1. INTRODUCTION

In nature, surface acoustic waves (SAWs) and localized surface plasmon resonance (LSPR) are two distinct physical phenomena; each has its unique principle and significance. SAW is an acoustomechanical phenomenon based on the piezoelectric property, whereas LSPR is based on optically excited surface plasmons. Both are widely used in biosensors and optoelectronics due to their extraordinary sensitivities and quality factors [1–7]. The interaction between SAW and LSPR has the potential to unveil an extraordinary optomechanical-plasmonic phenomenon that can significantly influence the future development of biophotonic devices. Since the SAW amplitude is tunable with applied voltage, the interaction can be regarded as voltage controlled, providing exceptional flexibility and control on device performance [8].

In the past few decades, the interaction between SAW and LSPR has been studied and understood in several ways with different design and observation tools. The interaction between Sezawa waves and localized surface plasmons (periodic metallic pillars) was explained [9] by analyzing two types of elastic modes, namely, the modes confined with local resonances near the metallic pillar and the modes propagating with deformed structures. Since acoustic periods are several orders of magnitude smaller than the optical cycles, a quasistatic approximation was considered to simulate the plasmonic behavior. As a result, a plasmonic shift was observed for different elastic phonon phases. Another study shows a coherent substrate phonon induces vibrational coupling between constituent atoms in a plasmonic molecule [10]. In this paper, vibrational modes of plasmonic molecules were explored by specially designed plasmonic molecules with varying complexity where an intermolecular coupling of the acoustic mode was observed by probing at the individual plasmonic molecular levels. A recent report claims that the plasmon drag effect can also modulate the plasmonic response [11] where the oscillating electrons in plasmon experience a drag force by an electric field applied in the lattice. In this context, an analogy can be made with SAW as a driving force instead of the applied field. A sustained drag effect can cause the surface redistribution of the electron cloud, which potentially affects LSPR responses. One of the major issues with all the above observations for plasmon-phonon interaction is the limited lifetime of plasmons due to faster energy relaxation through electron-phonon scattering and Landau damping [12]. Specifically, the dispersion followed by damping of plasmonic energy occurs due to a very steep energy gradient between energy of plasmons and energy of the surrounding phonons. This issue can be exploited by introducing high-energy phonons by increasing lattice energy. Therefore, interdigital transducers (IDTs) can be used to generate SAW-activated acoustic phonons with a wide range of resonant frequencies from megahertz to gigahertz (depending on the design) at room temperature [13–17]. The phonon-plasmon interaction can also be described numerically by two-temperature modeling where the energy exchange between the hot electron and the lattice phonon is expressed by an individual set of expressions [18].

Based on the above approach, a device structure is proposed in Fig. 1(a) where a set of symmetrically designed IDTs is fabricated on an X-cut ${\text{LiNbO}}_3$ (LN) substrate. The separation between two IDTs is 800 μm. The active area consists of a monolayer of Au nanoparticles, which can provide a plasmonic response. One of the IDTs can be used to generate the SAW, whereas, the other one is used as a detector. The surface morphology of the sample coated with Au nanoparticles is investigated by SEM-9000, shown in Fig. 1(b). The spherical-shaped uniform Au nanoparticles (40 nm in diameter) are random but compactly distributed on the surface as represented in Fig. 1(b-iv).

 

Fig. 1. (a) Illustration of the device, which is composed of a source IDT, randomly distributed Au nanoparticles, and a receiving IDT. (b) (i)–(iii) Scanning electron microscope (SEM) images of fabricated IDT, (iv) surface morphology captured by SEM where 40-nm uniformly sized Au nanoparticles are distributed on the surface.

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2. METHOD AND EXPERIMENTAL SETUP

A. Experimental Setup

The experimental setup is composed of two sections, optical and SAW setups as presented in Fig. 2. The optical setup consists of a broadband xenon light source, an attenuator, a set of lenses, and mirrors to achieve a well-collimated output beam with minimal aberration. A linear polarizer is employed to extract S- and P-polarized light. A spectrometer (Ocean Optics HR4000) is used to record the LSPR response in the receiving end. In the SAW measurement setup, a pulse generator (Anritsu MP1652A) is connected to the IDT to vary the input amplitude and frequency. The acoustic waves at the output end were read out by an oscilloscope.

 

Fig. 2. Experimental setup for SAW-varying LSPR. The optical setup for LSPR consists of a light source, optical components, and a spectrometer (blue line). The SAW setup includes a frequency generator to excite the source IDT and an oscilloscope to extract the SAW signals in the receiving IDT (red line).

