Tunable multipole resonances in plasmonic crystals made by four-beam holographic lithography

Plasmonic nanostructures confine light to sub-wavelength scales, resulting in drastically enhanced light-matter interactions.^1,2 Nanoplasmonics has enabled significant advances in chemical sensing via surface enhanced Raman scattering (SERS),^3,4 allowing Raman spectroscopy of even single molecules.⁵ Metallic nanostructures have also enabled thermal energy harvesting, eliminating the need for an external light source in chemical gas sensing.⁶ More recently, plasmonic nanogap antennas have been shown to enhance the photoluminescence (PL) emission of emitters with initially small quantum yield with remarkable results, such as 1340-fold enhanced PL emission from dye molecules coupled to bowtie antennas,⁷ 2000-fold enhancement from monolayer MoS₂,⁸ 30 000-fold enhanced PL from dyes coupled to nanopatch antennas,⁹ as well as Purcell enhancement factors exceeding 1000.¹⁰ 

One limiting factor of plasmonic nanostructures is their inherent loss, in particular, for radiative dipole modes of spherical nanoparticles that are strongly damped by population decay and nonradiative excitations, resulting in high loss rates of a few femtoseconds.^11,12 These loss rates give rise to rather low optical quality factors (Q-factors) around Q = 2 for the near-infrared resonant spectral response of spheres but can reach up to Q = 23 if the spherical symmetry is broken in the form of nanorods.¹² The reported Q-factors of nanorods significantly surpass the quasi-static limit of individual metal nanostructures with Q ≤ 12 for resonances below 1000 nm (Ref. 13) and highlight the importance of taking retardation effects into account. Further advances beyond the quasi-static limit have been made by diffraction coupling (radiative field coupling) in plasmonic crystals where the particle spacing is close to the plasmon resonance wavelength, leading to Q = 5–60 for delocalized in-plane modes^14–19 and beyond Q = 200 for out-of-plane lattice plasmon modes of tall metal nanoparticles.^20,21 Of particular interest are higher-order multipole modes of non-spherical, non-circular, or near-field coupled metal nanoparticles arranged with broken symmetry.^2,22–26 These modes have vanishing dipole moments that can store electromagnetic energy more efficiently than dipole modes, leading to high Q-factors that are particularly attractive to enhance the PL from single-photon emitters,²⁷ as well as for on-chip applications when quantum light is required to propagate along sub-diffraction limited channels with negligible radiative loss.²⁸ Interaction of narrow multipole modes with broad dipole modes can also give rise to asymmetric and tunable Fano-type resonances^{22,24,29–31} that can enable plasmon-induced transparency.²⁸ 

The majority of plasmonic nanostructures that feature multipole or Fano-type resonances were fabricated based on electron beam lithography (EBL). It was recognized that plasmonic losses are not entirely intrinsic and are partly caused by surface damping due to fabrication errors, metal graininess, and material loss of Cr adhesive layers.³² To some extent, fabrication losses of EBL can be overcome using sophisticated scanning helium-ion beam lithography (HIL) of coaxial gap antennas demonstrating Q-factors up to 11 that are close to the quasi-static limit.³³ EBL and HIL fabrication techniques, however, are not readily scalable to wafer size as required for practical applications.

In contrast, holographic lithography (HL) is an appealing large-area fabrication technique³⁴ which has already been utilized to create plasmonic crystals with predominantly circular disk motives arranged in simple square lattices.^35–39 In fact, simple-lattice plasmonic crystals with record high Q-factors above 200 for the out-of-plane lattice modes were made using two-beam HL templates.^20,21 In previous work based on two-beam HL the motive spacing was restricted to the lattice constant, which is on the order of the wavelength of light. Recently we demonstrated that four-beam HL enables possibilities to create nearly arbitrary motive shapes with doublet, triplet, and quadruplet symmetries that feature nanometer gap sizes.^40,41 While four-beam HL can potentially enable wafer-size plasmonic crystals featuring multipole dark-modes and Fano resonances, their optical properties have not yet been investigated systematically.

