Could be, if you find a way to store energy inside something consisting basically of nothing, without any conversion. 
Would that not have something to do with the type of light you are storing?
Would the difference be relevant compared to say, a lead acid battery?
Well, if I read all that has been posted, the trick is the substance or field that lines the inside of the container so the light is not lost, converted or dissipated.
It seems from a practical implementation standpoint the only missing invention is that “lining”?
Energy, in a form of light, would have to not change when in contact with that lining. But it would have to contain it.
Certainly a great challenge for physicists.
Yes, in principle a photon from the visible light spectrum can be stored in any atomic structure, that’s where electromagnetic energy comes from in the first place. However, it’s not a jar of photons … and the “best before” date is very short, even near absolute zero temperature.
AFAIK, humans have no method of permanently and directly storing any form of energy and that might be only be seen in nature with the energy stored in atoms. That needs to be realized.
So no man made energy storage is permanent and we usually think of energy storage in terms of what is practical. A rechargeable electric battery that maintains charge for just 24 hours can be practical in certain applications, but its usually more.
There is also the question of “what is storage”? We tend to think of storing matter and storing energy as the same thing, but its not. You put water in a bottle and store it directly. But putting electricity into a rechargeable battery does not directly store the electricity. Instead it creates a chemical alteration in the battery which can later be reversed to produce electricity.
Above people have offered methods of storing light indirectly. But I think the OP is asking if it can be stored directly, such as water can.
I theorize you could technically “sort of” store light in a very long optic fiber cable running in a loop, if you insert the light and close the loop fast enough. In a mathematical sense the loss of light would be low because optic fiber is pretty good at keeping the light moving without loss, but due to the speed at which the light would travel and the length of the cable it would be gone pretty fast according to our senses. I would be surprised if a loop of optic cable running around the equator would keep light in it for more than one second despite the 7 revolutions it might make. But I am no expert on any of this.
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