There is interest to develop optically generated radio frequency signals for systems such as radar, microwave-over-fiber, and high-frequency wireless communication because such systems have the potential for multi-channel broadband communication. We demonstrate the generation of terahertz optical subcarrier radio frequencies in a semiconductor optical amplifier. The circuit arrangement consists of a 1550 nm pigtailed laser diode driven below its lasing threshold to generate a spectrum of spontaneous emission. The spontaneous emissions signals are passes through a semiconductor amplifier driven into saturation. A fraction of the output signal emerging from the amplifier is fed back into the input of the amplifier. By appropriately arranging the phases of the input and the feedback signals, optical subcarrier frequencies of up to 3.75 terahertz were generated and measured.