What was the cause of foreign interest in Persia?

Persia adopted a cosmopolitan approach and developed culture and prosperity. The Greeks traveled there to look and profit.

This was added to by Persia's expansion westwards into the Greek world, taking over the Greek cities in Asia Minor which embroiled it in the endless Greek wars. Ultimately the richness of the Persian Empire attracted adventurers who attempted to take it over as a ready-made empire ripe for the picking.

Sparta's king Agesilaos was on the brink of success in Asia Minor when he was recalled to deal with troubles at home. Philip of Macedonia set up an expedition, but was assassinated before he could carry it through, and his son Alexander took over the project and successfully made the Persian Empire into an empire of his own.