CN-122026122-A - Planar Fresnel lens based on micro-step-dielectric constant gradual change and design method thereof

CN122026122ACN 122026122 ACN122026122 ACN 122026122ACN-122026122-A

Abstract

The invention discloses a plane Fresnel lens based on micro-step-dielectric constant gradient and a design method thereof, and belongs to the technical field of millimeter wave antennas and additive manufacturing. According to the method, the medium filling rate of the area is obviously improved by strategically and moderately reducing the height of the peripheral annular zone of the traditional multi-medium plane Fresnel lens according to the phase correction theory and the nonlinear coupling mechanism of the height-filling rate, and the method converts the annular zone with low filling rate, which is mechanically weak originally, into the stable annular zone with high filling rate on the premise of maintaining the original excellent electromagnetic performance, so that the integral mechanical reliability of the lens is obviously improved. The invention solves the problem of mechanical structure weakness caused by low filling rate of the peripheral ring belt in the same full-wave region in the traditional design process of the multi-medium plane Fresnel lens.

Inventors

GAO XINCHENG
ZHAO CHEN
Zhou Xuanrong
HE ENQI
LI YUE
ZHANG YANGYANG

Assignees

南京信息工程大学

Dates

Publication Date: 20260512
Application Date: 20260413

Claims (5)

1. Planar Fresnel lens based on micro-step-dielectric constant gradual change and provided with Lens of the order consists of A complete full wave region, each full wave region consisting of Each sub-zone is composed of medium endless belt with set height in each full-wave zone The heights of the medium endless belts of the sub-areas are First, the The equivalent dielectric constant of the medium ring belt of each sub-area is In the same full-wave region, the dielectric constants of the medium endless belts satisfy the following relationship: Characterized in that for the same full-wave region, the sub-region index Of the medium endless belt Nonlinear decrease along radial direction and corresponding equivalent dielectric constant Increasing with decreasing height.
2. A design method of a planar fresnel lens based on micro-step-dielectric constant gradient, for realizing the planar fresnel lens according to claim 1, comprising the steps of: s1, determining the working wavelength, focal length and order of a lens according to application requirements Calculating the outer radius of each subarea by utilizing a standard design formula of the Fresnel lens, and completing the geometric discretization of the lens plane; s2, calculating the theoretical filling rate of each medium zone of the lens under the 3D printing condition, and identifying the zone with the theoretical filling rate lower than a preset threshold as a mechanically weak zone; s3, calculating the height of the target endless belt according to a nonlinear height tuning formula for the identified mechanical weak endless belt And then the height of the target ring belt Calculating the equivalent dielectric constant of the target ring belt by using a phase correction formula, taking the equivalent dielectric constant as a target material parameter of the target ring belt, converting the equivalent dielectric constant into a filling rate required by 3D printing, and determining the structure of the lens; S4, verifying mechanical and electromagnetic properties of the designed lens according to the filling rate required by 3D printing, and confirming that the medium filling rate of the optimized target annular belt is larger than a preset threshold value and the antenna meets a preset radiation performance index.
3. The design method of the planar Fresnel lens based on micro-step-dielectric constant gradient according to claim 2, wherein in the step S2, the pre-evaluation is performed based on the traditional equal-height multi-medium theory, and all medium endless belts are set under the traditional equal-height multi-medium theory design and meet the equivalent dielectric constant required by phase correction; the medium endless belt with the theoretical filling rate lower than 30% is regarded as a mechanically weak endless belt, and is taken as a key reinforcement area.
4. The method for designing planar Fresnel lens based on micro-step-permittivity gradient as set forth in claim 2, wherein in step S3, the index of the sub-region is calculated according to a nonlinear height tuning formula in the same full-wave region Height of the medium endless belt The expression is as follows: , Wherein, the Representing the uniform medium zone height of a conventional multi-medium planar Fresnel lens for Is set to be full air filling for the annular belt of (2) Is set to be medium full filled.
5. The method for designing a planar fresnel lens based on micro-step-dielectric constant gradation according to claim 2, wherein in step S3, the phase correction formula is as follows: , wherein mod represents the remainder function; Is the operating wavelength of the light source, 。

