Fig. 3: Measured spectral response of the field distribution inside the DLA channel.

Our method for deep-subwavelength spatial imaging with sub-nm spectral resolution is applied to (a) the dual-pillar structure and (b) the inverse-designed structure. We observe a substantial change for the inverse-designed structure and hardly any change for the dual-pillar structure. c, d Measured field cross section (blue/purple dots) along the red marking lines in a and b. The black dashed lines (which can hardly be distinguished from the blue/purple dots since they almost perfectly overlap) are fits of the expected cosh/sinh field profile within the channel. They were multiplied by an exponential decay at the edges of the channel, where electrons lose energy due to inelastic scattering off the structure. A Gaussian convolution imitates the blurring effect mainly due to the imaging point spread function. The dual-pillar structure has a large sinh component in the fit, which corresponds to an anti-symmetric (odd) structural mode with zero field at the center. In contrast, the inverse-designed structure has a substantial cosh component in the fit, with large non-vanishing energy at the channel center corresponding to a low-order symmetric (even) mode.