We present the feasibility of a directional coupler composed of a tapered monomode fiber surrounded by a Liquid Crystal (LC) external cladding. After a short review of the different losses induced by bending or tapering of a fiber, we describe a method to couple light out of a tapered fiber, opening perspectives in the field of integrated optical couplers and we show how to control the direction of the losses, by electrically induced reorientation of LC.