A connection process between an optical fiber and an optical microguide, the microguide having on a substrate, a structure having two media and a core between the media and whose refractive index is higher than those of the media, wherein substantially anisotropic etching takes place of the structure from one end of the microguide, so as to eliminate from the structure a zone allowing the axis of the core as the median line and whose width is at least equal to the external diameter of the fiber. Etching by a dry process takes place of part of the substrate which is located beneath the thus eliminated zone and over a depth making it possible to bring into coincidence the core of the microguide and the core of the fiber, when the latter rests on the bottom of the recess formed in this manner in the substrate and the fiber is fixed in said recess.