Three or four years ago I grew Genovese basil just by sticking them under my 4-foot shoplights that I had mature tomato plants growing under. I did have some side-lighting using CFL's in brooder lamps, but I don't that was necessary for the basil. I'm sure they would have done just as well only using the shoplights with cool white tubes.
The basil did really really well. Had 4 or 5 basil plants in either an 8" or 10" container. Can't recall which is was. Unfortunately my current apartment gets too humid to grow herbs or even seedlings in the spring. It affects the leaves with tiny mold spores. One of these days I'll have to get a de-humidifier to see if that helps enough. I've lost most of my seedlings the last 2 years because of that problem, and the few survivors were weak and never flourished after transplanting.
I will say, fresh Genovese basil on the blackened (seasoned) salmon I used to buy really added a nice subtle flavor to it. The salmon was not the same without fresh basil leaves sprinkled on it. I actually didn't realize how much of a difference it made until the basil plants died out. Sam's Club sells the blackened salmon but they charge way too much for it these days. When I first bought it in Omaha it was less than $10 for a 2 lb. bag, which was 5 fairly small fillets. Now the price is around $15 and I've even seen it higher at times. I love it but considering I was eating two fillets per meal it wasn't worth the mark-up in price.
I got off track there as usual,
, but if you have a shoplight you should be able to grow herbs under it. Just remember to keep the plants very close to the light, the same as seedlings.