Antenna reflectors based on stretchable perforated thin films

Abstract

Systems and methods for parabolic antennas are disclosed. A reflector can include a film with a pattern. The pattern can include a repeating array of unit cells.

Description

[0001] ANTENNA REFLECTORS BASED ON STRETCHABLE PERFORATED THIN

[0002] FILMS

[0003] CROSS-REFERENCE TO RELATED APPLICATION

[0004] This application claims priority to U.S. Provisional Patent Application Serial No. 63 / 669,508, filed July 10, 2024, which is hereby incorporated by reference in its entirety.

[0005] GRANT INFORMATION

[0006] This invention was made with government support under HR001122C0054 by the Defense Advanced Research Projects Agency. The government has certain rights in the invention.

[0007] BACKGROUND

[0008] For parabolic antennas, a larger diameter can reduce the diffraction-limited divergence of the radio wave beam, which in turn enables greater pointing precision, lower power use, or increased transmission distance.

[0009] Large antennas, e.g., with diameters of approximately 100 m, can be highly beneficial in space, but launching such massive payloads can present significant technical and economic hurdles due to constraints like limited rocket fairing sizes and high launch costs. Robotic assembly in space is a potential solution but requires designs with minimal mass. Lowering the mass of the structural trusses can also require reflectors with lower pretension than the typical approximately 5 N / m used in metal fabric reflectors. Such high pretension can be required in metal fabric reflectors to ensure good electrical contact between metal threads and achieve microwave reflectance of over 90%.

[0010] Accordingly, there exists a need for antenna reflectors, which can address the challenges of creating large, lightweight, and cost-effective antennas. SUMMARY

[0011] Systems and methods for parabolic antennas are disclosed herein.

[0012] In certain embodiments, an example reflector can include a film with a pattern. The pattern can include a repeating array of unit cells.

[0013] In certain embodiments, each of the repeating arrays can include an axial cut and a diagonal cut. A plurality of the axial cut can be located orthogonally to each other, forming a rotating square, and a plurality of the diagonal cut can intersect at the center of the rotating square, creating triangular sections within each unit cell.

[0014] In certain embodiments, the film can be an aluminized film. In non-limiting embodiments, the repeating array can be a repeating two-dimensional array.

[0015] In certain embodiments, the film can be configured to be stretchable. In nonlimiting embodiments, the diagonal cut can be configured to increase a stretchiness of the film and allow the film to stretch independently in two in-plane directions. In non-limiting embodiments, the rotating square pattern can be configured to stretch in one in-plane direction causing an elongation in a perpendicular direction.

[0016] In certain embodiments, a mechanical property of the reflector can be configured to be adjustable. In non-limiting embodiments, the mechanical property can include Poisson’s ratio, tensile modulus, stress distribution, stiffness, reflectance, or combinations thereof. In non-limiting embodiments, an adjustable range of the Poisson’s ratio can be from about -1 to about 0.

[0017] In certain embodiments, the reflector can be configured to be coupled with an antenna.

[0018] In certain embodiments, the pattern can be non-periodic.

[0019] The disclosed subject matter provides a method using a reflector. An example method can include providing the reflector with a pattern. In certain embodiments, the pattern can include a repeating array of unit cells. Each of the repeating arrays can include an axial cut and a diagonal cut. A plurality of the axial cut can be located orthogonally to each other, forming a rotating square. A plurality of the diagonal cut can intersect at the center of the rotating square, creating triangular sections within each unit cell.

[0020] In certain embodiments, the method can further include adjusting a mechanical property of the reflector. In non-limiting embodiments, the mechanical property can be adjusted by modifying a geometric parameter of the reflector. In non-limiting embodiments, the mechanical property can include Poisson’s ratio, tensile modulus, stress distribution, stiffness, or combinations thereof. In non-limiting embodiments, the adjustable range of the Poisson’s ratio can be from about -1 to about 0. In non-limiting embodiments, the geometric parameter can include the length of the axial cut, the spacing between two axial cuts, the spacing between diagonal and axial cuts, the width of the axial or diagonal cut, or combinations thereof.

[0021] In certain embodiments, the reflector can be an aluminized film. In non-limiting embodiments, the diagonal cut can be configured to increase a stretchiness of the film and allow the film to stretch independently in two in-plane directions. In non-limiting embodiments, the rotating square pattern can be configured to stretch in one in-plane direction causing an elongation in a perpendicular direction.