Here we demonstrate that large-area gold and silver plasmonic crystals made by four-beam HL with deliberately broken circular symmetry can sustain in-plane lattice modes, dark modes, and Fano-resonances with high quality factors up to Q = 21. We also demonstrate static resonance tuning by changing the sub-lattice composition in the HL process as well as continuous tuning using the incident light polarization. The spectral position, Q-factor, polarization dependence, and multipole-order of the modes are also confirmed by finite difference time domain (FDTD) analysis and further reveal the electrical field enhancement and local charge distribution symmetries of the supported multipole modes.

To fabricate large-scale plasmonic crystals we utilized a four-beam HL setup in an umbrella geometry with azimuth angles φ = 0°,120°,180°, and 240°, respectively. (Figure 1(a)). Nanogap feature sizes were realized following our demonstrated scheme that is based on controlling the relative displacement of two sub-lattices of a compound lattice using phase, intensity, and/or polarization state of the four incident beams of a 488 nm Ar-ion laser operated at a power level of 15.6 mW.^40,41 Specifically, in this work the momentum vector $k→4$ and the polarization $e4→$ were used to realize dimer nanohole arrays with elliptical rather than circular hole shapes, and gap sizes that could be tuned from about 20–800 nm. The interference pattern was transferred into SU8 photoresist and the resulting nanohole templates were utilized to create metallic nanogap arrays by physical vapor deposition of Au or Ag films with 30 nm thickness on top of 3 nm Cr adhesive followed by mechanical tape-stripping of the polymer template. The scanning electron microscopy (SEM) images in Figures 1(b) and 1(c) show two plasmonic crystals with a gap-size of 180 ± 5 nm and 45 ± 5 nm, respectively. The measured long-axis diameter of 338 ± 5 nm and 342 ± 5 nm are nearly identical and reveal an aspect ratio (width/height) of about 10 for these elliptical disk-like structures.

The corresponding extinction and scattering spectra were recorded in transmission geometry with two distinct excitation angles. A regular bright-field excitation scheme was used to create a momentum vector of the incident white light that is perpendicular to the sample surface, thereby predominantly exciting plasmonic dipole modes. To efficiently excite the lattice modes and higher-order multipole modes that require an in-plane wave vector, a dark-field condenser with large numerical aperture (NA) of 0.75–0.9 was utilized, resulting in an average angle of incidence of about 35° with respect to the surface normal. For both bright-field and dark-field cases, the samples were excited with a halogen lamp white light source, and the transmitted or scattered light was collected with a 50 $×$ microscope objective (NA: 0.55) followed by a spatial filter before the spectrometer.

In the following we will first discuss the results under normal incidence excitation (bright-field). Extinction spectra for the 180 nm (45 nm) gap size plasmonic crystals are shown in Figures 2(a) and 2(d), respectively. The extinction (η_ext) was calculated from the measured transmission (T) spectra using η_ext = − log(T). The spectra show single-peak resonances centered around 950 nm that are typical for gold dimers with diameters of about 300 nm. As is well known, the bright-field dipole mode has a decay rate of a few femtoseconds, resulting in a rather broad continuum spectrum and thus rather low Q-factor of about 2.¹² For the plasmonic crystals made by four-beam HL, the Q-factor of the dipole modes was found to be Q = 1.8, in good agreement with previous findings of EBL fabricated structures. To demonstrate the nanogap effect, the data in Figures 2(a) and 2(d) show spectra for the two polarization cases, where p-pol refers to the incident electrical field vector oriented along the long axis of the dimer structure, and s-pol is the orthogonal case. At large gap separation the two resonances appear on top of each other with no clear sign of an energy splitting. In contrast, Figure 2(d) shows a pronounced energy splitting of ΔE = 148 meV (103 nm) between the s-pol and p-pol modes, clearly indicating near-field coupling of the plasmons.

