Babinet´s principle, percolation, and Kramers-Kronig relation in metallic checkerboard pattern with randomness

Terahertz transmission spectra of metallic checkerboard patterns with randomness have been investigated systematically. The spectrum changes from capacitive type to inductive one rapidly with the nominal size of the metal squares around the critical size with invariant-transmission at some frequencies. The characteristic properties of the transmission spectra are interpreted in terms of the Babinet´ principle, percolation, and Kramers-Kronig relation.