A surface lattice resonant metasurface device

Abstract

The application provides a surface lattice resonance (SLRs) super surface device, which comprises a substrate, a U-shaped split ring metal structure unit arranged in a periodic array on the substrate, and a buried material for burying the U-shaped split ring metal structure unit to provide a uniform refractive index background. When the period of the U-shaped split ring metal structure unit array is 1050 nm, and linearly polarized light is vertically incident on the super surface device, three resonance peaks appear in the transmission spectrum of the super surface device, wherein the half peak width of the resonance peak at the resonance wavelength of 1536 nm is 0.12 nm, and the resonance amplitude is 0.8, so that the super surface device realizes a Q factor of up to 12800. The Q factor is currently the highest not only in the metal array supporting SLRs, but also in other metal structures, which is of great significance for exploring the potential applications of high Q factor plasmonic resonance.

Description

Technical Field

[0001] This invention relates to the field of micro-nano photonic devices, and in particular to a surface lattice resonance metasurface optical device. Background Technology

[0002] Surface lattice resonances (SLRs) are collective resonance modes supported by periodic arrays of metallic nanostructures. The physical origin of SLRs lies in the coupling between localized surface plasmon resonances (LSPRs) excited by individual nanostructures and in-plane propagating diffraction orders generated by the entire periodic array. Since diffraction scattering effectively excites SLRs, rather than allowing the scattered beam to attenuate directly in free space, SLRs can significantly suppress radiation loss. Therefore, compared to other plasmon resonances, SLRs possess many attractive advantages, such as extremely narrow optical responses, significantly enhanced Q factors, and stronger field enhancements achievable on large volumes. These advantages, especially the high Q factor, make SLRs highly attractive in fundamental research and practical applications in areas such as strong coupling, nonlinear effects, directional emission, nanoscale lasers, and sensitive biosensing. Generally, the higher the Q factor, the wider its application range and the better its performance. In recent years, new methods for obtaining high Q-factor SLRs have been highly sought after.

[0003] To date, researchers have proposed various methods to improve the Q factor of SLRs. These methods include altering the shape, size, temperature, material, or adhesion layer of nanoparticles, utilizing light sources with better coherence, and changing the angle and polarization of the incident light, among others. However, these methods can only improve the Q factor to a few hundred, rarely reaching 10. 3 The order of magnitude is insufficient to meet the requirements of diverse applications.

[0004] Recent studies have focused on two main approaches to improving the Q factor of SLRs. One approach is to directly excite higher-order LSPRs, such as quadrupole resonances, and to utilize their dark-mode properties to enhance the Q factor [A. Yang, A. J. Hryn, MR. Bourgeois, W.-K. Lee, J. Hu, G. C. Schatz, and T. W. Dom, Proc Natl Acad Sci 113, 14201 (2016); X. Fang, L. Xiong, J. Shi, and G. Li, Opt Lett 46, 1546 (2021).]. On the other hand, complex particle arrays are used to achieve narrower spectral responses by realizing hybridization between different plasmonic modes and their antisymmetric modes, thereby improving the Q factor [A. Cuartero-González, S. Sanders, L. Zundel, A. I. Fernández-Domínguez, and A. Manjavacas, ACS Nano 14, 11876 (2020); L. Zundel, A. May, and A. Manjavacas, ACS Photonics 8, 360 (2021); A. D. Humphrey, N. Meinzer, A. T. Starkey, and W. L. Barnes, ACS Photonics 3, 634 (2016)]. To obtain higher-order LSPRs, it is usually necessary to use special vector illumination beams with in-plane phase distribution to excite in-plane quadrupoles in conventional symmetric nanostructure arrays, which is very difficult to achieve. The excitation of out-of-plane quadrupoles has strict requirements on the height of the nanostructure, which limits the use of ultrathin devices. Some studies have combined higher-order resonances and mode hybridization, such as using in-plane dipole and out-of-plane quadrupole coupling to improve the Q factor of SLRs [D. Wang, MR. Bourgeois, W.-K. Lee, R. Li, D. Trivedi, MP. Knudson, W. Wang, G. C. Schatz, and TWOdom, Nano Lett 18, 4549 (2018); C. Cherqui, MR. Bourgeois, D. Wang, and G. C. Schatz, Acc Chem Res 52, 2548 (2019)]. However, due to the inherent absorption and radiation losses being difficult to completely suppress, the Q factor of SLRs can only reach 10. 3 This is on the order of magnitude lower than the Q factor achieved in all-dielectric nanostructures. Summary of the Invention

