A method for enhancing the efficiency of bolometric photodetectors is presented. The method utilizes the analogy between the process of tunneling of a flux of quantum particles through a potential barrier and the propagation of electromagnetic waves within a nontransparent medium. The calculation results demonstrate that the fraction of radiation absorbed in a detector at a certain IR frequency may be close to unity if one chooses the right thickness and permittivity of the resonator substrate below a thin metal (superconductor) layer.