阅读说明：本技术 广义布鲁斯特效应的超表面设计方法 (super-surface design method for generalized Brewster effect ) 是由 祁嘉然 王常会 尹诗雄 于 2019-09-12 设计创作，主要内容包括：一种广义布鲁斯特效应的超表面设计方法,属于电磁场与微波技术领域。本发明针对现有经典布鲁斯特效应的应用受限于平行极化电磁波,对极化敏感的问题。它根据各向异性媒质分界面处布鲁斯特角的数学表达式,获得单元超表面需满足的基本条件；再根据所述基本条件构建在磁场激励下能产生预定量磁响应的所述单元超表面结构；将多个所述单元超表面结构依次组合在一起构成超表面层；将多个超表面层按预定方向有间距的依次排布,形成满足垂直与平行极化电磁波布鲁斯特效应的栅状超表面；所述栅状超表面的摆放方位为,垂直媒质分界面并且垂直电磁波入射面。本发明用于设计满足广义布鲁斯特效应的超表面。(a method for designing a super surface with a generalized Brewster effect belongs to the technical field of electromagnetic fields and microwaves. The invention aims at the problem that the application of the traditional classical Brewster effect is limited by parallel polarization electromagnetic waves and is sensitive to polarization. Obtaining basic conditions required to be met by the unit super-surface according to a mathematical expression of a Brewster angle at an anisotropic medium interface; constructing the unit super-surface structure which can generate a preset amount of magnetic response under the excitation of a magnetic field according to the basic conditions; sequentially combining a plurality of unit super-surface structures to form a super-surface layer; sequentially arranging a plurality of super surface layers at intervals in a preset direction to form a grid-shaped super surface meeting the Brewster effect of vertical and parallel polarized electromagnetic waves; the arrangement direction of the grid-shaped super surface is vertical to the medium interface and vertical to the electromagnetic wave incidence plane. The invention is used for designing the super surface meeting the generalized Brewster effect.)

1. A method for designing a super surface with a generalized Brewster effect is characterized by comprising the following steps:

Obtaining basic conditions required to be met by the unit super surface according to a mathematical expression of a Brewster angle at an anisotropic medium interface;

Constructing the unit super-surface structure which can generate a preset amount of magnetic response under the excitation of a magnetic field according to the basic conditions;

sequentially combining a plurality of unit super-surface structures to form a super-surface layer;

Sequentially arranging a plurality of super surface layers at intervals in a preset direction to form a grid-shaped super surface meeting the Brewster effect of vertical and parallel polarized electromagnetic waves;

The arrangement direction of the grid-shaped super surface is vertical to the medium interface and vertical to the electromagnetic wave incidence plane.

2. the method for designing a super surface with a generalized Brewster effect according to claim 1,

The mathematical expression of the Brewster angle at the interface of the anisotropic medium is as follows:

In the formula, theta B-TE is the Brewster angle of TE polarized electromagnetic waves, and theta B-TM is the Brewster angle of TM polarized electromagnetic waves;

is the dielectric constant of the first anisotropic medium, is the magnetic permeability of the first anisotropic medium,

the dielectric constant of the second anisotropic medium, the magnetic permeability of the second anisotropic medium,

Wherein epsilon iij, i ═ x, y, z; j is 1,2 represents the strength of electric polarization response along the i-axis direction generated in the anisotropic medium j under the excitation of the electric field along the i-axis direction; μ iij, i ═ x, y, z; j is 1, and 2 represents the strength of the magnetic polarization response generated in the anisotropic medium j along the i-axis direction under the excitation of the magnetic field along the i-axis direction; when the electromagnetic wave is incident from the first anisotropic medium to the second anisotropic medium according to the incidence of the electromagnetic wave from the free space to the grid-shaped super surface, the mathematical expression of the Brewster angle of the grid-shaped super surface is simplified as follows:

wherein:

the dielectric constant of the grid-shaped super surface and the magnetic permeability of the grid-shaped super surface are shown;

