Low-loss plasmon waveguide design method based on stretched metal

Abstract

The invention belongs to the technical field of surface plasmons, and discloses a low-loss SPP design method based on anisotropic stretched metal. The loss is accurately regulated and controlled through electron density dilution in different directions inside and outside the plane, so that the previous thought of reducing the electron body density of the material does not need to be continued. The theoretical limit of the waveguide loss of the SPP provided by the invention can be reduced to 50% of the original unstretched crystal lattice; according to the invention, the high-index single crystal copper can be used as a representative of an anisotropic stretching metal system, the restriction of a conventional metal lattice with a low-index crystal face exposed is broken through a pre-oxidation-reduction method, the copper single crystal with the high-index crystal face exposed is prepared, and relatively stable Cu (332) is taken as an example to prove that the dielectric imaginary part of the copper single crystal is lower than that of precious metal Ag of the same type, so that the copper single crystal with the high-index crystal face exposed is prepared. And the method can be compared with the lowest-loss alkali metal Na measured in the current experiment. In addition, periodic coupling grating structure design is carried out on Cu (332) to achieve SPP excitation, and the near-infrared propagation length of the Cu (332) can be measured to reach the hundred-micron level.

Description

[0001] The present invention mainly relates to the field of surface plasmon technology, and in particular to a method for designing a low-loss plasmon waveguide based on stretched metal. Background Art

[0002] Background: Traditional electronic integrated circuits face a series of physical limitations, including bandwidth bottlenecks, rising energy consumption, and interference from quantum effects. Optical and electrical integration is an inevitable trend in future integrated technology. Surface plasmon polaritons (SPPs)—surface-bound electromagnetic modes formed by the collective oscillations of free electrons on a metal surface coupling with electromagnetic waves and propagating along the metal-dielectric interface—can theoretically enable the integration of nanophotonic devices and electronic circuits in the same dimensionality due to their ability to reduce the diffraction limit. However, metal loss is one of the main issues limiting the practical application of SPP devices. At present, there are two main technical approaches to reducing plasmon loss: first, explore new materials with lower intrinsic loss. For example, the research group of Professor Zhu Jia of Nanjing University published a work in Nature in 2020, proposing a spin-coating preparation method for high-quality alkali metal Na, and successfully verified its low-loss characteristics (γ~10meV) relative to precious metals, and based on this, prepared high-performance low-threshold nanolasers. In addition, two-dimensional plasmonic materials have also attracted much attention, such as graphene with tunable electron density and borophene with semi-metallic properties. The common feature of these methods is to reduce the bulk electron density of the material system and thus reduce losses; second, design new composite waveguide structures. For example, the work of the research group of Professor Zhang Xiang of the University of Hong Kong, China, published in Nature Photonics in 2008, achieved low loss in the communication band while maintaining a subwavelength high localized mode field by combining traditional dielectric waveguides with metal plasmons.

[0003] The most similar prior art implementation to the present invention: Jacob Khurgin's theoretical work published in APL in 2010 first proposed the concept of "lossless metals." The design concept is that, through special band width and spacing design, the metal can neither meet the energy conservation matching for intra-band transitions nor overcome the inter-band transition barrier within a specific wavelength band. As a result, the metal cannot undergo intra-band or inter-band transitions, resulting in a lossless and non-absorbing state, manifested by the imaginary part of the metal's dielectric function being zero. Using the alkali metal Na as an example, Jacob Khurgin demonstrated that by three-dimensionally stretching its crystal lattice to twice its size in three directions, the increase in real space leads to reciprocal space band compression, thus achieving losslessness in the 1700-2500nm band.

[0004] Disadvantages of Existing Technologies: A common approach to reducing optical frequency loss in metals is to lower the bulk electron density of the material. For example, in existing three-dimensional material systems, developing low-loss alkali metal plasmons can reduce the carrier density of traditional precious metal systems by more than half. However, due to their chemically active nature, alkali metals exhibit poor stability, requiring specialized and complex packaging structures. Furthermore, as metals in the first main group of the periodic table, alkali metals already have a bulk electron density that is at a bottleneck for metal systems, making the continued pursuit of low-electron bulk density metal plasmon materials undesirable. Another approach to reducing electron density is to switch from three-dimensional to two-dimensional materials. However, due to the extremely low carrier density and limited tunability of two-dimensional plasmon materials, their SPP response band is often restricted to the infrared region, failing to cover high-frequency regions such as the visible spectrum. In summary, current technologies for reducing loss often compromise material stability, rely on complex structural designs, and limit the SPP response band. Summary of the Invention