[0005] To overcome the shortcomings of the aforementioned technologies, this invention utilizes a U-shaped split-ring resonator (U-SRR) array, achieving SLRs with an ultra-high Q factor by simultaneously exciting in-plane dipole and quadrupole resonances within it. Compared to traditional metal nanobulk arrays, this U-shaped nanostructure array significantly reduces its LSPR radiation, and the excitation of in-plane quadrupoles causes the U-SRRs to oscillate simultaneously in two orthogonal directions. When coupled with in-plane diffraction, standing waves are formed along the two mutually orthogonal directions, which confines more wave energy to the structural surface. This dual radiation suppression mechanism enables the SLRs to achieve a Q factor as high as 10. 4 This Q factor is currently the highest not only among metal arrays supporting SLRs, but also among other metal structures, which is of great significance for exploring the potential applications of high Q factor plasmon resonance.

[0006] It is worth noting that in practical applications, the Q factor is not the only performance indicator. The resonance amplitude, i.e. the signal intensity, is also very important in many applications involving detection. Therefore, in the design of surface lattice resonance metasurfaces, a trade-off is usually made between the resonance amplitude and the Q factor.

[0007] This invention employs both a numerical simulation method based on finite-difference time-domain (FDTD) and a semi-analytical method based on coupled dipole approximation (CDA). The consistency between the results obtained by the two methods demonstrates the reliability of the technical solution of this invention.

[0008] The technical solution of the present invention is as follows: The present invention provides a surface lattice resonance metasurface device, which includes:

[0009] Base;

[0010] U-shaped split-ring metal structural units arranged in a periodic array on a substrate; and

[0011] The U-shaped split-ring metal structural unit is buried within it to provide a uniform refractive index background as a burial material.

[0012] Preferably, the U-shaped split ring metal structure units are periodically arrayed on the substrate along the x and y directions of the x, y, z rectangular coordinate system; the U-shaped split ring metal structure units are made by symmetrically opening a groove with a width of s and a depth of w along the y direction on a square metal block with a side length of L and a thickness of H, where s = L / 3 and w = 2L / 3.

[0013] Optionally, the substrate is selected as a silica substrate, the burial material is selected as fused silica, and the U-shaped split ring metal structural unit is selected as being made of silver.

[0014] Preferably, the refractive index of the substrate and the burial material is 1.45.

[0015] Preferably, L is 240nm and H is 50nm.

[0016] Preferably, the period P of the U-shaped split ring metal structure units arranged in an array along the x and y directions is... x and P y All values ​​are taken as 1050 nm. When linearly polarized infrared light with electric field intensity along the x-direction is incident perpendicularly on the metasurface device, three resonance peaks appear in the transmission spectrum of the metasurface device, with resonance wavelengths of 930 nm, 1080 nm and 1536 nm, respectively. Among them, the resonance peak at the resonance wavelength of 1536 nm has a half-width of 0.12 nm and a resonance amplitude of 0.8. Thus, the metasurface device achieves a Q factor as high as 12800.

[0017] Optionally, the metasurface device can be numerically calculated using the finite-difference time-domain method and semi-analytically calculated using the coupled dipole approximation method. The resulting transmission spectrum of the metasurface device is consistent in terms of spectrum shape, resonance wavelength, resonance linewidth, and resonance amplitude.

[0018] Preferably, the resonance peak with a resonance wavelength of 930 nm in the transmission spectrum of the metasurface device is a localized surface plasmon resonance peak caused by a single U-shaped split-ring metal structural unit; while the resonance wavelengths of the resonance peaks with resonance wavelengths of 1080 nm and 1536 nm are consistent with the results calculated by the following theoretical formula:

[0019]

[0020] Where l and m are the diffraction orders of the Rayleigh anomaly, θ is the incident angle of the incident light incident on the metasurface device, φ is the azimuth angle characterizing the degree of deviation of the incident light from the defined incident surface, and when the incident light is incident perpendicularly on the metasurface device, θ = 0 and φ = 0; n is the refractive index of the buried material.

