Variable-beam control method for meta-grating leaky-wave antenna based on varactor

Abstract

The application discloses a variable-beam control method of a variable capacitance diode-based element grating leaky-wave antenna, and comprises the following steps: S1, researching and analyzing an ultra-grating beam conversion mechanism; researching the mechanism of a planar ultra-grating under anisotropic, uniform and continuous periodic boundary conditions; S2, according to the ultra-grating, researching a transmission mode and optimization design of a Floquet-Bloch theorem; researching an FB mode, and eliminating the bad FB mode by designing a tool for ultra-grating parameters; S3, analyzing and designing the ultra-grating leaky-wave antenna; researching the analytical field and current of the synthesized ultra-grating in the framework of the leaky-wave antenna, so as to customize the performance of phase, beam shape and polarization; S4, designing and analyzing an electrically-tuned beam control ultra-grating leaky-wave antenna; the application adopts the variable-beam control method of the variable capacitance diode-based element grating leaky-wave antenna, adopts a simple structure of a tunable material to tune an efficient structure platform, and lays a road for a new generation of efficient special gratings.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of optical gratings, in particular to a variable-beam control method for a meta-grating leaky-wave antenna based on a varactor. BACKGROUND

[0002] In the past few years, metagratings (also known as metasurfaces) have made unprecedented progress in light flow control as two-dimensional arrays of densely distributed polarizable particles, which have enabled their application in multiple research and technology fields such as energy harvesting, imaging and cloaking. Metagratings are important engineered surfaces that are widely used to redirect the reflection and transmission directions of incident waves. These metagratings are carefully designed to provide a gradually varying surface impedance to achieve the required local momentum, thereby guiding the incident waves to the desired direction. Although these gratings have achieved unprecedented functionality in regulating electromagnetic waves, recent independent studies have demonstrated that there are fundamental physical limitations on the conversion efficiency of the gradually varying metagratings designed based on the reflection and refraction generalized laws, provided that they are assumed to be local and passive. Notably, studies have shown that active or strongly non-local metagratings are required to achieve unit efficiency in redirecting incident or excited waves to the desired direction during reflection or transmission. In addition, since gradually varying metagratings need to provide carefully designed and rapidly varying gradually varying grating impedance characteristics, they require high-resolution discretization, which makes their manufacturing process complex.

[0003] Therefore, the basic design method followed by most reports is to try to establish an effective coupling with the ideal FB mode by selecting a period that allows only a few propagating modes to exist and using some heuristic methods or numerical optimization for a single period to reduce the coupling with all modes other than the prescribed mode. One of the fundamental functions used to measure the capabilities of metasurfaces (MTS) is anomalous refraction, i.e. a given incident plane wave is deflected to an ideal angle during transmission. SUMMARY

[0004] The purpose of the present application is to provide a variable-beam control method for a meta-grating leaky-wave antenna based on a varactor, which uses a simple structure of tunable material to tune an efficient structure platform, thereby paving the way for a new generation of high-efficiency special gratings.

[0005] The application provides a variable-beam control method for a meta-grating leaky-wave antenna based on a varactor, which comprises the following steps:

[0006] S1, researching and analyzing the beam conversion mechanism of the metagrating;

[0007] Researching the planar metagrating mechanism under anisotropic, uniform and continuous periodic boundary conditions;

[0008] The scalar electric impedance density and the magnetic admittance density of the superlattice are studied, and the performance of the electric impedance density and the magnetic admittance density as functions of the load impedance and the operating frequency is verified.

[0009] The surface wave to propagating wave method conversion of each physical quantity of the superlattice is studied.

[0010] S2, the transmission mode of the Floquet-Bloch theorem according to the superlattice is determined, and the design is optimized.

[0011] The FB mode is studied, and a tool for superlattice parameters is designed to eliminate undesirable FB modes.

[0012] The number of propagating FB modes is matched with the number of different superlattices in the periodic structure by local matching between the surface wave and the periodic superlattice and the infinite uniform periodic structure with the same amplitude and period.

[0013] S3, the superlattice leaky-wave antenna is analyzed and designed.

[0014] The analytical field and current of the synthesized superlattice are studied in the framework of the leaky-wave antenna to customize the performance of the phase, beam shape and polarization. The design considerations of the superlattice leaky-wave antenna are studied, focusing on the impedance characteristics of the superlattice, and the required feed system is described.

