CN108963464A - Meander line metamaterial unit and the super surface of focusing designed using the unit - Google Patents
Meander line metamaterial unit and the super surface of focusing designed using the unit Download PDFInfo
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Abstract
The invention discloses a kind of meander line metamaterial unit and utilize the super surface of focusing of unit design, meander line metamaterial unit is arranged on dielectric-slab, reference wave uses coaxial feed, form slab guide, to form cylindrical wave in dielectric-slab, model is established by Hankel function in magnetic field of the incident wave radiation on super surface；Based on holographic thought, needs to obtain reference wave and virtual focal point propagates back to the field distribution of super the interfered formation of surface holographic plate, therefore, for virtual focal pointPropagate back to the field distribution on super surface；In order to generate hologram on super surface, so that back-propagating field will be generated from reference wave guide mode, can be realized by the COMPLEX AMPLITUDE on the super surface with meander line metamaterial unit that is defined by the formula.Real-time, tunable control may be implemented in the present invention, can change in real time its control methods according to the movement of focus position object, enables the movement of focus point real-time tracking object.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a zigzag line metamaterial unit and a focusing super surface designed by using the unit.
Background
The size of a resonance unit is basically changed to realize the adjustable state of the current electromagnetic super surface, but after one electromagnetic super surface unit is manufactured, only a specific function can be completed for a certain specific frequency band; the corresponding functions of the system cannot be changed in real time according to the change of the actual application scene, and the system is inconvenient and inflexible.
The initial stage of the design of the novel artificial electromagnetic metamaterial is generally based on an arrangement rule simulating most natural materials, namely a simple periodic arrangement sequence. With the extensive and intensive research, researchers turn the attention to important degrees of freedom such as macroscopic sequence, arrange and design gradient specific media with slowly-changing sequence, and the newly-mentioned new technologies such as optical stealth, optical illusion and the like appear. In recent years, the metamaterial is moved to market application from the aspect of theoretical concept, and people can really realize the powerful function of the metamaterial. However, today with increasing intelligent demand, the market puts higher demands on metamaterials, namely, the metamaterials have to have flexibility of operation and convenience in mobility while ensuring excellent electromagnetic regulation and control performance. Thus, the planarization of metamaterials — the super-surface is emerging. The super surface is a novel electromagnetic specific medium surface with a complex macroscopic order, and is a planar tissue consisting of a plurality of small scatterers or apertures, and the super surface can achieve the same function as a super material in a plurality of researches at present. However, the physical space occupied by the super-surface is much smaller than the meta-material space fraction, and due to its two-dimensional construction, low energy consumption can be achieved, from which it follows that the super-surface perfectly fulfills one's desire for flexibility and easy handling of the meta-material.
The electromagnetic super surface is a novel structure for regulating and controlling electromagnetic waves by controlling wave front phase, amplitude, polarization and the like, is a novel structure for regulating and controlling the electromagnetic waves by controlling the wave front phase, the amplitude and the polarization based on the generalized Snell's law, is a metamaterial structure with the characteristics of small occupied space, low loss, easy preparation and the like, can be widely applied to electromagnetic wave regulation and control industries such as antenna engineering, intelligent equipment manufacturing, medical treatment and the like, and has a wide development prospect.
The electromagnetic super-surface can theoretically realize all electromagnetic wave phase control, and it is important that an operator knows which phase distribution the electromagnetic wave control function realized by the super-surface corresponds to. In order to realize the electromagnetic wave focusing or regulation of a desired point, researchers need to do a large amount of mathematical calculations in the front section and design a feedback circuit to realize the electromagnetic wave focusing or regulation, which often makes the electromagnetic wave regulation of the super surface complicated. Then does the super-surface have only this control method? The problem is solved in the holographic imaging idea, and the super-surface controllability is realized according to the holographic imaging wavefront recording and wavefront reproduction idea.
The electromagnetic super-surface is developed to the present, although amplitude and phase regulation of various conditions can be realized, one super-surface designed by the existing method can only correspond to one regulation mode, and if the regulation mode is changed, the electromagnetic super-surface needs to be redesigned.
