Violation of the Babinet principle in checkerboard complementary structures made of perfect electric conductors

The celebrated 1830's-era Babinet principle of classical electromagnetic theory is expected to hold universally for sufficiently thin perfect electric conductors. We demonstrate theoretically and using various numerical simulations that this principle can be severely violated in a family of complementary structures obtained by scaling the familiar checkerboard pattern, when in-plane electromagnetic wave components develop geometric resonances (standing wave patterns) in the screen openings. These resonances can occur even if the perfect conductor is infinitely thin.