Plasmonic hybridized modes empowered by strong plasmon interaction in the nanograting-dielectric-metal stacked structure

Surface plasmons (SPs), as special surface waves, have attracted remarkable attention in various research fields due to their strong spatial localization and electromagnetic field enhancement at the subwavelength scale [1, 2]. Owing to their strong coupling strength and ultra-small mode volume [3], the hybridized modes of SPs and various other modes, such as Tamm plasmon polariton [4], waveguide (WG) mode [5], Fabry–Perot (FP) resonance [6], and excitons [7], have been widely studied and confirmed in a variety of optical systems in recent years. A series of interesting physical phenomena are disclosed by plasmonic hybridization coupling, mainly including Fano resonance, plasmon-induced resonance energy transfer, and strong coupling at the quantum level [8, 9]. Hybridization coupling provides a new perspective for understanding the interaction between light and matter to promote the development of fundamental physics. New opportunities are offered in numerous application fields, such as high-performance biochemical sensors, quantum information processing, ultrafast optical switching, novel nanolasers, and the like [6, 10, 11].

Until now, the coupling between SPs and WG modes is still an enduring research hotspot in a variety of resonance structures [12, 13]. The hybridization coupling mechanism is employed to reveal some novel spectrum phenomena, thus laying a basis for their potential applications [14, 15]. However, most of the reported WG-surface plasmon polaritons (WG-SPPs) coupled modes are still excited by bulky prism setup and have strict requirements to oblique incidence [12–16]. To the best of our knowledge, the hybridization coupling of SPPs on a flat metal film and WG modes is mainly achieved under the oblique incidence, rather than normal incident light. This is not conducive to the simplification of optical paths and systems, limiting the integration of WG-SPPs hybridized mode devices and their further applications in various scenarios. In recent years, several grating-coupled metal-insulator-metal (MIM) nanostructures have been introduced [17, 18]. These structures not only demonstrate a remarkable capability for achieving hybridization coupling of plasmonic modes but also offer the potential for integration into compact optical systems. Nevertheless, these grating-coupled MIM structures have not yet achieved the hybridization coupling between SPPs on flat metal films and WG modes under normal incidence.

Herein, we present a three-layer nanograting-dielectric-metal (NDM) plasmonic structure. This structure enables the hybridization coupling between SPPs on the upper surface of a flat gold (Au) film and the plasmonic WG (PWG) mode within the dielectric cavity. This coupling can be fine-tuned by adjusting the thickness of the middle dielectric layer, leading to the emergence of two novel hybridized PWG-SPPs modes. The generation mechanisms of these two hybridized modes are investigated thoroughly through plasmonic hybridization and two coupled oscillator models. Meanwhile, other accompanied resonance modes are also analyzed systematically. Finally, the sensing performances of the generated PWG-SPPs hybridized modes are evaluated quantitatively, and the reasons for their distinct sensing characteristics are explained in detail. Different from most reported plasmonic nanostructured sensors, its excitation light source and sensing region are located on opposing sides of the sensing platform. Therefore, this configuration enables the separation of optical and fluidic pathways through reflection-mode sensing, facilitating the detection of analytes in turbid media. Moreover, these characteristics make it a promising candidate for integration of the end facet of optical fibers, offering the potential to achieve various metafibers.

