Frequency multiplexers that incorporate either a power divider network or a power coupling cavity in conjunction with photonic bandgap filters. The frequency multiplexers comprise a signal input and a plurality of signal outputs. In a first embodiment of the multiplexer, a 1-to-N power divider network is coupled to the signal input, and a predetermined number of photonic bandgap filters are coupled between the divider network and the plurality of signal outputs and that are driven by the divider network. Each photonic bandgap filter has an predetermined bandpass characteristic such that the plurality of filters cover the total input signal bandwidth. In a second embodiment of the multiplexer, a cavity is formed between the signal input and the plurality of filters. The spatial locations of the filters tailor the propagation properties of the cavity so that a corresponding plurality of propagating modes are established linking the different input frequency bands and the signal output. Each filter comprises a wave launching antenna, a waveguide-like cavity, a receiving antenna, and a photonic bandgap crystal disposed in the waveguide-like cavity that comprises a dielectric substrate having upper and lower metal boundaries that define lengths of dielectric members therein, and at least one switch interconnecting pairs of dielectric members formed in the substrate.