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B. Fabrication of IDTs

An X-cut LN substrate was cleaned with acetone, methanol, and isopropyl alcohol, dried with ${\mathrm{N}}_2$ gas, and then baked for 10 min at 120°C. The sample was spin coated with a bilayer photoresist consisting of LOR-5B and S1813. Photolithography was next performed, which developed the IDT structure on the photoresist. Ti/Au (40 nm/200 nm) metal layers were deposited by the electron gun deposition technique. The lift-off was then performed by MF319 and acetone.

C. Immobilization of Au Nanoparticles

A layer of 30-nm-thick ${\mathrm{SiO}}_2$ was deposited on the active area of the sample by plasma-enhanced chemical vapor deposition. The sample was then functionalized by a solution of 3-aminopropyltrithoxysilane (APTES) provided by Aldrich mixed with ethanol and de-ionized (DI) water with a ratio of 18:1:1 for 30 min. After the APTES treatment, the functionalized sample was dried by a heater, followed by a droplet of 40-nm uniformly sized Au nanoparticle solution. The nanoparticles were immobilized on the surface of the sample for 8 h. The sample was dried and rinsed with ethanol and DI water to wipe off extra unfixed nanoparticles.

3. RESULTS AND DISCUSSION

LN is a well-known material for its extraordinary optical and piezoelectric properties and widely used for SAW generation [19–23] and the LSPR experiment [24–27]. The localized surface plasmons are periodic oscillations of electrons in noble metallic nanoparticles with the incident optical excitation. The electron oscillation creates a localized electric field, and depending on the resonant condition, a particular wavelength is completely extinct in the transmittance spectrum as shown in Fig. 3(a). The resonant condition of an IDT is based on the device geometry and can be determined by Eq. (1),

 

Fig. 3. (a) Creation of LSPR where incident optical flux generates plasmonic oscillation of electrons, which results in the localized field and causes LSPR extinction. (b) The amplitude versus frequency plot of SAW where the resonant frequency can be observed at 710 MHz. (c) Magnitude versus frequency plot of SAW with respect to different applied external voltages. The amplitude of SAW varies linearly with the applied voltage.

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Before the experiment, the effect of environmental excitations, such as temperature and surface deformation, was studied and explained in Figs. 8 and 9 (Appendix A). The surface temperature which changes the carrier density can lead to a change in the refractive index. The surface temperature increases due to a longer duration of source illumination and the SAW (mechanical wave) propagation. To mitigate this issue, we extracted the data 10 ms after source illumination and SAW excitation. In addition, since LN is a piezoelectric material, the periodic SAW propagation creates elastic deformation on the surface. There might be chances of unintentional scattering and, thus, potential experimental noise. To verify, a separate study has been performed and discussed in Fig. 9 (Appendix A) where it is found that the effect is very negligible. The LSPR response with SAW activation was then explored. An RF signal was applied in the input terminal of IDT with an amplitude of $2V_{\mathrm{p}-\mathrm{p}}$. The resultant LSPR response is plotted in Fig. 4(a). It implies that the LSPR absorption increases with applied SAW and retracts back to its near-initial position by switching off the electrical supply. This process can be explained by considering the mechanical SAW activates the associated phonons to a higher energy of states as shown in Fig. 4(b). The higher-energy phonons interrupt the natural plasmon-phonon relaxation process and lead to a decrease in damping rate of plasmon-phonon relaxation energy. Therefore, an accumulation of excess energy occurs in the plasmonic state, which causes a transition of conduction electrons into the plasmonic state as represented in Fig. 4(c) [30,31]. The above phenomena enhance the electron density in the plasmonic state that results in an increase in absorption [32–35]. A variable SAW amplitude is applied by the electrical function generator, and respective LSPR responses are plotted in Fig. 4(d). The LSPR peak absorption increases with increasing SAW amplitude, demonstrating the exceptional voltage tunable LSPR property of the device. There is around a 19% change in absorption when the SAW voltage increases from $0.5V_{\mathrm{p}-\mathrm{p}}$ to $2V_{\mathrm{p}-\mathrm{p}}$. This behavior can be explained by considering phonons with a higher amplitude of SAW that correspond to a higher state of phononic energy as described in Eq. (2). Because LSPR is a result of periodic oscillation of electrons in the metallic and semimetallic nanoparticles [10,36–38] represented in Fig. 3(a), the oscillation relaxation can be through three main processes, i.e., electron-electron scattering, electron-phonon coupling, and phonon-phonon coupling [39–43]. For a stable phononic environment, these relaxation events are assumed to occur in a particular sequence with a specific relaxation time [44,45]. On the other hand, if the LSPR is observed in an exited phononic state, according to the energy conservation, the entire relaxation process is affected when altering the relaxation energy gradient. In other words, depending on the energy of external phonons, the damping rate of LSPR energy gets reduced or even becomes reversed [46–50]. In both cases, due to the change in the phonon-plasmon energy gradient, more electrons participate in plasmonic oscillation with respect to a stable phononic environment [35,51,52]. The higher density of electrons in plasmonic states increases LSPR absorption. Different SAW resonant conditions and their effects on the LSPR are plotted in Fig. 4(e). It is shown that at the resonant frequency of the IDT 710 MHz the change in LSPR absorption is greater than at the frequencies out of resonance, i.e., 560 and 1550 MHz. It confirms that the above phonon-plasmon interaction is dependent on the resonant condition of the IDT since the SAW amplitude is the highest at resonance. Frequencies not in resonance can generate smaller or negligible SAW amplitude as represented in Fig. 3(c). The smaller SAW amplitudes are unable to contribute enough energy to its associated phonons to actively affect the phonon-plasmon interaction. Hence, the resultant change in LSPR absorption is smaller or negligible compared to that at resonant frequency [53]. Therefore, the modulation efficiency is a function of resonant condition and maximum at the resonant frequency of the SAW device. Moreover, from the result at the resonant frequency, a linear approximation can be performed for the LSPR absorption and shown in Eq. (3), where $A_{\mathrm{init}.}$, $J_k$, and $V_{\mathrm{SAW}}$ represent initial LSPR absorption (without applying SAW), conversion factor, and applied SAW amplitude, respectively,

