This paper explores the possibility of designing nanoantennas that operate effectively in a wide range of infrared frequencies. To achieve a constant input impedance, we propose self-complementary nanoantennas composed of a high-permittivity dielectric and plasmonic metal. First, we present an approach to extend the applicability of Babinet's principle to the considered materials. We design several self-complementary nanoantennas made of silicon and silver with an optimal thickness of 12.7 nm whose input impedance is close to half the vacuum impedance, at least for frequencies from 50 THz to 300 THz. This approach facilitates the design of broadband nanoantennas operating in infrared. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)NanoantennasPlasmonics