Disclosure of Invention
The invention provides a zigzag line metamaterial unit and a focusing super surface designed by using the unit, aiming at solving the technical problem that the existing electromagnetic super surface cannot be regulated and controlled in real time.
The object of the invention is achieved in the following way:
the zigzag line metamaterial unit comprises a first vertical line segment, a second vertical line segment, a third vertical line segment, a first horizontal line segment and a second horizontal line segment, wherein the first vertical line segment, the first horizontal line segment, the second vertical line segment, the second horizontal line segment and the third vertical line segment are sequentially connected, a first diode is loaded on the first vertical line segment, a second diode is loaded on the second horizontal line segment, the second vertical line segment and the third vertical line segment are communicated through a third diode, and when the first diode and the second diode are conducted, the third diode is cut off; when the third diode is conducted, the first diode and the second diode are cut off; the first vertical line segment, the second vertical line segment and the third vertical line segment form the same equivalent resistance, and the first horizontal line segment and the second horizontal line segment form the same equivalent resistance; the first vertical line segment, the second vertical line segment, the third vertical line segment, the first horizontal line segment and the second horizontal line segment are all made of conductive materials.
The first vertical line segment, the second vertical line segment and the third vertical line segment are equal in length and are L; the widths of the first vertical line segment, the second vertical line segment, the third vertical line segment, the first horizontal line segment and the second horizontal line segment are equal and are tau, and the lengths of the first horizontal line segment and the second horizontal line segment are equal.
The lengths of the first horizontal line segment and the second horizontal line segment are equal and are both 4 tau.
The L is 450 mu m, tau is 25 mu m, and the resonant frequency of the zigzag metamaterial unit is 92.5 GHz.
The focusing super-surface designed by the zigzag metamaterial unit is arranged on a dielectric slab, a reference wave adopts coaxial feed to form a planar waveguide, so that a cylindrical wave is formed in the dielectric slab, and a magnetic field radiating incident waves on the super-surface is modeled by a Hankel function as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,λ represents the wavelength of the electromagnetic wave;εrrepresents the dielectric constant of the dielectric substrate; phi denotes the angle of the major axis of the meander at the surface, which would couple with the x-axis component of the reference wave if the major axis of the meander were along the x-axis, so multiplying by cos phi, which is 0 deg., and if along the y-axis, multiplying by sin phi, which is 90 deg., in the range of 0-90 deg., representing the angle of inclination of the major axis of the meander;is the location of a discrete point on the super surface;
based on the idea of holography, field distribution formed by interference of the reference wave and the virtual focusing point which reversely propagate to the super-surface holographic plate needs to be obtained, so that the virtual focusing point is subjected toThe field distribution, which propagates back to the super-surface, is defined as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,
to produce a hologram on a meta-surface such that the backward propagating field of equation (2) will be generated from the reference guided mode of equation (1), this can be achieved by a complex amplitude distribution on the meta-surface with meander line meta-material elements defined by:
wherein,representing the complex conjugate of the guiding magnetic field.
The Hankel function is derived from a Bessel function, and the specific formula is as follows:
the zigzag line metamaterial units are arranged on the dielectric plate in a matrix form.
The meander line metamaterial unit is 60 rows, each row is 60, and the size of the focusing metamaterial surface is 27mm multiplied by 18mm multiplied by 10 mu m.
The dielectric plate is a silicon substrate.