Epsilon ii, i-x, y, z represents the intensity of the electric polarization response generated in the grid-shaped super surface along the i-axis direction under the excitation of the electric field along the i-axis direction; μ ii, i ═ x, y, z represents the strength of the magnetic polarization response in the i-axis direction generated in the medium under excitation by a magnetic field in the i-axis direction;

The epsilon xx, the epsilon yy and the epsilon zz are not equal to 1, so that the Brewster effect of the parallel polarization electromagnetic wave is met;

let μ xx μ zz ≠ 1, satisfying the brewster effect of vertically polarized electromagnetic waves.

3. The method for designing a super surface with a generalized Brewster effect according to claim 2,

Constructing the unit super-surface structure includes:

the dielectric substrate F4B and two open metal rings, the open metal ring is set in the middle of the surface of the two sides of the F4B dielectric substrate, the opening of the open metal ring at one side is downward, the opening of the open metal ring at the other side is upward.

4. the method for designing a super surface with a generalized Brewster effect according to claim 3,

the dielectric constant of the F4B dielectric substrate is 2.2, the loss tangent is 0.001, the length and the width of the cell super surface are both 20mm, and the thickness is 0.8 mm.

5. the method for designing a super surface with a generalized Brewster effect according to claim 4,

The inner diameter of the opening metal ring is 3mm, the outer diameter of the opening metal ring is 9mm, and the opening width s is 3.5 mm.

6. The method for designing a super-surface with a generalized Brewster effect according to claim 5, wherein the Brewster angle of the grating-shaped super-surface to the electromagnetic wave is changed by changing the spacing between adjacent super-surface layers and the included angle between the super-surface layers and the horizontal plane.

7. the method for designing a broad brewster-effect super-surface according to claim 6, wherein the brewster angle range of the grating super-surface to electromagnetic waves comprises 20 ° to 80 °.

8. the method for designing a super surface with a generalized Brewster effect according to claim 5,

the spacing between adjacent super surface layers was 8 mm.

9. The method for designing a super surface with a generalized Brewster effect according to claim 8,

the super surface layer is vertical to the horizontal plane.

10. The method for designing a super surface with a generalized Brewster effect according to claim 9,

the brewster angle of the grid-shaped super surface for the vertically and parallelly polarized electromagnetic waves is 45 degrees at 10.3 GHz.

Technical Field

the invention relates to a method for designing a super surface with a generalized Brewster effect, and belongs to the technical field of electromagnetic fields and microwaves.

Background

since the Brewster effect has been observed and explained by both great guards Brewster (Sir David Brewster) and Malus (Malus), the classical Brewster effect has been widely used in the fields of optics, terahertz and even microwaves. Common applications are currently: polarizer, beam splitter prism, Brewster angle microscopy, measurement of medium optical characteristics, angle selection absorber, optical super transmission phenomenon and the like. However, these applications based on the classical brewster effect are often limited to parallel polarized (TM polarized, also called p polarized) electromagnetic waves. For example, in most typical laser resonators, the brewster window acts as a polarizer, and the resulting laser light is often only p-polarized (TM-polarized) light. This polarization limitation arises because for a vertically polarized (TE polarized, also called s polarized) electromagnetic wave, the brewster angle is only present when it is incident on the magnetic medium, but the magnetic response of most media in nature, especially in the optical band, is usually extremely weak.

Therefore, it is important to generalize the classical brewster effect and find a medium whose brewster angle is not limited by the polarization of incident waves.

