How are Maxwell equations satisfied in Raman scattering?

[fluidistic]

I had learned that at the interface between 2 regions such as vacuum and a material, if there's an incident light from a region to another, the boundary conditions on the $\vec E$ and $\vec B$ fields at the interface are such that for them to hold at all times, the frequency of the incident light must equal the frequency of both the reflected and refracted light.

If one looks at Raman scattering, where say a red laser is shun on a material, the reflection can occur with a different frequency. How are Maxwell equations still satisfied in that case?

 

[Paul Colby]

Because of energy levels in the material the electrical properties are non-linear.

 

[fluidistic]

Because of energy levels in the material the electrical properties are non-linear.

Does this imply that Maxwell equations "fail" to describe the system?

 

[Paul Colby]

Does this imply that Maxwell equations "fail" to describe the system?

Absolutely not in any way shape or form do Maxwell's equations fail. Maxwell's equations must be combined with the physics of the materials involved which in this case are not modeled by passive linear constitutive relations as is evident from the frequency evident in Raman scattering.