[0015] S4, the design and analysis of the electrically tunable beam steering superlattice leaky-wave antenna.

[0016] An analysis model of the wide-angle superlattice beam radiation field is established and studied in depth.

[0017] The beam control method is studied; the phase of the leaky-wave antenna is controlled to achieve electrical scanning; the phase of the superlattice is changed to control the radiation direction.

[0018] Preferably, in step S1, the superlattice is divided into two modeling methods by anisotropic continuous impedance, and the two modeling methods are opaque superlattice or transparent superlattice.

[0019] A specific grating pattern is constructed by the superlattice in the TE or transverse magnetic TM mode, and each wire of the superlattice is represented by a scalar electric impedance density. For wires with magnetic response, it is represented by a scalar magnetic admittance density.

[0020] Preferably, in step S2, the FB mode is a mode with a negative index, n=-1, and the phase number modulus is less than the wave number in free space. In addition, the mode n=-1 contributes to the far-field radiation pattern. The FB mode n=-1 is matched with the target aperture distribution to determine the periodic parameters of the superlattice.

[0021] Preferably, the dielectric layer or superlattice will be located above the ground plane, wherein the dielectric layer is characterized by a dielectric constant and thickness, and the superlattice will consist of metal strips or grooves of a width and periodicity determined by the analytical closed-form solution of the reactance.

[0022] Preferably, beam scanning is achieved by adjusting the superlattice elements, and without the need for complex and lossy beamforming networks.

[0023] Therefore, the present application adopts the above-mentioned variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method, and adopts a simple structure of tunable material to tune the efficient structure platform, thereby paving the way for a new generation of high-efficiency special gratings.

[0024] The technical solutions of the present application will be further described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 A flowchart of the variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method of the present application;

[0026] Figure 2 A superlattice leaky-wave antenna schematic diagram of the variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method of the present application;

[0027] Figure 3 A variable capacitance diode schematic diagram of the variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method of the present application;

[0028] Figure 4 A radiation angle schematic diagram in the superlattice leaky-wave antenna of the variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method of the present application;

[0029] Figure 5 An equivalent impedance matching circuit schematic diagram of a superlattice leaky-wave antenna unit cell of the variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method of the present application. DETAILED DESCRIPTION

[0030] The technical solutions of the present application will be further described in detail below with reference to the accompanying drawings and examples.

[0031] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meanings understood by those with ordinary skills in the art to which the present application belongs.

[0032] The terms "first," "second," and similar words used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0033] Example 1

[0034] like Figure 1 As shown, the present invention provides a method for adjustable beam control of a varactor diode-based grating leaky antenna, comprising the following steps:

[0035] S1. Research and analysis of the supergrating beam conversion mechanism;

[0036] The mechanism of planar supergrating under anisotropic, uniform, and continuous periodic boundary conditions is studied. It can conveniently handle the geometry and material parameters of arbitrary unit structures using periodic boundaries, and greatly reduce the size of the supergrating. The supergrating can be accurately characterized based on the uniform equivalent surface impedance.

[0037] When the surface impedance is uniform, the anisotropic and tangential fields of the surface must satisfy anisotropic boundary conditions. Therefore, a practical solution is to use small metal components (approximately λ / 10) printed on the dielectric substrate to achieve anisotropic boundary conditions, thereby giving them a preferred orientation. For example, the components can have a shape divided by small slits. When the slits are neither parallel nor orthogonal to the radial direction, the boundary conditions become anisotropic.

[0038] The scalar electrical impedance density and magnetic admittance density constituting the supergrating are studied, and the performance of electrical impedance density and magnetic admittance density as functions of load impedance and operating frequency is examined.

[0039] Supergratings are modeled in two ways based on anisotropic continuous impedance: opaque supergratings or transparent supergratings.

[0040] Supergratings can be modeled in two different ways using anisotropic continuous impedance, which we refer to as opaque supergratings or transparent supergratings, respectively. In the first case, the supergrating is represented as a tensor opaque reactance (X_op), which relates the average tangential electric field (Et) and magnetic field (Ht) at the interface of the supergrating, as shown below.