The core and innovation of the invention is the dynamically adjustable design of the meander line metamaterial unit. The idea of dynamic regulation and control of metamaterial units has been long, and in recent years, with the development of cognitive radio and computer software technologies, a dynamic reconfigurable technology (RRT) has become a new research hotspot of research teams at home and abroad. The advent of this technology has made the long-standing boundaries between hardware and software somewhat ambiguous, and through software processing, hardware systems are made more software. The nature of dynamic reconfigurability means that no large changes are made to the original system hardware and more functions are implemented. The resonance characteristics of the metamaterial unit are changed by loading microwave electronic devices or using a mechanical method, namely, under the same physical structure, the frequency characteristics, the resonance characteristics and the polarization characteristics of the metamaterial unit can be flexibly adjusted according to external requirements, so that the metamaterial unit has diversity and dynamic controllability. The dynamic adjustable technology has great influence on the metamaterial electromagnetic wave adjustment and control, so that the electromagnetic wave adjustment and control technology develops towards the direction of high-efficiency adjustment and control. The metamaterial has excellent performance in the aspect of regulating and controlling electromagnetic waves. In order to realize the complex and careful control of the electromagnetic wave propagation, the dielectric constant and the magnetic permeability of the metamaterial unit are required to be regularly arranged and changed on the dielectric plate theoretically, namely, certain special values are selected. Theoretically, each periodic unit of the metamaterial medium can be artificially controlled in resonant frequency.
The electromagnetic properties of the metamaterial unit are generally determined by the structural characteristics of the metamaterial unit, and the metamaterial unit with any structure can be an equivalent circuit consisting of a capacitor, an inductor and a resistor according to the theory of transmission lines. In the model, the equivalent capacitance and the inductance determine the resonant frequency of the metamaterial unit, so that the resonant frequency can be adjusted in real time by changing the inductance and the capacitance. Based on the above ideas, researchers have proposed various effective methods to realize real-time dynamic regulation and control of metamaterial units, and the mainstream regulation methods include real-time regulation and control technologies such as structural regulation (mechanical regulation), matrix regulation (controllable material regulation), loading lumped elements (switch regulation) and the like.
Structural adjustment, i.e., mechanical adjustment, is generally implemented by using an additional mechanical structure, such as a micro-electromechanical system. Generally speaking, the mechanically adjustable controllable metamaterial element is relatively easy to realize structurally, but the structure needs a precise and complex control system, and the situation results in a series of problems that the additional device is too large in size, the device cannot be moved frequently, the response time of the device is long when the device is adjusted and controlled, and the like, so that the method is not an ideal method for realizing the dynamically controllable metamaterial device. Based on the above drawbacks, mechanical regulation is not suitable for dynamic regulation of metamaterial devices in this paper.
And (3) adjusting the matrix, wherein theoretical research indicates that the electromagnetic parameters and the resonant frequency of the metamaterial can be adjusted by changing the dielectric constant, the magnetic permeability and the thickness of the metamaterial dielectric layer. If the dielectric layer of the metamaterial is set as a controllable dielectric material, the dielectric constant of the dielectric layer can be changed by regulating and controlling an external excitation signal, so that the dynamic controllable tuning of the resonant frequency is realized. The materials mainly comprise two categories of magnetic field response media and electric field response media. Theoretical research indicates that the electromagnetic parameters and the resonant frequency of the material can be adjusted by changing the dielectric constant and the thickness of the metamaterial dielectric layer. The materials mainly include two main types, namely a magnetic field response medium and an electric field response medium. The substrate-adjusting type adjustable metamaterial unit based on the dynamic controllable dielectric material can realize continuous and uniform adjustment and control of the electrical and magnetic characteristics of the metamaterial, and the adjusting mechanism is simple and easy, so that the substrate-adjusting type adjustable metamaterial unit is a promising real-time dynamic adjustable metamaterial unit design. However, the dynamic controllable metamaterial based on the material characteristics is limited by the properties of the material, the range of the electromagnetic parameter variation of the natural material is limited, the frequency adjustment range is small, a small amount of time is required for the dielectric material to respond to a certain response after receiving the excitation signal, and the response time of the dynamic controllable metamaterial is too long. That is, the substrate-regulated dynamically controllable metamaterial needs to be further developed and perfected, and the time delay is too long, so that the dynamic regulation of the zigzag metamaterial element in the paper is not applicable.
And (3) loading and adjusting, namely inserting a regulating switch into an equivalent circuit of the metamaterial, and controlling the on-off of the regulating switch to realize the real-time control of the resonant frequency, the magnetic conductivity and the dielectric constant. The diode is the most common regulating device, and is loaded into the metamaterial unit structure, and the equivalent capacitance value of the diode is continuously changed by regulating the bias voltage of each metamaterial unit, so that the continuously adjustable metamaterial medium is obtained. This is the controllable principle of loading the controllable metamaterial elements.
