The beam-propagation characteristics of the total internal reflection (TIR) induced by the thermo-optic effect are investigated. Based on the Fourier heat-transmission principle and the variable separation method, we derive an analytical transient expression of the thermal field for general thermo-optic devices. With the analytical expression, the time response and steady-state temperature distribution of thermo-optic devices are presented. The beam expansion rule of TIR in the thermal field is developed mathematically, and a quantitative calculation is given as well. To illustrate the application of the rule, an X-junction 2 x 2 TIR switch with high reflection efficiency is designed through theoretical calculation. The simulation shows that the structure exhibits a high reflection coefficient; the reflection loss is only -0.76 dB. The simulation results agree well with the theoretical calculation.
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Yu et al. (2005) studied this question.
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