[0041]

[0042] where the notation indicates the limit as z approaches 0 from above, z being perpendicular to the superlens, and assuming the existence of the time-harmonic relation exp(jωt), which is omitted. The opaque reactive admittance X_op is a function of frequency and surface wave wavevector Kt. On the other hand, an anisotropic transparent superlens can be defined using the transparent reactive admittance X, as follows:

[0043]

[0044] where J is the average current flowing in the transparent reactance, in this case, kt depends on the non-negligible opaque impedance, since it contains the electrical impedance of the shorted transmission line included in the network-forming system. Figure 3 A tunable meta-lens leaky-wave antenna using varactor diodes is shown. Input parameters include aperture field, frequency, substrate properties, and aperture size for setting initial values.

[0045] By constructing a specific grating pattern in the TE or transverse magnetic TM mode through the superlens, each wire constituting the superlens is represented by a scalar impedance density, or a scalar magnetic admittance density for a wire with a magnetic response;

[0046] S1.3, Study of the surface-to-propagating wave method conversion of physical quantities for super-magnetic fields; propose an alternative practical design of a converter based on a superlens, which achieves the engineering transmission of propagating plane waves by separating incident plane waves and surface waves of the same polarization in different half-spaces, which demonstrates the practical implementation of a converter based on a conventional printed circuit board, and confirms its high performance through full-wave three-dimensional simulation. In addition, the impedance matrix of the converter based on the superlens will be derived. Through this two-dimensional full-wave numerical simulation, the theoretical findings will be verified and a practically achievable topology of the superlens will be proposed,

[0047] S2, Transmission modes and optimization design according to the Floquet-Bloch theorem for superlenses;

[0048] Study all FB modes and eliminate undesirable FB modes by designing a tool for superlens parameters;

[0049] The FB expansion can be applied to the problem of a plane wavefront propagating on a periodic impedance superlens. This problem is posed for the case of a surface wave propagating on an impedance surface with a scalar impedance superlens. The fields and currents can be well approximated as those of a local plane wavefront on an infinite homogeneous medium with amplitude and period matching the local problem. In addition, by the same local plane approximation, the spectral GF function is evaluated at each local FB wavenumber, which provides an additional equation for the associated fields and currents. Thus, a local dispersion equation is established, and once this equation is solved, the local value of the surface wave complex wavenumber on the superlens is obtained.

[0050] The design tool for the superlens will give uniform periodic parameters (i.e. phase and amplitude) for the tensor impedance patch to match the radiating aperture field to the target aperture field. To achieve this goal, we will identify the FB modes that can be distinguished between the radiating or non-radiating modes. The radiating FB modes are the modes with negative index, typically n = -1, whose phase magnitude is less than the wavenumber of free space. In addition, the n = -1 mode has a dominant contribution to the far-field radiation pattern. Therefore, by matching the n = -1 FB mode to the target aperture distribution, the periodic parameters of the superlens can be determined. The phase of the superlens determines the phase of the radiating field. The depth of the superlens controls the amplitude of the aperture field and the amount of energy converted from the surface wave to the leaky wave. The polarization of the aperture field is controlled by the relative phase between the inputs of the tensor superlens.

[0051] By local matching between the surface wave interacting with the periodic superlens and the infinite homogeneous periodic structure with the same amplitude and period, the research will match the number of propagating FB modes with the number of different superlenses in the periodic structure;

[0052] The FB wave expansion is introduced for modeling and designing the superlens antenna fed by a microstrip line surface wave, which realizes a periodic impedance surface. The adiabatic expansion of the FB wave originates from the local matching between the problem of the microstrip line surface wave interacting with the periodic superlens and the problem of the plane wavefront on an infinite homogeneous periodic structure with the same amplitude and period. This model is the basis for the design tool of the superlens antenna with ideal radiation performance, and under the assumption that there is a single propagating exact solution in space, which is a non-uniform plane wave, the required local power balance can be accurately achieved by a system containing only one surface-bound mode and one propagating plane wave. The infinite region is lossless, and by operating as an ideal leaky-wave antenna, it only emits a plane wave in a given direction without storing any energy in higher-order FB modes. Theoretically, the conversion efficiency is expected to be ideal, and in numerical tests, it almost reaches 100%. As a reference solution for the periodic superlens impedance leaky-wave antenna, the radiation of the partially transparent wall is considered.

