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The Cotton mouton effect is observed when a linearly polarized electromagnetic wave passes through a dielectric medium and a magnetic field is applied perpendicular to the direction of propagation of electromagnetic wave. The linearly polarized electromagnetic wave is transformed to elliptically polarized wave.
What happens in inverse Cotton Mouton effect?
A quick Google search led me to this 2010 paper by Rizzo et al (that's arXiv link, here's the IOP science link). The article states,
...the inverse Cotton-Mouton effect (ICME in the following), [is] a non linear optical effect that in principle exists in any medium. In the presence of a transverse magnetic field, a linearly polarized light induces a magnetization in the medium in which it propagates. The optically induced magnetization depends linearly on the transverse magnetic field amplitude. ICME, as its name indicates, is related to the much more studied Cotton-Mouton effect...in a similar fashion as the Faraday effect and the inverse Faraday effect are related.
This group has published another paper (arXiv link, IOP link) that discusses the link between the ICME and the CME. They state more-or-less the same definition of the ICME in this paper, but add a diagram (Figure 1) of the system.