[0005] Existing bulk materials cannot achieve three-dimensional lattice stretching of metals, making the goal of achieving low optical frequency loss difficult to achieve. The present invention aims to provide a design method for low-loss plasmonic waveguides based on stretched metals, aiming to explore a relatively stable high-frequency, low-loss plasmonic system that does not rely on complex microstructure design, and to reduce the optical frequency loss of metal materials and the loss of SPP waveguides excited by the metal-dielectric interface. SPPs are bound electromagnetic waves that propagate in-plane and attenuate out-of-plane. Their loss is primarily due to collisional scattering of in-plane electrons with the lattice. The present invention proposes to precisely control the loss by diluting the electron density in different directions in and out of the plane (i.e., anisotropic dilution). For example, by stretching only the direction where loss reduction is desired, even if other directions are compressed while maintaining the lattice density, this method breaks the previous limitation of simply reducing the material's electron bulk density.

[0006] To achieve the above objectives, the present invention provides a method for designing a low-loss plasmon waveguide based on stretched metal, comprising the following steps: Step 1: Determine the main loss direction of SPP propagation in the metal structure; Step 2: Anisotropically stretch the metal structure while preserving the lattice volume, which involves applying tensile strain in the in-plane direction of the primary loss direction and compressive strain in the out-of-plane direction of the secondary loss direction in equal proportions. Step 3: Adjust the stretching parameters to reduce the SPP propagation loss while keeping the total volume of the metal lattice unchanged.

[0007] Furthermore, step 4 is also included: calculating the SPP loss that characterizes the anisotropic tensile metal.

[0008] Furthermore, there are two methods for calculating the SPP loss of anisotropic stretched metals: the method for calculating the SPP energy loss propagating along the anisotropic stretched metal-air interface and the method for calculating the imaginary part of the dielectric function for calculating the loss of different crystal planes themselves; The physical quantities that characterize SPP loss include three: the collision probability of electrons , the imaginary part of the dielectric function of the material , SPP energy loss Or the SPP propagation length L, the three physical quantities are positively correlated, expressed as (7).

[0009] Furthermore, a method for calculating the SPP energy loss along the anisotropic stretched metal-air interface includes a theoretical calculation method, which includes the following steps: T1: Based on the Drude model, the collision frequency of electrons on metals Corrected, the formula is (1), where represents the intrinsic damping of the metal itself without considering the lattice stretching, and denote the stretching coefficients along the in-plane x-direction and out-of-plane z-direction, respectively. represents the modified damping after considering the in-plane and out-of-plane stretching; T2: Based on the Drude model, the dielectric function of the metal is further modified. The formula is: (2); (3); (4); in, is the dielectric function under the free electron gas model, is the modified dielectric function after taking into account the different atomic arrangements of the lattice; T3: The electric field formula of SPP is (5), where is the propagation wave vector of the SPP along the plane, k is the attenuation wave vector of the SPP along the plane; T4: According to electromagnetic field theory, the skin depth is calculated as one original cycle The energy loss under the condition of , the formula for calculating SPP energy loss is: (6), where , and is the stretch coefficient.

[0010] Furthermore, according to formula (6), the stretching coefficient and calculate the energy loss under the corresponding stretching conditions; when When , it represents the anisotropic stretching while maintaining the lattice volume unchanged, which can be represented by the high-index crystal plane system of the metal. The specific crystal plane index (hkl) satisfies the relationship k=h,l=h-1.

[0011] Furthermore, the method for calculating the imaginary part of the dielectric function of the loss of different crystal planes includes a theoretical calculation method, which includes the following steps: S1: For anisotropically stretched high-index crystal face metal system with crystal face index (hkl) satisfying k=h,l=h-1, the corresponding SPP energy loss comparison can be expressed as follows from the rigid potential dispersion model RPM: (8), where and is the stretch coefficient; S2: According to formula (7), we can get (9); S3: According to the dielectric function of the Durde model, we can get (10), (11).