In summary, the mechanical adjustment mode and the matrix adjustment mode can theoretically complete the dynamic controllable design of the zigzag metamaterial, but the loading adjustment mode is the key point of the design in consideration of the operability in practical situations, so that the loading adjustment type controllable metamaterial is the breakthrough of the controllable metamaterial design.
Compared with the prior art, the invention provides a novel electromagnetic super-surface and a control method thereof. A brand-new electromagnetic super-surface dynamic adjustable and controllable method is provided based on the holographic idea. The method realizes dynamic regulation and control of the super-surface unit by loading a plurality of PIN diodes on the zigzag metamaterial resonance unit, so that the adjustable unit modules can be regularly arranged to form an adjustable holographic interference plate. The layout of the zigzag metamaterial units and the phase abrupt change state of the zigzag metamaterial units are determined by the holographic design principle, namely, the arrangement layout and the resonance state of the metamaterial units are determined by the phase distribution formed by the interference of the reference wave radiation field and the radiation field reversely propagated by the virtual focus.
The invention can realize real-time regulation and control, and can change the regulation and control mode of the object according to the movement of the object at the position of the focusing point, so that the focusing point can track the movement of the object in real time.
Drawings
Fig. 1 is a result of the different lengths of L such that the resonant cells correspond in amplitude and phase at that frequency.
FIG. 2 is a diagram showing the effect of a dynamically controllable meander-line type metamaterial element.
Fig. 3 is a PIN diode bias characteristic.
FIG. 4 is a forward bias metamaterial unit equivalent model.
FIG. 5 is a reverse bias metamaterial unit equivalent model.
FIG. 6 is a schematic view of a focusing super-surface configuration.
Fig. 7 is a phase distribution of the reference electromagnetic wave propagating to the super surface.
FIG. 8 is a phase distribution of the focal spot propagating back to the super-surface.
FIG. 9 is a phase distribution of an interference pattern of a reference wave counter-propagating to a focal point.
FIG. 10 is a graph of a meander line type metamaterial unit bias.
Fig. 11 is a focusing effect diagram.
Detailed Description
The zigzag line metamaterial unit comprises a first vertical line segment 1, a second vertical line segment 2, a third vertical line segment 3, a first horizontal line segment 4 and a second horizontal line segment 5, wherein the first vertical line segment 1, the first horizontal line segment 4, the second vertical line segment 2, the second horizontal line segment 5 and the third vertical line segment 3 are sequentially connected, a first diode 6 is loaded on the first vertical line segment 1, a second diode 7 is loaded on the second horizontal line segment 5, the second vertical line segment 2 and the third vertical line segment 3 are communicated through a third diode 8, and when the first diode 6 and the second diode 7 are conducted, the third diode 8 is cut off; when the third diode 8 is turned on, the first diode 6 and the second diode 7 are turned off; the equivalent resistances formed by the first vertical line segment 1, the second vertical line segment 2 and the third vertical line segment 3 are the same, and the equivalent resistances formed by the first horizontal line segment 4 and the second horizontal line segment 5 are the same; the first vertical line segment 1, the second vertical line segment 2, the third vertical line segment 3, the first horizontal line segment 4 and the second horizontal line segment 5 are all made of conductive materials.
The first vertical line segment 1, the second vertical line segment 2 and the third vertical line segment 3 are equal in length and are L; the first vertical line segment 1, the second vertical line segment 2, the third vertical line segment 3, the first horizontal line segment 4 and the second horizontal line segment 5 are equal in width and are tau, and the first horizontal line segment 4 and the second horizontal line segment 5 are equal in length.
The different lengths of L are such that the amplitude and phase response of the resonant cell at that frequency is as shown in figure 1.
