Here we propose a new scheme to testify the half-wave loss through both theory and experimental demonstration. The scheme uses Jones matrix to analyze the transforming of optical state and calculates the outputs of two different kinds of Sagnac interferometers after light propagation. The results clearly show a π phase shift in a Faraday mirror. It is noted that the structure is simple since the structure is based on a developed Sagnac interferometer and some commercial optical components such as X type coupler

polarization beam splinter

Faraday mirror. The experimental results also indicate that the interference phenomenon is obvious

with interference contrast as high as 99%.