Fig. 2: Example of a reduction in frequency of the entire superoscillatory field with the proper phase distribution.

a The amplitude of the 1D optical field is given by f(x) = {[A_s + cos[2π(x + 0.5)]}·exp[iφ(x)], where the corresponding phase is given by φ(x) = π × ∑Rect(2πn + x/2d) and rect(∙) is defined as 1 within [−0.5, 0.5] and 0 elsewhere, and b a comparison of the Fourier spectra between the optical field amplitude f(x) and the entire optical field E(x) = f(x)∙exp[−iφ(x)] = A_s + cos[2π(x + 0.5)], consisting of components with wavenumber values of 0 and 1, which are much smaller than those of the amplitude