In this paper, the beam-propagation characteristics of the total internal reflection induced by the thermo-optic effect are investigated. Based on the Fourier heat transmission principle and variable separation method, we derive the analytical transient expression of thermal field for general thermo-optic (TO) devices. Based on the analytical expression, time response and steady-state temperature distribution of thermal-optic devices are presented. The expansion rule of total internal reflection (TIR) in the thermal field is developed mathematically, and quantitative calculation is given about specific expansion value. As an illustration and application of this rule, a X-junction 2×2 TIR switch is designed to accomplish the object of high reflection efficiency. The computer simulation results show the structure presents a high reflection coefficient indeed, the reflection loss is only -0.76dB. The computer simulation results agree with the calculation well.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.