[0053] S3, analyzing and designing the superlens leaky-wave antenna;

[0054] The analysis of the synthesized EBGs' electric field and current in the leaky-wave antenna framework is performed to tailor the performance in terms of phase, beam shape and polarization;

[0055] An analytical approach will be presented to predict the beam pointing angle achieved by phase EBGs in such leaky-wave antennas. The primary goal is to extend the synthesis of multi-EBG-fed antennas to pattern shaping. The approach is based on a synthesis technique that relies on the direct inversion of the electric field integral equation (EFIE) after expanding the surface currents and patch impedances in terms of Fourier-Bessel basis functions (FBBFs). Proper phasing of the feeds allows continuous beam pointing within an angular range equal to the 3-dB beamwidth.

[0056] Design considerations of EBG leaky-wave antennas will be investigated, focusing on the characterization of the EBGs' impedance properties and the description of the required feeding system to ensure the correct excitation of the surface wave while controlling the total field leakage.

[0057] The far-field radiation patterns will be investigated through equivalent EBG leaky-wave antennas, which can be obtained by using a rigorous spectral Green's function approach for the fundamental sources in the E- and H-planes at the center frequency. In fact, for dielectric materials, the presence of this mode leads to the appearance of a side lobe in the direction close to the Brewster angle. This peak effect can also be observed for capacitive slot-grid-based EBGs, but at a slightly larger angle. For inductive strip-grid-based EBGs, the peak disappears, thus improving the directivity. Compared to dielectric solutions, as shown in Figure 5 EBG MG antennas are a versatile class of planar antennas that can achieve beam shaping and pattern control through periodic boundary conditions while keeping the antenna structure unchanged. This feature makes them suitable for dynamic EBGs. They can be applied to any unit cell structure, regardless of its complexity, and can take into account all the difficult-to-calculate scattered fields, achieving high directivity and reducing the beamwidth angle through radiating grating elements.

[0058] S4, Design and analysis of EBG leaky-wave antennas for electrically steered beam manipulation

[0059] An analytical model of the wide-angle EBG beam radiation field is established and studied in depth; a new periodic EBG for beam control in EBG leaky-wave antennas is configured, which controls the radiation phase by changing the inductance / capacitance (LC) elements, thereby controlling the pointing angle of the radiation beam. Several prototypes are designed and fabricated for operation at X-band frequencies. Each grating has an input impedance that can be adjusted by carefully adjusting the element spacing and geometry to achieve a wide range of controllable phases in the z direction. All gratings are connected to a feed port with an input impedance of 50 Ω. The far-field radiation pattern measurement results of the fabricated prototypes are in good agreement with the simulation results, and show a wide beam control range of nearly 120°.

[0060] The method of beam control is studied; the phase of the leaky-wave antenna is controlled to achieve electrical scanning;

[0061] The phase of the leaky-wave antenna is controlled to achieve electrical scanning, and a prototype of a fixed-frequency electrical scanning EBG leaky-wave antenna is proposed, which is based on the concept of EBG. By adding an adjustable substrate, continuous beam scanning at a fixed frequency can be achieved, thereby providing a wide range of scanning angles that can be controlled by applying a bias voltage, while maintaining a constant characteristic impedance for good matching. In addition, the antenna uses microstrip technology, and the low profile characteristics make the proposed antenna easier to manufacture and more suitable for integration into microwave or millimeter wave systems

[0062] The phase of the EBG is changed (-90°<θ<90°) to control the radiation direction.

[0063] In particular, by adjusting the EBG elements, beam scanning can be achieved without the need for complex and lossy beamforming networks, and instead of controlling the dielectric substrate material, the subwavelength size of the unit cell can be used to control the equivalent impedance (or equivalently the properties of the scattering elements), and different tuning methods and various technical solutions can be used to achieve beam scanning. Two possible methods of beam scanning: global control for one-dimensional or two-dimensional scanning, and here the design related to the implementation of tuning the EBG in the first method using varactor diodes is proposed.

[0064] Therefore, the present application adopts the above-mentioned variable capacitance diode-based element grating leaky-wave antenna adjustable beam control method, and uses a simple structure of tunable material to tune an efficient structure platform, which lays the foundation for a new generation of high-efficiency special gratings.

