Silicon Photonics: Fundamentals and Devices

10.2 Ray Optic Theory for Light Guidance

The condition for light guiding may be established by using Snell's law of refraction. Consider that a light ray E_i propagating in a medium of refractive index (RI) n₁ is incident at the interface between two media at an angle . The ray will be partially reflected (E_r) with angle and partially refracted (E_t) with angle into the other medium of RI n₂ (Fig. 10.1). Snell's law states that

(10.1)

When n₁ > n₂, there exists an incident angle , known as the critical angle, for which the refracted angle is 90̊, and the above relation reduces to

(10.2)

For angles of incidence greater than , there is total internal reflection and no light is transmitted into medium 2.

Consider now the three-layer structure in which medium 1 having RI n₁, called the core layer ...