In textbooks one is told that, two beams of light shall propagate independently without any interactions. However, from QED, we have learned that, they can actually interact with each other, but the effective strength is remarkably tiny and hardly discernible. This insignificance is largely due to the considerable energy required to excite an electron-positron pair. Nonetheless, the energy to generate an exciton in a solid, which acts as the the counterpart of electron-positron pair, is not big. Thus, the photon-photon interaction might be greatly enhanced. Another factor that may help is the slowdown of photons in solid. This slowdown may prolong the interaction duration. Thus motivated, I did a simple calculation. The result is somewhat surprising: the slowdown does not always help but might be adverse. How could one understand this ?