A method is shown for the extension in higher spatial dimensions of deterministic, aperiodic structures which exhibit strong aperiodic effects and have overall compatibility with the planar technology of integrated optical circuits. Disclosed devices are operative in response to incident electromagnetic energy to create a distribution of electromagnetic energy having localized electromagnetic field enhancement, wherein the device includes a dielectric or plasmonic material having a region of interaction with the incident electromagnetic energy. The region of interaction has a deterministic, aperiodic patterning with an array of individual patterning elements of distinct refractive indices such that a variation of refractive index of the device occurs over distances comparable with a wavelength of the incident electromagnetic energy, the array being a multi-dimensional extension of a corresponding one-dimensional sequence such that a spectral response of the array is a multi-dimensional equivalent of a spectral response of the one-dimensional sequence. Specific examples employing so-called Rudin-Shapiro, Thue-Morse and Fibonacci sequences are shown.