As shown in fig. 2(1), each meander-line type metamaterial element includes 3 PIN diodes arranged in a certain rule, and for each PIN diode, a circuit equivalent model of the PIN diode is assumed as shown in fig. 3. For a single PIN diode, the PIN diode is modeled as an RL circuit with a negligible forward resistance and an inductor in series, as shown in fig. 3. When reverse biased, the PIN diode can be modeled as an LC circuit, exhibiting high reverse resistance (i.e., effectively an open circuit).
As shown in fig. 2(1), when the first diode 6 and the second diode 7 are forward biased and the third diode 8 is reverse biased, the first diode 6 and the second diode 7 are turned on and the third diode 8 is turned off, so that the whole coupling unit is fig. 2(2), and the length is L. When the first diode 6 and the second diode 7 are reverse-biased and the third diode 8 is forward-biased, the first diode 6 and the second diode 7 are turned off and the third diode 8 is turned on, so that the whole coupling unit is shown in fig. 2(3), and the length is L/2 at this time.
By varying the length of L, one can achieve varying amplitude and phase relationships of the resonant cells to signal changes.
The first horizontal line segment 4 and the second horizontal line segment 5 are equal in length and both are 4 τ.
The resonant frequency of the meander line metamaterial unit is determined by a length parameter L, wherein L is 450 μm, τ is 25 μm, and the resonant frequency of the meander line metamaterial unit is 92.5 GHz.
The meander line metamaterial unit dynamically regulates and controls the length parameter L of the meander line metamaterial unit through a loading diode, flexibly realizes the continuous change of the phase on the super surface, utilizes the forward current conduction and reverse cut-off characteristics of the diode to dynamically regulate and control the microwave, and designs the dynamically controllable meander line metamaterial element shown in figure 2.
The on-off control of the PIN diode controls the size of the length parameter L of the zigzag metamaterial to indirectly control the resonant frequency, and further controls the coupling response of the element to the reference wave. Each metamaterial unit is loaded with 3 PIN diodes.
In forward bias, as shown in fig. 4, the first diode 6 and the second diode 7 are turned on, and the third diode 8 is turned off, and at this time, the meander line super unit L is 450 μm, and a 45 ° phase jump in the 92.5GHz band can be realized.
When the reverse bias is performed, as shown in fig. 5, the first diode 6 and the second diode 7 are turned off, the third diode 8 is turned on, and the zigzag line superunit L participating in resonance is 350 μm at this time, so that 90-degree phase jump in a 92.5GHz band can be realized. That is, the dynamically adjustable meander-line type metamaterial element can realize a phase jump of 0 to 180 °.
Before designing the hologram, the reference wave needs to be determined.
The focusing super-surface designed by the meander line metamaterial unit is arranged on the dielectric slab, as shown in fig. 6, the reference wave adopts coaxial feed to form a planar waveguide, so that a cylindrical wave is formed in the dielectric slab, and a magnetic field of incident wave radiation on the super-surface is modeled by a Hankel function as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,λ represents the wavelength of the electromagnetic wave;εrrepresents the dielectric constant of the dielectric substrate; phi denotes the angle of the major axis of the meander line on the surface, ifThe major axis of the meander is along the x-axis, the meander will couple with the x-axis component of the reference wave, so multiplying by cos φ, which is 0, if along the y-axis, by sin φ, φ being 90, in the range of 0-90 degrees, representing the skew angle of the major axis of the meander;is the location of a discrete point on the super surface;
after the reference wave guiding mode is defined, based on the holographic idea, the field distribution formed by the interference of the reference wave and the virtual focusing point which reversely propagate to the super-surface holographic plate needs to be obtained, therefore, the virtual focusing point is used for the virtual focusing pointThe field distribution, which propagates back to the super-surface, is defined as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,
to produce a hologram on a meta-surface such that the backward propagating field of equation (2) will be generated from the reference guided mode of equation (1), this can be achieved by a complex amplitude distribution on the meta-surface with meander line meta-material elements defined by:
wherein,representing the complex conjugate of the guiding magnetic field.