Figure 1(a) demonstrates a schematic of the proposed three-dimensional NDM plasmonic structure, consisting of a bottom Au nanograting, a middle dielectric spacer, and an uppermost Au film. This NDM structure can be integrated on a flat quartz substrate by ultraviolet (UV) curing adhesive transferring technology [19]. Due to the diffraction effect of nanograting embedded inside UV curing adhesive, the normally incident transverse magnetic polarized light from the bottom can simultaneously excite SPPs on the upper surface of the Au film and the PWG mode inside the dielectric layer. In this designed structure, periodicity (P), nanowire width (w), and thickness (h₃) of the bottom Au grating are fixed at 452 nm, 120 nm, and 35 nm, respectively. The thicknesses of the uppermost Au film and dielectric spacer are labeled as h₁ and h₂, respectively. To demonstrate the optical properties of the proposed nanostructure, its optical spectra and electromagnetic field distributions are calculated by employing the finite-difference time-domain (FDTD) method. In the simulation, the refractive indexes (RIs) of the dielectric layer (n₂) and UV curing adhesive (n₃) are taken as the constants of 1.6 and 1.56 [20], respectively. The permittivity of Au in the visible region is from Johnson and Christy [21]. According to the structural feature of the NDM structure, a two-dimensional simulation is employed in the x–z direction and one structural unit is considered, where the periodic and perfectly matched layers boundary conditions are applied along the x and z directions, respectively. The normal plane wave, with the amplitude of electric field of 1 V m⁻¹, illuminates the nanograting from the bottom of the NDM structure (along +z direction). To excite the SPPs mode, its polarization direction is perpendicular to the nanograting (along x direction). Besides, a refined mesh of 1 nm × 1 nm is applied to ensure the accuracy of the results. Notably, the top surface of the structure is immersed in a pure water solution (n₁ = 1.33). The simulation model in FDTD solution is shown in figure S1 of the supplementary information. Furthermore, UV glue is considered as a bulk substrate because the thickness of the UV glue is much greater than the overall thickness of the above three-layer nanostructure. Hence, the UV glue is assumed to be semi-infinitely thick, and only the spectra reflected into the UV glue are calculated. The simulated reflection spectrum of the NDM nanostructure with a 730-nm-thick dielectric layer is demonstrated in the top panel of figure 1(b). There are two reflection dips appearing at 634 nm and 656 nm, marked by the light blue region. As a direct comparison, when the thickness of the middle dielectric layer decreases to 100 nm, there is just one reflection dip at 649 nm, attributed to the excitation of SPPs on the top Au film [22]. Therefore, the generation of two reflection dips in the case of the thicker dielectric layer is correlated with more physical phenomena to be explained.

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As demonstrated in figure 1(b), the thickness of the middle dielectric layer is a critical factor for the generation of two reflection dips in the proposed NDM nanostructure. Figure 2(a) illustrates the dependence of the reflection spectrum of the NDM nanostructures on the thickness of the middle dielectric layer (h₂), where the uppermost Au film thickness is fixed at 40 nm. When the thickness h₂ of the dielectric layer is at 100 nm, there is one reflection dip of SPPs (marked as M2 mode) at 649 nm. Its resonance wavelength is mainly determined by the following equation:

$$\begin{align}{\lambda _{{\text{SPPs(}}i{{)}}}} = P\sqrt {\frac{{{\varepsilon _i}{\varepsilon _{\text{m}}}}}{{{\varepsilon _i} + {\varepsilon _{\text{m}}}}}} \end{align} \tag{ 1 }$$

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where, ε_i and ε_m represent the permittivity of the ambient surroundings (n₁ ²) and Au film, respectively. λ_SPPs(i) refers to the resonance wavelength of the SPPs. However, as the thickness of h₂ gradually increases, the reflection dip at 649 nm splits into two new resonance dips, located at its high-frequency and low-frequency locations, respectively. When the thickness h₂ is larger than 400 nm, it returns to one reflection dip of SPPs. The above process is repeated as the thickness h₂ continues to be increased. As a direct comparison, the case of the NDM structure with an opaque 140-nm-thick Au film is also considered in figure 2(b). In this structure, SPPs at the uppermost Au film cannot be excited, namely, the reflection dip at 649 nm disappears. Obviously, as the thickness of h₂ increases, its spectral variation around 649 nm in figure 2(b) is completely different from the case in figure 2(a). A new reflection dip (marked as M1 mode) appears periodically without any splitting. The resonance wavelength of M1 mode at the fixed order has a redshift with the increase of the thickness h₂. Therefore, it is deduced that the mode splitting around 649 nm originates from the hybridization coupling of M1 and M2 modes. Furthermore, as shown in figure 2(a), there is an evident narrowband dip in the vicinity of 705 nm (marked as M3 mode). Its resonant position can be expressed as:

$$\begin{align}{\lambda _{{\text{WA}}}} = {n_{\text{3}}}P.\end{align} \tag{ 2 }$$

Interestingly, the M3 mode exhibits a slight redshift and an increase in resonance depth as the thickness h₂ increases. This is because a thicker dielectric layer can eliminate the substrate effect and create a local environment equivalent to suspending Au nanograting in free space, enhancing the resonance intensity of M3 mode. This periodic disappearance of the M3 mode is attributed to its hybridization coupling with different-order M5 modes. Among these, the presence of the M5 mode is induced by the asymmetric FP cavity in the middle dielectric layer. Its resonance wavelength needs to satisfy the following phase-matching condition:

$$\begin{align}{\lambda _{{\text{FP}}}} = {{4{n_2}\pi {h_2}} \mathord{\left/ \right. } {\left( {m2\pi - {\varphi _1} - {\varphi _2}} \right)}}\end{align} \tag{ 3 }$$