A time-resolved photoluminescence (TRPL) experiment is also conducted to study the plasmon-phonon damping behavior and plotted in Fig. 5(a). The carrier lifetime ($\tau$) is increased with increasing input SAW amplitude as represented in Fig. 5(b). The increase in carrier lifetime is a result of reduced damping rate, which leads to an increase in plasmonic population or absorption.

 

Fig. 4. Variation of plasmonic response with respect to applied acoustic wave amplitude. (a) LSPR response with respect to different switching conditions of the IDT where the LSPR absorption increases when SAW is on and retracts back when SAW is off. (b) Diagram of phonon-plasmon interaction with and without SAW-activated acoustic phonons. The plasmonic electron density increases with the applied SAW pulse as compared to the case without SAW. (c) Illustration of SAW-activated electron transition to the plasmonic state. The SAW-activated phonons participate in phonon-plasmon coupling and increase the plasmonic population. (d) Change in LSPR absorption with varying amplitude of SAW. (e) Amplitude-varying LSPR response with respect to different SAW resonant conditions where at the SAW resonant frequency (710 MHz), the change in LSPR absorption is highest.

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Fig. 5. TRPL analysis. (a) Plasmonic damping with increasing SAW wave amplitude. The change in gradient is clearly suggested; the change in damping behavior with applied SAW amplitude. (b) Change in normalized time constant with respect to applied SAW voltage analyzed by TRPL.

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An equivalent theoretical model is constructed by COMSOL Multiphysics based on the Lorentz–Drude approximation. The model is developed by considering electrons as damped harmonically bound particles subject to external electric fields and widely used for plasmonic simulation in the metal-dielectric interface. In this model, the relative permittivity is related to plasma frequency and calculated from Eq. (4), where ${ϵ}_{\infty }$ is the high-frequency contribution to the relative permittivity, ${\omega }_p$ is the plasma frequency, $f_j$ is the oscillation strength, ${\omega }_{0j}$ is the resonance frequency, and ${\mathrm{\Gamma }}_j$ is the damping coefficient. SAW is formulated by an appropriate secondary directional electromagnetic field [53,54],

An increase in population of the plasmonic electron is observed with increasing applied SAW power as shown in Fig. 6(a), and the corresponding increase in absorption is plotted in Fig. 6(b). Change in electron population can be approximated by considering Mie theory where the absorbance is related to the extinction cross section as shown in Eq. (5),

 

Fig. 6. Equivalent model analysis. (a) Change in electron population in the plasmonic state with increasing SAW power. (b) Increase in absorption with increasing SAW power.

