IKEA has these backlit fake windows they use in store displays in their curtain section. I wish they would sell the fake windows as well. The light actually looks natural.
In Germany they sell these LED Panels, though not with the same dimensions used for their curtain installations. But unfortunately it looks like they are discontinuing these products. I just searched for "LED Panel" on their website and all listings say "Letzte Chance! Nur noch kurze Zeit erhältlich." (Last chance! Still available for a short time only).