Introduction

Nano-scale structures usually show completely different characteristics from block structures1,2. For example, our common quantum dot structure not only shows very high luminous efficiency, but also the luminous wavelength can be freely regulated by structural parameters3,4. For metal materials, when it is of nanometer size, the electron cloud on the particle surface will resonate under the irradiation of incident light. The resonance effect can localize the incident light on the surface of metal nanoparticles (MNP), resulting in a great enhancement of the electric field strength on the surface of MNP5. The local electric field intensity on the surface of MNP and the position of resonance peak are closely related to the morphology, size, material and surrounding dielectric environment of MNP6,7,8,9. Therefore, these optical properties enable us to study the surface structure, plasmon mode, carrier lifetime and charge-energy transfer of MNP10,11,12,13. Based on these important properties, MNP show potential applications in many fields, such as surface-enhanced Raman scattering, fluorescence enhancement, photovoltaic efficiency, random laser, photocatalysis, wave-absorbing stealth and so on14,15,16,17,18,19.

The morphology and size of MNP can affect the position of resonance peak in a large range, and MNP with tip structure can also form hot spot effect, which can greatly enhance the local electric field on the surface of MNP, especially nano-stars, nano-sea urchins and other morphologies20,21. It is found that the hot spot effect comes not only from the tip structure of metal nanoparticles, but also from two metal nanoparticles close to each other22. In addition, when metal nanoparticles are placed on the mirror, they will also form a hot spot effect in their gaps23. Some interesting characteristics will appear in the nanoparticle-on-mirror (NPOM) structures, such as mixed plasmon mode, great local field enhancement at hot spots, shift of resonant wavelength of plasmon, and so on. Among them, NPOM structure has the advantages of simple preparation, stable structure, wide-band adjustable and highly repeatable optical properties, so it can be designed as a promising platform for application in many fields. At present, the NPOM structure has aroused great interest among researchers23,24,25,26. Jin-Woo Oh group23 studied the coupling effect between silver nanoparticles and gold thin films. They mainly analyze the influence of the thickness of the dielectric layer between the particles and the film on the maximum local electric field and the position of resonant wavelength. The results show that gap mode mainly appears when the thickness of the dielectric layer is small (≤ 4 nm), and nanoparticle mode will appear with the increase of the thickness of the dielectric layer. T. Hutter team24 proposed a coupling model of silver nanoparticles and dielectric substrates. When the thickness of gap is kept at 2 nm, it is found that the maximum local electric field at gap is proportional to the refractive index of the substrate material. M. L.Chapelle25 studied the coupling between cylindrical gold nanoparticles and gold thin films. He observed that the electric field enhancement mainly occurs on the surface of cylindrical gold nanoparticles, and the position of the resonance peak can be adjusted by changing the parameters of the nanoparticles. However, in previous studies, the regulation range of local electric field resonance peak wavelength is narrow, which limits the follow-up application of this structure. In order to solve this limitation problem, many researchers choose ellipse, mushroom, bowtie array structure27,28,29. Among them, B. Gu team27 compared the SERS substrate detection work of the above three array structures. The results show that the ellipsoidal array has higher Raman enhancement properties than the mushroom and bowtie array when it is used as SERS substrate.

Based on the above analysis, we report a NPOM structure composed of gold ellipsoidal nanoparticles (GENP) and gold thin films. The enhancement characteristics of the local electric field on the surface of vertical and horizontal GENP by incident light with the same polarization direction are compared theoretically. At the same time, based on the coupling characteristics between the GENP and the mirror in the NPOM structure, the maximum value and wavelength position of the local electric field in the gap are studied by changing the thickness of the dielectric layer between them. The proposed gap plasmon structure provides a new opportunity for the design of MNP with excellent properties. It has a broad prospect in spectrum, sensing and other application fields.

