Though visible light communication (VLC) systems are contained to a given room, improving their security is an important criterion in any practical deployment. In this paper, the design of artificial noise (AN) to enhance physical layer security in VLC systems is studied in the context of input signals with no explicit amplitude constraint (e.g., multicarrier systems). In such systems, clipping is needed to constrain the input signals within the limited linear ranges of the LEDs. However, this clipping process gives rise to non-linear clipping distortion, which must be incorporated into the AN design. To facilitate the solution of this problem, a sub-optimal design approach is presented using the Charnes-Cooper transformation and the convex-concave procedure (CCP). Then, a novel AN transmission scheme is proposed to reduce the impact of clipping distortion, thus improving the secrecy performance. The proposed scheme exploits the common structure of LED luminaries that they are often composed of several light-emitting chips. Capitalizing on this property, LED chips in each luminaire are divided into two groups driven by separate driver circuits. One group is used to transmit the information-bearing signal, while the other group transmits the AN. Numerical results show that the clipping distortion significantly reduces the secrecy level, and using AN is advantageous over the no-AN scheme in improving the secrecy performance. Moreover, the proposed AN transmission scheme is shown to achieve considerable secrecy improvements compared with the traditional transmission approaches (e.g., about 1 bit/s/Hz improvement in the achievable secrecy rate when the standard deviation of the LEDs' modulating current is 0.25 A and the signal-to-interference-plus-noise ratio of the eavesdropper's received signal is limited to $0$ dB).