Three novel designs of adaptively modulated optical orthogonal frequency division multiplexing modems using subcarrier modulation (AMOOFDM-SCM) are proposed, for the first time, each of which requires a single IFFT/FFT operation. These designs has a number of salient advantages including a significantly simplified modem configuration due to the involvement of a single IFFT/FFT operation, input/output reconfigurability, dynamic bandwidth allocation capability, cost reduction and system flexibility and performance robustness to variations in transmission link conditions. Investigations show that these three modems are capable of supporting >60Gb/s AMOOFDM-SCM signal transmission over 20km, 40km and 60km single-mode fibre-based intensity modulation and direct detection transmission links without optical amplification and chromatic dispersion compensation