Increase path length for a photon with two mirrors vs optical fiber

Is it possible to build two mirrors in vacuum such that a light pulse (single photon) gets refleted many times in order to increase the distance it travels? For example like that?

Say I want the photon to travel 1 km. The two mirrors have a length of 1m and a distance of 10 cm. Hence I need the pulse to bounce back and forth approximately 10,000 times.

Is it possible to build something like that?

Another question is: What happens to the pulse? Will it disperse? How will the incident pulse differ from the outgoing pulse?

And at least: Is there any advantage over an optical fiber with a length of 1 km? Or is it even worse (concerning losses and dispersion)?

For every reflection in the mirror you will loose some light. In my knowledge the best polished mirror has ~ 99% reflecting ability. But lets stick to 90%. A common mirror has less than 10% reflectivity. After 10000 reflections the intensity of the out going light is $(0.9)^{10000}$ of the incoming light. On the other hand, optical fiber uses total internal reflection. So there is no loss of light. You don't need a optical fiber 1km long. If you know the radius of the fiber and you know the critical angle, with a similar method you can find out the length of the fiber you need.