Simulation model and methods

We use the finite element method to study the NPOM structure proposed in this paper, in which the GENP and the mirror are separated by the dielectric layer, and hot spots will be formed in the gaps of the nanometer scale. The specific structural model is shown in Fig. 1a. The parameters of the material are set as follows: the radius of the major axis of the GENP ra is fixed as 30 nm. The minor axis radius rb of the ellipsoid is determined by the aspect ratios of the GENP. The thickness of the dielectric layer is expressed by t. Because the size of t has an important influence on the local field at the gap, we will study the electric field distribution and electric field intensity at gap by adjusting t. The section view of the simulation model is shown in Fig. 1b. Throughout the paper, the refractive index of the dielectric layer n = 1.36 remains unchanged. The refractive index n0 of the medium around the GENP remains unchanged (n0 = 1). The thickness of the gold thin films is 100 nm. We set up a perfect matching layer around the whole model. Its main function is to completely absorb the scattered electromagnetic waves in the model and prevent the scattered electromagnetic waves from being reflected back. In the absence of MNP, we first set the perfectly matched layer to 100 nm, and the calculation results show that the thickness has been able to fully absorb the scattered electromagnetic waves. The mesh size at the gap is set to 0.2 nm to ensure the accuracy of the calculation results. The grid size around the MNP and the gold thin films region is set to 2 nm, which not only ensures the accuracy of the calculation results, but also saves the calculation time. The direction of incident light is vertical downward, and the direction of the electric field is horizontal, as shown in Fig. 1b. The optical parameters of GENP and gold thin films are mainly referred to the literature30. The electric field in this paper is calculated in the form of ratio, that is, E/E0. Where E represents the electric field in the presence of GENP, and E0 represents the value of the incident electric field. The near field discussed refers to the maximum value of E/E0.

Fig. 1
figure 1

Schematic configuration (a) and calculation model (b) with NPOM structures separated by a dielectric layer.

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Results and discussion

Electric field intensity of vertical and horizontal GENP surfaces

Under the excitation of incident light, a strong local electric field will be formed on the surface of MNP. This characteristic has important applications in SERS, fluorescence enhancement, solar cell efficiency enhancement and so on. We first calculate the local electric field distribution of a vertical and horizontal GENP in a uniform medium, as shown in the illustration in Fig. 2a-b. The aspect ratios of the GENP are both 2.0. The insets in Fig. 2a-b are electric field distributions of GENP with an incident wavelength of 520 nm. It can be seen from the figure that the electric field is mainly localized on the surface of MNP, and the electric field intensity decreases rapidly with the increase of the distance from the surface. In order to determine the attenuation of the electric field intensity on their surface, we draw the electric field intensity value in the horizontal direction between the GENP (Fig. 2a-b inset green line), and the specific electric field intensity position coordinate curve is shown in Fig. 2a-b. The results show that the electric field intensity on the surface of GENP is the largest, and there is an obvious decrease after leaving the surface of GENP, but there is a significant difference between them. We chose the position from the surface 60 nm as the furthest distance, and its specific value is shown in the right circle in the Fig. 2a-b. In the figure, we use the red thick arrow to indicate the changing trend of the maximum electric field on the surface of the GENP to the 60 nm position from the surface, and calculate their electric field attenuation ratio, the results are shown in Fig. 2c. Through the bar chart of Fig. 2c, we can clearly see that the electric field attenuation ratio of vertical and horizontal GENP are 70% and 31%, respectively. Because the electric field is mainly localized in the sub-wavelength range, the electric field strength will attenuation rapidly after leaving the GENP surface. Therefore, when MNP are used for fluorescence enhancement, it is particularly important to regulate the thickness of the spacer layer between the luminescent material and the surface of the MNP31.

Fig. 2
figure 2

Corresponds to the electric field value of the horizontal line (green line) in the middle of (a) Vertical GENP, (b) Horizontal GENP, (c) The electric field decay rate of 60 nm away from the horizontal surface of the GENP. (The arrows pointing to the left in Fig. 2(a) and (b) are the local electric field intensity on the surface of the nanoparticles. The arrow pointing downward is the local electric field intensity at the distance from the 60 nm on the surface of the nanoparticles.)