[0012] Furthermore, a method for calculating the SPP energy loss along the anisotropic stretched metal-air interface includes an experimental calculation method, which includes the following steps: T5: Before measurement, design SPP coupling grating structures for metals with different crystal planes to meet SPP excitation conditions; T6: Use the built reflective far-field test optical path to collect SPP propagation images; T7: The SPP propagation length L is obtained by performing exponential fitting on the outcoupling light intensity I at different propagation distances d. T8: The longer the SPP propagation length L, the smaller the SPP energy loss; the shorter the SPP propagation length L, the greater the SPP energy loss.

[0013] Furthermore, the method for calculating the imaginary part of the dielectric function of the loss of different crystal planes includes an experimental calculation method, which includes the following steps: S4: Before measurement, the single crystallinity of the sample was characterized by XRD; S5: Use AFM to calibrate the crystal axis orientation of single crystal metals with different crystal planes; S6: Perform dielectric function measurement using an ellipsometer, ensuring the incident angle is 60°. S7: Fit the raw data obtained by the ellipsometry with the Drude-Lorentz model to obtain the dielectric functions of metals with different crystal planes , by measuring the dielectric imaginary part of samples with different crystal planes By comparison, we can obtain the rule that loss decreases when transitioning from the low-index surface of the metal to the high-index surface.

[0014] Furthermore, the metal may be high-index single crystal copper.

[0015] Furthermore, the dielectric function of bulk copper can be used instead of Cu(110), which can be expressed as (12), (13).

[0016] The present invention provides a low-loss SPP design method based on anisotropically stretched metal. The present invention proposes that the waveguide loss of SPP is mainly caused by the collision of electrons with the in-plane lattice. Therefore, stretching the lattice along the in-plane SPP propagation direction (diluting the electron density) has a more significant effect on reducing loss. In addition, anisotropic stretching (in-plane stretching, out-of-plane compression) that maintains the electron body density unchanged can still achieve loss reduction. The theoretical limit is that it can be reduced to 50% of the original lattice.

[0017] The present invention proposes that high-index single-crystal copper can be used as a representative of anisotropic tensile metal systems. Theoretically, taking Cu (998) as an example, it is proved that it maintains a negative real part of the dielectric constant and an imaginary part of the dielectric function that can reach 0.01 in the visible to near-infrared frequency band, comparable to the transparent semiconductor ITO. Experimentally, a copper single crystal with exposed high-index crystal faces was prepared by a pre-oxidation-reduction method, and taking the relatively stable Cu (332) as an example, it was proved that its imaginary part of the dielectric constant is lower than that of the same type of precious metal Ag, and is comparable to the lowest loss alkali metal Na currently measured experimentally. In addition, by designing a periodically coupled grating structure for Cu (332) to achieve the excitation of SPPs, its propagation length in the near-infrared is measured to be up to hundreds of microns. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 1 is a comparison diagram of the theoretical effects of metals stretched along different directions on SPP loss reduction according to an embodiment of the present invention; Figure 2 This is a diagram showing the effect of anisotropic stretching on reducing SPP loss while maintaining the lattice density unchanged, according to an embodiment of the present invention; Figure 3 1 is a diagram of copper SPP energy loss on different crystal planes calculated by a rigid potential model according to an embodiment of the present invention; Figure 4 1 is a design diagram of the coupled grating structure of the SPP involved in an embodiment of the present invention; Figure 5 Schematic diagram of a test optical path for SPP propagation length according to an embodiment of the present invention; Figure 6Schematic diagram of the SPP propagation length of high-index single crystal copper relative to low-index single crystal copper involved in an embodiment of the present invention; Figure 7 is a graph of the imaginary parts of the dielectric functions of copper on different crystal planes calculated by the rigid potential model according to an embodiment of the present invention; Figure 8 Schematic diagram of material characterization of single crystal copper with different crystal plane orientations involved in an embodiment of the present invention; Figure 9 This is a comparison chart of the imaginary part of the dielectric function of high-index single-crystal copper according to an embodiment of the present invention, compared with low-index single-crystal copper and other metals. DETAILED DESCRIPTION

[0019] The preferred structure and implementation method of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0020] like Figures 1 to 9 As shown, an embodiment of the present invention discloses a technical solution for a low-loss SPP design method based on anisotropic stretched metal.

[0021] Surface Plasmon Polaritons (SPPs) are surface-bound electromagnetic modes formed by the coupling of the collective oscillations of free electrons on the metal surface with electromagnetic waves and propagating along the metal-dielectric interface. Due to their ability to reduce the diffraction limit and the ability to transmit light, they can theoretically realize the integration of nanophotonic devices and electronic circuits in the same dimension.

