The dynamic behavior of an optical micro ring resonator (OMRR) with an amplitude modulator positioned in the micro ring is investigated quantitatively by adopting a recently introduced quantifier, the permutation entropy (PE). The effects of modulation depth are focused on, and the roles of input power are considered. The two-dimensional (2D) maps of PE showing dependence on both modulation depth and input power are presented as well. PE values nearly increase with modulation depth. On the other hand, the optimal value of input power is achieved when the PE reaches its maximum. Thus, PE can successfully quantify the dynamics of modulated OMRR. Selecting the parameters in the region with high PE values would contribute to the complexity-enhanced OMRR-based chaotic communication systems.