where ϕ₁ and ϕ₂ represent the reflection phase shifts between the dielectric and the top Au film/the bottom Au nanograting. m represents the order of the resonance mode. Except for FP interference in the dielectric cavity, the reflected light of the nanograting and the top Au film into the UV glue will also form constructive interference to enhance reflection. The position of this enhanced reflection effect is determined by the following formula:

$$\begin{align}{\lambda _{\text{R}}} = {{4\pi \left( {{n_2}{h_2}{{ + }}{n_{\text{3}}}{h_{\text{3}}}} \right)} \mathord{\left/ \right. } {\left( {m2\pi {{ + }}{\varphi _{\text{1}}} - {\varphi _{\text{3}}}} \right)}}\end{align} \tag{ 4 }$$

where ϕ₃ represents the reflection phase shift between bottom Au grating and UV glue. The schematic diagrams of these two interference effects and the values of the reflected phase shifts are summarized in figure S2 of the supplementary information. Interestingly, when the resonance mode in the NDM structure is close to the position of this enhanced reflection, the resonance intensity will be strongly attenuated. Besides, it is noticed that there is also a resonance dip appearing around 769 nm (labeled as M4 mode). It stems from the SPPs at the bottom surface of the Au film excited by the evanescent field of nanograting. Its resonance wavelength also satisfies equation (1) except that ε_i is equal to the permittivity of the dielectric layer (n₂ ²). When the dielectric layer is relatively thin, its resonance wavelength is redshifted relative to the calculated result of equation (1). This is a result of the coupling between the SPPs and the local SPs (LSPs) excited by the Au grating. Besides, it will eventually disappear when the thickness of h₂ is larger than 550 nm in figure 2(a). This is because the evanescent field of nanograting has the inability to excite SPPs at the bottom surface of Au film when the dielectric layer is too thick. Compared to figure 2(a) to figure 2(b), the increase of the Au film's thickness h₁ has little effect on M3, M4, and M5 modes. In addition to the thickness of the dielectric layer, the effects of other structural parameters on the characteristic spectra are also shown in figures S3 and S4 of the supplementary information in detail.

To further elaborate the hybridization coupling between M1 and M2 modes supported by this NDM nanostructure, plasmonic hybridization [23] and two coupled oscillator models [24] are employed to analyze the interaction between M1 and M2 modes in detail. Figure 3(a) displays the energy level diagram of M1, M2, and two hybridized modes, where M1 and M2 modes are excited independently by two compared structures in figure 3(a), respectively. Since M1 and M2 modes have small frequency detuning, hybridization coupling between them can be achieved to form two high-frequency and low-frequency hybridized modes. Furthermore, the sum of the energy of the independently excited M1 and M2 modes is equal to the sum of the energy of the two hybridized modes. This proves that the hybridization coupling is caused by the energy exchange between the two modes. To demonstrate the electromagnetic characteristics of hybridized modes, the corresponding spatial distributions of electric field intensity |E|² and amplitude of the y-component H_y of the magnetic field of individual M1 and M2 modes, and two hybridized modes are depicted in figures 3(c)–(f). When the middle dielectric layer has an appropriate thickness, the electromagnetic fields of M1 mode are strongly concentrated inside the gap between Au nanograting and the Au film, resulting in the generation of a new PWG mode. For this mode, H_y exhibits alternating positive and negative periodic arrangement in both the x and z directions, indicating that a standing wave-like mode formed in the z direction can propagate along the x direction in the cavity. When the thickness of the dielectric layer cannot meet the phase-matching conditions of the PWG mode, there is only the feature of M2 mode in the structure. The electromagnetic field is localized on the top surface of the Au film and propagates along the x direction. Interestingly, these two hybridized modes possess the electromagnetic field characteristics of both SPPs and PWG modes, but the characteristics of the dominant mode are different. The high-frequency PWG-SPPs hybridized mode is mastered by PWG mode, where the strong electric field enhancement is localized inside the cavity. Meanwhile, a relatively weak electric field is confined on the surface of the Au film. Differently, the SPPs mode dominates the low-frequency PWG-SPPs hybridized mode, and the electric field is enhanced greatly on the upper surface of the Au film, while the electric field is weak in the cavity. Besides, the coupling strength between the SPPs and PWG modes can also be calculated by fitting the characteristic spectra using the two coupled oscillators model. The fitting formula is shown as follows [25]:

$$\begin{align}{\sigma _{{\text{abs}}}}\left( \omega \right) = a\omega \text{Im} \left[ {\frac{{\omega _{_{{\text{PWG}}}}^2 - {{\left( {\omega + {{i{\gamma _{{\text{PWG}}}}} \mathord{\left/ \right. } 2}} \right)}^2}}}{{\left( {\omega _{_{{\text{PWG}}}}^2 - {{\left( {\omega + {{i{\gamma _{{\text{PWG}}}}} \mathord{\left/ \right. } 2}} \right)}^2}} \right)\left( {\omega _{{\text{SPP}}}^2 - {{\left( {\omega + {{i{\gamma _{{\text{SPP}}}}} \mathord{\left/ \right. } 2}} \right)}^2}} \right) - 4{K^2}{\omega ^2}}}} \right]\end{align} \tag{ 5 }$$

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where σ_abs (ω) represents the absorption spectrum of structure, a, as a constant, represents the amplitude. γ_PWG and γ_SPPs represent the damping rates (related to the full width at half-maximum) of the PWG and SPPs modes, respectively. ω_SPPs and ω_PWG denote the resonance angular frequencies of the unhybridized SPPs and PWG modes, respectively, and K is the coupling strength between the two modes. In the equation (5), γ_PWG, γ_SPPs and K are obtained by fitting the absorption spectrum of the structure. As shown in figure 3(b), the fitted result using equation (3) (blue curve) shows that the simulated absorption spectrum is well described by the coupled oscillators model. The fitting parameters γ_PWG, γ_SPPs, and K are calculated as 46, 83, and 45 THz, respectively, which can also be taken as evidence of hybridization coupling between SPPs and PWG modes. Some fitting discrepancy is also observed, which may be attributed to the following two aspects: firstly, the PWG and SPPs modes in the proposed structure are not perfect harmonic oscillators and do not have a perfect Lorentzian spectrum profile. This is distinguished from the fact that two ideal harmonic oscillators are considered in two coupled oscillators model. Secondly, due to the complexity of the structure, the interaction between PWG and SPPs modes might not conform strictly to the linear relationship of coupling interaction in two coupled oscillators model.

Except for the generated mechanisms of the M1 and M2 modes as well as their hybridized modes, the spatial electric field intensity distributions of M3-5 modes in the x-z plane are also calculated to further prove their generation mechanisms. As shown in figure 3(g), the electric field enhancement of the M3 mode is confined around two corners of the lower surface of the Au nanograting, which is consistent with the typical characteristics of the LSPs mode. Additionally, its wavelength is mainly determined by the wood's anomaly (WA) mode on the lower surface of the nanograting. Thereby, the M3 mode is attributed to the coupling of the LSPs mode with the WA mode, commonly known as the surface lattice resonance. The electric field of M4 mode as shown in figure 3(h) is mainly localized on the lower surface of the Au film, while its intensity decreases exponentially along the direction perpendicular to the Au film. Besides, there are also obvious LSPs characteristics in the upper surface of the Au nanograting. Therefore, M4 mode originates from the coupling of SPPs on the lower surface of the Au film and LSPs on the upper surface of the Au grating. With the increase of dielectric layer thickness, the resonance condition of M5 mode is satisfied. As shown in figure 3(i), there are three obvious electric field interference fringes in the NDM WG. The electric field varies periodically in the z-direction, and the electric field is relatively uniform in the x direction, which is a typical electric field characteristic of FP resonance mode. Furthermore, its transverse wave vector component is nearly zero, which indicates the M5 mode is mainly excited by the zero-order diffracted transmitted light of the nanograting. Above all, the NDM structure can support the generation and hybridization coupling of more resonance modes compared with the traditional MDM structure. This provides a novel and flexible plasmonic platform to tailor the electromagnetic properties of the metal nanostructure.

Due to their local electric field enhancement and localization effect on the upper surface, the hybridized PWG-SPPs modes (marked as dip 1 and dip 2) possess the potential for RI sensing and biochemical detection. To comprehensively evaluate their sensing performance, the bulk RI and surface sensitivities of the hybridized PWG-SPPs modes are investigated quantitatively. Figure 4(a) demonstrates the reflection spectra of the proposed NDM structure when the RI of ambient surroundings varies from 1.33 to 1.40. Evidently, both dip 1 and dip 2 have an obvious redshift with the increase of the RI but their redshift amount are distinct. Besides, there is a slight decrease in reflection intensity for dip 1 while the case is justly opposite for dip 2. This may be caused by the resonance detuning of PWG and SPPs modes. The PWG mode gradually approaches the location of its maximum resonance intensity while SPPs mode progressively moves away. As shown in figure 4(b), the wavelength shifts amount of dip 2 is linearly related to the RI of ambient surroundings, and its bulk RI sensitivity (S) can be calculated as 333 nm/RIU by linearly fitting data in figure 4(b). Different from dip 2, the wavelength redshift of dip 1 exhibits an exponential variation trend and approaches a plateau at high RI of ambient surroundings.

