In this question, I ask about the existence of a smooth curve that traps light in a certain direction in a confined domain. I get a nice answer. Here is an extension of that question.
Is there a closed smooth planar curve and a nonzero length interval of angles satisfying the following property?
The closed smooth curve separates the plane into two disconnected domains, one interior the other exterior. Cut a finite connected segment, called opening, out of the curve. "Shoot" a "photon" through the opening into the interior along a direction in the aforementioned angle interval. The photon bounces off of the curve with the same angle as the incident line with respect to the normal vector of the curve. The photon will remain trapped inside the interior after traversing an infinitely long distance.