The Persian Empire ceased to exist after Alexander defeated Darius at Gaugamela in 331 BCE. There were subsequent major mopping up operations over the following five years in Central Asia, but the Persian power was broken and the Persian king murdered by his own people.
Plataea of the last battle in the Persian war.
The Achaemenid Empire.
The Battle of Pteria in 547 BCE, between the Persian forces of Cyrus the Great and the Lydian army of Croesus.
Darius III.
Artaxerxes V.
No, the Persian Empire did not last from 1500 BC to 185 BC. The Persian Empire, also known as the Achaemenid Empire, was established in 550 BC and lasted until it was conquered by Alexander the Great in 330 BC.
The Battle of Salamis involved the Persian Empire - it was part of the invasion led by King Xerxes to try to bring the Greek city-states under control to stop their internecine warring spilling over into his empire.
Thermopylae.480 BCE.
The battle of Thermopylae.
Greek city-states vs Persian Empire
550 to 330 BCE.
The Persian Empire.