Actually I thought about it a little more, if you use repeater and multiplex and a long fiber line, it is like dynamic RAM that you reflesh with the repeater, then you can read or write new data through the mux. You keep track of the bit in the loop with counter which serve as address lines in DRAM.
Problem is the speed in fiber might vary slightly, it is not exactly like charge in discrete cell. Also the data storage is limited and depends on the fastest repeater and mux. Say using OC192 10Gbs. Say each data occupied 1" on the line, you need 1000' to store 12000 bits of data. Say if you use very advance modulation like QAM, you might say improving 16 times, still that is a lot of hardware for very little data storage. Might be cheaper to do storage in static RAM of very wide data so you get the equivalent speed up.