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Effect of aspect ratio on electric field intensity of GENP surface

The resonance characteristics of MNP are closely related to their morphology. Next, we will study the effect of aspect ratios on the local electric field on the surface of GENP. We selected five kinds of GENP of aspect ratios (1.5, 2.0, 2.5, 3.0, 3.5) as the research object. When building the models, the polarization direction of incident light in these two models was kept unchanged. The LSPR characteristics of vertical and horizontal GENP under the same incident light polarization direction were studied respectively. Firstly, the effect of aspect ratios on the surface electric field of vertical GENP is studied, and the electric field distribution is shown in Fig. 3a1-a5. It can be seen from the figure that transverse plasmon oscillations are formed on the surface of vertical GENP. At the same time, it can be seen that the electric field is mainly localized on the surface of vertical GENP. In order to accurately obtain the effect of aspect ratios on the surface electric field, we calculated the resonance spectra of the GENP of each aspect ratios, as shown in Fig. 3c. As can be seen from Fig. 3c, the wavelength of the resonant peak shifts 8 nm with the change of aspect ratio. At the same time, the electric field intensity of the resonant peak decreases with the increase of aspect ratio. This shows that the larger the aspect ratios is, the smaller the local electric field on the surface is. Under the condition of the same polarization direction of incident light, the electric field distribution of horizontal GENP is significantly different from that of vertical, as shown in Fig. 3b1-b5. It can be seen from the figure that longitudinal plasmon oscillations are formed on the surface of horizontal GENP. Then we calculate the resonance spectrum of horizontal GENP, as shown in Fig. 3d. As can be seen from the figure, the wavelength of the resonance peak has a red shift of 18 nm with the increase of aspect ratio. In addition, it can be seen that the intensity of the resonance peak increases with the increase of aspect ratios, which is opposite to that of vertical GENP. The main reason is that the hot spot effect is formed at the tip of horizontal GENP, which produces a stronger local electric field under the excitation of incident light.

Fig. 3
figure 3

(a1-a5) Electric field distribution of vertical GENP with different aspect ratios, (b1-b5) Electric field distribution of horizontal GENP with different aspect ratios, (c) Resonance spectra of vertical GENP with different aspect ratios, (d) Resonance spectra of horizontal GENP with different aspect ratios.

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Coupling effect of NPOM structure composed of GENP and gold thin films