[0022] In certain embodiments, the method can further include perforating the pattern on the reflector.

[0023] The accompanying drawings, which are incorporated and constitute part of this disclosure, illustrate certain embodiments and serve to explain the principles of the disclosed subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 illustrates a kirigami pattern disclosed in accordance with the disclosed subject matter.

[0025] FIG. 2 illustrates the characteristics of an example antenna in accordance with the disclosed subject matter.

[0026] FIG. 3 illustrates the characteristics of an example antenna in accordance with the disclosed subject matter.

[0027] FIG. 4 illustrates the characteristics of an example antenna in accordance with the disclosed subject matter.

[0028] FIG. 5 illustrates the characteristics of an example antenna in accordance with the disclosed subject matter.

[0029] FIG. 6 illustrates an example eigenmode of a periodic kirigami structure in accordance with the disclosed subject matter.

[0030] FIG. 7 illustrates the characteristics of an example antenna in accordance with the disclosed subject matter.

[0031] FIG. 8 illustrates the effects of geometric parameters on reflectance in accordance with the disclosed subject matter.

[0032] FIG. 9 illustrates example geometry optimization results in accordance with the disclosed subject matter.

[0033] FIG. 10 illustrates example characteristics of an example antenna in accordance with the disclosed subject matter.

[0034] FIG. 11 illustrates example laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0035] FIG. 12 illustrates example laser-cut aluminized polyimide films in accordance with the disclosed subject matter. FIG. 13 illustrates example laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0036] FIG. 14 illustrates example laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0037] FIG. 15 illustrates example laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0038] FIG. 16 illustrates example geometry optimization results of laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0039] FIG. 17 illustrates example geometry optimization results of laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0040] FIG. 18 illustrates example geometry optimization results of laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0041] FIG. 19 illustrates example geometry optimization results of laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0042] FIG. 20 illustrates example geometry optimization results of laser-cut aluminized polyimide films in accordance with the disclosed subject matter.

[0043] FIG. 21 illustrates example geometries of the disclosed film with additional parameters in accordance with the disclosed subject matter.

[0044] DETAILED DESCRIPTION

[0045] The disclosed subject matter provides antenna reflectors, which can address the challenges of creating large, lightweight, and cost-effective antennas. An example antenna can include kirigami patterns for perforating thin films, which can be used as reflectors in antennas (e.g., parabolic antennas). The use of perforated films can allow for improved prestress levels in these antennas. “Approximately” as used herein refers to a value or range that is close to the stated value or range, as would be understood by a person of ordinary skill in the art. The term allows for reasonable variations, deviations, or tolerances that do not materially affect the intended function or result.

[0046] In certain embodiments, the disclosed kirigami pattern for perforating thin film can be optimized for antenna reflectors. For example, as shown in Fig. 1, the pattern can include a repeating 2-dimensional array of unit cells, each containing two types of cuts: axial and diagonal. Axial cuts can be located orthogonally to each other forming a so-called rotating squares pattern if there are no diagonal cuts. In addition, the disclosed subject matter also uses two diagonal cuts that intersect at the center of this square, creating four smaller triangular sections within each unit cell. The additional diagonal cuts can further increase the stretchiness of the film and allow it to stretch independently in two in-plane directions, in contrast to the rotating squares pattern where stretching in one in-plane direction also causes similar elongation in the perpendicular direction (corresponding to the Poisson ratio close to -1). In non-limiting embodiments, the intersecting diagonal cuts can reduce the stiffness of the entire structure of the disclosed reflector by letting all four rotating squares shear or buckle under tensile load.

[0047] In certain embodiments, mechanical properties can be improved or adjusted by controlling geometric parameters. For example, four independent geometric parameters control the entire geometry of the structure: the length of the axial cut (Lxiai), the spacing between two axial cuts (Saxiai), the spacing between diagonal and axial cuts (Sdiag), and the width of the cut (Wcut). The range of geometric parameters can be selected based on the fabrication and diffraction limitations. For example, the spacings and cut lengths can vary from 100 micrometers to 1 mm, from 10 microns to 3 mm, from 10 nanometers to 10 microns, or larger. The maximum size of the spacing and other cut lengths can be limited by the fact that the period of the structure needs to be less than the wavelength of the electromagnetic radiation and the antenna can be designed for in order to avoid parasitic diffraction peaks during the operation of the antenna. In non-limiting embodiments, the maximum reflector size can be 20 meters, 100 meters, 1000 meters, 10,000 meters, or larger.

