I know this is severely late, but I wanted to address some points now that I have some time.

First, I am going to assume that "our culture" refers to western culture. But this is a dangerous assumption to make, so please be sure to avoid such generalizations in the future. This is an important distinction to make because the reception of the Persians in the West is much, much different from the reception of the Persians in, for example, modern Iran. These are just two extremes in a the wide spectrum of modern societies that have studied and analyzed materials and documents from Achaemenid Persia.

All that being said, I want to point out just one major document that has impacted Western culture: the Cyrus Cylinder. Since its discovery in the 19th century in Babylon, the Cyrus Cylinder has often been heralded as a document of peace, magnanimity, and the universal tolerance of mankind. It has been argued that in the document, King Cyrus the Great guaranteed the freedoms and liberties of all citizens of the Persian Empire.

Of course, reality is much different (and less exciting). The document was merely a dedication to the gods of the rebuilding of a sacred temple in the city of Babylon. In the text, Cyrus stated numerous platitudes about being destined to be king, and to protect these gods of Babylon, and to do the bidding of the gods, etc. But there is no "universal charter of mankind" in this document.

Nonetheless, scholarship in the early 20th century focused heavily on this early interpretation of the text, and Cyrus was aggrandized into an ancient guardian of liberty and freedom. The modern state of Iran has also developed and furthered this legend, even placing an image of the Cyrus Cylinder on some official documents and currency. Of course, there are also the biblical connections, with Cyrus being tied to the return of the Jews to Israel. Of course, the Cyrus Cylinder itself is silent on the Israelites, but his supposed magnanimity and his mention in the book of Isaiah 45 tied the Cyrus Cylinder to this growing legend of Cyrus 'the Great.'

For further reading, I recommend Irving Finkel's The Cyrus Cylinder, which has compiled all of the most recent research and thinking on the document and its history and reception.