size, making it suitable for wireless communication fields such as automotive radar.
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Figure CN116683172B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to an artificial surface plasmon full-space beam scanning leaky antenna, belonging to the field of antenna technology. Background Technology
[0002] Artificial surface plasmons are surface waves excited on periodic metal surfaces, exhibiting characteristics such as deep subwavelength, localized field enhancement, and nonlinear dispersion curves. Novel electromagnetic devices designed using this mode offer advantages such as compact structure, light weight, and low cost, and have broad application prospects in highly integrated wireless communication systems.
[0003] Currently, leaky wave antennas mainly include leaky wave antennas based on artificial surface plasmons and traditional periodic microstrip leaky wave antennas. However, leaky wave antennas based on artificial surface plasmons and traditional periodic microstrip leaky wave antennas still have the following problems: 1) Existing leaky wave antennas based on artificial surface plasmons have limited beam scanning range, making it difficult to achieve full-space scanning of the beam from back-firing to end-firing; 2) Traditional periodic microstrip leaky wave antennas, due to their linear dispersion curve, often require a large operating bandwidth to achieve large-angle scanning from back-firing to front-firing.
[0004] For example, Chinese patent application CN202111227242.0 discloses a wide-angle omnidirectional leaky wave antenna based on artificial surface plasmon polaritons, which also suffers from problems such as occupying a large operating bandwidth, limited beam scanning range of the leaky wave antenna, and difficulty in achieving full-space scanning.
[0005] The above-mentioned problems should be considered and solved in the design and production of artificial surface plasmon full-space beam scanning leaky wave antennas. Summary of the Invention
[0006] The purpose of this invention is to provide an artificial surface plasmon full-space beam scanning leaky antenna to solve the problems of existing technologies, such as large operating bandwidth, difficulty in achieving full-space scanning, and the need to improve the beam scanning range of leaky antennas.
[0007] The technical solution of this invention is:
[0008] An artificial surface plasmon full-space beam scanning leaky antenna includes a dielectric substrate. The upper and lower surfaces of the dielectric substrate form a top dielectric substrate and a bottom dielectric substrate, respectively. The top dielectric substrate has a balun structure, an artificial surface plasmon strip group, and several metal stubs. The two ends of the artificial surface plasmon strip group are symmetrically provided with balun structures. The upper and lower sides of the artificial surface plasmon strip group are periodically arranged and symmetrically provided with several metal stubs. The artificial surface plasmon strip group includes a pair of slidingly symmetrical artificial surface plasmon strips. The two ends of the bottom dielectric substrate are respectively provided with ground metal layers corresponding to the balun structures. The ground metal layers are respectively connected to the balun structures through ground metal vias. The balun structures respectively realize differential feeding to the two ends of the artificial surface plasmon strips.
[0009] Furthermore, the balun structure includes a first microstrip line, a second microstrip line, and a tapered double-slot line. The first microstrip line is a tapered first microstrip line. One end of the first microstrip line is the feed port of the antenna, and the other end of the first microstrip line is connected to the second microstrip line. One branch of the tapered double-slot line is connected to the second microstrip line, and the other branch of the tapered double-slot line is connected to the corresponding ground metal layer through a ground metal via. The upper and lower ends of the tapered double-slot line are respectively connected to artificial surface plasmon strips.
[0010] Furthermore, the artificial surface plasmon strip includes an artificial surface plasmon transition section and an artificial surface plasmon radiation section. The two ends of the artificial surface plasmon radiation section are connected to the balun structure through the artificial surface plasmon transition section. Metal branches are located on the outer side of the artificial surface plasmon radiation section. Several trapezoidal grooves are spaced apart on the inner side of the artificial surface plasmon transition section, and several rectangular grooves are spaced apart on the inner side of the artificial surface plasmon radiation section.
[0011] Furthermore, the rectangular trenches have the same depth, width, and period, while the trapezoidal trenches have the same height and period, and the depth of the trapezoidal trenches increases from the plasmon radiation section far from the artificial surface to the plasmon radiation section near the artificial surface.