[0048] In certain embodiments, the disclosed thin films with linear perforations (i.e., Kirigami metamaterials) can provide tunable Young’s modulus and Poisson’s ratio. For example, as shown in Fig. 2, the Poisson's ratio of the disclosed reflector can be adjusted by modifying the axial cut lengths, di agonal -to-axi al spacing ratio, or a combination thereof. Making the Poisson ratio close to zero can allow the films to be stretched independently in two perpendicular in-plane directions in contrast to, for example, the rotating squares pattern, where stretching in one direction makes the film expand in the perpendicular direction. In non-limiting embodiments, as shown in Figs. 3-5, stress distribution at hinges can be adjusted by controlling the ratio of Sdiag / Saxiai. Such adjustable mechanical properties of the disclosed reflector facilitate the construction and deployment of the antenna, reduce deflections of the antenna from the ideal (e.g., parabolic) shape and enable the increased size of the reflector and / or antenna.

[0049] In certain embodiments, the use of the disclosed perforated films as reflectors enables the use of lower prestress in antennas. For example, the disclosed antennas can include the intersecting diagonal cuts added on the rotating squares pattern. These intersecting diagonal cuts can reduce the tensile stiffness of the entire structure by letting all rotating squares shear or buckle individually under stretching in any direction. The Tensile Stiffness Enhancement (or Reduction) Factor (TSEF or TSRF) is a ratio of Young’s modulus of the bulk material to the effective Young’s modulus of the perforated film. It can be used to estimate the prestress at a strain where the reflecting antenna can be exposed during operation due to thermal gradients in space. The increased axial cut and the decreased spacings can provide decreased prestress.

[0050] In certain embodiments, when stretched, the disclosed reflector can buckle, or deform out of plane, in a specific pattern corresponding to a buckling mode of a periodic kirigami structure. A buckling mode refers to buckling modes represent potential instability pattern, i.e., the specific shape or pattern that a structure deforms into when it buckles under tensile (or compressive) loads. Fig. 6 provides an example buckling mode of a periodic kirigami structure. In non-limiting embodiments, the prestress can be controlled by varying cut parameters as well as the thickness of the reflector. For example, as shown in Fig. 7, the geometry of the reflector can be further optimized to minimize the prestress by varying cut parameters as well as the thickness of Kapton and Aluminum. In further non-limiting embodiments, the pattern can be non-periodic (i.e., randomized), for example, by introducing random variations of the regular geometries. These non-periodic patterns are expected to perform similarly.

[0051] In certain embodiments, the disclosed subject matter can provide improved reflectance. For example, the reflectance of the disclosed film can be improved by minimizing axial cuts and increasing the spacing between two axial cuts (Saxiai) and the spacing between diagonal and axial cuts (Sdiag). To assess the effects of perforation on its effectiveness as a microwave reflector, the reflectance of the perforated Kapton films aluminized on one side (100 nm Al and 7.6, 12.7, and 25.4 um thick Polyimide) was simulated with varying geometric parameters in COMSOL Frequency Domain Wave Electromagnetics module at 10 GHz and zero-degree incidence. As shown in Fig. 8, the results of parametric assessments for undeformed perforated films suggest that reflectance can be maximized at minimized axial cut length and maximized axial and diagonal spacings. Similarly, Figs. 16 and 17 illustrate that reflectance can be maximized at minimized axial cut length and increased uniaxial strain for both p- and s- polarizations. The reflectance at zero strain is much lower for some geometries due to formation of wrinkles. Applying a 1% or larger tensile strain reduces the wrinkles and increases the reflectance. For tested geometries (2- and 3-mm axial cuts and 0.1 mm spacings), buckling has reduced effects on the reflectance: the changes in reflectance are at most approximately 1% even at the largest incidence angles and strains (including post-buckling at 6% strain). Figs. 18-20 show reflectance as a function of frequency for example different polarization models (e.g., s- polarization and p-polarization) and different axial cut lengths. Fig. 10 shows reflectance as a function of the incidence angle for different combinations of the film’s stretching strain (0 and 6%) and the polarization of the electromagnetic wave (TM, TE or the average of the two). The results of combined mechanical and electromagnetic simulations show that there can be a trade-off between minimizing prestress and maximizing reflectance, however, as shown in Fig. 9, there can be various geometries that can offer reflectance of >90% and prestress of <0.5N / m (i.e., more than an order of magnitude lower than what is used with metal fabric meshes). This tradeoff between the optical and mechanical properties can be improved by optimizing the thickness of the aluminum and polyimide layers as well as the in-plane geometric parameters shown in Fig. 1.

