Deducing critical coupling condition to achieve perfect absorption for thin-film absorbers and identifying key characteristics of absorbing materials needed for perfect absorption

Equations are deduced to describe the critical coupling condition to achieve perfect absorption for the thin-film absorbers of absorbing layer/spacer layer/substrate. By numerically solving these equations, a linear inequality is obtained to describe key characteristics of the absorbing layer needed for perfect absorption at a given wavelength. Guided by this finding, various materials including metals and semiconductors are identified as the absorbing layer to achieve perfect absorption at a randomly chosen wavelength within the visible wavelength range of 400–800 nm. Finally, it is found that absorption in an ultrathin absorbing layer can approach 100% with the use of highly reflective substrate.