We demonstrate that FDSOI transistors co-integrated with a diode implemented below the buried oxide (BOX) become strongly sensitive to visible light. The carriers photogenerated in the diode create a Light-Induced Vt Shift (LIVS) in both NFET & PFET transistors by means of capacitive coupling, without direct electrical connection between the photodiode and the sensing transistor. This optical back biasing effect is carefully examined as a function of both transistor and diode technological parameters. The experimental results are supported by TCAD simulations, suggesting that the proposed FDSOI/photodiode co-integration scheme can be used for efficient photodetectors. We also study the transient effects, and propose an efficient reset mechanism. Finally, we demonstrate for the first time that SRAM cells can be made controllable by light illumination.