[0052] In certain embodiments, the disclosed subject matter can provide various unexpected improvements on the antenna functionalities. According to the COMSOL finite element modeling package, various advantages were identified. For example, Poisson’s ratio can be controlled from -1 to 0 by diagonal -to-axial spacing ratio. If the spacing between diagonal and axial cuts is much smaller than the spacing between two axial cuts, in the linear elastic regime, shearing of the squares is dominating the rotation, which leads to near-zero Poisson’s ratio. If the spacing between diagonal and axial cuts is much larger than the spacing between two axial cuts, rotation of the squares is dominating the shearing, which leads to Poisson’s ratio approaching -1. In this case, the disclosed pattern can behave similar to a rotating squares pattern. If the spacing between diagonal and axial cuts is equal to the spacing between two axial cuts, rotation of the squares is slightly dominating the shearing and the Poisson’s ratio is approximately -0.3.

[0053] In certain embodiments, the effective tensile modulus of the disclosed subject matter can be controlled by axial cut-to-diagonal spacing and axial cut-to-axial spacing ratios. To quantify how stretcher the perforated film when compared to the unpattemed planar material, Tensile Stiffness Reduction Factor (TSRF), which is a ratio of the Young’s modulus of a bulk material to the Young’s modulus of perforated film, was introduced. To achieve maximum stretchiness, the length of axial cuts needs to be maximized while the axial and diagonal spacings needs to be minimized.

[0054] In certain embodiments, the disclosed subject matter provides reduced tensile modulus, consequently, lead to a lower prestress required for a thin film. Prestress can be defined as the force needed to cause a certain displacement divided by the width of the film and can be inversely proportional to the TSRF.

[0055] In certain embodiments, the disclosed subject matter can include the smallest axial and diagonal spacing to achieve the combinations of increased reflectance and lowered prestress is achieved with films that have the smallest axial and diagonal spacing.

[0056] In certain embodiments, the disclosed reflector can be a laser-cut aluminized polyimide film with various geometric parameters. In other embodiments, other combinations of metals and polymers can be used. For example, gold, silver, (e.g., on biaxially oriented polyethylene terephthalate or polyethylene or polytetrafluoroethylene) or combinations thereof. Figs. 11 and 12 show example laser-cut aluminized polyimide films with different cut lengths and spacings. Fig. 13 shows deformation shapes of example lasercut aluminized polyimide films with controlled lengths and spacings when stretched at various strains. Fig. 14 shows tensile test results of an example laser-cut aluminized polyimide film (with a controlled cut length of 3 mm) stretched uniaxially in three different directions with pretension at 1% strain ranging from approximately 0.18N / m to approximately 0.56N / m and the stretching limit (before tearing) ranging from approximately 20% to approximately 42% strain depending on the stretching direction. Fig. 15 shows tensile test results of an example laser-cut aluminized polyimide film (with a controlled cut length of 4 mm) stretched uniaxially in three different directions with pretension at 1% strain ranging from approximately 0.08N / m to approximately 0.27N / m and the stretching limit ranging from approximately 24% to approximately 52% strain depending on the stretching direction.

[0057] In certain embodiments, the disclosed film can have various geometries. For example, in addition to the disclosed four geometric parameters (i.e., the length of the axial cut, the spacing between two axial cuts, the spacing between diagonal and axial cuts, and the width of the cut), two additional parameters can be introduced: notches at the ends of the axial and diagonal cuts. These notches can be added either simultaneously or individually, resulting in three different cases, as shown in Fig. 21. For example, by adjusting the length of the notches at the ends of axial cuts (naxiai) and / or the length of the notches at the ends of diagonal cuts (naiag), reflectors with a different geometry can be produced. In non-limiting embodiments, the additional parameters can alter mechanical properties of the film. For example, adjusting the additional parameters (e.g., naxiai and / or naiag) can allow the film to be more stretchable.

[0058] In certain embodiments, the disclosed reflector can be used for various antennas.

