Research on Surface Plasmon Resonance Sensing of Metal Nano hollow Elliptic Cylinder

In this article, a new three-dimensional multi-layered nanoscale elliptical cylinder structure-based surface plasmon resonance sensor is designed, which utilizes the finite difference time domain method and FDTD simulation software for numerical simulation. The top of the structure is an elliptical cylinder array attached to a gold film with nanoholes. The middle layer is a dielectric layer, which can restrict the electromagnetic field. The bottom layer is an Au film and Si substrate. Surface plasmon resonance is excited by a vertically incident plane wave structure, and the incident electromagnetic wave is coupled to local surface plasmon through gold nanoscale elliptical cylinders. By adjusting the relevant structural parameters, the structure’s resonance wavelength and resonance depth can be well adjusted. The optimized sensing structure has a smaller half-width than the traditional solid elliptical cylinder, higher sensitivity, and a larger quality factor. This structure can detect refractive indices in both gaseous and liquid environments, overcome the disadvantage of only being able to sense in a single environment, and provide a new approach for surface plasmon resonance sensing in biology and chemistry.


Introduction
Surface plasmon resonance (SPR) is an optical phenomenon [1] that is widely used in fields such as medical detection, food testing, and environmental monitoring [2].The effective regulation of localized surface plasmon resonance (LSPR) effects through the artificial design and preparation of metal nanoperiodic arrays have been widely applied in fields such as optical communication and sensing, demonstrating advantages over traditional detection technologies [3].Compared to traditional detection techniques, SPR sensors have the advantages of real-time biological detection, high refractive index sensitivity, and no need for labeled samples.With the continuous development of nanofabrication and manufacturing technology [4], metal nanostructures that can excite surface plasmon resonance phenomena [5] have been widely applied in surface plasmon resonance sensing [6].In recent years, there have been many studies on the sensing and performance characteristics of nanoparticle shapes, including rod-shaped [7][8][9], spherical [10], square [11], and cylindrical structures [12,13].This article focuses on studying the cylindrical structure.
In 2016, Xu et al. proposed a simple method for preparing large-scale nanostructure arrays and studied the feasibility of using different diameters and periods of nanoarrays for refractive index sensing, which increased sensitivity by 60% and quality factor by 190% [14].In 2018, Wang et al. designed a periodic gold nanoring array structure and analyzed the influence of structural parameters on refractive index sensitivity.Finally, the structure was prepared and validated by laser holographic lithography technology, achieving a sensitivity of 577 nm/RIU [15].In 2019, Sioma Debela designed a surface plasmon resonance sensor for three layers of bimetallic nanoparticles in various geometric shapes.By changing the geometric shape, shell thickness, dielectric constant of the intermediate medium, thickness of the intermediate medium, and aspect ratio of the three layers of bimetallic nanoparticles, the surface plasmon resonance frequency can be tuned to the desired spectral range [16].In 2020, Jialin Ji studied the surface plasmon resonance of silver nanospheres on a silicon substrate gold film and achieved an adjustment of the absorption peak from 590 to 510 nm by increasing the thickness of the gold film [17].
The classic structure of metal-dielectric-metal (MDM) plasmon resonance is closely related to its surface morphology, metal particle size, shape, the refractive index of the environment, and so on [18].The particle size, shape, and spacing of gold nanoparticles have a significant impact on the wavelength and intensity of surface plasmon resonance.In addition, the gold-dielectric-gold surface plasmon resonance is also affected by the medium.In 2020, Y. F. C. Chau designed a structurally simple surface plasma polarization sensor consisting of a metal-insulator-metal waveguide containing multiple silver nanorod defects and numerically studied it using the finite element method for refractive index sensors and temperature sensors.The simulation results show that the presence of a single silver nanorod defect has a significant effect on the sensitivity performance, which provides an additional degree of manipulation of the system response at the nanoscale [19].In 2021, Y. F. C. Chau et al. used the finite element method to numerically investigate a plasma filter with a center-coupled ring resonator containing silver nanorod defects in a metal-insulator-metal structure.It is characterized by the time-coupled mode theory.The structure has high sensitivity and excellent coefficients [20].In 2021, Shengxi Jiao designed a three-layer periodic artificial metamaterial sensing structure composed of silver nanodisks, intermediate dielectric layers, and bottom silver reflectors.By optimizing the parameter structure, an absorption rate of 98.68% was achieved at a half-wave peak width of 3.5 nm, and the refractive index sensitivity reached 542 nm/RIU [21].
