In this paper directional modulation (DM) transmitters, designed for orthogonal frequency-division multiplexing (OFDM) wireless data transfer are proposed using time-modulated arrays (TMAs). It is shown that by properly designing the switch controlling time sequences the proposed time-modulated OFDM DM systems exhibit promising features, such as i) requires only one radio frequency (RF) chain, ii) the conventional efficient OFDM signal construction approach, i.e., by using inverse fast Fourier transform (IFFT) modules, can be adopted, iii) it is 'DM synthesisfree', meaning that there is no need to re-synthesize the array excitation vectors for different secure communication directions, different modulation schemes, and different DM power efficiencies; and iv) the trade-off between secrecy performance and power efficiency can be flexibly adjusted. Index Terms-Directional Modulation (DM), orthogonal frequencydivision multiplexing (OFDM), physical-layer wireless security, timemodulated array (TMA) Readers who are following DM developments may be aware of a number of recent DM works, which claim that the FDA concept (and its variants such as non-linear frequency increments and random subcarrier selections) can be incorporated into DM transmitters, achieving free-space wireless security in range-domain, e.g. the random-subcarrier-selection-based OFDM DM transmitters in [19] and some of the references wherein. However, in those works one important factor was overlooked, which is that 'FDA range-angle dependent beamforming patterns are also functions of time'. This