We have fiber optic, and our old rotary dial phone works just fine with it. Here's how our system works: the box on the outside of the house is Optical Network Terminal - this converts the signal to work with the house's copper wire. Since there is no longer a copper wire connection from the phone company (which previously carried power), the home's internal phone wiring needs to be powered from the home's regular AC power. There is a converter box in the basement that provides this charge to the ONT, but it is, of course, subject to household power outages. To protect against this, the converter box contains a rechargeable backup battery, which will power the home's phone system for eight hours of talk-time (supposedly - I have never had to test the battery life yet).
We have Verizon Fios phone service, which I believe is fiber optic, right?
In any case, the backup battery only lasts for 8-12 hours whether you use the phone or not.
We got to test it out last year after the hurricane when a transformer was taken down by a tree a few blocks away.
Our power lines are actually underground, but that transformer above ground apparently serves our lines.
After about 8-12 hrs (I can't remember exactly) the battery died and we had no home phone service. Instead we charged our cell phones in our car.