The bright-field extinction spectra in Figures 2(a) and 2(d) have been simulated based on the FDTD method and are shown in Figures 2(b) and 2(e), respectively. A total-field scatter-field source was used to excite the plasmonic crystals on a 1 nm uniform mesh size with perfectly matched-layer boundary conditions. Geometry parameters are taken directly from SEM images. All spectral signatures, including occurrence of a single resonance peak, spectral position, linewidth (Q-factor), and splitting energy are well reproduced. The charge distribution plots show that the 950 nm peak has dipole character. Figures 2(c) and 2(f) show that polarization splitting is accompanied by a strong enhancement of the local electric intensity within the gap area. The intensity enhancement factor P increases from about P = 29 for the 180 nm gap sample to P = 160 for the 45 nm gap sample. As the gap-size is further reduced to 20 nm, which is the smallest size we have fabricated so far using the HL technique,⁴¹ P reaches 500 for the dipole mode.

To investigate the lattice mode and higher order multipole modes, we have utilized a dark-field condenser that effectively creates an in-plane wave vector in the optical excitation. Figure 3(a) shows a silver plasmonic crystal with a simple trigonal lattice featuring circular disks as characterized by a negligible ellipticity of ε = 3%, defined by ε = (a − b)/a, where a and b are the semi-axes of the ellipse. In this case one expects that only dipole lattice modes are visible and higher-order multipoles are suppressed since this lattice has neither a significant symmetry breaking nor a strong near-field dipole coupling of the plasmons, given the large lattice constant of 1.1 μm, as measured by the center to center distance. The corresponding scattering intensity spectrum in Figure 3(b) indeed displays only one dominant resonance peak centered around 700 nm. Its full width at half maximum (FWHM) is 112.3 nm corresponding to Q = 6.4, which is more than 3-fold narrower than the dipole mode recorded under normal incidence excitation. Note that the x-axis scaling in Figure 3 is zoomed in about twofold compared with Figure 2. The higher Q-factor is attributed to the excitation of the in-plane lattice mode that has significantly reduced radiative losses due to diffractive coupling of the plasmon resonances.^15,19

In contrast, the silver plasmonic nanogap crystal shown in Figure 3(c) has been designed to reveal higher-order multipole resonances by deliberately breaking the circular symmetry in the form of elliptical disk arrays with an ellipticity parameter of ε = 25%, and by introducing an average dimer gap size of 40 nm. The optical response in Figure 3(d) is more complex compared with that of the bright-field results, now featuring three distinct and spectrally narrow peaks centered at 653 nm, 760 nm, and 875 nm. The polarization dependence of the 653 nm peak displays a very pronounced intensity contrast up to 75%, which is indicative of an underlying dipole mode nature. The assignment of the highest energy mode to the lattice dipole mode is also in agreement with previous findings for broken symmetry.²⁹ The lower energy peaks display significantly less polarization modulation and are attributed to higher-order multipole modes.

To gain further insights into the underlying nature of the multipole plasmon modes we carried out FDTD simulations to find the corresponding electric field intensity maps and charge distributions plots for each peak. The intensity profile shown in Figure 3(e) for the prominent resonance peak at 875 nm strongly deviates from a pure dipole field while the charge distribution map clearly reveals a quadrupole character with multipolar expansion order l = 2. The Q-factor of the quadrupole mode is with Q = 12.2 (FWHM = 71.8 nm), significantly higher than the dipole lattice mode of the circular disk lattice in Figure 3(b). Similarly, the middle peak around 760 nm, or more precisely the dip on its high energy side at 710 nm, features additional nodes in the intensity profile shown in Figure 3(f), while the corresponding charge distribution in Figure 3(h) reveals it as an octupole mode with l = 3.