[0012] Furthermore, gaps are provided between the artificial surface plasmon strips in the artificial surface plasmon strip group.
[0013] Furthermore, the length of the grounding metal layer is greater than the sum of the lengths of the first and second microstrip lines in the balun structure.
[0014] Furthermore, the balun structure enables two currents with a 180° phase difference to transition to the artificial surface plasmon radiation section via the artificial surface plasmon transition section. This allows the slidingly symmetrically arranged artificial surface plasmon radiation section to form a dipole array with the metal stubs loaded on the outside of the artificial surface plasmon radiation section, thereby achieving full-space beam scanning of the antenna from back-firing to front-firing.
[0015] Furthermore, by adjusting the spacing between adjacent metal stubs, the dispersion curve of multiple spatial harmonics of the plasmon radiation strips on the artificial surface can be controlled, thereby adjusting the antenna's operating frequency and bandwidth: when the spacing between the metal stubs increases, the antenna's operating frequency decreases and its operating bandwidth widens; when the spacing between the metal stubs decreases, the antenna's operating frequency increases and its operating bandwidth narrows.
[0016] Furthermore, by adjusting the number of rectangular trenches and metal stubs in the artificial surface plasmon radiation segment, the length of the artificial surface plasmon radiation segment can be controlled, thereby controlling the antenna gain: when the number of rectangular trenches and metal stubs increases, the length of the artificial surface plasmon radiation segment increases, allowing the electromagnetic waves transmitted on the artificial surface plasmon strip to radiate further into free space, thus improving the antenna gain; conversely, when the number of rectangular trenches and metal stubs decreases, the length of the artificial surface plasmon radiation segment decreases, and the antenna gain decreases.
[0017] The beneficial effects of this invention are:
[0018] I. This artificial surface plasmonic full-space beam scanning leaky antenna can realize continuous scanning of the main beam from back-firing to front-firing, and has the capability of full-space beam scanning. It has the advantages of small bandwidth occupation, high radiation efficiency, high directivity, high gain, low profile and relatively small overall size, and can be applied to wireless communication fields such as automotive radar.
[0019] II. In this invention, the balun structure provides a pair of antiphase currents, which then transition to the artificial surface plasmon radiation section via the artificial surface plasmon transition section. The artificial surface plasmon radiation section, together with the metal stubs loaded on the outside of the artificial surface plasmon radiation section, serves as the radiation part, enabling full-space scanning with the main beam direction varying with frequency, thus achieving full-space scanning effect.
[0020] Third, this artificial surface plasmon full-space beam scanning leaky antenna, by symmetrically loading metal stubs on the upper and lower sides of the artificial surface plasmon strip group to excite multiple spatial harmonics for radiation, can reduce the occupied bandwidth of the antenna while achieving high directional radiation from back-firing to forward end-firing direction, and can reduce the relative size of the antenna while achieving high gain, thereby achieving high radiation efficiency. Attached Figure Description
[0021] Figure 1 This is a schematic diagram of the structure of the artificial surface plasmon full-space beam scanning leaky antenna according to an embodiment of the present invention;
[0022] Figure 2 This is a schematic diagram of the top surface structure of the artificial surface plasmon full-space beam scanning leaky wave antenna in the embodiment.
[0023] Figure 3 yes Figure 2 A magnified view of part A in the diagram;
[0024] Figure 4 yes Figure 2 A magnified view of part B in the diagram;
[0025] Figure 5 yes Figure 2 A magnified view of part of C;
[0026] Figure 6 This is a schematic diagram of the bottom structure of the artificial surface plasmon full-space beam scanning leaky antenna in the embodiment.
[0027] Figure 7 This is a schematic diagram of the simulated and measured S-parameters of the artificial surface plasmon plasmon full-space beam scanning leaky wave antenna in the embodiment.
[0028] Figure 8 This is a schematic diagram of the simulated radiation patterns of the artificial surface plasmon full-space beam scanning leaky wave antenna at 4.45G, 4.75G, 5.00G, 5.65G, 6.15G, 6.40G and 6.60G.