Disclosure of Invention

Aiming at the problems that the application of the conventional classical Brewster effect is limited by parallel polarization electromagnetic waves and is sensitive to polarization, the invention provides a method for designing a super-surface with the generalized Brewster effect.

the invention discloses a method for designing a super-surface with a generalized Brewster effect, which comprises the following steps:

obtaining basic conditions required to be met by the unit super surface according to a mathematical expression of a Brewster angle at an anisotropic medium interface;

Constructing the unit super-surface structure which can generate a preset amount of magnetic response under the excitation of a magnetic field according to the basic conditions;

sequentially combining a plurality of unit super-surface structures to form a super-surface layer;

sequentially arranging a plurality of super surface layers at intervals in a preset direction to form a grid-shaped super surface meeting the Brewster effect of vertical and parallel polarized electromagnetic waves;

the arrangement direction of the grid-shaped super surface is vertical to the medium interface and vertical to the electromagnetic wave incidence plane.

according to the super-surface design method of the generalized Brewster effect of the invention,

The mathematical expression of the Brewster angle at the interface of the anisotropic medium is as follows:

In the formula, theta B-TE is the Brewster angle of TE polarized electromagnetic waves, and theta B-TM is the Brewster angle of TM polarized electromagnetic waves;

is the dielectric constant of the first anisotropic medium, is the magnetic permeability of the first anisotropic medium,

the dielectric constant of the second anisotropic medium, the magnetic permeability of the second anisotropic medium,

Wherein epsilon iij, i ═ x, y, z; j is 1,2 represents the strength of electric polarization response along the i-axis direction generated in the anisotropic medium j under the excitation of the electric field along the i-axis direction; μ iij, i ═ x, y, z; j is 1, and 2 represents the strength of the magnetic polarization response generated in the anisotropic medium j along the i-axis direction under the excitation of the magnetic field along the i-axis direction; when the electromagnetic wave is incident from the first anisotropic medium to the second anisotropic medium according to the incidence of the electromagnetic wave from the free space to the grid-shaped super surface, the mathematical expression of the Brewster angle of the grid-shaped super surface is simplified as follows:

wherein:

The dielectric constant of the grid-shaped super surface and the magnetic permeability of the grid-shaped super surface are shown;

Epsilon ii, i-x, y, z represents the intensity of the electric polarization response generated in the grid-shaped super surface along the i-axis direction under the excitation of the electric field along the i-axis direction; μ ii, i ═ x, y, z represents the strength of the magnetic polarization response in the i-axis direction generated in the medium under excitation by a magnetic field in the i-axis direction;

The epsilon xx, the epsilon yy and the epsilon zz are not equal to 1, so that the Brewster effect of the parallel polarization electromagnetic wave is met;

Let μ xx μ zz ≠ 1, satisfying the brewster effect of vertically polarized electromagnetic waves.

According to the method for designing the super surface with the generalized Brewster effect, the step of constructing the unit super surface structure comprises the following steps:

the dielectric substrate F4B and two open metal rings, the open metal ring is set in the middle of the surface of the two sides of the F4B dielectric substrate, the opening of the open metal ring at one side is downward, the opening of the open metal ring at the other side is upward.

According to the method for designing the super-surface of the generalized Brewster effect, the dielectric constant of the F4B dielectric substrate is 2.2, the loss tangent is 0.001, the length and the width of the super-surface of the unit are both 20mm, and the thickness of the super-surface of the unit is 0.8 mm.

according to the generalized Brewster effect super-surface design method, the inner diameter of the opening metal ring is 3mm, the outer diameter of the opening metal ring is 9mm, and the opening width s is 3.5 mm.

according to the method for designing the super-surface with the generalized Brewster effect, the distance between adjacent super-surface layers and the included angle between the super-surface layers and the horizontal plane are changed, so that the Brewster angle of the grid-shaped super-surface to electromagnetic waves is changed along with the change.

According to the method for designing the broad-brewster-effect super surface, the brewster angle range of the grating super surface to electromagnetic waves comprises 20-80 degrees.

According to the method for designing the super surface with the generalized Brewster effect, the distance between the adjacent super surface layers is 8 mm.

according to the method for designing the super surface with the generalized Brewster effect, the super surface layer is vertical to the horizontal plane.