[0022] X-ray diffraction (XRD) is a technique for characterizing a material's crystal structure by analyzing its X-ray diffraction pattern. Its core principle is based on Bragg's law: when X-rays strike a crystal, coherent diffraction occurs when the interplanar spacing (d) satisfies nλ = 2dsinθ (where λ is the X-ray wavelength, θ is the incident angle, and n is an integer), resulting in characteristic diffraction peaks. XRD characterization can be used for lattice structure identification, lattice parameter and strain analysis, crystallinity and defect characterization, orientation and structural analysis, and phase analysis.

[0023] AFM (Atomic Force Microscope) is a high-resolution surface topography characterization technique based on probe-sample interaction forces. It belongs to the scanning probe microscope (SPM) family. Its core principle is to detect changes in the force exerted by a microcantilever probe on the sample surface, enabling three-dimensional topography imaging and physical property measurement at the nanoscale or even atomic level.

[0024] Existing bulk materials cannot stretch the metal's three-dimensional lattice in three directions, making it difficult to achieve low optical frequency loss. This invention precisely controls loss by diluting the electron density in different directions, in and out of the plane (i.e., anisotropic dilution). For example, by stretching only the direction where loss is desired, the lattice volume can be maintained. This anisotropically stretched metal system can be experimentally realized using high-index plane-oriented single crystal metals, eliminating the need to simply reduce the material's electron density.

[0025] Methods for achieving anisotropic stretching of metals: Traditional metals are usually single crystals or polycrystals composed of three types of low-index planes: (100), (110), and (111). However, the difference in the atomic arrangement period between the in-plane and out-plane of these three types of crystal planes is very small, and they often show isotropy in optical properties. However, when metals are composed of high-index crystal planes, the difference in the in-plane and out-plane lattice arrangement changes significantly. Specifically, the in-plane lattice is significantly stretched relative to the low-index crystal plane, that is, the in-plane lattice atomic arrangement period increases, while the out-plane lattice is significantly compressed, that is, the out-plane lattice atomic arrangement period decreases. Therefore, when the metal transitions from the low-index plane to the high-index plane, it is equivalent to anisotropic stretching of the traditional metal. The anisotropic stretching here refers to the in-plane stretching and out-of-plane compression that maintains the lattice volume unchanged. Taking high-index copper Cu(221), Cu(332), and Cu(998) as examples, their specific in-plane lattice parameters are shown in Table 1. It can be seen that the atomic period along the in-plane x-direction is significantly increased, while at the same time the atomic period along the out-of-plane z-direction is significantly decreased, which is consistent with the anisotropic stretching situation.

[0026] Table 1 Specific in-plane lattice parameters of high-index copper Cu(221), Cu(332), and Cu(998) Example

[0027] This example uses high-index single-crystal copper as an example to demonstrate the feasibility of anisotropic stretched metal as a new low-loss plasmon system through theoretical calculations and experimental tests.

[0028] Based on the classic Drude model that describes the optical properties of metals, the present invention further considers the regulation of SPP loss by the different arrangement periods of lattice atoms inside and outside the plane. The rigid potential model (RPM) is used to calculate the differences in the effect of stretching metals in different directions on reducing SPP energy loss. Taking high-index single-crystal copper as an example, the SPP energy loss propagating along different crystal planes of copper and the imaginary part of the dielectric function that characterizes the loss of copper on different crystal planes are further calculated, thereby theoretically verifying the effect of anisotropic stretching of metals on loss reduction.

[0029] A low-loss SPP design method based on anisotropic stretched metal mainly includes the following steps: Step 1: Determine the main loss direction of SPP propagation in the metal structure; Step 2: Anisotropically stretch the metal structure while preserving the lattice volume, which involves applying tensile strain in the in-plane direction of the primary loss direction and compressive strain in the out-of-plane direction of the secondary loss direction in equal proportions. Step 3: Adjust the stretching parameters to reduce the SPP propagation loss while keeping the total volume of the metal lattice unchanged.

[0030] Step 4: Calculate the SPP losses that characterize the anisotropic stretched metal.