[0029] Figure 9 This is a schematic diagram of the measured radiation patterns of the artificial surface plasmon full-space beam scanning leaky wave antenna at 4.35G, 4.65G, 4.85G, 5.55G, 5.95G, 6.25G and 6.45G, as described in the embodiment.
[0030] Figure 10 This is a schematic diagram of the simulation and measured gain and radiation efficiency of the artificial surface plasmon full-space beam scanning leaky wave antenna in the embodiment.
[0031] Wherein: 1-dielectric substrate, 2-balun structure, 3-metal branch, 4-artificial surface plasmon strip, 5-ground metal layer, 6-ground metal via, 7-gap;
[0032] 11-Top layer of dielectric substrate, 12-Bottom layer of dielectric substrate
[0033] 21-First microstrip line, 22-Second microstrip line, 23-Gradual double groove line;
[0034] 41-Artificial surface plasmon transition section, 42-Artificial surface plasmon radiation section, 43-Trapezoidal groove, 44-Rectangular trench. Detailed Implementation
[0035] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0036] Example
[0037] An artificial surface plasmonic full-space beam scanning leaky antenna, such as Figure 1 , Figure 2 and Figure 6 The device includes a dielectric substrate 1, with a top dielectric substrate 11 and a bottom dielectric substrate 12 formed on the top and bottom surfaces of the dielectric substrate 1, respectively. The top dielectric substrate 11 is provided with a balun structure 2, an artificial surface plasmon strip group and several metal branches 3. The two ends of the artificial surface plasmon strip group are symmetrically provided with balun structures 2. The top and bottom sides of the artificial surface plasmon strip group are periodically arranged and symmetrically provided with several metal branches 3. The artificial surface plasmon strip group includes a pair of slidingly symmetrical artificial surface plasmon strips 4. The two ends of the bottom dielectric substrate 12 are respectively provided with ground metal layers 5 corresponding to the balun structure 2. The ground metal layers 5 are respectively connected to the balun structure 2 through ground metal through holes 6. The balun structure 2 respectively realizes differential power feeding to the two ends of the artificial surface plasmon strip 4.
[0038] This artificial surface plasmonic full-space beam scanning leaky antenna can achieve continuous scanning of the main beam from back-firing to front-firing, and has the capability of full-space beam scanning. It has the advantages of small bandwidth occupation, high radiation efficiency, high directivity, high gain, low profile and relatively small overall size, and can be applied to wireless communication fields such as automotive radar.
[0039] like Figure 3 The balun structure 2 includes a first microstrip line 21, a second microstrip line 22, and a tapered double-slot line 23. The first microstrip line 21 is a tapered double-slot line, with one end serving as the antenna feed port and the other end connected to the second microstrip line 22. One branch of the tapered double-slot line 23 is connected to the second microstrip line 22, and the other branch is connected to the corresponding ground metal layer 5 via a ground metal via 6. The upper and lower ends of the tapered double-slot line 23 are connected to artificial surface plasmon strips 4, respectively. In the balun structure 2, the feed at the front end of the first microstrip line 21 is connected to one of the tapered double-slot lines 23 via the second microstrip line 22, and the other branch of the tapered double-slot line 23 is connected to the corresponding ground metal layer 5 via the ground metal via 6. This results in two currents with a 180° phase difference being formed at the end of the tapered double-slot line 23. The first microstrip line 21 is a 50-ohm microstrip line, which is used to match the impedance of a 50-ohm coaxial connector.
[0040] like Figure 2The artificial surface plasmon strip 4 includes an artificial surface plasmon transition section 41 and an artificial surface plasmon radiation section 42. Both ends of the artificial surface plasmon radiation section 42 are connected to the balun structure 2 via the artificial surface plasmon transition section 41. Metal branches 3 are located on the outer side of the artificial surface plasmon radiation section 42. The inner side of the artificial surface plasmon transition section 41 is provided with several trapezoidal grooves 43 at intervals, and the inner side of the artificial surface plasmon radiation section 42 is provided with several rectangular grooves 44 at intervals. Gaps 7 are provided between the artificial surface plasmon strips 4 in the artificial surface plasmon strip group.