The near-field enhancement property of single MNP is weak, and even the hot spot effect formed by MNP with tip structure can only be enhanced by a few hundred times. However, the near-field enhancement caused by the coupling effect of NPOM structure is very strong. We first analyze the coupling effect of the NPOM structure composed of vertical GENP and gold thin films, and the model is shown in Fig. 1. The aspect ratios of GENP remains unchanged at 2.5. In the NPOM structure, the thickness of the dielectric layer t is the most important factor affecting the near field strength of the gap. Therefore, we change the value of t from 0 nm to 10 nm while keeping other parameters unchanged, and the local field-enhanced resonant spectrum is shown in Fig. 4a. It can be seen from the figure that the smaller t is, the greater the local electric field intensity is. When t is equal to 0 nm, the maximum electric field intensity is close to 2200 (V/m). With the increase of t, the effect of local electric field intensity becomes weaker. When t increases to 4 nm, the peak value of the local electric field is less than 120 (V/m). As the t continues to increase, the decrease of the local electric field becomes smaller and smaller, as shown in Fig. 4b. On the other hand, the wavelength of the resonant peak of the local electric field is blue-shifted with the increase of the t. This is because there is a strong coupling effect between the GENP and the gold substrate, thus forming a “hot spot” at the gap. The extra surface charge mode appears in the gap formed in metal-insulator-metal. Under this very small gap size, the additional contribution from the surface of the planar gold film is mirrored coupled with the GENP, resulting in a larger near-field enhancement in the gap region. When the thickness of the dielectric layer increases, the additional contribution from the gold film substrate will decrease, resulting in a blue shift of the resonance peak wavelength at the gap of the NPOM structure. Through Fig. 4b, we can also find that with the increase of t, the change of the wavelength position corresponding to the local electric field resonance peak is less and less obvious. The peak value of the local electric field resonance spectrum and its wavelength position are affected by t. Using the data in Fig. 4a, we draw a detailed trend between them, as shown in Fig. 4c. It can be seen from Fig. 4c that the peak intensity and wavelength position of the local electric field resonance spectrum are inversely proportional to the t. When the t is very small (< 1 nm), they will decrease rapidly with the increase of t. When the t exceeds that of 2 nm, the trend of their change becomes smaller and smaller. If we further increase t, the peak intensity and wavelength position of the local electric field resonance spectrum will not change. This is mainly because the coupling effect between GENP and metal films is very weak when t is large. Finally, we draw the electric field position distribution map of the NPOM structure, and the result is shown in Fig. 4d. The abscissa is the white line coordinate in the illustration of Fig. 4d. As you can see from Fig. 4d, there is a minimum value in the central position within the gap of the NPOM structure. On the other hand, there is a maximum local electric field on both sides, and the result of electric field distribution is consistent with that in reference24.

Fig. 4
figure 4

NPOM structure of vertical GENP and gold thin films. (a) Local field enhanced spectra at gap with different t. (b) The amplified local field enhanced spectrum in Fig. 4a, the t is 4–10 nm. (c) The maximum resonance peak and its wavelength of the local field enhanced spectrum corresponding to different t are shown in Fig. 4a. (d) The normalized value of the local field intensity on the horizontal line at the gap between the vertical GENP and the dielectric layer (white line coordinates of the illustration).

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As shown in Fig. 5, the electric field distribution section (XZ) of vertical GENP and gold thin film NPOM structure at different t, in which the selected wavelength is the corresponding position to the resonance peak in Fig. 4a. It can be seen from the figure that when t is less than 1.4 nm, the electric field is mainly distributed in the gap position of the NPOM structure. With the increase of t, there is a strong electric field distribution on both sides of the surface of vertical GENP. When t reaches 4 nm, this phenomenon is already obvious. If we continue to increase the thickness of t, the local electric field at gap in NPOM structure becomes weaker gradually. This is consistent with the analysis results in Fig. 4. The coupling effect between vertical GENP and gold thin films decreases gradually and disappears with the increase of t. It can be seen in Fig. 5g that there is no local electric field at the gap position in the NPOM structure. Therefore, when we apply the NPOM structure to practice, we must fully consider the thickness of the dielectric layer.

Fig. 5
figure 5

Cross-sectional (XZ) electric field distribution of vertical GENP with different t. (The wavelength is the position of the resonance peak.)

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In the NPOM structure, the dielectric environment around the MNP can also affect the local electric field intensity in the gap region. When we simulate in Fig. 4, the surrounding medium is air, and the refractive index n0 of the dielectric environment around the GENP is 1. In order to compare the influence of the surrounding dielectric environment on the local electric field in the gap region, six groups of different refractive indexes are compared, and the calculated results are shown in Fig. 6a. In the process of building the model, the aspect ratio of the ellipsoid is 2.5, the thickness t of the gap layer is 2 nm, the refractive index n of the gap layer is 1.36. The results of Fig. 6a show that the resonance peak of the local electric field resonance curve increases with the increase of refractive index n0. The value of the resonance peak increases from the initial 175 V/m to 277 V/m. The wavelength position of the resonance peak is red-shifted with the increase of refractive index n0. However, the larger the refractive index n0 is, the more obvious the red-shift trend is. The wavelength position red-shifts 45 nm with the increase of refractive index n0 from 1 to 1.5. In fact, the refractive index n of gap layer in NPOM structure is also a part of the dielectric environment. We set the refractive index n0 to 1 and change the refractive index n of the gap layer to compare the change of the local electric field intensity. As shown in Fig. 6b, the intensity of the local electric field resonance peak increases with the increase of refractive index n. The local electric field resonance peak intensity of n = 1.1 is 120 V/m, while when n is 1.6, the local electric field resonance peak intensity has increased to 280 V/m. The wavelength of the local electric field resonance peak is red-shifted with the increase of gap refractive index n. The resonance peak wavelength of n = 1.1 is 530 nm, while when n is 1.6, the resonance peak wavelength has increased to 535 nm. Through the above results, it can be found that the wavelength of the resonance peak in the gap region is more sensitive to the change of n0.

