Substrate-Independent Lattice Plasmon Modes for High-Performance On-Chip Plasmonic Sensors
We systematically study the lattice plasmon resonance structures, which are known as core/shell SiO2/Au nanocylinder arrays (NCAs), for high-performance, on-chip plasmonic sensors using the substrate-independent lattice plasmon modes (LPMs). Our finite-difference time-domain simulations reveal that new modes of localized surface plasmon resonances (LSPRs) show up when the height-diameter aspect ratio of the NCAs is increased. The height-induced LSPRs couple with the superstrate diffraction orders to generate the substrate-independent LPMs. Moreover, we show that the high wavelength sensitivity and the narrow linewidth of the substrate-independent LPMs lead to the plasmonic sensors with high figure of merit (FOM) and high signal-to-noise ratio (SNR). In addition, the plasmonic sensors are robust in asymmetric environments for a wide range of working wavelengths. Our further study of both far- and near-field electromagnetic distribution in the NCAs confirms the height-enabled tunability of the plasmonic “hot spots” at the sub-nanoparticle resolution and the large field enhancement in the substrate-independent LPMs, which are responsible for the high FOM and SNR of the plasmonic sensors.
KeywordsLattice plasmon modes Plasmonic sensors Spectral tunability Figure of merit Hot spots
Noble metal nanoparticles (NPs) such as Au NPs and Ag NPs support localized surface plasmon resonances (LSPRs), which are the light-coupled coherent oscillations of free electrons confined within the NPs [1, 2, 3, 4, 5]. Various applications such as enhanced spontaneous or stimulated emission [6, 7, 8], solar energy harvesting [9, 10, 11, 12, 13, 14], surface-enhanced Raman spectroscopy, [15, 16, 17, 18] and cancer phototherapy [19, 20] have been investigated. Due to the strong electromagnetic field confinement and enhancement at the nanoscale, LSPRs are highly sensitive to the refractive index (RI) of local environments of the NPs, enabling the development of plasmonic sensors based on the analyte-induced changes in the peak wavelength and/or intensity of LSPRs [21, 22, 23, 24, 25, 26].
The performances of plasmonic sensors can be characterized by their figure of merit (FOM), which is defined as ratio of the wavelength sensitivity and the resonance linewidth. Usually, Ag nanospheres  and Au nanospheres  as single NPs or uncoupled arrays [32, 33, 34] have FOM between 1 and 3. The FOM is limited by the broad linewidth of LSPRs caused by radiative damping [35, 36, 37, 38]. Immobilizing NPs on substrates as required for on-chip applications also reduces FOM due to the reduced sensing areas from the contact between the NPs and the substrates. Strategies have been developed to improve the FOM of on-chip plasmonic sensors. For example, substrate undercutting has been applied to reduce the NP-substrate contact areas in order to increase the wavelength sensitivity . The design of NPs with sharp tips, like Ag nanotriangles  or Au nanostars,  has enhanced the FOM up to 5. A significant improvement of FOM has been achieved by breaking the symmetry in two or more NPs (or nanoholes) to introduce the Fano resonances with narrow linewidth, [41, 42] which result from interaction between a discrete state and a continuum of states .
Another effective approach towards narrowing the resonance linewidth of LSPRs is to arrange NPs in a highly ordered array so that far-field diffractive coupling occurs [44, 45]. When the diffraction orders change from evanescent to radiative, a strong dipolar interaction occurs, resulting in lattice plasmon modes (LPMs) or collective modes [46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57]. Significant suppression of the radiative damping leads to an ultra-narrow resonance linewidth of LPMs. Both theoretical and experimental studies have shown that the narrow linewidth leads to the enhanced performance in sensing [58, 59, 60, 61]. However, the LPMs have intrinsic drawback for sensing applications due to their requirement of homogeneous environments surrounding the arrays of NPs. The LPMs are suppressed when the NPs are immobilized on substrates because the diffraction orders are cut off at the nanoparticle-substrate interfaces . One can avoid this drawback by either introducing an index-matching layer on the top of NPs to generate a quasi-symmetric environment or increasing the size of the NPs to obtain coupling at the higher polarizability [51, 60, 62]. However, the index-matching layer prevents the interactions between analytes and NPs, and the use of larger NPs reduces the range of working wavelengths, limiting the applications of LPMs in the on-chip sensors [59, 60, 63]. Recently, an extremely high FOM of 108 is reported for LPMs in the Au mushroom arrays . However, the weak coupling in this type of structures leads to a low signal-to-noise ratio (SNR). As a result, the development of LPM-based plasmonic sensors with both high FOM and SNR for a wide range of working wavelengths in the asymmetric environment has remained challenging.