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Besides the bulk RI sensitivity, surface sensitivities of the hybridized PWG-SPPs modes are also considered by continuously increasing the thickness of a simulated molecular layer on the top surface of the uppermost Au film. In these simulations, the molecular layer is simulated by a thin dielectric layer with an RI of 1.56. Dip 1 and dip 2 show a similar variation tendency in figure 4(c) with the case in figure 4(a) as the thickness of the molecular layer increases from 0 nm to 80 nm in a step of 10 nm. Figure 4(d) summarizes the wavelength-redshift amount versus the thickness of the molecular layer. Obviously, the wavelength redshifts of both dip 1 and dip 2 are well-fitted exponentially, but dip 1 quickly reaches the plateau while the redshift amount of dip 2 continues to increase. Furthermore, dip 1 is susceptible to reaching a plateau when the resonance wavelength is close to the unhybridized PWG mode. Therefore, the insensitivity of dip 1 to the external environment may be attributed to the weakening of the coupling strength between PWG and SPPs modes. This stems from the increase of frequency detuning of PWG and SPPs modes caused by environmental changes. To demonstrate the weakening of coupling strength, the dependency of the maximum electric field enhancement of hybridized PWG-SPPs modes on the RI of ambient surroundings and the thickness of the simulated molecular layer are depicted in figures 4(e) and (f), respectively. The detailed spatial electric field distributions of resonance modes and corresponding electric field extraction points are demonstrated in figures S5 and S6 in the supplementary information. As ambient RI and molecular layer thickness increase, the maximum electric field intensity of dip 1 on the structural upper surface gradually decreases and approaches zero. This can be taken as direct evidence of a gradual reduction in the coupling strength. Besides, the maximum electric field intensity of dip 2 on the structural upper surface has a slight increase with the increase of the ambient RI but is always smaller than the electric field intensity before the coupling (blue dotted line). This is because dip 2 is dominated by SPPs mode, the inherent characteristics of SPPs mode will be more obvious as the coupling strength decreases. The decrease of the maximum electric field intensity of dip 2 in figure 4(f) is attributed to the effect of the presence of the molecular layer on the electric field distribution of dip 2 on the upper surface. There are three main reasons for the non-uniform variation in electric field intensity: (1) the non-uniformity in the variation of coupling strength between the two modes; (2) the change in resonance intensity due to wavelength shifts; (3) the stratification of the upper surface electric field resulting from the presence of the simulated molecular layer.

In summary, we have demonstrated theoretically a three-layer NDM plasmonic structure, which can achieve the hybridization coupling of the SPPs and the PWG mode by altering the thickness of the dielectric layer. In contrast to traditional angle-dependent total internal reflection excitation, the hybridization coupling in the proposed plasmonic nanostructure is achieved by the diffraction effect of nanograting. This approach eliminates the limitation of the oblique incidence and simplifies the complex optical path system, effectively facilitating the miniaturization and integration of resonance structures. In order to reveal hybridization coupling, plasmonic hybridization and two coupled oscillator models are employed to provide insights into the formation of hybridized modes and their optical properties. Furthermore, the potential applications of the hybridized PWG-SPPs modes in the field of biochemical detection are discussed in detail. The different responses of the two hybridized modes to the external environment are graphically explained by the coupling strength between SPPs and PWG modes. The sensing structure can detect turbidity analytes due to the decoupling of the excitation light source and the sensing region, which is impossible for traditional plasmonic nanostructure sensors. Furthermore, the proposed plasmonic nanostructure provides an effective strategy for the generation and modulation of a variety of resonance modes. Since the resonance characteristics of the NDM structure are highly dependent on the middle dielectric layer, it is also expected to promote the development of integrated active plasmonic devices, such as electro-optic modulators and metafibers.

All data that support the findings of this study are included within the article (and any supplementary files).

National Natural Science Foundation of China (NSFC) (12274052 and 62171076), Liaoning Province Natural Science Foundation (2022-MS-134), Shanxi Province Applied Basic Research Program (20210302123267), the Fundamental Research Funds for the Central Universities (DUT22YG120).

The authors declare no conflicts of interest.