GaN/AlN multiple quantum wells (MQWs), designed for intersubband (ISB) absorption in the telecommunication range, are grown by molecular beam epitaxy. We demonstrate that the use of both AlN template and optimized growth temperature allows to reach ISB transition energy in the telecom range, i.e. above 0.8 eV (lambda = 1.55 mu m). Absorption spectra exhibit narrow linewidth (< 50 meV) with a relative energy broadening of 8%. An electro-optical modulator based on electron tunnelling in coupled QWs is then fabricated. A modulation bandwidth of 2 GHz at -3 dB cut off frequency is achieved for 15x15 mu m(2) mesas. We show that the modulation rate is limited by the device geometry rather than by the material quality, which makes this technology a good candidate for THz regime.