Abstract: Rotation effect is one of the important contents of college physics. Faraday rotation spectroscopy based on Faraday effect is proofed to be an effective method to investigate spin polarization and spin relaxation in materials.In this article，we study the theory of Faraday rotation and ellipticity which is caused by effective magnetic field induced by ultrafast circular polarization laser pulse by using Jones matrix.

Key words: Faraday effect, Jones matrix, rotation, ellipticity