[0041] like Figure 4 and Figure 5 The rectangular groove 44 has the same depth, width and period, and the trapezoidal groove 43 has the same height and period. The depth of the trapezoidal groove 43 increases from the far artificial surface plasmon radiation section 42 to the near artificial surface plasmon radiation section 42.
[0042] This type of artificial surface plasmonic full-space beam scanning leaky antenna, such as Figure 6 The length of the grounding metal layer 5 is greater than the sum of the lengths of the first microstrip line 21 and the second microstrip line 22 in the balun structure 2.
[0043] This type of artificial surface plasmon full-space beam scanning leaky antenna uses a balun structure 2 to realize two currents with a 180° phase difference, which are transitioned to the artificial surface plasmon radiation section 42 via the artificial surface plasmon transition section 41. The slidingly symmetrical artificial surface plasmon radiation section 42 and the metal stubs 3 loaded on the outside of the artificial surface plasmon radiation section 42 form a dipole array, thereby realizing full-space beam scanning of the antenna from back-firing to front-firing.
[0044] This artificial surface plasmon full-space beam scanning leaky antenna achieves control over the dispersion curve of multiple spatial harmonics of the artificial surface plasmon radiation strip by adjusting the spacing between adjacent metal stubs 3, thereby adjusting the antenna's operating frequency and bandwidth: when the spacing between the metal stubs 3 increases, the antenna's operating frequency decreases and its operating bandwidth widens; when the spacing between the metal stubs 3 decreases, the antenna's operating frequency increases and its operating bandwidth narrows.
[0045] This artificial surface plasmon full-space beam scanning leaky antenna can adjust the dispersion curve of the artificial surface plasmon radiation strip by adjusting the depth of the rectangular groove 44 of the artificial surface plasmon radiation section 42, thereby enabling the adjustment of the antenna's operating frequency and bandwidth: when the groove depth of the artificial surface plasmon radiation section 42 is increased, the antenna's operating frequency decreases and the operating bandwidth narrows; when the groove depth of the artificial surface plasmon radiation section 42 is decreased, the antenna's operating frequency increases and the operating bandwidth widens.
[0046] This artificial surface plasmon full-space beam scanning leaky antenna achieves frequency control by adjusting the spacing of the rectangular metal stubs 3 distributed along the transverse axis of the artificial surface plasmon radiation segment 42 and / or the depth of the periodic rectangular grooves 44 on the artificial surface plasmon strip 4.
[0047] This artificial surface plasmon full-space beam scanning leaky antenna achieves gain control by adjusting the number of rectangular grooves 44 and metal stubs 3 in the artificial surface plasmon radiation segment 42. Increasing the number of rectangular grooves 44 and metal stubs 3 increases the length of the artificial surface plasmon radiation segment 42, allowing the electromagnetic waves transmitted on the artificial surface plasmon strip 4 to radiate further into free space, thus improving the antenna gain. Conversely, decreasing the number of rectangular grooves 44 and metal stubs 3 decreases the length of the artificial surface plasmon radiation segment 42, resulting in a lower antenna gain.
[0048] This artificial surface plasmon full-space beam scanning leaky antenna uses a balun structure 2 with differential input as its feed section. The current through the balun structure 2 passes through the vertically sliding symmetrical artificial surface plasmon transition section 41, achieving impedance matching and thus a wider bandwidth. The gradual transition of the vertically sliding symmetrical artificial surface plasmon trapezoidal slot 43 achieves electromagnetic wave matching, enabling the electromagnetic waves to be effectively transmitted into the artificial surface plasmon strip 4. Finally, by periodically loading vertically symmetrical metal stubs 3 on both sides of the artificial surface plasmon strip 4, the electromagnetic waves are effectively radiated into free space, achieving high gain and radiation efficiency.