The phase distribution represented by the formula (3) is formed by interference of a reference wave and a virtual focus point counter-propagating field, and according to the principle of holography, the subsequent work only needs to construct the phase distribution represented by the formula (3) to complete focusing on a desired focus point. Therefore, this stage dominates the formation of the late focus point, so the phase distribution implied by the reconstruction equation (3) is of crucial importance.
It should be noted that the implementation of a super-surface hologram requires a DC bias circuit to drive the PIN diode. From the current relatively efficient solution, one approach is to etch sub-wavelength wide lines (narrow enough to prevent reference wave distortion) on the dielectric plate to accommodate the bias circuit. Alternatively, a thin dielectric laminate may be added to the metal vias of the diode for PIN-biased design. The biasing of the diodes may also be achieved using Arduino to drive a set of shift registers, or the switching speed may be achieved using a Field Programmable Gate Array (FPGA).
The Hankel function is derived from a Bessel function, and the specific formula is as follows:
the zigzag line metamaterial units are arranged on the dielectric slab in a matrix form, the matrix is M rows and N columns, and M and N are positive integers.
The number of the zigzag metamaterial units is 60 × 60, namely M ═ N ═ 60, and the size of the focusing metamaterial surface is 27mm × 18mm × 10 μ M.
The dielectric plate is a silicon substrate.
Simulation test:
the frequency selection for the simulation was 20G,is 0, i.e. the long axis coincides with the x-direction.
The formula for the simulation is as follows:
fun ═ bessel (0,1, pr); % calculation to obtain Hankel function value
This program simulates the hankel function formula listed above.
Firstly, a super-surface xy plane coordinate system x [ -0.2: step:0.2], y [ -0.2: step:0.2] is set, and a sampling interval step [ -0.01 ] is taken.
We model the reference electromagnetic wave as a Hankel function, then the propagation of the reference electromagnetic wave to the hyper-surface phase distribution is shown in fig. 6.
In order to illustrate the high-efficiency electromagnetic wave regulation capability of the reconfigurable holographic super surface, four spatial points are arbitrarily selected on a focus plane 0.5m away from the super surface: f1 (x-0.1 m, y-0.1 m, z-0.5 m), F2 (x-0.1 m, y-0.1 m, z-0.5 m), F3 (x-0.1 m, y-0.1 m, z-0.5 m) and F2 (x-0.1 m, y-0.1 m, z-0.5 m). The phase distributions represented by the four points propagating back to the super-surface are different, and therefore the phase distribution of the focal point propagating back to the super-surface should be the sum of the four virtual focal point phase distributions. The phase distribution of the focal point back-propagating to the super-surface is shown in fig. 7 by MATLAB simulation.
Therefore, the generation and phase distribution simulation of the reference electromagnetic wave and the virtual focus point counter-propagating electromagnetic wave is completed. Based on the holographic idea, we need to record the interference pattern of the reference wave and the backward propagating electromagnetic wave of the focusing point, so the phase distribution of the interference pattern of the reference wave and the backward propagating electromagnetic wave of the focusing point obtained through the MATLAB calculation is shown in fig. 8.
In the simulation of the electromagnetic super-surface regulation and control technology, the phase distribution of the interferogram is simulated and approximated, so that the super-unit arrangement of the super-surface is completed, and then the original reference wave is used as an incident wave to irradiate the super-surface holographic plate, so that the regulation and control purpose of the electromagnetic wave is realized. The interference phase distribution was calculated by MATLAB using equation (3). One small square represents a phase feature corresponding to the macroscopic super-surface, and one small square represents a zigzag metamaterial unit, wherein the gray small square represents the forward bias of the zigzag metamaterial unit, and the black small square represents the reverse bias of the zigzag metamaterial unit, as shown in fig. 9, as described above, the bias state of the PIN diode on the zigzag metamaterial unit controls the polarization characteristic of the metamaterial unit, thereby forming the super-surface with phase gradient change.
And finishing the preparation of the super-surface holographic plate. Next, we illuminate the super-surface hologram plate with the original reference wave acting as the incident electromagnetic wave in order to achieve the four-focus focusing, as shown in fig. 10, the super-surface perfectly achieves the desired four-focus focusing.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the overall concept of the present invention, and these should also be considered as the protection scope of the present invention.
