'Second Sophistic' was a Greek cultural movement of the second and third centuries CE, very important to the emperor Hadrian.
A teaching guide, The Second Sophistic (PFD) gives a brief overview. Quotes:
[Greek] cultural Renaissance, centered in Athens and the cities of Asia, such as Ephesus, Smyrna, and even Laodicea. Rome itself [was] heavily involved, chiefly through Hadrian and Marcus Aurelius but as early as Nero and as late as the troubles of the third century [.An] encompassing literary and cultural movement …
A number of sophists, such as Nicetes of Smyrna, Scopelian of Smyrna, and Polemo of Laodicea were active between the reigns of Nero and Hadrian. Second century sophists such as Lollianus of Ephesus, Herodes Atticus, and Aelius Aristides were even more prominent.
Herodes Atticus was a friend of Hadrian and later became a teacher of Marcus Aurelius and Lucius Verus.
A JSTOR search on the Second Sophistic yields only this article: Cultural Choice and Political Identity in Honorific Portrait Statues in the Greek East in the Second Century A.D., R. R. R. Smith, Journal of Roman Studies, Vol. 88, 1998 (1998). [check with your local public or university library for JSTOR access]
Postscript 2/27: the above JSTOR file seems to be damaged and unrecoverable.