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The observed phenomenon can be further discussed using the two-temperature model [18]. Considering the activated phonon energy as the lattice energy source, plasmon dynamics can be analyzed by equations given in Appendix B. The forward damping is observed when the effect of electron-phonon coupling ${\alpha }_{e\to \mathrm{ph}}$ is positive as represented in Eq. (B5) of Appendix B. It indicates that if the energy of electrons in the plasmon is greater than the phonon energy, the plasmon energy is dissipated through lattice phonons, and the energy of plasmonic electrons ($\partial T_e$) is reduced. Furthermore, the plasmon-phonon interaction reaches equilibrium when ${\alpha }_{e\to \mathrm{ph}}$ becomes zero as represented in Eq. (B6) at which there is no energy dissipation. Similarly, Eq. (B7) suggests the damping is reversed when ${\alpha }_{e\to \mathrm{ph}}$ is negative at which the energy of electrons ($\partial T_e$) increases through phonon-electron coupling.

Furthermore, we also investigated the effect of plasmonic relaxation for S- and P-polarized incident fluxes [as represented in Fig. 7(a)]. Without applying SAWs, the corresponding LSPR spectra are plotted in Fig. 7(b). Next, a similar SAW amplitude-varying experiment was conducted for S- and P-polarized incident fluxes. The spectra are shown in Figs. 7(c) and 7(d), respectively. The LSPR absorption spectra versus IDT voltage amplitude of both polarizations are plotted in Fig. 7(e). S-polarized light has a better absorption gradient than P-polarized light. This phenomenon initially can be understood by comparing different electromagnetic polarization fields. The field is parallel to the surface plane for the S-polarized wave, leading to a better coupling with surface plasmons and traveling SAWs. For the P-polarized wave, the field component is perpendicular to the SAW traveling direction and generally has less interaction with surface plasmons.

 

Fig. 7. Effect of light polarization on interaction between the localized surface plasmon and the SAW-activated acoustic phonon. (a) Diagram of S and P polarizations with respect to incident flux and Au nanoparticle. (b) LSPR response of S- and P-polarized light without applying SAWs. (c) LSPR absorption spectra with varying SAW amplitudes with S-polarized incident optical flux. (d) LSPR absorption spectra with varying SAW amplitudes with P-polarized incident optical flux. (e) Peak absorption of LSPR with respect to SAW amplitudes for S- and P-polarized light, which suggests that the absorption tuning gradient with respect to applied voltage is better for S-polarized flux than for P-polarized incident flux.

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4. CONCLUSION

We report for the first time to the best of our knowledge the effect of the amplitude-varying surface acoustic waves on the damping of localized surface plasmon resonance. The results successfully demonstrate the amplitude tunability of the plasmonic response in which the LSPR absorption varies near linearly with the input SAW amplitude. The absorption is increased by about 19% when the IDT applied voltage shifts from $0.5V_{\mathrm{p}-\mathrm{p}}$ to $2V_{\mathrm{p}-\mathrm{p}}$. The result is explained by considering SAW-activated phonon-plasmon interaction where the effective energy gradient between the surface plasmon and the SAW-activated phonons is reduced, enhancing the effective electron density in the plasmonic state. We also investigate the effect of SAW on localized surface plasmons with respect to S- and P-polarized incident optical fluxes. It is shown that the S-polarized wave has a better response gradient than the P-polarized incident flux.

APPENDIX A: MODULATION OF PLASMONIC RELAXATION DAMPING BY SURFACE PHONONS

The effect of SAW generated temperature on LSPR absorption is explained in Fig. 8. A constant SAW ($2V_{\text{p-p}}$) amplitude is applied and the corresponding absorption is plotted. There is a small change in absorption observed with increasing time which corresponds to an increase in surface temperature. Hence to eliminate this effect, the data is measured at a very short duration of excitation (10 ms). The effect of surface deformation is investigated by changing the switching condition of SAW in the absence of LSPR, as shown in Fig. 9. The observation shows that the surface bending has very negligible effect on the output of optical transmission. Hence the effect can be neglected in our measurement system.

 

Fig. 8. Effect of SAW generated temperature on LSPR absorption.

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Fig. 9. Effect of surface deformation.