The octupole mode in nanostructures with broken symmetry is often found to interfere with the spectrally broader dipolar continuum mode resulting in a Fano-type resonance profile,^22,24,29,30 as schematically illustrated in Figure 4(a). It is thus plausible to assume that the middle peak at 760 nm is not a resonance on its own but rather the result of the superposition of the octupole mode, with the broader dipole lattice mode creating an intensity dip around 710 nm due to destructive interference. Additional insights can thus be gained by a full lineshape analysis of the polarization dependent spectra that takes into account spectral modifications due to Fano-type mode interference. To better highlight the components of the lineshape analysis we labelled the quadrupole mode with a black arrow and the Fano related intensity dip around 710 nm with a red arrow in Figures 4(b)–4(f). The scattering spectra (open dots) have been fitted analytically (solid lines) using a revised Fano-Lorentzian lineshape function given by:

where $ωb$ and $Γb$ describe the resonance frequency and line width of the dipole mode, respectively.

represents the Fano-type interference, where $κ$ is the reduced frequency, q the asymmetry parameter, and b the screening parameter.⁴² Good fits have been found for Γ_b = 42 nm, q = −3.6, and b = 0.13. The additional quadrupolar resonance at 875 nm was fitted by adding a Lorentzian lineshape to $σ(ω)$ while relative peak intensities are adjusted by three amplitude parameters with values 0.3, 0.2, and 0.7. The experimental scattering spectra in Figure 4 are well reproduced by the analytic lineshape functions, further supporting the assignment of the 710 nm dip to a Fano-type destructive interference of the dipole lattice mode with the octupole mode. While the dipole resonance dominates for the polarization orientation along the dimer axis (Figure 4(b), polarizer at 0°), it almost completely vanishes at orthogonal polarization (Figure 4(d), polarizer at 90°), making the quadrupole mode the dominant response. Continuous tunability of the oscillator strength between dipole and quadrupole modes is achieved at intermediate polarizer angles.

In addition, we fabricated gold plasmonic crystals with nearly identical geometrical dimensions and symmetry breaking as compared to the silver plasmonic crystals presented in Figures 3 and 4. Dark-field excitation of these gold dimer plasmonic crystals also reveal three-peak resonance spectra but with even narrower peaks with a FWHM of 40.6 nm for the quadrupole mode resulting in Q = 21, as shown in Figure 5. The higher Q-factor for gold is somewhat surprising given that the quasi-static limit predicts a three-fold higher Q-factor for silver nanoparticles as compared with gold. It is however well-known that silver nanostructures are prone to oxidation even under ambient conditions where submonolayer coverage of silver oxide significantly reduces the SERS activity.^43,44 We note that previous work has demonstrated optimization of the Q-factor by systematically varying the interplay of lattice constant and nanoparticle size,^15,17 which we have not yet carried out systematically, leaving room to further enhance the Q-factor of the a priori wafer-scale plasmonic crystals made by 4-beam HL in future work.

In summary, we have demonstrated that large-area gold and silver plasmonic crystals made by four-beam HL with deliberately broken symmetry can sustain in-plane lattice modes, multipole-modes, and Fano-resonances. Under normal incidence excitation conditions, we found signatures of plasmonic near-field coupling in dimer-gap arrays displaying pronounced energy splitting of ΔE = 148 meV, albeit with rather broad spectral response characterized by a Q-factor of 1.8. In contrast, we demonstrated more than one order of magnitude improvement of the plasmonic Q-factors (Q = 21) when the quadrupole mode is activated by the controlled symmetry breaking of the plasmonic crystal and the in-plane excitation scheme. In addition, we have demonstrated continuous tuning of higher-order multipole modes and Fano-like resonance profiles using the polarization state of the incident light beam. The demonstrated high Q-factor of the quadrupole mode in the 900 nm frequency band originates from strong suppression of radiative decay, which makes them particularly attractive for on-chip enhancement of single photon emission from individual (6,4)-chirality carbon nanotubes.^45,46 Finally, we note that the demonstrated utility of the polarization-controlled 4-beam HL technique opens possibilities to extend the rich physics of multipole plasmonic modes and Fano-resonance profiles to wafer-scale applications that demand low-cost and high-throughput.

We gratefully acknowledge the financial support by the National Science Foundation (NSF), CAREER Award Nos. ECCS-1053537 and DMR-1506711. Metal deposition was carried out at the Micro Device Laboratory supported by Stevens Institute of Technology. This research effort used microscope resources in the LMSI facility at Stevens that are partially funded by NSF through Grant No. DMR-0922522.