Fig. 1

Curvature-induced broadband field enhancement. a Left panel: A desired but unrealistic distribution of refractive index of air above a flat substrate that can achieve light confinement. The permittivity ε′ is presented in cylindrical coordinates (r′, θ′, z′). Right panel: Transformed structure obtained by applying a coordinate mapping (x, y, z) = Ω(x′, y′, z′), with permittivity above the substrate equal to 1. The spatial variation of ε′ in left panel is mapped to the spatial curvature without changing the dynamics of the electromagnetic waves. b, c 3D FDTD simulations for a Ag nanoparticle on flat Au substrate with 10 nm thick silica spacer in between. The inset in b is a schematic of the setup. d, e 3D FDTD simulations for a Ag nanoparticle on warped Au substrate. The inset in d is a schematic of the setup. A prominent field enhancement is demonstrated due to the effective gradient of permittivity described in a. f A summary of the averaged field enhancement factor \(\gamma = \overline {|{\mathbf{E}}|} _{{\mathrm{curv}}}{\mathrm{/}}\overline {|{\mathbf{E}}|} _{{\mathrm{flat}}}\) for different wavelength λ and particle radius r. A broadband enhancement is illustrated for all nanoparticles with different sizes, owing to the wavelength independence permittivity gradient induced by curvature