We present the first demonstration of reproducible harmonic modelocked operation from a novel design of monolithic semiconductor laser comprising a compound cavity formed by a 1-D photonic-bandgap (PBG) mirror. Modelocking is achieved at a harmonic of the fundamental round-trip frequency with pulse repetition rates from 131 GHz up to a record high frequency of 2.1 THz. The devices are fabricated from GaAs/AlGaAs material emitting at a wavelength of 860 nm and incorporate two gain sections with an etched PBG reflector between them, and a saturable absorber section. Autocorrelation studies are reported, which allow the device behaviour for different modelocking frequencies, compound cavity ratios, and type and number of intra-cavity reflectors to be analyzed. The highly reflective PBG microstructures are shown to be essential for subharmonic-free modelocking operation of the high-frequency devices. We have also demonstrated that the multi-slot PBG reflector can be replaced by two separate slots with smaller reflectivity. These lasers may find applications in terahertz imaging, medicine, ultrafast optical links, and atmospheric sensing.