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1 SUPPLEMENTARY INFORMATION doi: /nnano Tunable Subradiant Lattice Plasmons by Out-of-plane Dipolar Interactions Wei Zhou and Teri W. Odom Optical measurements. The gold nanoparticle arrays were mounted on a computer-controlled stage that can rotate at incident angle (θ) from θ = with 0.02 accuracy. Collimated TMpolarized or TE-polarized white light from a 100-W halogen source was incident on the nanoparticle array, and the reflected (transmitted) light was directed to a spectrometer (Triax 522/LN2-cooled CCD, Horiba Jobin Yvon). Zero-order transmittance and reflectance spectra of the nanoparticle arrays were measured under TM-polarized and TE-polarized light from θ = The incident excitation plane was aligned along the high symmetry lattice direction. To create a uniform dielectric environment around the nanoparticle array, we indexed matched the PU-substrate (n PU = 1.55) with an immersion oil-superstrate (n oil = 1.525). FDTD simulations. We performed 3D finite-difference time-domain (FDTD) simulations using commercial software (FDTD solution, Lumerical Inc. Vancouver, Canada). A uniform mesh size of 2 nm (x, y, and z directions) was used. The optical constants of gold were taken from Johnson and Christy 30 in the spectrum range from 400 nm to 1000 nm. The dielectric dispersion profiles of the materials were fitted by the multi-coefficient model. To calculate the angle and frequency dependent transmittance, perfectly matched layer (PML) boundary conditions were set for the z direction, and Bloch boundary conditions were applied to x and y directions of the simulation region. Minor differences between experiment (Fig. 3a) and calculations (Fig. 3b) were present from simplifications in the simulations: (1) the shape of the nanoparticles is modeled as a perfect cylinder; and (2) a homogenous dielectric environment (n = 1.52) is used although experimental environment is slightly asymmetric (n PU = 1.55 and n oil = 1.525). nature nanotechnology 1 1

2 Optical cross-section analysis. We used the following equations to evaluate extinction (σ ext ), scattering (σ scat ), and absorption (σ abs ) cross-section of individual nanoparticles in an array: σ ext = (1-T)*(a 2 0 cos θ), 2 σ scat = R*(a 0 cos θ), 2 σ ext = (1-T-R) (a 0 cos θ), where T is transmittance, R is reflectance, a 0 is the lattice period, and θ is the incident angle. In the experiment, we measured the zero-order transmittance and reflectance. In the simulation, we calculated the total transmittance and reflectance. 2

3 Figure S1. Electric field and phase distributions in strong coupled gold nanoparticle arrays are different for in-plane and out-of-plane components. FDTD simulated extinction (black line), scattering (red line) and absorption (blue line) cross-section spectra and phase maps of (ac) a single nanoparticle (θ = 15 ) and (d-f) a 2D nanoparticle array (θ = 15 ). 3

4 Figure S2. Energy flux from the incident light is trapped and propagates in the plane of the nanoparticle array at the subradiant resonance wavelength (λ out = 758 nm). Poynting vector maps at wavelengths within the broad in-plane lattice plasmon resonance (738 nm and 778 nm) indicate that light is not efficiently trapped when not at the out-of-plane resonance wavelength. The circulating energy flows around the particles in the left and right images is characteristic of localized plasmon modes. 4

5 Figure S3. Far-field and near-field spectra of gold 2D nanoparticle arrays change as θ increases. Angle-dependent spectra of (a) absorption cross-section σ abs, (b) local field intensity E loc 2 (2-nm away from the edge of the gold nanoparticle, +), and (c) average field intensity E ave 2 (center-plane of gold nanoparticle arrays, z = 0). 5

6 Figure S4. 2D nanoparticle arrays show different far-field spectral line shapes and nearfield optical properties at high θ compared to low θ. (a) FDTD simulated extinction (black line), scattering (red line) and absorption (blue line) cross-section spectra and (b-d) electric field intensity maps of 2D nanoparticle arrays (θ = 40 ). At high θ, the out-of-plane lattice plasmon spectrally shifts beyond the broad in-plane lattice plasmon. Hence, the far-field spectra exhibit a Fano lineshape because of interference between the narrow out-of-plane lattice plasmon and the scattered light continuum, and the near-field distribution map reveals a dominate contribution from out-of-plane dipolar plasmons. 6