Experimental investigation of Kramers–Kronig relations in chiral metasurfaces with reduced rotational symmetry

Abstract

We examine the Kramers–Kronig relations between the circular dichroism and the optical rotation dispersion in the k-space obtained from a chiral metasurface with a reduced rotational symmetry. We operate a leakage-radiation microscopy system to probe the near-field plasmonic modes and measure the polarization effects of the grating. By using our system we were able to capture and analyze the plasmonic modes at both air/gold and gold/glass interfaces. The k-space mapping of the chirality parameters allows us to fully analyze the optical activity of the metasurface. We experimentally find that the reduction in rotational symmetry affects the locality condition which unavoidably leads to the deviation from the Kramers–Kronig relation.

Directional Plasmonic Excitation by Helical Nanotips

“…One can notice a very clear helical structure of the measured maps with opposite handedness, which we link to the strong symmetry breaking by the tips. In chiral system, two enantiomers can be interconverted by a spatial inversion rather than by a time reversal [34,35]. As we observed, also the k-space CD maps geometrically behave as two enantiomers.…”

Directional Plasmonic Excitation by Helical Nanotips

“…One can notice a very clear spiral structure of the measured maps with opposite handedness which we refer to the strong symmetry breaking by the tips. In chiral system, two enantiomers can be interconverted by a spatial inversion rather than by a time reversal [29,30]. As we observed, also the k-space CD maps geometrically behave as two enantiomers.…”

Topological Diffraction from Grating with Space Variant Chirality

“…39 Accordingly, numerous features of the kspace map presented in Figure 6 can be identified as the replicated plasmonic resonance lines surrounding different diffraction orders. It appears that the secondary plasmonic resonances at metal−dielectric interfaces (∼1.5k SP ) 34,40 have dominant signatures in this system, which results in χ enhancement around the line crossings. In order to obtain a sufficient range of χ and θ we chose to avoid working in saturated regions (rightmost and the leftmost parts of the map) as well as the null region around the center of the map.…”

“…It is known that a chiral medium leads to an optical activity manifested by the refractive index having different values for the RCP and LCP illumination. This results in a circular birefringence: Δ n = Δ n ′ + i Δ n ″, where Δ n ′ , ′′ = n RCP ′,″ – n LCP ′,″ , and the ′ and ″ mark the real and the imaginary parts of the index, respectively. , The real part of Δ n is responsible for the retardation between the circular polarization states, and the imaginary part leads to a differential absorption resulting in the ellipticity change (linear birefringence) . While adding a phase between circular states results in the rotating of a linear polarization, varying the retardation between linear states is equivalent to the rotating of the reference frame in the circular basis.…”

“…32,33 The real part of Δn is responsible for the retardation between the circular polarization states, and the imaginary part leads to a differential absorption resulting in the ellipticity change (linear birefringence). 34 While adding a phase between circular states results in the rotating of a linear polarization, varying the retardation between linear states is equivalent to the rotating of the reference frame in the circular basis. This can be described 3b.…”