[0031] There are two methods for calculating the SPP loss of anisotropic stretched metals: the method for calculating the SPP energy loss along the anisotropic stretched metal-air interface and the method for calculating the imaginary part of the dielectric function of the loss of different crystal planes themselves. There are three physical quantities that characterize SPP loss. At the microscopic level, it is the collision probability of electrons. , the material level is the imaginary part of the dielectric function , energy loss of SPP at the device level Or the SPP propagation length L, the three physical quantities are positively correlated, expressed as (7).

[0032] like Figure 1 This is a comparison chart of the theoretical effects of stretching the lattice in different directions on reducing SPP loss in the embodiments of the present invention. The red line represents stretching only in the in-plane x-direction, the black line represents stretching only in the out-of-plane z-direction, and the blue line represents stretching in both the x and z directions. There are two conclusions: first, stretching the lattice in the in-plane x-direction is more effective in reducing SPP loss than stretching in the out-of-plane z-direction; second, simply diluting the in-plane electron density is sufficient to reduce SPP loss, such as Figure 1 As shown, the red line and the blue line have similar effects on loss reduction.

[0033] Figure 2 is Figure 1 On this basis, we further considered the effect of anisotropic stretched metal system on SPP loss reduction and found that under the premise of maintaining the lattice density unchanged, in-plane stretching and out-of-plane compression can still achieve loss reduction, and this situation can be replaced by the high-index crystal plane of metal.

[0034] Figure 3Figure 2 shows the SPP energy loss of copper on different crystal planes, calculated using a rigid potential model, according to an embodiment of the present invention. The SPP energy loss under these conditions is calculated based on the corresponding stretch coefficients of copper on different index crystal planes. It is found that the highest-index Cu (998) plane achieves a nearly 50% reduction in loss compared to the lower-index Cu (110) plane. Furthermore, the larger the crystal plane index, the lower the loss due to the greater in-plane stretch coefficient.

[0035] This shows that anisotropic stretched metal is theoretically feasible as a new low-loss plasmonic material system. Example

[0036] This embodiment is substantially the same as embodiment 1, except that the method for calculating the SPP energy loss propagating along the anisotropic stretched metal-air interface includes a theoretical calculation method and an experimental calculation method; The theoretical calculation method includes the following steps: T1: First, based on the Drude model, the collision frequency of electrons on metals Corrected, the formula is (1), where represents the intrinsic damping of the metal itself without considering the lattice stretching, and denote the stretching coefficients along the in-plane x-direction and out-of-plane z-direction, respectively. represents the modified damping after considering the in-plane and out-of-plane stretching; T2: Based on the Drude model, the dielectric function of the metal is further modified. The formula is: (2); (3); (4); in, is the dielectric function under the free electron gas model, is the modified dielectric function after taking into account the different atomic arrangements of the lattice; T3: The electric field formula of SPP is (5), where is the propagation wave vector of the SPP along the plane, k is the attenuation wave vector of the SPP along the plane; T4: According to electromagnetic field theory, the SPP propagation unit length is calculated to be 1 μm, and the skin depth is calculated to be one original cycle. The energy loss under the condition of , the formula for calculating SPP energy loss is: (6), where , and is the stretch coefficient.

[0037] According to formula (6), the stretch coefficient And calculate the energy loss under the corresponding stretching conditions. Specifically, when When , it represents the anisotropic stretching while maintaining the lattice volume unchanged (the electron density unchanged), which can be represented by the high-index crystal plane system of the metal. The specific crystal plane index (hkl) satisfies the relationship of k=h,l=h-1.

[0038] In the theoretical calculation method, the inter-band transition in the frequency band considered in this embodiment is negligible, and the problem can be explained using only the Drude model.

[0039] The methods for calculating the SPP energy loss along the anisotropic stretched metal-air interface include theoretical calculation methods and experimental calculation methods. The experimental calculation method includes the following steps: T5: Before measurement, design SPP coupling grating structures for metals with different crystal planes to meet SPP excitation conditions; T6: Use the built reflective far-field test optical path to collect SPP propagation images; T7: The SPP propagation length L is obtained by performing exponential fitting on the outcoupling light intensity I at different propagation distances d. T8: The longer the SPP propagation length L, the smaller the SPP energy loss; the shorter the SPP propagation length L, the greater the SPP energy loss.

