1. Introduction

In the past decade, couplings between excitonic materials and metal nanostructures have attracted increasing interest because of their potential applications in the biological and chemical sensing [1–4], surface enhanced spectroscopy [5,6], quantum information processing [7,8], and solar cells [9,10]. In general, optical responses in metal nanostructures include localized surface plasmon (LSP), surface plasmon polariton (SPP), and plasmonic nanocavity (NC) [11], whereas excitons mainly exist in semiconductor materials [12], quantum wells [13], quantum dots [14], biomolecules [15], etc. There are two types of coupling: weak coupling and strong coupling [16]. The weak coupling often enhances absorption or light-emitting of the excitonic materials [17–21]. In the strong coupling regime, new hybrid modes are formed and separated by the Rabi splitting [22,23]. Such new modes have different optical properties and have been widely used in quantum cryptography [24], nanoscale lasers [25], plasmon-enhanced light harvesting [26], and chemical reaction promotion [27].

Similar to the exciton–plasmon interactions in visible, couplings between molecular vibrational transitions and plasmons have received great attention recently due to fundamental and practical interests [22,23,28]. Cetin et al. [22] reported that two vibrational modes of PMMA molecules can couple with two plasmonic modes, providing more reliable sensing information. Wan et al. [23] not only achieved the strong couplings between the LSP mode and the PMMA vibrational mode, but also demonstrated that the coupling strength can be modulated by changing the thickness of the PMMA film and hence the forbidden energy gap due to the mode splitting could be adjusted accordingly. Memmi et al. [28] demonstrated that the strong coupling between SPPs and the vibration of the ketone-based polymer arises new eigenstates, which hold strong potential for applications in chemistry and optoelectronics. However, the weak couplings in the molecular vibration–plasmon structure were seldom studied, especially the mutual transformation between the weak coupling and the strong coupling was not reported. As we know, there are various plasmonic modes which are closely related with metal structure parameters. There is great opportunity that coupling regimes can be changed by utilizing different plasmonic modes in the same system. It was found in some exciton–plasmon couplings in visible region that the coupling strength could be controlled by the geometry [18], exciton concentrations [29,30] and metal oxidation [31], etc.

In this paper, we investigate the mid-infrared molecular vibration–plasmon coupling in a hybrid structure, consisting of a silver grating filled with polymethyl methacrylate (PMMA) molecules (SG–PMMA). The localized plasmon resonance could be modulated to match with the vibrational band (C = O) of PMMA molecules by tuning the height of the grating elements. We further study the influences of the grating structure parameters on the molecular vibration–plasmon couplings in the SG–PMMA. It is surprising that the molecular vibration–plasmon coupling transfers from the weak coupling into the strong coupling by reducing the distance between adjacent elements. These couplings are different from those in the traditional cavity quantum electrodynamics (CQED) systems, which is essential for interesting physics in quantum information science [32,33]. Our system is semi-classical and can be studied by the coupled oscillator model [34,35].

2. Molecular vibration–plasmon hybrid model

Figure 1(a) shows the cross-section schematic of the SG–PMMA hybrid structure. The period and element width of the 1–D silver grating are defined as P and w, respectively. The height of the grating elements is h and PMMA molecules are filled in grooves. The dielectric function of silver could be described by the Drude model ${\epsilon }_{Ag}={\epsilon }_{\infty }-{\omega }_p^2/\left({\omega }^2+i{\gamma }_1\omega \right)$, where ω is the angular frequency, the plasma frequency ω_p = 9 eV, and the damping constant γ₁ = 0.1 eV. The high frequency constant term ε_∞ is set as 4.6 [36]. The permittivity of the PMMA medium could be modeled by the Lorentz oscillator model ${\epsilon }_{PMMA}={\epsilon }_2-A{\omega }_0^2/\left({\omega }^2-{\omega }_0^2+i{\gamma }_2\omega \right)$ [22], where background permittivity ε₂ = 2.36, oscillator strength A = 0.0115, Lorentz resonance frequency ω₀ = 0.215 eV (5.77 μm), and damping frequency γ₂ = 0.00245 eV. These parameters make the model fit the reported experimental data well [22]. The Lorentz model means there is a narrow absorption band around ω₀, but the absorption is weak.

 

Fig. 1 (a) Schematic of the cross section of SG-PMMA hybrid structure. (b) Absorption spectra of the SG–PMMA, the silver grating, and the PMMA molecules in the grooves, respectively. Here, the period P = 3000 nm, the element width w = 2000 nm, and the height of the elements h = 775 nm.

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Finite element method (FEM) has been performed to calculate the optical responses and electric field distributions of the SG–PMMA hybrid structure based on the software COMSOL Multiphysics. A TM plane wave with electric field E₀ normally impinges onto the SG–PMMA hybrid structure. The periodic boundary conditions are employed on both left and right to account for the periodic arrangement. Perfectly matched layers are set at the top and bottom to avoid multiple reflections.