[0049] In this invention, the balun structure 2 provides a pair of antiphase currents, which then transition to the artificial surface plasmon radiation section 42 via the artificial surface plasmon transition section 41. The artificial surface plasmon radiation section 42, together with the metal stub 3 loaded on the artificial surface plasmon, serves as the radiation part, enabling full-space scanning with the main beam direction varying with frequency, thus achieving a full-space scanning effect.
[0050] This artificial surface plasmon full-space beam scanning leaky antenna achieves high directional radiation from back-firing to forward-firing direction by symmetrically loading metal stubs 3 on both sides of the artificial surface plasmon strip group to excite multiple spatial harmonics. It can reduce the occupied bandwidth of the antenna while achieving high gain, and can reduce the relative size of the antenna while achieving high gain, thus achieving high radiation efficiency.
[0051] This artificial surface plasmon full-space beam scanning leaky antenna uses a balun structure 2 to feed a pair of vertically parallel and slidingly symmetrical artificial surface plasmon strips 4 and metal stubs 3 symmetrically loaded on the upper and lower sides of the artificial surface plasmon strips 4. This avoids the pattern tilt problem caused by the asymmetrical structure and enables high-directional radiation from back-firing to front-firing direction.
[0052] This artificial surface plasmon (ASP) full-space beam-scanning leaky antenna differs significantly from other existing ASP leaky antennas. Structurally, existing ASP leaky antennas typically employ asymmetric structures or use magnetically coupled patch radiators, while this ASP full-space beam-scanning leaky antenna uses a vertically sliding symmetrical structure. In principle, ASPs have strong field confinement, preventing efficient energy radiation into free space. To achieve free space radiation from ASPs, their field distribution must be disrupted. Existing ASP leaky antennas use ASP transmission lines as antenna feed, coupling energy from the transmission lines to patch radiators for radiation, or employ asymmetric structures. This invention's ASP leaky antenna uses a conical microstrip balun slotted wire structure to differentially feed dipole-type ASPs, thereby achieving efficient energy radiation.
[0053] The simulation and experimental verification results of the embodiments are as follows:
[0054] Figure 7 This is an S-parameter diagram of the artificial surface plasmon full-space beam scanning leaky-wave antenna of the embodiment. Figure 7 It can be seen that the antenna has an operating bandwidth of 4.35-6.45 GHz, a relative bandwidth of 40%, a high scan rate of 4.6° / %, and the advantage of occupying little bandwidth.
[0055] Figure 8 This is a schematic diagram of the simulated radiation patterns of the artificial surface plasmon full-space beam scanning leaky wave antenna at 4.45G, 4.75G, 5.00G, 5.65G, 6.15G, 6.40G and 6.60G. Figure 9 This is a schematic diagram of the measured radiation patterns at 4.35G, 4.65G, 4.85G, 5.55G, 5.95G, 6.25G, and 6.45G for the artificial surface plasmon full-space beam scanning leaky-wave antenna of the embodiment. (From...) Figure 8 and Figure 9 It can be seen that the main beam can continuously scan from back-firing to front-firing, and has the capability of full-space beam scanning.
[0056] Figure 10This is a schematic diagram of the simulated and measured gain and radiation efficiency of the artificial surface plasmon full-space beam scanning leaky wave antenna in the 4.35-6.45 GHz frequency band, obtained by taking points every 0.1 GHz. The antenna has a maximum gain of 12.5 dBi and an average radiation efficiency of over 90%, achieving high gain and radiation efficiency, and enabling efficient energy radiation.