According to the method for designing the broad-brewster-effect super-surface, the brewster angle of the grid-shaped super-surface for the vertically and parallelly polarized electromagnetic waves is 45 degrees at 10.3 GHz.

The invention has the beneficial effects that: the invention adopts a simplified anisotropic medium model analysis method to deduce a digital expression of the Brewster effect based on the model, design the super surface and obtain a grid-shaped super surface structure with electromagnetic response meeting the requirement, thereby realizing the generalized Brewster effect. The grid-shaped super surface obtained by the method realizes that any polarized electromagnetic wave has the same Brewster angle and realizes simple and adjustable Brewster angle for the first time.

simulation experiments prove that when the super-surface layer of the grid-shaped super-surface obtained by the method is vertical to the horizontal plane, the grid-shaped super-surface works in an X wave band and has a Brewster angle of 45 degrees for any polarization electromagnetic wave of 10.3 GHz; the simple adjustment and control of the Brewster angle can be realized by changing the strip pitch or the inclination angle of the super surface layer. The method solves the problem that the application of the classical Brewster effect is limited by parallel polarized electromagnetic waves, the Brewster angle of the obtained grating-shaped super surface is not limited by incident wave polarization, the function of an angle filter can be realized, and the polarization is insensitive, so that more efficient energy directional collection, such as directional interception of optical energy in the optical field, improvement of the signal-to-noise ratio of a receiver in directional wireless communication, information encryption by using a geometric angle and the like, can be realized.

Drawings

FIG. 1 is a schematic structural diagram of a grating-shaped super surface obtained by the method of the present invention, which is irradiated by natural light; in the figure, 1 represents an incident plane, and 2 represents a boundary surface of two mediums; d represents the thickness of the grid-shaped super surface, namely the width of the unit super surface; px represents the spacing between adjacent super surface layers;

FIG. 2 is a schematic structural view of a cell super-surface; the dashed line frame in the figure represents an opening metal ring correspondingly arranged on the super surface of the unit; in the figure, S represents the opening width of the opening metal ring; py represents the length of the cell super-surface;

FIG. 3 is a graph of input reflection coefficient versus frequency for a grating-like super-surface reflection amplitude simulation;

FIG. 4 is a graph of input reflection coefficient as a function of angle of incidence in a grating-like super-surface reflection amplitude simulation;

FIG. 5 is a graph of return loss of a grid-like metasurface as a function of frequency;

FIG. 6 is a graph of return loss of a grid-like metasurface as a function of angle of incidence;

FIG. 7 is a diagram showing an electric field distribution when TE-polarized electromagnetic waves are incident on an equivalent anisotropic medium;

FIG. 8 is a plot of the TE polarized electromagnetic wave incident on the grid-like metasurface in accordance with the present invention; may be used for comparison with fig. 7;

FIG. 9 is a diagram of an electric field distribution when a TM polarized electromagnetic wave is incident on an equivalent anisotropic medium;

FIG. 10 is an electric field profile of a TM polarized electromagnetic wave incident on a grid-like metasurface in accordance with the present invention; may be used for comparison with fig. 9;

FIG. 11 is a schematic diagram illustrating the control of the inclination angle Θ of the grid-shaped super surface to change the super surface layer;

FIG. 12 is a graph showing the Brewster's angle and corresponding frequency of the grating-shaped super-surface for TE-polarized electromagnetic waves when Px is changed;

FIG. 13 is a plot of changes in brewster angle and corresponding frequency of a grating-shaped super-surface versus TM polarized electromagnetic waves when Px is changed;

FIG. 14 is a graph showing the effect of a grating-like super surface on the Brewster angle at different frequency points of a TE polarized electromagnetic wave when the inclination angle Θ of the super surface layer is changed;

FIG. 15 is a graph showing the effect of a grating-like super surface on the Brewster angle at different frequency points of a TM polarized electromagnetic wave when the inclination angle theta of the super surface layer is changed.

Detailed Description

the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

it should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.

the invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.