In 2022, Jiabao Jiang designed a surface plasmon resonance sensor based on the metal-dielectric-metal (MDM) structure, which is composed of AU gratings and Al 2 O 3 gratings.The maximum sensitivity can reach 362 nm/RIU [22].
There are also many types of research on hybrid MDMbased plasmonic nanostructure.In 2011, Yuan-Fong Chau for the first time used the finite element method to achieve near-field interaction and local surface plasmon resonance of a pair of silver-shell nanospheres with different dielectric pores embedded on a dielectric substrate.An electromagnetic pattern is different from that of solids of the same volume is excited inside and outside the shell surface, resulting in increased strength in the particle pair gap around the particle-substrate interface [23].
The two-dimensional periodic cavity resonance-based (CRB) plasmonic nanoantennas (PNAs) on the tailoring near field enhancement and optical spectrum of surface plasmon resonance (SPR) modes is numerically investigated by using the finite element method.The CRBPNAs consist of a single or double cavity on each antenna arm.A detailed physical explanation of the simulation results and the consistent dependence of SPR characteristics on CRBPNA structure and material parameters are given [24].
Most of the above-mentioned SPR sensors can only conduct high-sensitivity detection in a single environment and lack strong adaptability to the environment.In response to this problem, this article proposes a new type of refractive index sensor based on a gold nanohollow elliptical cylinder multilayer film structure that is based on the MDM classic structure.The proposed structure is simulated and calculated using the FDTD method, revealing that the surface plasmon resonance wavelength is extremely sensitive to the refractive index.Compared to traditional elliptical cylinder-induced surface plasmon resonance sensors and other classic MDM structure sensors, the proposed structure has higher sensitivity and quality factors.At the same time, the structure can be used in both gas and liquid environments, with maximum sensitivities of 602 nm/RIU and 578 nm/RIU achieved in gas and liquid environments, respectively.This sensor has great application value for use in a single environment.

Sensing Structure and Theoretical Methods
The designed composite structure is shown in Fig. 1, consisting of a three-dimensional structure with a top layer of gold nanohollow elliptical cylinder array capable of generating surface plasmon resonance phenomenon on its surface, a dielectric layer in the middle, and a bottom layer of Si substrate, forming a metal-dielectric-metal multilayer film.The entire array extends periodically in the X and Y directions, as shown in the figure.The height of the top gold film is denoted as t 1 , the thickness of the dielectric layer is denoted as d 1 , the thickness of the bottom gold film is denoted as t 2 , and the thickness of the Si substrate is denoted as d 3 .The height of the gold nanohollow elliptical cylinder and the hollow cavity is denoted as h, the short axis length of the elliptical cylinder is denoted as R 1 , the long axis length of the elliptical cylinder is denoted as R 2 , and the radius of the hollow cavity is denoted as R 3 .The period of the structure is denoted as p.
Analysis was performed using the three-dimensional finite-difference time-domain (FDTD) method and simulation software.The simulation software uses Lumerical Solutions' FDTD software, version 8.19.This method is widely used in optical simulation and can obtain the reflection spectrum and field strength of composite material structures.Perfectly matched layer (PML) boundary conditions were used on the upper and lower boundaries in the Z direction, the XY direction adopts the periodic boundary condition, the monitor records the monitoring point set to 400, and the mesh grid size is 20 nm.The incident light is a plane wave.The direction of the incident light is vertically incident along the negative half axis of the Z axis, and there is no inclination angle, the wavelength is 700-900 nm, and the polarization direction is XY direction.According to the Drude model [25], metals contain a large number of free electrons, which are influenced by external electromagnetic fields, resulting in oscillations that form plasmons.Under different conditions, there are three different modes of this resonance: one is the plasmon oscillation that occurs inside the structure, the second is the surface plasmon mode that can propagate along the structure surface, and the third is the localized surface plasmon resonance that oscillates in standing wave form.
