Persian EmpirePersian Empire
Collocation of 'Persian' (as a demonym of Latinate Persia in the sense of Greek Persis, Old Persian Pārsa) and 'empire'. Translates Latin Imperium Persarum, as attested e.g. in the 1st century (e.g. Quintus Curtius Rufus "Life and exploits of Alexander the Great" 3.3.8).
In English from the 17th century, invariably in reference to the Achaemenid Empire (550–330 BCE) conquered by Alexander the Great. Sometimes expanded to Medo-Persian Empire (translating Imperium Persarum et Medorum, "empire of (ruled by) Persians and Medians"). The 'et Medorum' is not a reference to Median empire (625–550 BCE), but rather to (1) the tribal affiliation and shared status of the Persians and Medians, (2) the mixed Persian-Median parentage of the founder of the dynasty, Cyrus I.
The term 'Persian empire' has sometimes been extended to the later, "restored" empire ruled by the Sassanid dynasty, the ruling dynasty of which was also from Persia in the sense of Greek Persis, Old Persian Pārsa. It is sometimes taken more loosely to refer to the Achaemenid, Parthian and Sassanid states taken together (so Encyclopædia Britannica 2009: "historical empire from about 550 BCE-640 CE")