Herein, we introduce an approach towards increasing the FOM of on-chip plasmonic sensors for a wide range of working wavelengths, which synergizes the sub-nanoparticle engineering of plasmonic “hot spots” for high sensitivity and narrow linewidth of the LPMs. Previous work has demonstrated that the height-induced LPMs in the core/shell SiO2/Au nanocylinder arrays (NCAs) [65, 66] shift the plasmonic “hot spots” from the nanoparticle-substrate interface to the nanoparticle-superstrate interface to form the substrate-independent modes. In this study, we focus on evaluating the sensing capability of the substrate-independent LPMs. Our studies are based on finite-difference time-domain (FDTD) simulations, and the far-field sensing performances are supported by the studies of near-field electromagnetic field distribution.
Results and Discussions
Hot Spots Engineering in Single NC
We hypothesize that one can enhance the wavelength sensitivity of the LSPRs of single NCs to the superstrate RI (i.e., analytes) by shifting the plasmonic “hot spots” away from the nanoparticle-substrate interface to maximize their interactions with analytes. To test this hypothesis, we achieve the spatial control of the plasmonic “hot spots” within NCs at the sub-nanoparticle resolution by tuning the height-diameter aspect ratio of the NCs. Figure 2b shows the simulated scattering spectra and the near-field electromagnetic fields of single NCs with different heights for superstrate RI = 1.0. We observe a strong dependence of the LSPRs on the height of the NCs. Firstly, the D1 mode makes a slight redshift with the increased height. Secondly, a new dipole-bonding mode (D2 mode) shows up at the shorter wavelength of the D1 mode. With the “hot spots” located at the side of the NC (see upper panel of Fig. 2b), the D2 mode makes a redshift with the increased height. Lastly, a quadrupole mode (Q mode) appears at the higher energy side of the D2 mode when the height of the NC is further increased (i.e., h > 300 nm). This higher-order mode has the “hot spots” both within the core at the bottom of the NC and at the outer part of the Au shell on the top of the NC. Compared with the FOM of D1 mode (<0.98) in Fig. 2a, the D2 mode and Q mode have larger FOM, which are 3.15 (h = 200 nm; RI = 1) and 5.95 (h = 400 nm; RI = 1) (not shown here). The higher FOM for the D2 and Q modes justifies our hypothesis that the shift of the “hot spots” away from the nanoparticle-substrate interface increases the FOM. We focus on the height-induced D2 mode because it provides the opportunity to couple with the superstrate diffraction orders to generate the substrate-independent LPMs in 2D NCAs, which enables the development of the high-FOM plasmonic sensors.
Enhanced FOM in the Core/Shell NCAs
To enable the plasmonic-photonic coupling for the LPMs in the NCAs, we tune the lattice constants to make the diffraction orders overlap with the LSPRs, in particular, the D2 mode. We focus on the D2 mode because its plasmonic “hot spots” located at the sides of the NCs can couple with the superstrate diffraction waves to generate the substrate-independent LPMs for the enhanced sensing performance. Figure 3b shows a series of transmission spectra of the NCAs (D = 200 nm, h = 400 nm, and a⊥ = 900 nm), which exhibit the coupling and the LPMs, when the superstrate RI changes from 1.0 to 1.2. A strong dip at the wavelength of 937 nm in the spectrum (for RI = 1) is assigned to the LPM that arises from the coupling between the (0, ±1) superstrate diffraction orders and the D2 mode. This LPM makes a continuous redshift when the RI is increased, leading to a sensitivity of 733 nm/RIU. The increased sensitivity of the LPM is attributed to the high sensitivity of the superstrate diffraction orders to the changes of superstrate RI. As radiative damping is suppressed in this collective mode, the LPM has a linewidth that is much smaller than that of the LSPRs of single NCs. Even if we take an intermediate FWHM value from the spectrum with RI = 1.08, a high FOM of 17.9 is obtained. In contrast, the LPM that arises from the coupling between the (0, ±1) substrate diffraction orders and the D1 mode is not sensitive to the superstrate RI. Such a LPM is identified as a dip around the wavelength of 1258 nm in the spectra of Fig. 3b. When the superstrate RI changes from 1.0 to 1.2, the dip wavelength of this substrate-related LPM has almost remained unchanged.
