Total internal reflection

Total internal reflection is a special case of transmission with Snell’s law. We define the critical angle as the angle of incidence where the transmitted angle is aligned with the media interface.

$${\theta }_c=\arcsin \left(\frac{n_t}{n_i}\right)$$

In the critical angle case, the reflected angle is perpendicular to the incident angle.

There are two conditions for TIR:

• $n_i>n_t$, i.e., the incident light wave is in the denser medium.
• ${\theta }_i>{\theta }_c$, i.e., the incident angle is greater than the critical angle.

Some important things to note about TIR:

• No power propagates across the boundary, i.e., the reflected wave carries all of the power of the incident wave. $R=1$, $T=0$.
• However, there does exist an evanescent field in the second medium that decays exponentially with distance.
• TIR introduces a polarisation-dependent phase shift.
• The Fresnel coefficients become complex: $r_{TE}=e^{i{\phi }_{TE}}$, $r_{TM}=e^{i{\phi }_{TM}}$. And note that ${\phi }_{TE}\ne {\phi }_{TM}$.