Giant colloidal silver crystals for low-loss linear and nonlinear plasmonics

The development of ultrasmooth, macroscopic-sized silver (Ag) crystals exhibiting reduced losses is critical to fully characterize the ultimate performance of Ag as a plasmonic material, and to enable cascaded and integrated plasmonic devices. Here we demonstrate the growth of single-crystal Ag plates with millimetre lateral sizes for linear and nonlinear plasmonic applications. Using these Ag crystals, surface plasmon polariton propagation lengths beyond 100 μm in the red wavelength region are measured. These lengths exceed the predicted values using the widely cited Johnson and Christy data. Furthermore, they allow the fabrication of highly reproducible plasmonic nanostructures by focused ion beam milling. We have designed and fabricated double-resonant nanogroove arrays using these crystals for spatially uniform and spectrally tunable second-harmonic generation. In conventional ‘hot-spot'-based nonlinear processes such as surface-enhanced Raman scattering and second-harmonic generation, strong enhancement can only occur in random, localized regions. In contrast, our approach enables uniform nonlinear signal generation over a large area.

The double-resonance design allows both the fundamental and second harmonic fields to be greatly enhanced, leading to more than 2,000 times stronger SH emission in comparison to that from an unpatterned silver surface.

Supplementary Note 1. Atomic force microscopy (AFM)
AFM images (see Supplementary Fig. 1) were acquired by a commercial AFM system (Park system XE-100). The table in Supplementary Fig. 1 shows the root-mean-square (RMS) roughness values from different horizontal and vertical line profiles. The RMS roughness is about 0.5 nm over 1  1 m 2 and 0.9 nm over 10  10 m 2 .

Supplementary Note 2. Optical measurements for the determination of SPP propagation lengths at different wavelengths a. White light interference (WLI, Method 1)
Our objective is to extract the propagation lengths of SPP on the Ag crystal using the Fabry-Pérot (FP) interference patterns resulting from multiple SPP reflections between two grooves, as illustrated in Supplementary Fig. 2. Because of the incoherent nature of the excitation source and the oblique incident angle, the SPP intensity launched from groove 1 is stronger. Therefore, in the following discussion, we only consider SPPs launched from groove 1, reflecting back from groove 2 and subsequent multiple reflections between two grooves. The SPPs propagating along the x-direction on the Ag surface can be describe by , where E is the amplitude of the detected scattering light from one groove, and E follows the plasmonic resonance of a single nanogroove. The coefficient C is the SPP coupling coefficient, and is the SPP wavenumber. The real part of k SPP (k r ) determines the peak and dip positions of the interference pattern, and the imaginary part of k SPP (k i ) determines the propagation length of SPP such that .
The scattered light amplitude arising from the FP modes formed between two grooves separated by a distance D can be described as the following, , where and the r is the reflection coefficient, which is proportional to the plasmonic resonance spectral shape and the SPP reflection cross-section. Then, the scattering intensity from groove 1 can be written as .
We first extract , which only depends on the peak and dip positions of the scattering spectrum (Fig.   S3a). The precise values of E, C, r, and k i do not affect the fitted values of . We can simplify them by assuming E = C = r = 1, and such that .
We can then extract the k r () from Eq. (S5). After that, we substitute the k r into Eq. (S3) to fit the interference pattern shown in Fig. 2c to extract . To extract one needs to simulate the field distribution and spectral response of SPP launched from the groove, which have been included in the reflection coefficient r. Furthermore, we also use this model to fit interference patterns formed between several double-grooves with different separation distances (see Supplementary Fig. 3) and the resulting effective index (n eff = /(2)·k r ()) is self-consistent for all fitted curves (see Supplementary Fig. 4)

b. Direct scattering intensity (DSI, Method 2)
For DSI experiments, the incident laser was focused to a spot size of 10 m in diameter onto the short launching grooves via a lens of focal length 18 mm. The decoupled light from the long output groove was collected by a 50 long working distance objective. The incident light was polarized at 45 degree relative to the groove. A linear polarizer at 45 degree was used to remove the background from incident light in the r i 2 2 2 1 1 The far-field intensity of scattering light was obtained from CCD images of the output coupler after subtracting a background. Signal from an area of 10 µm (perpendicular to output groove) by 45 µm (parallel to output groove) was used to obtain the integrated output intensity.