[0021] According to formulas (1), (2), and (3), the resonance peaks at wavelengths of 1080 nm and 1536 nm are both resonance peaks generated based on surface lattice resonance. The Rayleigh anomalous diffraction order of the former is l = 1, m = 1; and the Rayleigh anomalous diffraction order of the latter is l = 0, m = 1 and l = 1, m = 0.

[0022] The beneficial effects of this invention are as follows: This invention utilizes a U-shaped split-ring metal nanoarray to realize a metasurface device for SLRs with an ultra-high Q factor. By simultaneously exciting in-plane dipole and quadrupole resonances in the U-shaped split-ring metal nanoarray, SLRs with an ultra-high Q factor are achieved. Compared with conventional metal nanoblock arrays, this U-shaped split-ring nanostructure array can significantly reduce its LSPRs radiation. Moreover, the excitation of in-plane quadrupoles causes the U-SRR to oscillate simultaneously in two orthogonal directions. When coupled with in-plane diffraction, standing waves are formed along the two mutually orthogonal directions, which confines more wave energy to the structural surface. This dual radiation suppression mechanism enables the SLRs to achieve a Q factor as high as 10. 4 This Q-factor is currently the highest not only among metal arrays supporting SLRs, but also among other metal structures, which is of great significance for exploring the potential applications of high-Q-factor plasmon resonance. Furthermore, this invention has the advantages of simple structure, ease of fabrication, and convenient integration. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the surface lattice resonance metasurface device according to an embodiment of the present invention;

[0024] Figure 2 This is a dimensional diagram of the U-shaped split ring structure unit described in an embodiment of the present invention;

[0025] Figure 3 The transmission spectrum of the surface lattice resonance metasurface device obtained by the FDTD method in this embodiment of the invention;

[0026] Figure 4 The images show the transmission spectrum of the surface lattice resonance metasurface device calculated using the FDTD method and the CDA method respectively in the embodiments of the present invention, and the curves showing the variation of two key parameters in the CDA method, polarizability 1 / α and lattice and S, with the incident light wavelength. Detailed Implementation

[0027] To better understand the present invention, the following description, in conjunction with embodiments and accompanying drawings, further illustrates the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0028] like Figure 1 As shown, in this embodiment, the present invention provides a surface lattice resonance metasurface device, which includes: a substrate; U-shaped split ring metal structure units arranged in a periodic array on the substrate; and a burial material in which the U-shaped split ring metal structure units are buried to provide a uniform refractive index background.

[0029] In this embodiment, the U-shaped split-ring metal structural units are periodically arrayed on the substrate along the x and y directions of the x, y, z rectangular coordinate system. For example... Figure 2As shown, the U-shaped split ring metal structure unit can be made by symmetrically opening a groove with a width of s and a depth of w along the y direction on a square metal nanoblock with a side length of L and a thickness of H, where s = L / 3 and w = 2L / 3.

[0030] In this embodiment, the substrate is selected as a silicon dioxide substrate, the burial material is selected as fused silicon dioxide, and the U-shaped split ring metal structural unit is selected as being made of silver, a precious metal with a high cost-performance ratio.

[0031] In this embodiment, we use the finite-difference time-domain (FDTD) method to perform numerical calculations on the metasurface device. In the calculations, the refractive index of the silicon dioxide substrate and molten silicon dioxide is taken as 1.45. The dielectric of the noble metal silver used to fabricate the U-shaped split-ring metal structure unit is often taken from existing experimental data [PB Johnson, and R.-W. Christy, Phys Rev B 6, 4370 (1972)]. L is taken as 240 nm, H as 50 nm, and correspondingly, s = 80 nm and w = 160 nm. Therefore, the width of the metal strips constituting the U-shaped split-ring metal structure unit is equal along any direction. Furthermore, the period of the U-shaped split-ring metal structure unit array along the x and y directions is also taken as equal, i.e., P... x =P y =P, which simplifies the discussion of the parameters that affect the performance of this metasurface device.

