A single mode resonant cavity is adapted to absorb energy via a single excitation mode in a plurality of overlapping absorption bands having different respective resonant frequencies, thereby increasing the resonant bandwidth of the cavity. The high Q-factor cavity may form part of a microwave powered catalytic converter for exhaust gas, and has the advantage that as the cavity warms up and physically expands the coupling efficiency between the cavity and a relatively narrow waveband microwave source remains good.