$2\mathrm{.}5\mathrm{.}3$ Light can enter a semiconductor slab waveguide in different polarization states. Describe what happens when light in each of the following input polarization states is coupled into the waveguide: $($a$)$ linearly polarized in a direction parallel to the boundaries of the core layer, $($b$)$ linearly polarized in a direction perpendicular to the boundaries of the core layer, $($c$)$ linearly polarized in a direction that is neither parallel nor perpendicular to the boundaries of the core layer, and $($d$)$ circularly polarized.