Claims (9)
1. Zigzag line metamaterial unit, its characterized in that: the LED display panel comprises a first vertical line segment (1), a second vertical line segment (2), a third vertical line segment (3), a first horizontal line segment (4) and a second horizontal line segment (5), wherein the first vertical line segment (1), the first horizontal line segment (4), the second vertical line segment (2), the second horizontal line segment (5) and the third vertical line segment (3) are sequentially connected, a first diode (6) is loaded on the first vertical line segment (1), a second diode (7) is loaded on the second horizontal line segment (5), the second vertical line segment (2) and the third vertical line segment (3) are communicated through a third diode (8), and when the first diode (6) and the second diode (7) are communicated, the third diode (8) is cut off; when the third diode (8) is conducted, the first diode (6) and the second diode (7) are cut off; the equivalent resistances formed by the first vertical line segment (1), the second vertical line segment (2) and the third vertical line segment (3) are the same, and the equivalent resistances formed by the first horizontal line segment (4) and the second horizontal line segment (5) are the same; the first vertical line segment (1), the second vertical line segment (2), the third vertical line segment (3), the first horizontal line segment (4) and the second horizontal line segment (5) are all made of conductive materials.
2. The meander line metamaterial unit according to claim 1, wherein: the first vertical line segment (1), the second vertical line segment (2) and the third vertical line segment (3) are equal in length and are L; the widths of the first vertical line segment (1), the second vertical line segment (2), the third vertical line segment (3), the first horizontal line segment (4) and the second horizontal line segment (5) are equal and are tau, and the lengths of the first horizontal line segment (4) and the second horizontal line segment (5) are equal.
3. The meander line metamaterial unit according to claim 2, wherein: the lengths of the first horizontal line segment (4) and the second horizontal line segment (5) are equal and are both 4 tau.
4. The meander line metamaterial unit according to claim 2, wherein: the L is 450 mu m, tau is 25 mu m, and the resonant frequency of the zigzag metamaterial unit is 92.5 GHz.
5. A focusing super-surface designed using the meander line metamaterial unit as described in any one of claims 1-4, wherein: a plurality of meander line metamaterial units are arranged on a dielectric slab, a reference wave adopts coaxial feed to form a planar waveguide, so that cylindrical waves are formed in the dielectric slab, and a magnetic field radiating incident waves on a super surface is modeled by a Hankel function as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,λ represents the wavelength of the electromagnetic wave;εrrepresents the dielectric constant of the dielectric substrate; phi denotes the angle of the major axis of the meander at the surface, which would couple with the x-axis component of the reference wave if the major axis of the meander were along the x-axis, so multiplying by cos phi, which is 0 deg., and if along the y-axis, multiplying by sin phi, which is 90 deg., in the range of 0-90 deg., representing the angle of inclination of the major axis of the meander;is the location of a discrete point on the super surface;
based on the idea of holography, field distribution formed by interference of the reference wave and the virtual focusing point which reversely propagate to the super-surface holographic plate needs to be obtained, so that the virtual focusing point is subjected toThe field distribution, which propagates back to the super-surface, is defined as follows:
where k represents the wave number of electromagnetic wave propagation in vacuum,
to produce a hologram on a meta-surface such that the backward propagating field of equation (2) will be generated from the reference guided mode of equation (1), this can be achieved by a complex amplitude distribution on the meta-surface with meander line meta-material elements defined by:
wherein,representing the complex conjugate of the guiding magnetic field.
6. The focusing super-surface of claim 5, wherein: the Hankel function is derived from a Bessel function, and the specific formula is as follows:
7. the focusing super-surface of claim 5, wherein: the zigzag line metamaterial units are arranged on the dielectric plate in a matrix form.
8. The focusing super-surface of claim 7, wherein: the meander line metamaterial unit is 60 rows, each row is 60, and the size of the focusing metamaterial surface is 27mm multiplied by 18mm multiplied by 10 mu m.
9. The focusing super-surface of claim 5, wherein: the dielectric plate is a silicon substrate.
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