Middle eastern orange

After I heard the last show where the question was about whether the word for "orange" came from the fruit or the color first, I kept thinking about the similarity in several Middle Eastern languages for the word orange. Martha, this one's for you. In Greek, the word for orange is "πορτοκαλί"; in Turkish, it's "portakal"; and in Arabic, it's "burtuqaala". These seem very similar and I would guess trace to the same root. I seem to recall that the word "portugal" once was used for "orange". Were oranges once shipped to the Middle East through Portugal. Is that the connection?