Optical fiber anchors accomplishing low creep confinement or fixing of a section of optical fiber in an assembly compact enough to be used conveniently as an anchor or as an enabling part of a strain or temperature sensor while retaining low optical losses and the original buffer coating to prevent the fiber from being exposed to abrasion and other influences that could lead to breakage. A rigid body is used that is mechanically stiff and hard enough to prevent the fiber from cutting into it or distorting the medium or substrate when subjected to stress, even over a long period of years. Trapping can be accomplished by molding the bent fiber into the substrate or body, adhesively bonding or soldering the optical fiber into a confining curved groove in a body or substrate.