We report that, for an evanescent-wave (EW) based fiber-optic sensor, the less skewed tunnelling rays and a small number of very steep guided rays experience total internal reflection (TIR) at one end-face of the air-clad fiber segment. As a result, they demonstrate nine times greater efficiency in collecting EW-power than rays that do not exhibit end-face- TIR. This tunneling ray group originates from a launching ring that is seven times wider than that of end-face-TIR capable guided rays, enabling it to dominate the overall detected EW-power level. Strongly supporting this conclusion is the counter-intuitive experimental observation that the detected power at one end of the fiber abruptly drops 91% when the back reflection at the opposite end is eliminated, while an isotropic light source is placed at the core-cladding interface between these two ends. The mechanism of non-propagating ray excitation accounts for this high efficiency. We also indicate that many highly skewed tunnelling rays are naturally isolated from the external world because, outside the fiber core, they are accessible only via their EW fields even at the fiber end-faces. The findings reported here have significant implications for the design of future high-performance EW-based fiber sensing devices for the analysis of surface-event.