3. Results and discussion

In Fig. 1(b), the solid, dashed, and dotted lines represent the absorption spectra of the SG–PMMA, the silver grating filled with dielectric material of ℇ₂ = 2.36, and the PMMA molecules, respectively. Here, the period P = 3000 nm, the element width w = 2000 nm, and the element height h = 775 nm. The absorption is defined as A = 1–R–T, where R is the reflection and T is the transmission. Two virtual boundaries B_top and B_bottom are drawn in the upstate and substrate to calculate the reflection R and transmission T, respectively. Each of them is 50 nm away from the PMLs to avoid numerical errors [37]. The thickness of the silver substrate is much larger than the skin depth of the silver, which makes the transmission T = 0. The pure PMMA molecules are kept as many as those in the hybrid structure. There is a weak absorption peak at about 5.77 μm for PMMA molecules due to vibrational transitions. We observe two plasmon modes in the absorption spectrum of the silver grating. One peak at around 3 μm is the SPP mode, which is directly determined by the grating period under normal incidence. The reciprocal grating vector provides the wavenumber for SPP k_SPP = 2mπ/P [6]. Here m = 1. The broad peak at around 5.77 μm arises from the LSPs of the grating elements [38]. This mode originates from the collective oscillations of free electrons in metallic elements and is determined by the element width w and the height h [39]. Here, the values of w and h are well designed so that the LSP matches with the molecular vibrational mode of PMMA. As the dielectric material in the silver grating is replaced by PMMA molecules, the absorption around 5.77 μm is increased to nearly 1 and the other peak at about 3 μm is almost unchanged. Even if the metal absorption from the silver grating is subtracted, the remaining absorption at 5.77 μm is 7 times larger than that of the pure PMMA molecules. Usually, such molecule absorption enhancement results from the weak couplings between the molecular vibrational transitions and the plasmon resonances [40].

Then we systematically investigate the absorption enhancement in the SG–PMMA hybrid structure to clarify the weak coupling. Figure 2(a) shows the contour plot of the absorption spectra of the silver grating as a function of grating element height h. Here, the period P and width w are fixed at 3000 and 2000 nm, respectively. As the h-value increases from 600 to 900 nm, the LSP redshifts almost lineally from about 4.7 to 6.5 μm, moving across the vibrational mode of PMMA (~5.77μm). As the h-value increases, the relaxation effect in metal elements grows and hence the LSP shows a redshift accordingly [39]. Figure 2(b) represents the contour plot of the absorption spectra of the SG–PMMA as a function of h-value. The dashed and dotted lines denote the uncoupled LSP mode and the molecular vibrational mode, respectively. It is observed that the spectrum position of the absorption peak at around 5.77 μm isn’t affected by the approaching LSP mode. This means the molecular vibrational transition and the plasmon do not exchange energies and their interaction is definitely in the weak coupling regime. The absorption of the SG–PMMA at around 5.77 μm increases first and then decreases with the increase of the h-value, as shown in Fig. 2(c). At h = 775 nm, the LSP appears at about 5.77 μm while the local electric fields near the grating elements is the largest, resulting in the greatest absorption.

 

Fig. 2 (a) Contour plot of the absorption spectra of the silver grating as a function of element height h. (b) Contour plot of the absorption spectra of the SG–PMMA as a function of h. The dashed and dotted lines represent variations of the LSP mode and molecular vibrational mode, respectively. (c) Maximal absorption of the SG–PMMA at 5.77 μm as a function of h. Here, the period P and width w are fixed at 3000 nm and 2000 nm, respectively.

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Next, we focus on the influence of the grating period P on the plasmon modes of the silver grating. Figure 3(a) shows the absorption spectra of the silver gratings with period P of 3000 nm (solid line), 2700 nm (short dashed line), 2400 nm (short dotted line). Here the element width w and height h are fixed at 2000 and 700 nm, respectively. It is observed that by decreasing the P-value from 3000 to 2400 nm the SPP of the silver grating shows a distinct blue-shift from around 3 to 2.4 μm, which follows the resonance condition of the SPP [6]. Meanwhile, the LSP shows a negligible blue–shift. The LSP is mainly determined by the element width and height and the interaction between neighboring elements causes this weak shift [41]. Figure 3(b) shows the near-field distribution of the silver grating with P = 3000 nm at the LSP resonance (5.30 μm). The electric fields are strongly localized at the top corners and extend outward, which is one feature of the LSP reported in [29]. With the decreasing P-value, the distance between grating elements grows narrow as the element width w is fixed at 2000 nm. When the groove width becomes very small, plasmonic nanocavity (NC) mode of the silver grating is achieved and generates stronger localized field enhancements [11,42]. Figure 3(c) shows the absorption spectra of the silver gratings with P-values of 2100, 2090, and 2080 nm. The SPP at around 2.1 μm is almost unchanged because of the very small variation in the P-value. On the other hand, another peak red shifts with the decrease of P-value, which means this mode is different from the LSP mode in Fig. 3(a). Strong interactions between neighboring grating elements form the NC mode, which is related with the shape of the cavity. As the groove height h is fixed here, narrower groove leads the resonance to move towards longer wavelength [43,44]. Figure 3(d) shows the electric field distribution of the silver grating with P = 2100 nm at the NC resonance of 5.73 μm. The cavity between grating elements is filled with higher electric fields compared with Fig. 3(b). Also, it has strongest electric field at the mouth of the groove and the weakest field at the bottom [45]. Therefore, by decreasing the grating period, the LSP mode of grating elements could be changed to the NC mode between grating elements, accompanied with higher electric fields in grooves. By this way, the light-matter interactions should be strengthened.

