I've written quite a bit about this topic elsewhere, which I hope provides quite a comprehensive overview of this period as a whole. The most relevant is my answer on why the Arab conquests succeeded, focusing particularly on Roman losses and the collapse of the Persian Empire, but other answers on how Christians at the time saw Islam, on whether Islam was seen as a Christian heresy, and on whether Rome and Persia had any warning before the conquests began might be interesting for you as well. /u/textandtrowel's answer on just how Islamic the conquests were is relevant too, especially given recent historiographical developments. There are quite a few book recommendations included in these answers, but I'm happy to talk more about the sources here if it is needed :)