Resonant to broadband searches for cold dark matter consisting of weakly interacting slim particles

Dark matter may consist of light, very weakly interacting bosons, produced nonthermally in the early Universe. Prominent examples of such very weakly interacting slim particles are axions and hidden photons. Direct detection experiments for such particles are based on the conversion of these particles into photons. This can be done in resonant cavities, featuring a resonant enhancement, or by using suitably shaped reflecting surfaces that allow for broadband searches. In this paper we want to elucidate the relation between the two setups and study the transition from resonant to broadband searches. This then allows us to determine the sensitivity of off-resonance cavity searches for cavities much larger than the wavelength of the generated photons.