Description

Planar Fresnel lens based on micro-step-dielectric constant gradual change and design method thereof Technical Field The invention relates to the technical field of millimeter wave antenna and additive manufacturing, in particular to a planar Fresnel lens based on micro-step-dielectric constant gradient and a design method thereof. Background The traditional planar Fresnel lens is mainly realized by a multi-medium method and a grooving method. The grooving method uses the same dielectric constant and achieves phase regulation by varying the groove depth (as shown in fig. 1). The grooving method generally adopts a solid medium structure, has high mechanical strength, but is easy to generate shadow shielding phenomenon due to larger groove depth, so that the antenna gain is reduced. The multi-medium method adopts a medium lens with uniform height, and realizes lens phase regulation through gradually changing dielectric constants (shown in figure 2). The lens has higher antenna gain due to no shadow shielding phenomenon, so that the lens is widely applied. In practical application, the natural dielectric constant of the material is difficult to realize, and the equivalent dielectric constant gradual change is often realized through modes such as punching, 3D printing and the like. The punching method is easy to introduce micro cracks when processing high-hardness media, and is extremely easy to cause structural collapse when realizing an outer ring belt with low filling rate requirement. With the development of additive manufacturing technology, 3D printing has become the mainstream technology, and by adjusting and controlling the mixing ratio of air and medium, the required equivalent dielectric constant can be flexibly realized. However, this freedom of manufacture also presents a new problem in that, according to the fresnel lens phase correction theory, the outer zones lying in the same full-wave region often need to have a fairly low equivalent dielectric constant. This constraint is particularly pronounced in higher order lens designs, which forces the filling rate of the outer rim annulus to be reduced to very low levels (e.g., the filling rate of the outermost rim annulus in the same full wave region of an eighth order lens often needs to be below 12%). The extremely low filling rate seriously weakens the mechanical performance of the lens, so that the peripheral girdle becomes a weak link of the structure in severe environments such as vibration, impact and the like, the structural collapse is extremely easy to cause in the 3D printing process, and the overall reliability of the lens is restricted. Disclosure of Invention The invention aims to provide a planar Fresnel lens based on micro-step-dielectric constant gradual change and a design method thereof, aiming at solving the problem that the mechanical strength of the same full-wave zone outer edge girdle is insufficient due to low filling rate in the 3D printing multi-medium planar Fresnel lens. The invention utilizes a nonlinear coupling mechanism of the height and the filling rate, and reduces the height of the outer edge ring belt in a strategic way to obviously improve the medium filling rate of the outer edge ring belt, thereby improving the structural weak link on the premise of maintaining excellent electromagnetic performance and realizing the improvement of the integral mechanical reliability of the lens. Technical proposal is that a plane Fresnel lens based on micro-step-dielectric constant gradual change is provided withLens of the order consists ofA complete full wave region, each full wave region consisting ofEach sub-zone is composed of medium endless belt with set height in each full-wave zoneThe heights of the medium endless belts of the sub-areas areFirst, theThe equivalent dielectric constant of the medium ring belt of each sub-area isIn the same full-wave region, the dielectric constants of the medium endless belts satisfy the following relationship: for the same full-wave region, sub-region index Of the medium endless beltNonlinear decrease along radial direction and corresponding equivalent dielectric constantIncreasing with decreasing height. A design method of a planar Fresnel lens based on micro-step-dielectric constant gradual change is used for realizing the planar Fresnel lens and comprises the following steps: s1, determining the working wavelength, focal length and order of a lens according to application requirements Calculating the outer radius of each subarea by utilizing a standard design formula of the Fresnel lens, and completing the geometric discretization of the lens plane; s2, calculating the theoretical filling rate of each medium zone of the lens under the 3D printing condition, and identifying the zone with the theoretical filling rate lower than a preset threshold as a mechanically weak zone; s3, calculating the height of the target endless belt according to a nonlinear height tuning formula for the identi