To better understand the two types of LPMs in Fig. 3b, we describe the (0, ±1) diffraction orders as λ0,j = na⊥/|j| according to Eq. 4. We can see that the resonance wavelength is proportional to the RI of media surrounding the NCAs (i.e., n in Eq. 4) and to the lattice constants that are perpendicular to the external electric field Ex of incident light. Since n can be the RI of either superstrate or substrate, two sets of diffraction orders exist. For the LPM that arises from the coupling between the D2 mode and the (0, ±1) superstrate diffraction orders, the increase of superstrate RI makes a redshift in both the superstrate diffraction orders and the D2 mode, leading to the redshift of the LPM accordingly. The Fano-like LPM can be explained by the coupling between the discrete state (diffraction orders) and a continuum of states (LSPRs), and therefore, the coupling wavelength is slightly deviated from the (0, ±1) superstrate diffraction orders. This deviation is responsible for the difference in the wavelength sensitivity between the LPM and the (0, ±1) superstrate diffraction orders, i.e., 733 nm/RIU versus 900 nm/RIU (according to Eq. 4).
Electromagnetic Field Distribution and SNR
To further examine the plasmonic enhancement of the field in the diffraction orders, we simulate the magnetic field distributions for both the bare SiO2 NCAs (without Au shells) and the core/shell SiO2/Au NCAs. The orthogonal diffraction orders lead to the horizontal propagating magnetic field, i.e., Hz component propagating along y axis (see Fig. 1) [65, 66]. Figure 4c shows that, for the bare SiO2 arrays, the superstrate diffraction order of a low intensity is extended from the sides of the NC into the superstrate with two lobes parallel to z axis. The similar lobes with weaker intensity exist in the substrate, which arises from the imaginary part of Hz rather than the diffraction orders. When the plasmonic-photonic coupling occurs in the core/shell NCAs, the Hz intensity is enhanced with a factor of 20∼30, indicating an energy transfer from the plasmonic mode to the photonic diffraction modes (Fig. 4d).
Working Wavelengths of Plasmonic Sensors
Figure 6d summarizes the FWHM and the coupling wavelength for the core/shell NCAs with the different structural parameters and superstrate RIs. The FWHM decreases when the RI increases due to the weakening coupling strength. By taking the FWHM for the NCAs with strong plasmonic-photonic coupling (i.e., RI = 1.12, 1.08, and 1.04 for D = 50, 100, and 250 nm), we calculate the FOM as 23.7, 22.4, and 13.2, respectively. The highest FOM obtained at D = 50 nm suggests that reducing the FWHM is critical in enhancing the FOM of the LPM-based plasmonic sensors. The high FOM for both large and small NCAs is also supported by theoretical analysis. According to Eq. 4, the wavelength sensitivity is determined by a⊥, which decreases for the arrays with smaller NCs. However, the FWHM also decreases for the smaller NCs, which maintains the high FOM for the NCAs.
In summary, the substrate-independent LPMs, which arise from the coupling between superstrate diffraction orders and the height-induced modes of LSPRs in the lattice plasmon resonance structures of high aspect ratio (e.g., SiO2/Au core/shell NCAs), presents a tremendous opportunity for the development of the high-performance, on-chip plasmonic sensors. The narrow linewidth and the high wavelength sensitivity of the substrate-independent LPMs lead to the sensors of high FOM for a wide range of working wavelengths. The high SNR of the plasmonic sensors is enabled by the LPM-associated large field enhancement in the NCAs. The proposed structures can be fabricated with low-cost and high-throughput nanofabrication techniques, including nanoimprinting lithography. With the high FOM, high SNR, and robustness of the substrate-independent LPMs, the on-chip plasmonic sensors will find a wide range of applications in molecular analysis, biomedicine, and environmental protection.
The authors acknowledge the financial support of the Beckman Young Investigator Program. We also thank the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. URL: http://www.tacc.utexas.edu. We thank B. Bangalore Rajeeva, X. Peng, M. Wang, and Z. Wu for their helpful discussions on the simulation results and proofreading the manuscript.
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