In Fibre-Wireless (Fi-Wi) links, conversion devices between wireless microwave/millimetre-wave and lightwave signals are required. In this paper, we propose a wireless millimetre-wave-lightwave signal converter using an electro-optic (EO) modulator with Quasi-Phase-Matching (QPM) array of orthogonal-gapembedded patch-antennas on a low-k dielectric material. Wireless millimetre-wave signals can be received and converted directly to lightwave signals using the proposed device. It can be operated with no external power supply and extremely-low millimetre-wave losses. The orthogonal-gap-embedded patch-antennas can be used for receiving dual-linearized or circular polarizations of wireless millimetre-wave signals. The QPM array structure can be adopted for enhancing modulation efficiency by transit-time effects consideration. Structure, analysis, and experimental of the proposed device are discussed for 40GHz operational millimetrewave bands.