Under the excitation of an external electric field, longitudinal plasma oscillations are generated inside the metal.By introducing appropriate boundary conditions into the metal Maxwell equations, the expression for the oscillation frequency inside the metal can be obtained: where n is the degree of electron freedom in the metal, e is the electron charge, m is the electron mass, and ε is the dielectric constant of the metal in a vacuum.According to the Drude model, the dielectric constant of the metal is expressed as where the plasma frequency p = 2 × 2.175 × 10 15 Hz , and metal scattering frequency c = 2 × 6.49 × 10 14 Hz , When incident light excites surface plasmon resonance in a composite structure, surface plasma waves become highly sensitive to changes in the environmental medium.Therefore, the deviation of the resonance wavelength corresponds to the refractive index (RI) change of the object to be measured.RI sensing can be achieved by establishing a curve corresponding to the RI of the object to be measured and the resonance wavelength.Refractive index sensitivity [26] and figure of merit (FOM) are important indicators of sensor performance [27], and their values increase with better sensor performance.The refractive index sensitivity can be expressed as and the FOM can be expressed as FOM = S FWHM , where FWHM is the full width at half maximum of the plasmon resonance peak, and the smaller the FHWM, the higher the quality factor.

Discussion and Analysis
Numerical simulations of the sensor were conducted using the 3D FDTD method, where the corresponding structural parameters were set as h = 40 nm, R 1 = 100 nm, R 2 = 175 nm, t 1 = 50 nm, d 1 = 60 nm, t 2 = 200 nm, d 2 = 2000 nm, and p = 620 nm. Figure 2(a) shows the reflectance spectrum of plasmonic resonance, where the energy of the incident light wave resonates with the surface plasmon wave, resulting in a resonance peak in the spectrum.The corresponding incident wavelength is the resonance wavelength, which can be found to be at 765 nm, and the width of the spectrum is the half-maximum width that is 8.6 nm.Reflectance is the ratio of the flux reflected to that incident on a surface.The resonance depth is the difference between the maximum reflectance and the peak reflectance, and it can also be represented as the coupling efficiency between the incident light and the metal surface plasmon wave.The deeper the depth, the greater the coupling efficiency.When the depth reaches half of the corresponding wavelength, the width of the spectrum is the half-maximum width (FWHM).FWHM represents the loss degree of the surface plasmon polariton, where a wider FWHM leads to greater loss and poorer sensing performance.Figure 2(c) shows the plasmon resonance reflection spectra of the traditional elliptical cylinder structure.Compared with Fig. 2 (a) and (c), it can be found that the ellipsoidal structure designed in this study has greater resonance depth and higher coupling efficiency than the cylindrical structure.
Figure 2(b) shows the surface electric field diagram of the gold nanostructure at 765 nm of the plasmon formant of the elliptical cylinder structure, and Fig. 2(d) shows the surface electric field diagram of the nanostructure corresponding to the cylinder structure.Compared with the traditional cylindrical surface plasmon resonance, the elliptic cylindrical structure designed in this study has higher electric field intensity and more intense plasmon resonance.The surface electric field distribution after surface plasmon resonance can be more clearly obtained from the electric field diagram of the metal surface.When light is irradiated onto the metal surface, there are many electrons on the surface of the metal, which collectively resonate with the light wave, resulting in a large amount of energy accumulation, numerically represented by the strength of the electric field.As shown in the figure, the electric field strength on both sides of the hollow elliptical cylinder is larger, while that at the hollow position is smaller, indicating that resonance occurs at the interface between the metal and the dielectric.The electric fields on both sides of the metal are highly concentrated, indicating that the plasmonic resonance is stronger in this area due to the sharper edges of the elliptical cylinder, which can accumulate a large number of electrons.At the same time, it can also be found that the electric field strength is larger on the surface of the hollow elliptical cylinder and smaller inside, which can fully prove that the plasmonic resonance occurs on the metal surface.The structural parameters will affect the performance of the plasmonic resonance sensor.To obtain the optimal performance of the sensor, it is necessary to optimize and analyze the structural parameters of the sensor.The parameters of the sensing structure mainly include the height of the gold nanocylinder, the ratio of its major and minor axes, the size of the hollow region, the period size, and the thickness of the dielectric layer.
