It saddens me greatly, and in numerous ways, to find out that "How do they get light?" is a killer question.
Of course, it's slightly different if you've got plentiful energy, but no good way to transmit/store it. Lots of solar panels all over the city to power its greenhouses. Or windmills in Chicago.
If this is the case, than we may be able to grow crops more efficiently indoors than out. But we will be replacing acres of crops with acres of solar panels. And it's unclear to me why we would want these buildings to be skyscrapers, which are much more expensive per square foot than large warehouses in the middle of nowhere.
That's utter nonsense!
You can only get as much light as you have surface area - so now instead of fields of crops, you have fields of solar collectors!
Did you think there was some magical light multiplier device that could give you more output light than you started with?
Plants already use the best parts of the visible spectrum to collect light. The small amounts of infra-red you might barely be able to collect and frequency up-convert are not worthwhile - especially since you'd need to throw away all the energy from the higher frequencies in order to get it.
Solar cells are terrible as far as efficiency is concerned - and not because of engineering, because that's simply how they work. (Unless you want a multijunction solar cell but those are very very expensive.)
And for engineering challenges there simply doesn't exist in the world enough rare earth elements to make enough solar cells for everyone - and that's just for regular electrical usage, forget about growing plants. We do have enough silicon, but silicon based solar cells have poor efficiency.
You'll also have a garden full of black plants, which is both creepy and cool.
More accurately, below the frequency cutoff they ignore the light, above the cutoff any, extra energy is wasted as heat.
And plants don't need a narrow frequency anyway.
And, even if evolution automatically did win, plants did not evolve to feed us. They evolved to reproduce themselves, and we have incidentally hijacked them to use as food sources.
Of course you need to transmit electricity and re-emit the light efficiently. You will still end up with acres of solar panels, as I said. Before you jump on someone for getting their science wrong, make sure YOURS IS RIGHT!
You mis-recall. It has two peaks in the absorption spectra but they are not narrow. In other words, a plant is green. There's no way to absorb only two frequencies and still be green.
"Wheat is say 1% efficient at solar collection"
Using http://en.wikipedia.org/wiki/Photosynthetic_efficiency as a guide, about 28% of sunlight energy is collected by chlorophyl. Of that, much is used to keep the plant alive (sugar production, respiration, growing roots). About 1% is left for human use.
It's the 28% that's relevant here, not the 1%.
In other words, 28% for plants beats "crappy solar cells" at 8%. Now, 47% of the energy is outside the 400-700nm range that chlorophyll can process so you might be able to double the energy use if you can find a good way to upconvert/downconvert light into that range. That would at best double what you can grow.
Which is still nowhere close to getting viable farming in an urban center.