What is the origin of my last name?

My last name is Azulay. Now before you suggest that I am of distant Jewish descent (As this is a popular name in Israel) I have found that my last name was originally spelled out as "Azulae" before my family moved to America from Portugal (I asked my Grandpa). I have tried to research my last name, yet I have found literally nothing except for Azulay. I found though, that Jewish "amazingh" (No that is not a spelling error; I can't remember what that means, but I think it's their original last name) settlers immigrated to Spain, and their name translated to Azulay. So, does anybody have any answers as to where my last name came from?