After the conquest of Iran by Arabs, spoken Persian(Farsi) headed towards the East, and the military troops and merchants brought it to the Transoxiana, and the area in which Afghanistan is located today. Arab conquerors used Persian far more than Arabic to propagate and promote Islam among the residents of that region. Thus, Persian(Farsi) finally overshadowed the regional languages such as Sogdian, and became the literary language of the communities in these regions in the Eastern borders of Iran.
Literary Middle Persian of Sassanid era was not completely obsolete at that time, as it was spoken and written by Zoroastrians; however, another literary language based on Dari Persian came to existence during that era. It is the contemporary written Persian.
Using the Arabic script for writing Persian(Farsi) began in the province of Khorasan, since in Southern and Western regions of Iran such as Fars Province, there were large groups of Zoroastrians and mobads who wrote their texts in Middle Persian (Pahlavi); thus, Pahlavi script was still resisting against new scripts and writing systems.
Therefore, Persian was the local dialect of southernmost region of Iran, gradually extending from south to north and east as a spoken language, and finally becoming the literary language of farthest northeast regions of Iran; the prevalence of Persian language (Farsi) expanded to the western and southern Iran, and finally established its roots in vast areas of Asia.
Since Middle Persian (with Pahlavi script) continued its existence and influence in parallel with Modern Persian for a while, those people who used to write in new literary Persian, initially insisted that their language was not the prior literary Persian, but another type of Persian, named "Dari Persian", and written using the Arabic script. Henceforth, when literary Pahlavi became effectively obsolete (except among Zoroastrians), there was no reason to express "Dari", and the new language was merely referred to as Persian (Farsi or Parsi).
Shortly after mid-9th century A.D., the first verses of Modern Persian poetry were written. However, it was in Transoxiana and during the Samanid Empire that the first prominent works of Persian Poetry were created by poets such as Shahid Balkhi, Abu-Shakur Balkhi, Abu-Mansur Daqiqi, and Ferdowsi; this new wave inspired many poets in the Iranian-language world and also in India, Central Asia, and Turkic language countries in Anatolia since 10th century.
Ferdowsi played a major part in restoring many lost words of Persian language(Farsi), and he himself has declared this influence. If it was not for Ferdowsi's spontaneous efforts, the identity of Persian language would be in jeopardy all the more. The trend of speaking in Persian in major cities of Central Asia was well-established during the final years of Sassanid Empire, and the Arabic language was substituted by the Persian language(Farsi) as the official written language in the Samanid and then Qara Khitai era.