doi: 10.1038/nature07247 nature METHODS ption of Figs 3c and 4d, e, we used a RCWA, which expands the electromagnetic field into 3 X 13 diffraction orders and matches the boundary conditions at each inter- face. Specifically, the numerical refractive index in Fig. 3b, the dispersion curv in Fig. 4a-c and the numerical figure of merit in Fig. 5 were calculated using a alysis given in ref. 22. Figures 3c and 4d, e were calculated with com- finite-difference time-domain software( CST Microwave Studio ). In the ions, a Drude model was used for the dielectric parameters of silver, with 9.0 eV and scattering frequency ,=0.054 ev.The ompared to that of th bulk silver in order to account for the additional loss of surface scattering. In the experimental setup(Fig. 2c), light from the optical parametric oscillator Spectra-Physics)was focused onto the prism with an achromatic lens (lens 1) the second lens (lens 2)was placed at its focal position. The position of the beam at the focal distance of lens 2(2)was used to calculate the angle of refraction.As a result of limited camera imaging area, only the zero-order Fourier image was recorded. To obtain the absolute angle of refraction, a window with an area equal to that of the prism was etched through the multilayer stack to serve as a ref. erence. The windows Fourier image was measured at all wavelengths, giving a reference position corresponding to a refractive index of 1. The centres of the beam spot for both the window and prism samples were determined by fitting the intensity with a 2D Gaussian profile and the total beam shift(O) at the position of the camera was calculated by taking the difference between the beam spot centres. @2008 Macmillan Publishers Limited All rights reservedMETHODS In the numerical studies of the 3D fishnet metamaterial, with the exception of Figs 3c and 4d, e, we used a RCWA, which expands the electromagnetic field into 13 3 13 diffraction orders and matches the boundary conditions at each inter￾face. Specifically, the numerical refractive index in Fig. 3b, the dispersion curves in Fig. 4a–c and the numerical figure of merit in Fig. 5 were calculated using a modal analysis given in ref. 22. Figures 3c and 4d, e were calculated with com￾mercial finite-difference time-domain software (CST Microwave Studio). In the simulations, a Drude model was used for the dielectric parameters of silver, with plasma frequency vp 5 9.0 eV and scattering frequency c 5 0.054 eV. The scattering frequency is increased by a factor of three compared to that of the bulk silver30 in order to account for the additional loss of surface scattering. In the experimental setup (Fig. 2c), light from the optical parametric oscillator (Spectra-Physics) was focused onto the prism with an achromatic lens (lens 1); the second lens (lens 2) was placed at its focal position. The position of the beam at the focal distance of lens 2 (f2) was used to calculate the angle of refraction. As a result of limited camera imaging area, only the zero-order Fourier image was recorded. To obtain the absolute angle of refraction, a window with an area equal to that of the prism was etched through the multilayer stack to serve as a ref￾erence. The window’s Fourier image was measured at all wavelengths, giving a reference position corresponding to a refractive index of 1. The centres of the beam spot for both the window and prism samples were determined by fitting the intensity with a 2D Gaussian profile and the total beam shift (d) at the position of the camera was calculated by taking the difference between the beam spot centres. doi:10.1038/nature07247 ©2008 Macmillan Publishers Limited. All rights reserved