Babinet’s principle states that if you have an opaque object and its complementary aperture, they should produce identical diffraction patterns when light passes through them. Ex. A thin metal rod blocking light should create the same diffraction pattern as a slit of the same shape cut into a metal sheet.
Babinet’s principle does not hold for nonlinear optics.
super-resolution effect:
In linear optics, only Fourier components inside the fundamental resolution limit (2π/λ) contribute to the far-field pattern. This means that small details in the near-field do not appear in the far-field image.
In nonlinear optics, The third-harmonic wave has a much shorter wavelength (λ/3), so the far-field image contains Fourier components up to 3 times and allows finer details visible.
Eddy current in slits:
In the rod, the polarization is mostly cosine-shaped, aligned with the electric field.
The Third Harmonic Generation process is highly localized and depends on the third power of the electric field.
The eddy currents in slits create extra localized hot spots, which do not appear in rods.
These extra hot spots cause the THG pattern of slits and rods to be completely different, violating Babinet’s principle.
Source:
https://arxiv.org/html/2503.14773v1
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