[0040] First, for the design of the coupled grating structure, the key parameter, period p, is determined by the incident wavelength and the dielectric function of the material (for example, for Cu(332), the grating period is 870 nm under 900 nm excitation). Other parameters, such as length L of 25 μm, width d of 100 nm, and depth h of 200 nm, remain consistent. Furthermore, the propagation structure in each direction is set to four propagation distances of 50, 60, 70, and 80 μm, respectively. After the grating structure is designed, the SPP propagation image is collected using a reflective optical path. The specific optical path diagram is illustrated in the attached figure. The test principle is that the supercontinuum light source passes through a filter in a specific band (430-1450 nm), is reflected by the reflector for the first time, enters the microaperture, and then passes through a semi-transparent and semi-reflective mirror to reach the 50x objective lens. After focusing, it hits the coupling structure of the sample. Because the periodic structure of the grating meets the momentum matching condition of the SPP, the SPP is excited and propagates in a specific direction. When it propagates to the next coupling structure, the SPP is converted into spatial free light. Therefore, the spot image during propagation will be reflected by the sample and return to the original path. It is reflected by the semi-transparent and semi-reflective mirror and enters the CCD of a specific band. The images of the SPP from coupling, propagation, and decoupling are collected. Subsequently, the brightness exponential fitting of the coupled light at different propagation distances is performed to obtain the propagation length of the SPP.

[0041] like Figure 4 This is a design diagram of the SPP coupled grating structure involved in an embodiment of the present invention. According to the wave vector period matching of the SPP grating coupling, the corresponding grating period p and four groups of propagation distances d (50 / 60 / 70 / 80mμm) are designed. By collecting the outcoupled light signal under each group of propagation distance d, different light intensities I under different distances d are obtained. Through the exponential relationship The corresponding SPP propagation length LSPP is obtained by fitting.

[0042] like Figure 5 This is a schematic diagram of the optical path for testing the SPP propagation length involved in an embodiment of the present invention. After passing through a filter in a specific wavelength band (430-1450 nm), the supercontinuum light source is reflected by a reflector for the first time and enters the microaperture diaphragm. It then passes through a semi-transparent and semi-reflective mirror to reach a 50x objective lens. After being focused, it hits the sample's coupling-in structure. Because the periodic structure of the grating meets the momentum matching condition for the SPP, the SPP is excited to propagate in a specific direction. When it propagates to the next coupling-out structure, the SPP is converted into spatial free light. Therefore, the spot image during propagation will be reflected by the sample and return along the original path. It is reflected by the semi-transparent and semi-reflective mirror and enters the CCD in the specific wavelength band for signal acquisition.

[0043] like Figure 6 This is a schematic diagram of the SPP propagation length of high-index single-crystal copper relative to low-index single-crystal copper involved in an embodiment of the present invention. The low inherent loss of the material (small imaginary part of the dielectric function) brings about a longer SPP propagation length. Therefore, it can be seen from the figure that the SPP propagation length of high-index single-crystal copper Cu(332) in the near-infrared band is longer than that of low-index single-crystal copper Cu(111), reaching the level of hundreds of μm. Moreover, the longer the wavelength band, the more obvious the advantage of high-index single-crystal copper is. This proves the potential of high-index single-crystal copper in optical waveguide devices compared to traditional low-index copper. Example

[0044] This embodiment is basically the same as Example 1, except that the method for calculating the imaginary part of the dielectric function of the loss of different crystal planes includes a theoretical calculation method, which includes the following steps: S1: For anisotropically stretched high-index crystal face metal system with crystal face index (hkl) satisfying k=h,l=h-1, the corresponding SPP energy loss comparison can be expressed as follows from the rigid potential dispersion model RPM: (8), where and is the stretch coefficient; S2: According to formula (7), we can get (9); S3: According to the dielectric function of the Durde model, we can get (10), (11).

[0045] Since bulk Cu metal is generally composed of low-index surfaces, the properties of single crystal Cu(110) are basically the same as those of bulk Cu. The dielectric function of bulk copper can be used instead of Cu(110), which can be expressed as (12), (13).

[0046] The method for calculating the imaginary part of the dielectric function of different crystal plane losses includes an experimental calculation method, which includes the following steps: S4: Before measurement, the single crystallinity of the sample was characterized by XRD; S5: Use AFM to calibrate the crystal axis orientation of single crystal metals with different crystal planes; S6: Perform dielectric function measurement using an ellipsometer, ensuring the incident angle is 60°. S7: Fit the raw data obtained by the ellipsometry with the Drude-Lorentz model to obtain the dielectric functions of metals with different crystal planes , by measuring the dielectric imaginary part of samples with different crystal planes By comparison, we can obtain the rule that loss decreases when transitioning from the low-index surface of the metal to the high-index surface.