 

Fig. 3 (a) Absorption spectra of the silver gratings with grating period P of 3000 nm (solid line), 2700 nm (short dashed line), 2400 nm (short dotted line). (b) Electric field distribution in the silver gratings with P = 3000 nm at resonance wavelength of 5.30 μm. (c) Absorption spectra of the silver gratings with grating period P of 2100 nm (solid line), 2090 nm (short dashed line), 2080 nm (short dotted line). (d) Electric field distribution in the silver grating with P = 2100 nm at resonance wavelength of 5.73 μm. Here, the element width w and element height h are fixed at 2000 nm and 700 nm, respectively.

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Finally, we study the couplings between the molecular vibrational mode and the plasmonic NC mode in the SG–PMMA. Figure 4(a) shows the contour plot of the absorption spectra of the uncoupled silver grating as a function of the element height h. Here, the element width w and period P is fixed at 2000 and 2100 nm, respectively. When the h-value increases from 610 to 810 nm, the NC mode of the silver grating redshifts from 4.9 μm to 6.8 μm almost linearly. The NC mode is mainly determined by the ratio of the cavity [43,44]. Since the width of the gap is fixed, it red shifts with the increase of the gap depth h. Figure 4(b) shows the contour plot of the absorption spectra of the SG–PMMA as a function of h. The uncoupled NC modes and molecular vibrational modes are represented by the dash and dotted lines, respectively. When the h-value is small, the broad NC mode is far away from the molecular vibrational mode and hence the interaction between these two modes results in a Fano-like resonance, i.e., the Fano lineshape occurs. As the h-value increases to around 710 nm, the strong molecular vibration–plasmon coupling results in two new hybrid modes [46] and the Rabi splitting happens, as shown in Fig. 4(b). Such transition from Fano resonance to Rabi splitting has been carefully investigated in previous papers [47,48]. The solid and dash-dot lines show the hybridized high-energy mode (HM) and low-energy mode (LM), respectively. There is an obvious anti-crossing behavior and the obtained Rabi splitting energy Ω_Rabi is about 15 meV. The full-width at half-maximum (FWHM) of the uncoupled plasmon resonance and molecular vibrational transition are Γ_plasmon ≈22.90 meV and Γ_PMMA ≈2.45 meV, respectively. It is known that the Rabi splitting occurs when the Rabi splitting energy Ω_Rabi is larger than (Γ_plasmon + Γ_PMMA)/2 [49]. Based on the above calculations, we can confirm that the coupling in Fig. 4 can satisfy this criterion, as (Γ_plasmon + Γ_PMMA)/2 ≈12.68 meV. Furthermore, we investigate the strong coupling strength in the SG–PMMA structure, which can be studied by the classic coupled oscillator model [34]:

 

Fig. 4 (a) Contour plot of the absorption spectra of the silver grating as a function of h. (b) Contour plot of the absorption spectra of the SG–PMMA hybrid structure as a function of h. Here, the period P and width w are fixed at 2100 nm and 2000 nm, respectively. The solid and dash-dot lines show the hybridized HM and LM, respectively. The dashed and dotted lines represent the uncoupled nanocavity mode (NC) of the silver grating and molecular vibrational mode of PMMA, respectively.

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4. Conclusion

We have investigated the molecular vibration–plasmon couplings in the SG–PMMA hybrid structure in mid-infrared region. When the period of the silver grating is large, the weak coupling between the LSP of grating elements and PMMA molecular vibration could greatly enhance the absorption of the PMMA molecules. The maximal absorption enhancement is more than 7 times when the LSP matches with the molecular vibrational mode. As the grating period decreases and hence the distance between adjacent elements becomes small, the LSP mode turns into the plasmonic nanocavity mode. This plasmonic mode introduces higher local electric fields and promotes light-matter interactions greatly in the SG-PMMA hybrid structure. Strong couplings between molecular vibrations and plasmon NC modes are achieved and the obtained Rabi splitting energy is about 15 meV. The tunable couplings in this molecular vibration–plasmon hybrid structure may be beneficial to their further biochemical and biophysical applications.