Okay, I imagined it. Converting electricity into light is inefficient (maxing out around 44% [1] excluding ballast losses), and converting light into electricity is also inefficient (topping out at 47%[2] efficiency). So you'd end up with a battery that stores energy at extremely low efficiency (less than 21% combined), relying on a hypothetical exotic material that can slow light transmission to ~0.00000001c, assuming you don't mind using a hypothetical box that is 1km long, and you can shine the light and replace the light with a mirror in <1 second. And that's before even accounting for the fact that perfect mirrors do not exist, so you'd be losing another 0.1% of remaining energy with every cycle (i.e. every second)
Or you could buy a lithium-ion battery off the shelf today at 95% round trip efficiency and low self discharge.
[1] https://en.wikipedia.org/wiki/Luminous_efficacy#Lighting_eff...
[2] https://en.wikipedia.org/wiki/Solar_cell_efficiency