[0047] Theoretically, based on the traditional Drude model, the difference in the influence of the atomic arrangement inside and outside the lattice plane on the probability of electroacoustic scattering was corrected. By introducing the Rigid Potential Model (RPM), the influence of electron density dilution in different directions on SPP propagation loss was calculated and processed, and then it was demonstrated that the electron density in the in-plane SPP propagation direction is the main factor of loss.

[0048] Figure 7 is a graph of the imaginary part of the dielectric function of copper on different crystal planes calculated by the rigid potential model according to an embodiment of the present invention, Figure 7 It can be seen that from a material perspective, the loss of high-index crystal surface copper is lower than that of low-index crystal surface copper.

[0049] like Figure 8 This is a schematic diagram of the material characterization of single-crystalline copper with different crystal plane orientations involved in an embodiment of the present invention. The XRD test results of the prepared copper foils with different crystal planes show that the single crystallinity is excellent and meets the test requirements. The illustration is an optical photograph of the single-crystalline copper foil with the corresponding crystal plane orientation.

[0050] like Figure 9 This is a comparison chart of the imaginary part of the dielectric function of high-index single-crystal copper relative to low-index single-crystal copper and other metals involved in the embodiment of the present invention. The physical meaning of is the inherent optical frequency loss of metals. As can be seen from the figure, the loss of high-index copper Cu(332) is reduced by nearly 90% compared with the conventional low-index copper Cu(111). Figure 7 The theoretical results are generally consistent, with losses reduced by nearly 80% compared to low-loss precious metal Ag, and comparable to the extremely low-loss alkali metal Na currently measured experimentally. This demonstrates that high-index single-crystalline copper overcomes the high-loss limitations of low-index copper, outperforming the commonly used precious metal Ag. While maintaining comparable losses to alkali metal Na, it offers the advantages of relatively stable chemical properties and the absence of packaging.

[0051] The present invention provides a low-loss SPP design method based on anisotropic stretched metals. Taking copper as an example, the present invention proposes that the waveguide loss of SPPs is mainly caused by the collision of electrons with the in-plane lattice. Therefore, stretching the lattice along the in-plane SPP propagation direction (diluting the electron density) has a more significant effect on reducing loss. In addition, anisotropic stretching (in-plane stretching, out-of-plane compression) that maintains the electron body density unchanged can still achieve loss reduction, with the theoretical limit being 50% of the original lattice. The present invention proposes that high-index single-crystal copper can be used as a representative of anisotropic stretched metal systems. Theoretically, using Cu(998) as an example, it is demonstrated that it maintains a negative real part of the dielectric constant and an imaginary part of the dielectric function can reach a level of 0.01 in the visible to near-infrared band, comparable to the transparent semiconductor ITO. Experimentally, a copper single crystal with exposed high-index crystal faces was prepared by a pre-oxidation-reduction method. Taking the relatively stable Cu(332) as an example, it is demonstrated that its imaginary part of the dielectric constant is lower than that of the same type of precious metal Ag and is comparable to the lowest loss alkali metal Na currently measured experimentally. In addition, a periodically coupled grating structure was designed for Cu(332) to achieve SPP excitation, and its propagation length in the near-infrared was measured to be on the order of hundreds of microns.

[0052] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent replacements for some of the technical features therein. However, any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A low-loss SPP design method based on anisotropic stretched metal, characterized in that: The following steps are involved: Step 1: Determine the main loss direction of SPP propagation in the metal structure; Step 2: Anisotropically stretch the metal structure while preserving the lattice volume, which involves applying tensile strain in the in-plane direction of the primary loss direction and compressive strain in the out-of-plane direction of the secondary loss direction in equal proportions. Step 3: Adjust the stretching parameters to reduce the SPP propagation loss while keeping the total volume of the metal lattice unchanged.

2. The low-loss SPP design method based on anisotropic stretched metal according to claim 1 is characterized in that: Also included is step 4: calculation of the SPP losses characterizing the anisotropic tensile metal.