Figure 3 shows the variation of the reflectance spectrum with the height of the gold nanohollow elliptical cylinder in the wavelength range of 700-900 nm through FDTD simulations.When the height of the top gold nanohollow elliptical cylinder changes from 30 to 60 nm, the reflectance spectrum undergoes a redshift, and the resonance depth gradually decreases, while the FWHM slightly increases.When the height is 30 nm, the resonance depth reaches 99.9%, the coupling efficiency is the highest, the reflectance is the largest, and the resonance effect is optimal.
For a cylinder, the main resonance mode is the transverse electromagnetic wave, and its resonance frequency is related to the height of the cylinder.When the height of the cylinder is small, the resonance frequency is high, while when the height of the cylinder is large, the resonance frequency is low.Therefore, the height of the cylinder affects the resonance mode [28].At the same time, the height of the cylinder also affects the local electric field strength and energy transfer efficiency of plasma resonance.When the height of the cylinder is within a certain range, the electric field strength is stronger and the energy transfer efficiency is higher, which leads to a stronger plasma resonance [29].When the height of the cylinder exceeds a threshold, the energy transfer efficiency decreases, resulting in a weakening of the plasma resonance intensity.
The length of the major and minor axes of the elliptical cylinder is also an important parameter that affects the sensor performance.When the length of the long axis and the Fig. 3 The reflectance spectrum varies with the height of elliptical cylinders Fig. 4 Variation of reflectance spectrum with the ratio of major and minor axes of elliptical cylinders Fig. 5 The reflectance spectrum varies with hollow aperture short axis are 290 nm and 200 nm, respectively, that is, the ratio of the long axis to the short axis is 1.45:1, as shown in Fig. 4, the resonance peak is at 755 nm.With the increasing ratio of the length of the major axis to that of the minor axis, the resonance peak continuously shifts towards longer wavelengths, and the resonance depth gradually increases.When the ratio of the length of the major axis to that of the minor axis is 1.75:1, the resonance depth reaches over 99% at 762 nm, achieving the best resonance effect.When the ratio of the long axis to the short axis is 1:1, the elliptical cylinder becomes a cylinder.When the radius is 350 nm, the resonance depth is only 76%, which also shows that the ratio of the length of the long axis and the short axis affects the effect of the surface plasma resonance, and also plays a crucial role in the performance of the sensor.When the ratio of the length of the major axis to that of the minor axis is larger, the ends become sharper and a large number of electrons gather at the edges.It can also be seen from the edge intensity comparison between Fig. 2b and d that the electric field intensity at both ends of the elliptical cylinder structure is significantly higher than that of the cylinder structure, and the localized near-field characteristic of the metal nanostructure becomes more obvious [30].
The more concentrated the free electrons are, the greater and more concentrated the energy generated by the free electron resonance will be.The excitation effect of this elliptical cylinder structure is significantly higher than the resonance strength of the cylinder, which provides a new idea for exciting plasma resonance in the cylinder.
Figure 5 shows the influence of the size of the hollow elliptical cylinder aperture on the resonance depth of the sensing structure.The reflection spectrum changes with Fig. 6 The reflectance spectrum of periodic changes in the gold-electrolyte-gold structure Fig. 7 Reflectance spectrum as a function of refractive index in a gas environment the variation of the hollow aperture radius by simulation experiments.When the elliptical cylinder has no hole, its resonance depth is the smallest compared to that with a hole, indicating that the hollow structure affects the performance of the sensor [31,32].
When the aperture size increases, the spectrum shifts towards longer wavelengths, and the resonance depth increases accordingly.The maximum resonance depth is achieved when the aperture size is 40 nm.The size of the hollow aperture directly affects the surface area of the excitation body, thereby affecting its resonance frequency and leading to changes in its coupling efficiency.When the elliptical cylinder has no hole, the surface area is small, and the resonance frequency is low; when there is a nanohole, the surface area of the excitation body increases, leading to an increase in resonance frequency and resonance depth, thereby improving the performance of the sensor.However, the resonance depth does not continue to increase when the aperture size reaches a threshold.Compared with the elliptical cylinder without a hole as the excitation body, the hollow elliptical cylinder has a higher coupling efficiency and superior sensing performance.