[0059] For example, parabolic dish antennas for microwave radiation in L, S, C, X, Ku, etc., bands, or radiofrequency antennas in VHF and HF bands, as well as other shapes of antennas (e.g., cylindrical or horn) and other parts of the electromagnetic spectrum, such as terahertz or infrared or low-frequency radio waves.

[0060] In non-limiting embodiments, the disclosed subject matter can used for space antennas. The disclosed subject matter can serve as reflectors with minimal prestress for large (e.g., approximately 100 meter) RF parabolic antennas. For example, polyimide films with thicknesses between 1 / 3 and 1 mil (approximately 8 to 25 microns) coated with a thin (approximately 100 nm) layer of aluminum can effectively reflect microwaves without increased pretension since they are always electrically interconnected. Compared to unperforated films, the Kirigami perforation pattern can enhance the reflector's ability to withstand large strains (up to 50%) and reduce the prestress needed to compensate for the approximately 1% thermal strain caused by temperature cycling in space, where the antenna alternates between exposure to intense sunlight and being in Earth's shadow.

[0061] All patents, patent applications, publications, product descriptions, and protocols cited in this specification are hereby incorporated by reference in their entirety. In case of a conflict in terminology, the present disclosure controls.

[0062] While it will become apparent that the subject matter herein described is well calculated to achieve the benefits and advantages set forth above, the presently disclosed subject matter is not to be limited in scope by the specific embodiments described herein. It will be appreciated that the disclosed subject matter is susceptible to modification, variation, and change without departing from the spirit thereof. Those skilled in the art will recognize or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments described herein. Such equivalents are intended to be encompassed by the following claims.

Claims

What is claimed is:

1. A reflector, comprising: a film comprising a pattern, wherein the pattern comprises a repeating array of unit cells.

2. The reflector of claim 1, wherein each of the repeating arrays comprises an axial cut and a diagonal cut, wherein a plurality of the axial cut are located orthogonally to each other forming a rotating square, wherein a plurality of the diagonal cut intersect at a center of the rotating square, creating triangular sections within each unit cell.

3. The reflector of claim 1, wherein the film is an aluminized film.

4. The reflector of claim 1, wherein the repeating array is a repeating two- dimensional array.

5. The reflector of claim 1, wherein the film is configured to be stretchable.

6. The reflector of claim 5, wherein the diagonal cut is configured to increase a stretchiness of the film and allow the film to stretch independently in two in-plane directions.

7. The reflector of claim 5, wherein the rotating square is configured to stretch in one in-plane direction causing an elongation in a perpendicular direction.

8. The reflector of claim 1, wherein a mechanical property of the reflector is configured to be adjustable.

9. The reflector of claim 8, wherein the mechanical property comprises Poisson’s ratio, tensile modulus, stress distribution, stiffness, reflectance, or combinations thereof, wherein an adjustable range of the Poisson’s ration is from about -1 to about 0.

10. The reflector of claim 1, wherein the reflector is configured to be coupled with an antenna.

11. The reflector of claim 1, wherein the pattern is non-periodic.

12. A method of using a reflector, comprising providing the reflector with a pattern, wherein the pattern comprises a repeating array of unit cells.

13. The method of claim 11, wherein each of the repeating arrays comprises an axial cut and a diagonal cut, wherein a plurality of the axial cut are located orthogonally to each other forming a rotating square, wherein a plurality of the diagonal cut intersect at a center of the rotating square, creating triangular sections within each unit cell.

14. The method of claim 11, further comprising adjusting a mechanical property of the reflector.

15. The method of claim 13, wherein the mechanical property is adjusted by modifying a geometric parameter of the reflector.

16. The method of claim, 13, wherein the mechanical property comprises Poisson’s ratio, tensile modulus, stress distribution, stiffness, or combinations thereof.

17. The method of claim 15, wherein an adjustable range of the Poisson’s ration is from about -1 to about 0.

18. The method of claim 14, wherein the geometric parameter comprises a length of an axial cut, a spacing between two axial cuts, a spacing between diagonal and axial cuts, a width of the axial or diagonal cut, or combinations thereof.

19. The method of claim 12, wherein the reflector is an aluminized film.

20. The method of claim 12, further comprising perforating the pattern on the reflector.

21. The method of claim 12, wherein the diagonal cut is configured to increase a stretchiness of the film and allow the film to stretch independently in two in-plane directions.15

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