Fig. 6
figure 6

(a) Local electric field intensity of gap region at different n0 in vertical GENP NPOM structure. (b) Local electric field intensity of gap region at different n in vertical GENP NPOM structure.

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We have compared the resonance enhancement characteristics of vertical and horizontal GENP in the same polarization direction in Fig. 2. It has been proved that the direction of polarization has an important influence on the GENP with different placement methods. So is it the same conclusion about the structure of NPOM? We keep the polarization direction of the incident light unchanged, and place the GENP horizontally on the gold thin film. By comparing with the calculated results in Fig. 4, we can find out whether the GENP are affected by the polarization direction. As shown in Fig. 7a, we have studied the local electric field resonance enhancement characteristics of different t on horizontal GENP. It can be seen from the figure that when t is 0 nm, the maximum local electric field exceeds 9400 (V/m), which is much larger than the maximum local electric field when vertical GENP are coupled with gold thin films. It shows that the polarization direction of incident light has an important influence on the local electric field resonance enhancement of the surface of GENP. With the increase of t, the maximum value of local electric field at gap of NPOM structure decreases gradually. In addition, we found that there are two resonance peaks in the resonance spectra of the GENP when t is less than 2 nm. When t exceeds 4 nm, the sub-resonance peak in the resonance spectrum of GENP disappears, which is consistent with the simulation results in reference23. Because the sub-resonance peak disappears, we only consider the wavelength position of the main resonance peak. With the increase of t, the wavelength corresponding to the main resonance peak is blue-shifted. With the increase of the thickness of the dielectric layer, the additional contribution from the gold film substrate will decrease, resulting in a blue shift of the resonance peak wavelength in the gap region between the GENP and the gold film. In order to directly see the changing trend of the intensity of the resonance peak and its wavelength position with t, we draw their corresponding relationship according to Fig. 7a, as shown in Fig. 7b. It can be seen from Fig. 7b that the change trend of resonance peak intensity and wavelength position is the same. When t is small, the trend of change is greater. This trend slows down as t increases, which is consistent with the trend in Fig. 4c.

Fig. 7
figure 7

NPOM structure of horizontal GENP and gold thin films. (a) Local electric field spectra at gap with different t. (b) The intensity and wavelength position of the main resonance peak of the local electric field with different t in Fig. 6a.

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In the above study, it can be found that for the same t 0 nm, when the GENP vertical are placed in the gold film, the maximum local electric field at their gap is 2200 (V/m) (Fig. 4a). Under the same conditions, when the GENP are placed horizontally, the maximum local electric field at the gap is more than 9400 (V/m) (Fig. 6a). Therefore, their electric field distribution must be different. We select the wavelength of the main resonance peak in Fig. 7a and intercept the electric field distribution of XZ cross section in NPOM structure under different t, the results are shown in Fig. 8. As can be seen from the figure, the smaller t is, the stronger the local electric field at gap is. With the increase of t, the coupling effect at the gap of NPOM structure becomes weaker, and the internal local electric field decreases. As can be seen from Fig. 8g, when t is 6 nm, the electric field is mainly localized in the gap region and particularly concentrated (green coil), so the calculated electric field value is very strong. In Fig. 8g, it can be seen that the electric field is no longer very concentrated and localized in the gap region (green coil). Compared with the NPOM structure formed by vertical GENP, the gap region formed between horizontal GENP and gold substrate is more compact. Therefore, there is a stronger coupling effect between horizontal GENP and gold film substrate. As a result, the extra surface charge localized in the gap is also more, resulting in a stronger local electric field intensity. This is also consistent with the comparison of the local electric field intensity calculated in Figs. 4 and 7.