c. Film thickness effect in SPP propagation length
The silver thickness would affect the SPP propagation length only when the thickness is below 100 nm.
We use the FDTD method to simulate SPP propagation lengths on Ag films with different thicknesses (45 nm, 100 nm, 200 nm and infinite thickness, as shown in Supplementary Fig. 5a). In these simulations, an incident light with = 532 nm excites a single nanogroove on the silver film to generate SPPs. The propagation length on a 45-nm-thick silver film is clearly shorter than that in other films (see Supplementary   Fig. 5a) because of the presence of an additional leaky mode (mode 2) in Supplementary Fig. 5b. The propagation length no longer depends on film thickness when it exceeds 100 nm (see Supplementary Fig.   5a).

Supplementary Note 3. SHG measurement a. Field distribution of fundamental plasmonic resonance
We used the two-dimensional FDTD method to simulate the near-field distributions at 532 nm and 1064 nm (see Fig. 3d and Supplementary Fig. 6). The permittivity function of silver is adopted from ref. 16.

b. Optical setup of reflectance measurement
We used a halogen white light as the incident light to excite the nanogroove array at normal incidence through a 100× objective lens (Olympus, N.A. = 0.8) and a polarizer. The reflection light was collected by the same objective lens. All the reflectance spectra shown in Figs. 3c and 4d are normalized to the reflection spectrum from a bare silver single crystal.

c. Optical setup for SHG measurement
We used a homemade confocal microscope to map the SHG signal by scanning the sample under the excitation laser spot. The signal was projected onto a photomultiplier tube (PMT) and a charge-coupled device (Andor, iDus DU420A-BU2), which was cooled to 60˚C. A short-pass filter (Semrock, FF750-SDi02) separated the SHG signal from the excitation light. The excitation source is a 1064 nm pulsed laser (Fianium, FemtoPower 1060-532-s) with a 300 fs pulse width and a repetition rate of 40 MHz. The optical excitation and collection of the SHG signal from the nanogroove arrays were through the same 100× objective lens (Nikon, N.A. = 0.9) at normal incidence/collection geometry. Furthermore, the spot diameter is 1.4 m.

d. More detailed descriptions for Supplementary Figs. 7, 8, 9 and 10
In Supplementary Figure 7, we show the quadratic relationship between the SH signal and the incident excitation peak energy density in a log-log plot. The SHG conversion efficiency (P (2) /p () ) depends on various conditions including the excitation pulse, the focused spot size and excitation cross-section, thus difficult to compare between different structures. With an incident average power of 2.4 mW, we measured a value of 1.2 × 10 -8 , which is comparable with other plasmonic nanostructures 30 . We note that this SHG efficiency is limited by the nonlinear coefficient of Ag itself. A higher efficiency can be achieved by placing other dielectric nonlinear materials in plasmonic hot spots or hot areas. In Supplementary Figure 8, we show the histogram of SH emission from a square area (5  5 m 2 ). This statistical analysis shows that the standard deviation of SH intensity is about 10% of the mean value. In Supplementary Figure 9, we provide more data about tunable plasmonic resonant structures for enhanced SHG (Fig. 4). In comparison to the H-polarized incident light, the V-polarized incident light (i.e., E field parallel to the nanogroove) cannot excited the plasmonic modes in nanogrooves; thus, no reflection color change can be observed in Supplementary Fig. 9a. The SHG signal is spatially uniform as shown in Supplementary Fig. 9b,c.
Supplementary Figure 10 shows that the double resonant structure allows more than 2,000 times stronger SH emission, in comparison with that from an unpatterned surface.