3. The low-loss SPP design method based on anisotropic stretched metal according to claim 2, characterized in that: There are two methods for calculating the SPP loss of anisotropic stretched metals: the method for calculating the SPP energy loss along the anisotropic stretched metal-air interface and the method for calculating the imaginary part of the dielectric function of the loss of different crystal planes themselves. The physical quantities that characterize SPP loss include three: the collision probability of electrons , the imaginary part of the dielectric function of the material , SPP energy loss Or the SPP propagation length L, the three physical quantities are positively correlated, expressed as (7).

4. The low-loss SPP design method based on anisotropic stretched metal according to claim 3 is characterized in that: The method for calculating the SPP energy loss along the anisotropic stretched metal-air interface includes a theoretical calculation method, which includes the following steps: T1: Based on the Drude model, the collision frequency of electrons on metals Corrected, the formula is (1), where represents the intrinsic damping of the metal itself without considering the lattice stretching, and denote the stretching coefficients along the in-plane x-direction and out-of-plane z-direction, respectively. represents the modified damping after considering the in-plane and out-of-plane stretching; T2: Based on the Drude model, the dielectric function of the metal is further modified. The formula is: （2）； （3）； （4）； in, is the dielectric function under the free electron gas model, is the modified dielectric function after taking into account the different atomic arrangements of the lattice; T3: The electric field formula of SPP is (5), where is the propagation wave vector of the SPP along the plane, k is the attenuation wave vector of the SPP along the plane; T4: According to electromagnetic field theory, the skin depth is calculated as one original cycle The energy loss under the condition of , the formula for calculating SPP energy loss is: (6), where , and is the stretch coefficient.

5. The low-loss SPP design method based on anisotropic stretched metal according to claim 4 is characterized in that: According to formula (6), the stretch coefficient and Calculate the energy loss under the corresponding stretching conditions; when When , it represents the anisotropic stretching while maintaining the lattice volume unchanged, which can be represented by the high-index crystal plane system of the metal. The specific crystal plane index (hkl) satisfies the relationship k=h,l=h-1.

6. The low-loss SPP design method based on anisotropic stretched metal according to claim 3, characterized in that: The method for calculating the imaginary part of the dielectric function of the loss of different crystal planes includes a theoretical calculation method, which includes the following steps: S1: For anisotropically stretched high-index crystal face metal system with crystal face index (hkl) satisfying k=h,l=h-1, the corresponding SPP energy loss comparison can be expressed as follows from the rigid potential dispersion model RPM: (8), where and is the stretch coefficient; S2: According to formula (7), we can get (9); S3: According to the dielectric function of the Durde model, we can get (10), （11）。 7. The low-loss SPP design method based on anisotropic stretched metal according to claim 3, characterized in that: The method for calculating the energy loss of SPP propagating along the anisotropic stretched metal-air interface includes an experimental calculation method, which includes the following steps: T5: Before measurement, design SPP coupling grating structures for metals with different crystal planes to meet SPP excitation conditions; T6: Use the built reflective far-field test optical path to collect SPP propagation images; T7: The SPP propagation length L is obtained by performing exponential fitting on the outcoupling light intensity I at different propagation distances d. T8: The longer the SPP propagation length L, the smaller the SPP energy loss; the shorter the SPP propagation length L, the greater the SPP energy loss.

8. The low-loss SPP design method based on anisotropic stretched metal according to claim 3, characterized in that: The method for calculating the imaginary part of the dielectric function of different crystal plane losses includes an experimental calculation method, which includes the following steps: S4: Before measurement, the single crystallinity of the sample was characterized by XRD; S5: Use AFM to calibrate the crystal axis orientation of single crystal metals with different crystal planes; S6: Perform dielectric function measurement using an ellipsometer, ensuring the incident angle is 60°. S7: Fit the raw data obtained by the ellipsometry with the Drude-Lorentz model to obtain the dielectric functions of metals with different crystal planes , by measuring the dielectric imaginary part of samples with different crystal planes By comparison, we can obtain the rule that loss decreases when transitioning from the low-index surface of the metal to the high-index surface.

9. The low-loss SPP design method based on anisotropic stretched metal according to claims 1-8, characterized in that: The metal may be high index single crystal copper.

10. The low-loss SPP design method based on anisotropic stretched metal according to claims 6 and 9, characterized in that: The dielectric function of bulk copper can be used instead of Cu(110), which can be expressed as (12), (13).

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