[0032] In the calculations, linearly polarized light with an electric field intensity E along the x-direction was selected as the incident light, and the incident light was made to be perpendicular to the metasurface device. We obtained the Q factor of the metasurface device by simulating its transmission spectrum. It is worth noting that in practical applications, the Q factor is not the only performance indicator. The resonance amplitude, i.e., the signal intensity, is also very important in many applications involving detection. Therefore, in the design of surface lattice resonance metasurfaces, a trade-off is usually made between the resonance amplitude and the Q factor. Calculations show that the period P of the U-shaped split ring metal structure unit array is an effective structural parameter for balancing the Q factor and the resonance amplitude. In addition, the detuning between LSPRs and Rayleigh anomaly (RA) can also be adjusted by adjusting P, thereby adjusting the Q factor. In the calculations, we first scanned the values ​​of parameter P and determined the optimal value of parameter P while taking into account both the Q factor and the resonance amplitude. In this embodiment, the optimal value of P is 1050 nm. When P takes this optimal value, the transmission spectrum of the metasurface device is as follows. Figure 3 As shown.

[0033] from Figure 3It can be seen that three resonance wavelengths appear in the transmission spectrum of this metasurface device, namely 930nm, 1080nm and 1536nm. Among them, the full width at half maximum (FWHM) of the resonance peak at the resonance wavelength of 1536nm is 0.12nm and the resonance amplitude is 0.8. Thus, this metasurface device achieves a Q factor as high as 12800 with a relatively high resonance amplitude, which exceeds the Q factor of metal structure arrays in the prior art.

[0034] Considering the potential convergence issues in numerical simulations of ultra-high Q-factor resonances, we further employ a semi-analytical method using the Coupled Dipole Approximation (CDA) to analyze the optical response of the metasurface device to verify the reliability of the numerical results. The effectiveness of the CDA method in analyzing various optical responses of different nanostructure arrays has been confirmed. In the CDA method, the effective polarizability α of a single nanoparticle represents its optical response, while the lattice size and arrangement (S) represent the combined influence of the lattice size and arrangement. The total polarizability α of the nanostructure array is calculated using the combined influence of the individual nanoparticle and the entire lattice. * The contribution can be expressed by the following formula:

[0035]

[0036] When Re(1 / α) equals Re(S), α * Taking the maximum value corresponds to the resonance response caused by various mechanisms. For the transmission spectrum, this can be achieved through the extinction cross section E. xt To calculate transmittance:

[0037]

[0038] Where k is the wave vector in the background medium, k = 2πn / λ, n is the refractive index of the background medium, in this embodiment the background medium is the burial material, its refractive index is n = 1.45, and λ is the wavelength of the incident light; P x and P y These are the periods of the structural unit array along the x and y directions, respectively. In this embodiment, P x =P y =1050nm.

[0039] Figure 4 The middle figure shows the transmission spectrum of the U-shaped split-ring metal structural unit array calculated using the CDA method. For comparison, in Figure 4The results calculated using the FDTD method are also presented at the top. A comparison shows that the transmission spectra obtained by both methods contain three resonance peaks with different linewidths and resonance wavelengths of 930 nm, 1080 nm, and 1536 nm, respectively. Furthermore, the two methods are completely identical in shape, resonance position, resonance linewidth, and resonance amplitude. The consistency between the results obtained by the FDTD numerical method and the CDA semi-analytical method confirms the reliability of the results in this embodiment.

[0040] In order to reveal the resonance mechanism, Figure 4 At the bottom, the curves showing the variation of two key parameters in the CDA method, polarizability (1 / α) and lattice strength S, with the incident light wavelength are also given. According to CDA theory, all resonance sites originate from the intersection of the curves showing the variation of these two parameters with the incident light wavelength, i.e.

[0041]

[0042] and Figure 4 The three resonance positions of the two spectra in the top two figures perfectly coincide with the three intersection points of the two curves in the bottom figure. The resonance peak at the widest wavelength of 930 nm is the LSPR resonance peak, whose characteristics are only related to a single U-shaped split-ring metallic structural unit, and its resonance type can be determined by the scattering cross-section. The other two Fino linear resonance peaks are SLR resonance peaks of different orders, and their specific resonance wavelengths can be determined by the following formula:

[0043]

[0044] Where l and m are the diffraction orders of the Rayleigh anomaly (RA), θ is the incident angle of the incident light incident on the metasurface device, φ is the azimuth angle characterizing the degree of deviation of the incident light from the defined incident surface. In this embodiment, the incident light is incident perpendicularly on the metasurface device, so θ = 0 and φ = 0; n is the refractive index of the buried material, and in this embodiment, n = 1.45.