[0057] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. An artificial surface plasmon full-space beam scanning leaky-wave antenna, comprising a dielectric substrate, the upper and lower surfaces of the dielectric substrate forming a dielectric substrate top layer and a dielectric substrate bottom layer respectively, characterized in that: The medium substrate top layer is provided with a balun structure, an artificial surface plasmon strip group and a plurality of metal branches, the balun structure is symmetrically arranged at both ends of the artificial surface plasmon strip group, the artificial surface plasmon strip group is periodically arranged and symmetrically provided with a plurality of metal branches on the upper and lower sides, the artificial surface plasmon strip group comprises a pair of sliding symmetric artificial surface plasmon strips, the artificial surface plasmon strip comprises an artificial surface plasmon transition section and an artificial surface plasmon radiation section, the artificial surface plasmon radiation section is connected with the balun structure through the artificial surface plasmon transition section at both ends, the metal branches are arranged on the outer side of the artificial surface plasmon radiation section, a plurality of trapezoidal grooves are arranged on the inner side of the artificial surface plasmon transition section, and a plurality of rectangular grooves are arranged on the inner side of the artificial surface plasmon radiation section; the depth, width and period of the rectangular groove are the same, the height and period of the trapezoidal groove are the same, and the depth of the trapezoidal groove increases from the artificial surface plasmon radiation section to the artificial surface plasmon transition section; the bottom layer of the medium substrate is provided with a grounding metal layer corresponding to the balun structure at both ends, the grounding metal layer is connected with the balun structure through a grounding metal through hole, and the balun structure realizes differential feeding of both ends of the artificial surface plasmon strip.
2. The artificial surface plasmon full-space beam scanning leaky-wave antenna of claim 1, wherein: The balun structure comprises a first microstrip line, a second microstrip line and a gradually changing double groove line, the first microstrip line adopts a tapered first microstrip line, one end of the first microstrip line is a feeding port of the antenna, the other end of the first microstrip line is connected with the second microstrip line, one of the gradually changing double groove lines is connected with the second microstrip line, the other of the gradually changing double groove lines is connected with the corresponding grounding metal layer through a grounding metal through hole, and the upper and lower ends of the gradually changing double groove line are connected with the artificial surface plasmon strip.
3. The artificial surface plasmon full-space wave-beam scanning leaky-wave antenna according to claim 1 or 2, wherein: The artificial surface plasmon strips of the artificial surface plasmon strip group are provided with a gap.
4. The artificial surface plasmon full-space beam scanning leaky-wave antenna according to claim 1 or 2, wherein: The length of the grounding metal layer is greater than the sum of the lengths of the first microstrip line and the second microstrip line in the balun structure.
5. The artificial surface plasmon full-space beam scanning leaky-wave antenna of claim 1, wherein: The balun structure realizes two currents with a phase difference of 180 degrees, which are transferred to the artificial surface plasmon radiation section through the artificial surface plasmon transition section, so that the dipole array is formed by the sliding symmetric artificial surface plasmon radiation section and the metal branches loaded on the outer side of the artificial surface plasmon radiation section, thereby realizing the full-space beam scanning of the antenna from back to front.
6. The artificial surface plasmon full-space wave-beam scanning leaky-wave antenna of any one of claims 1 or 2, wherein: By adjusting the spacing of adjacent metal branches, the dispersion curve of multiple spatial harmonics of the artificial surface plasmon radiation strip is controlled, and the working frequency and working bandwidth of the antenna are adjusted: when the spacing of the metal branches increases, the working frequency of the antenna decreases and the working bandwidth becomes wider; when the spacing of the metal branches decreases, the working frequency of the antenna increases and the working bandwidth becomes narrower.
7. The artificial surface plasmon full-space wave-beam scanning leaky-wave antenna of claim 1, wherein: By adjusting the number of rectangular grooves and the number of metal branches of the artificial surface plasmon radiation section, the length of the artificial surface plasmon radiation section is controlled, so that the gain of the antenna is controlled: when the number of rectangular grooves and the number of metal branches increase, the length of the artificial surface plasmon radiation section increases, so that the electromagnetic wave transmitted on the artificial surface plasmon strip is further radiated into the free space, and the gain of the antenna is improved; on the contrary, when the number of rectangular grooves and the number of metal branches decrease, the length of the artificial surface plasmon radiation section decreases, and the gain of the antenna decreases.
Citation Information
Patent Citations
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