Periodicity is also an important parameter that affects the sensor performance.Figure 6 shows the variation of the reflection spectrum with the change of the period.As the period increases, the reflection spectrum shifts towards longer wavelengths.The resonance depths of the reflection spectra at 560 nm, 580 nm, 600 nm, and 620 nm all reach over 99%.For this structure, changing the period size can tune the resonance wavelength of the sensing structure.The optimal value of the period is 620 nm.
In summary, the optimal geometric parameters of the composite material structure after parameter optimization are obtained.The height of the gold nanoeccentric cylinder is 30 nm, the length of its major axis is 175 nm, the length of its minor axis is 100 nm, the height of the top gold film is 40 nm, the height of the dielectric layer is 50 nm, the height of the bottom gold film is 60 nm, and the height of the Si substrate is 2000 nm, which is the optimal parameter.To further explore the sensor performance, the sensitivity of the sensor was analyzed.Refractive index sensing is achieved by measuring the shift of the resonant peak position in the corresponding reflection spectrum with the change of refractive index.The larger the resonant peak shift per unit RI, the better the sensing performance and the higher the sensitivity.The figure below shows the reflection spectra of the sensor under different environmental refractive index changes in both liquid and gas conditions.It can be seen from the reflection spectra that as the refractive index of the measured object increases, the resonance wavelength shifts towards longer wavelengths, and the half-peak width and resonance depth of the spectrum are unaffected, so it can be used as a refractive index sensing device.
As shown in Fig. 7, the refractive index range of the measured gas is from 1.1 to 1.15.Changes in the environmental refractive index cause a shift in the resonance wavelength.
Fig. 8 The fitting curve of refractive index change in a gas environment Fig. 9 The refractive index changes the reflectance spectrum in a liquid environment Figure 8 shows the fitting curve of refractive index changes in the gas environment, and the sensitivity in the gas environment was calculated to be 602 nm/RIU.As shown in Fig. 9, the refractive index range of the measured liquid is from 1.3 to 1.35.Figure 10 shows the fitting curve of refractive index changes in the liquid environment, and the sensitivity in the liquid environment was calculated to be 578 nm/RIU.As shown in Table 1, compared to other surface plasmon resonance structures, this structure is highly sensitive to refractive index changes in both gas and liquid environments.
Compared with traditional elliptical cylinder nanostructure sensors with sensitivities of only a few tens, this structure has greatly improved sensitivity.The quality factor is also important for measuring the performance of plasmon resonance sensors, represented by the ratio of sensitivity to FWHM.The FOM value is related to the propagation loss of SPR.When the diffraction field of the incident light is coupled with the surface mode to form a resonance, it is reflected as the ratio of stored energy and lost energy in the composite structure after a certain time.In the frequency domain, it is also equal to the ratio of the center frequency of the resonance mode to the half-height width of the mode frequency.The higher the FOM value, the smaller the loss per unit of time, and the stronger the time localization of the composite structure.The quality factors in gas and liquid environments were calculated to be 78.1 RIU-1 and 66.8 RIU-1, respectively.
Both the sensitivity and quality factors demonstrate that this sensing structure has superior performance and great potential for applications in detecting small refractive index changes and as a tunable metal device.It also demonstrates high adaptability to gas and liquid environments, making it highly applicable for sensing in single-medium environments.

Conclusion
In conclusion, surface plasmon resonance has become a hot research area, and the AU-dielectric-AU nanoperiodic array sensing structure designed based on this theoretical foundation has good stability.Simulating and optimizing its electromagnetic and spectral characteristics through finite difference methods can achieve high refractive index sensitivity detection in dual gas and liquid environments.Compared with traditional elliptical cylinder structures, it has higher sensitivity and quality factor in the visible light band, with a sensitivity of 578 nm/RIU and 602 nm/RIU in gas and liquid environments, respectively.The structure will provide new ideas for the wide application of surface plasmon resonance sensors in biochemistry sensing.

Fig. 2
Fig. 2 Sensor performance: a elliptic cylinder reflectance spectrum, b elliptic cylinder surface electric field, c cylinder reflectance spectrum, and d cylinder surface electric field