[0045] According to formulas (4), (5), and (6), the resonance peak at 1080 nm is the SLR resonance peak with l=1 and m=1, while the resonance peak at 1536 nm is the SLR resonance peak with l=0 and m=1 and l=1 and m=0.

[0046] In summary, this invention utilizes a U-shaped split-ring metal nanoarray to realize a metasurface device for SLRs with an ultra-high Q factor. By simultaneously exciting in-plane dipole and quadrupole resonances within the U-shaped split-ring metal nanoarray, SLRs with an ultra-high Q factor are achieved. Compared to conventional metal nanobulk arrays, this U-shaped split-ring nanostructure array significantly reduces its LSPR radiation. Furthermore, the excitation of in-plane quadrupoles causes the U-SRR to oscillate simultaneously in two orthogonal directions. When coupled with in-plane diffraction, standing waves are formed along the two mutually orthogonal directions, which confines more wave energy to the structural surface. This dual radiation suppression mechanism enables the SLRs to achieve a Q factor as high as 10. 4 This Q factor is currently the highest not only among metal arrays supporting SLRs, but also among other metal structures, which is of great significance for exploring the potential applications of high Q factor plasmon resonance.

[0047] It should be noted that those skilled in the art should understand that all modifications or combinations made to the present invention based on the technical content described in the above embodiments are within the scope of protection of the claims of the present invention.

Claims

1. A surface lattice resonance metasurface device, characterized in that, include: Base; U-shaped split-ring metal structural units arranged in a periodic array on the substrate; as well as The U-shaped split-ring metal structural unit is buried therein as a burial material to provide a uniform refractive index background; The U-shaped split ring metal structure units are periodically arrayed on the substrate along the x and y directions of the x, y, z rectangular coordinate system; The U-shaped split ring metal structure unit is made by symmetrically opening a groove with a width of s and a depth of w along the y direction on a square metal block with a side length of L and a thickness of H, where s=L / 3 and w=2L / 3; The substrate is selected as a silicon dioxide substrate, the burial material is selected as fused silicon dioxide, and the U-shaped split ring metal structural unit is selected as being made of silver; The refractive index of the substrate and the buried material is 1.45; L is set to 240nm, and H is set to 50nm; The period P of the U-shaped split ring metal structural units arranged in an array along the x and y directions x and P y All are taken as 1050nm; When linearly polarized infrared light with electric field strength along the x-direction is incident perpendicularly on the metasurface device, three resonance peaks appear in the transmission spectrum of the metasurface device, with corresponding resonance wavelengths of 930 nm, 1080 nm and 1536 nm, respectively. Among them, the resonance peak at the resonance wavelength of 1536 nm has a half-width of 0.12 nm and a resonance amplitude of 0.

8. Thus, the metasurface device achieves a Q factor as high as 12800.

2. The metasurface device as described in claim 1, characterized in that, The resonance peak with a resonance wavelength of 930 nm in the transmission spectrum of the metasurface device is a localized surface plasmon resonance peak caused by a single U-shaped split ring metal structural unit. The resonance wavelengths of the resonance peaks at 1080 nm and 1536 nm in the transmission spectrum of the metasurface device are consistent with the results calculated by the following theoretical formula: （1） （2） （3） Where l and m are the diffraction orders of the Rayleigh anomaly; θ is the incident angle of the incident light incident on the metasurface device; φ is the azimuth angle characterizing the degree of deviation of the incident light from the defined incident surface; when the incident light is perpendicularly incident on the metasurface device, θ=0 and φ=0; n is the refractive index of the buried material. According to formulas (1), (2), and (3), the resonance peak with a resonance wavelength of 1080 nm is a Rayleigh anomalous diffraction order of l=1 and m=1 generated by surface lattice resonance; the resonance peak with a resonance wavelength of 1536 nm is a Rayleigh anomalous diffraction order of l=0 and m=1 and l=1 and m=0 generated by surface lattice resonance.

Images