[0065] The above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them. Although the present application is described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still make modifications or equivalent replacements to the technical solutions of the present application, and these modifications or equivalent replacements should not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for beam steering of a meta-grating leaky-wave antenna based on varactor diodes, characterized in that, The method comprises the following steps: S1, researching and analyzing the supergrating beam conversion mechanism; Researching the planar supergrating mechanism under the anisotropic, uniform, and continuous periodic boundary conditions; conveniently processing the geometric shape and material parameters of an arbitrary unit structure by using the periodic boundary, and greatly reducing the size of the supergrating; the supergrating is accurately characterized according to the uniform equivalent surface impedance; Researching the scalar resistance and inductance density constituting the supergrating, and testing the performance of the resistance and inductance density as the function of the load impedance and the working frequency; the supergrating is divided into two modeling modes through the anisotropic continuous impedance, and the two modeling modes are the opaque supergrating or the transparent supergrating; In the first case, the superlattice is represented as a tensor opaque reactance X op which relates the average tangential electric field Et and magnetic field Ht at the upper interface of the superlattice as follows: ；（1） where the notation denotes the limit as z approaches 0 from above, z is perpendicular to the superlattice, and assuming a time-harmonic relationship exp(jωt), the opaque reactive antiz_op is a function of frequency and surface wave wavevector Kt; on the other hand, the anisotropic transparent superlattice uses a transparent reactive antiz_op defined as follows: X where the notation denotes the limit as z approaches 0 from above, z is perpendicular to the superlattice, and assuming a time-harmonic relationship exp(jωt), the opaque reactive antiz_op is a function of frequency and surface wave wavevector Kt; on the other hand, the anisotropic transparent superlattice uses a transparent reactive antiz_op defined as follows: ；（2） Wherein J is the average current flowing in the transparent reactance, and kt depends on the non-negligible opaque impedance; Researching the surface wave to propagation wave method conversion of each physical quantity of the supermagnetic field; realizing the engineering transmission of the propagation plane wave by separating the same polarization incident plane wave and surface wave in different half spaces; S2, transmitting mode and optimization design of the Floquet-Bloch theorem according to the supergrating; Researching the FB mode, and eliminating the bad FB mode by designing a tool for supergrating parameters; Researching the matching of the number of propagation FB modes and the number of different supergratings in the periodic structure through the local matching between the surface wave and the periodic supergrating and the infinite uniform periodic structure with the same amplitude and period; S3, analyzing and designing the supergrating leaky-wave antenna; Researching the analytical field and current of the synthesized supergrating in the framework of the leaky-wave antenna, so as to customize the performance of the phase, beam shape, and polarization; researching the design considerations of the supergrating leaky-wave antenna, focusing on characterizing the impedance characteristics of the supergrating, and describing the required feed system; S4, designing and analyzing the electrically tunable beam steering supergrating leaky-wave antenna; Establishing an analysis model of the wide-angle supergrating beam radiation field, and conducting in-depth research; controlling the pointing angle of the radiation beam by changing the inductance / capacitance LC element to control the radiation phase; designing and manufacturing a prototype for working at an X-band frequency; Researching the beam control method; Controlling the phase of the leaky-wave antenna to realize electric scanning; realizing continuous beam scanning at a fixed frequency by adding an adjustable substrate, so as to provide a wide range of scanning angles, which are controlled by applying a bias voltage, while maintaining a constant characteristic impedance, realizing good matching; Changing the phase of the supergrating to control the radiation direction.

2. The varactor-based meta-groove leaky-wave antenna adjustable beam control method according to claim 1, wherein, In step S1, a specific grating pattern is constructed by the supergrating in the TE or transverse magnetic TM mode, and each wire constituting the supergrating is represented by a scalar resistance density, or a scalar inductance density for a wire with a magnetic response.

3. The varactor-based meta-groove leaky-wave antenna adjustable beam control method according to claim 1, wherein, In step S2, the FB mode is a mode with a negative index, n=-1, and the phase number modulus is less than the wave number in free space; in addition, the n=-1 mode has a contribution to the far-field radiation pattern, and the n=-1 FB mode is matched with the target aperture distribution to determine the periodic parameters of the supergrating.

4. The varactor-based meta-groove leaky-wave antenna adjustable beam control method according to claim 1, wherein, The dielectric layer or superlattice will be located above the ground plane, where the dielectric layer is characterized by a dielectric constant and thickness, and the superlattice will consist of metal strips or metal slots determined by a width and periodicity due to the reactive analytic closed form.

5. The varactor-based meta-groove leaky-wave antenna adjustable beam control method according to claim 1, wherein, Beam scanning is achieved by adjusting the superlattice elements without the need for complex and lossy beamforming networks.

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