Fig. 8
figure 8

Cross-sectional (XZ) electric field distribution of horizontal GENP with different t. (The wavelength is the position of the resonance peak.)

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As shown in Fig. 6, the dielectric environment n0 and n around vertical GENP can have a significant impact on the local electric field intensity in the gap region. So whether the horizontally placed GENP is also affected by the dielectric environment n0 and n. We set the same parameters in the NPOM structure model, that is, the aspect ratio of the GENP is 2.5, the thickness of the gap layer t is 2 nm, and the calculated results are shown in Fig. 9. Figure 9a shows the effect of the change of refractive index n0 on the local resonant electric field in gap. It can be seen that two resonant peaks appear in the gap region. This means that a multipole resonance mode appears in the electric field in the gap region. The results show that the intensity of the local electric field resonance peak decreases with the increase of the refractive index n0, from the maximum 3287 V/m to 1778 V/m. The reason for this may be the interference and dispersion of the secondary resonant peak energy on the primary resonant peak. This is contrary to the relationship between the local electric field intensity and the refractive index n0 obtained by the NPOM structure composed of vertical GENP shown in Fig. 6a. When the refractive index n0 is 1, the wavelength of the resonance peak is at 690 nm. With the increase of refractive index, the wavelength of the resonance peak is red-shifted. When the refractive index n0 is 1.5, the wavelength of the resonance peak is at 800 nm, and its wavelength has a total red shift of 110 nm. Similarly, keep the refractive index n0 constant and change the refractive index n of the gap layer, and the result is shown in Fig. 9b. We can see from the figure that the intensity of the resonance peak increases rapidly with the increase of refractive index n. When the refractive index n is 1.6, the intensity of the local electric field resonance peak is higher than that of n is 1, which increases 2052 V/m. The wavelength of the resonance peak is red-shifted with the increase of refractive index n. When the refractive index n is 1, the wavelength of the resonance peak is at 655 nm. When the refractive index n is 1.6, the wavelength of the resonance peak is at 725 nm, and its wavelength has a total red shift of 70 nm. The results show that compared with the regulation of refractive index n, the wavelength of resonance peak is more sensitive to the regulation of refractive index n0.

Fig. 9
figure 9

(a) Local electric field intensity of gap region at different n0 in horizontal GENP NPOM structure. (b) Local electric field intensity of gap region at different n in horizontal GENP NPOM structure.

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Conclusion

In conclusion, we propose a numerical study of NPOM structure based on GENP and gold thin films. The local field enhancement properties of vertical and horizontal GENP in homogeneous media are compared by finite element method. The results show that the surface of horizontally placed GENP has a larger electric field under the same conditions. Based on the structural characteristics of GENP, we systematically studied the local field enhancement properties of NPOM structures composed of vertical and horizontal GENP and gold films. The results show that the local field of gap system formed by horizontal GENP is much larger than that in the vertical case. However, for the NPOM structure composed of these two kinds of GENP, the local field intensity at gap is inversely proportional to t. Based on the coupling effect between GENP and gold thin films, the maximum local electric field at gap in NPOM structure is more than 9400 (V/m) (t = 0 nm). The larger the t is, the weaker the coupling effect between them is, and the smaller the maximum local electric field at gap is. The proposed NPOM structure has a broad application prospect in the fields of plasmon, sensing, electronics and optics.