This was the time of the Safavid Dynasty (and empire).
I had no idea - until I listened to this excellent In Our Time podcast :
... In 1501 Shah Ismail, a boy of fifteen, declared himself ruler of Azerbaijan. Within a year he had expanded his territory to include most of Persia, and founded a ruling dynasty which was to last for more than two hundred years. At the peak of their success the Safavids ruled over a vast territory which included all of modern-day Iran. They converted their subjects to Shi'a Islam, and so created the religious identity of modern Iran - although they were also often ruthless in their suppression of Sunni practices. They thrived on international trade, and their capital Isfahan, rebuilt by the visionary Shah Abbas, became one of the most magnificent cities in the world. Under Safavid rule Persia became a cultural centre, producing many great artists and thinkers...The role of Armenian Christians in the dynasty puts the infamous Turkish genocide in a historical perspective. The Ottamans and Safavids were great rivals, and the Christian Armenians seem forever caught in the crossfire.
This history, and the myths that arose from it, explain a lot about modern Iran and the great Shia-Sunni struggles of the 21st century.
 This link is to the almost impossible to find archived podcast. Despite the BBC's stated podcast policy these are no longer discoverable from the primary In Our Time episode archives. You can find them on on the hidden BBC IOT Podcast archive. You may be able to also extract them from the iTunes archive or the BCC IOT Podcast feed. I blame it on Cameron.
 The last of the Iranian Shahs, prior to the latest revolution, was accused of favoring Zoroastrian ideas, including divine rule. The God-King is a worldwide tradition. (Aside, I met one on his sons when I was at Williams College in @ 1979/80.)