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APPENDIX B: DERIVATION OF PLASMON DAMPING BY USING THE TWO-TEMPERATURE MODEL

The general equation for the two-temperature model is given by [18]

(B1)$$C_e\frac{\partial T_e(r,t)}{\partial t}=K_e\mathrm{\Delta }{T}_e(r,t)-G[T_e(r,t)-T_l(r,t)]+S_1(r,t),$$

(B2)$$C_l\frac{\partial T_l(r,t)}{\partial t}=K_l\mathrm{\Delta }{T}_l(r,t)-G[T_l(r,t)-T_e(r,t)]+S_2(r,t),$$

where $C_e$, $C_l$ are heat capacities of electron and lattice, respectively; $K_e$, $K_l$ are thermal conductivities of electron and lattice, respectively; $T_e(r,t)$ is temperature of electron and $T_l(r,t)$ is temperature of lattice ion at position $r$ and time $t$; $G$ is electron-phonon coupling constant; $S_1(r,t)$ is the light source term that represents the deposition of photon energy per unit time per unit area; and $S_2(r,t)$ is an energy source term from lattice phonons.

Generally without any external excitation in lattice, $S_2(r,t)$ is negligible as the energy only flows through electrons to phonons; whereas, with surface acoustic waves, the source $S_2(r,t)$ is essential and can be written as

$$S_2(r,t)=\kappa \frac{\partial E_{\mathrm{mesh}.}}{\partial t},$$

where $\kappa$ is energy conversion coefficient. It represents the portion of mechanical energy that can be transferred to phonon-electron coupling [8].

By considering Eq. (2) given in the main text,

(B3)$$\begin{gathered} S_2(r,t)=\frac{\kappa d^2}{{\epsilon }_0{\epsilon }_{r}s}\frac{\partial E_{\text{elec.}}}{\partial t}, \\ {C}_l\frac{\partial T_l(r,t)}{\partial t}=K_l\mathrm{\Delta }{T}_l(r,t)-G[T_l(r,t)-T_e(r,t)]+\frac{\kappa d^2}{{\epsilon }_0{\epsilon }_{r}s}\frac{\partial E_{\text{elec.}}}{\partial t}. \end{gathered}$$

From Eq. (B3), it is shown that the input lattice energy is a function of input electrical energy applied through the interdigital transducer.

The temperature difference between electron and lattice indicates the effect of electron-phonon coupling, represented as ${\alpha }_{\mathrm{e}\to \mathrm{ph}}$, which is expressed as

(B4)$${\alpha }_{\mathrm{e}\to \mathrm{ph}}=T_e(r,t)-T_l(r,t).$$

For a very short incident light pulse (at $t\to 0):S_1(r,t)\to S_1$.

Now by increasing $S_2(r,t)$, $T_l$ increases.

Condition 1: At $t\to 0$, $T_l<T_e$, in Eq. (B4), electron-phonon coupling, ${\alpha }_{\mathrm{e}\to \mathrm{ph}}$, becomes

$${\alpha }_{\mathrm{e}\to \mathrm{ph}}=T_e(r,t)-T_l(r,t)\sim \text{positive (forward energy damping)}.$$

Equation (B1) becomes

(B5)$$C_e\frac{\partial T_e(r,t)}{\partial t}=K_e\mathrm{\Delta }{T}_e(r,t)-G{\alpha }_{\mathrm{e}\to \mathrm{ph}}+S_1.$$

Condition 2: At $t\to 0$, $T_l=T_e$,

$${\alpha }_{\mathrm{e}\to \mathrm{ph}}=T_e(r,t)-T_l(r,t)=0(\text{at equilibrium}).$$

Equation (B1) becomes

(B6)$$C_e\frac{\partial T_e(r,t)}{\partial t}=K_e\mathrm{\Delta }{T}_e(r,t)-G[0]+S_1.$$

Condition 3: At $t\to 0$, $T_l>T_e$,

$${\alpha }_{\mathrm{e}\to \mathrm{ph}}=T_e(r,t)-T_l(r,t)\sim \text{negative}(\text{reverse damping}).$$

Equation (B1) becomes

(B7)$$C_e\frac{\partial T_e(r,t)}{\partial t}=K_e\mathrm{\Delta }{T}_e(r,t)+G[{\alpha }_{\mathrm{e}\to \mathrm{ph}}]+S_1.$$

Funding

Ministry of Science and Technology, Taiwan (108-2221-E-002-014-MY3).

Acknowledgment

We acknowledge the Ministry Science and Technology, Taiwan for funding and acknowledge R. Gupta and other laboratory mates for their help in editing and discussion. We would also like to acknowledge the Advance Spectroscopy Laboratory, Department of Physics at National Taiwan University for TRPL analysis.

Disclosures

The authors declare no competing interests.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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