Non-linear phenomena impact the quality of optical transmission along the dielectric fiber. The theoretical analysis of non-linear interaction of light and matter assumes that certain parameters are either positive or within a bounded range. However, these assumptions although pragmatic may overshadow other possible outcomes that lead to paradoxical consequences of interest. In this paper, we review the theory of optical propagation and particularly the non-linear interaction between adjacent optical channels that propagate in a dielectric medium such as fiber, and we challenge traditional mathematical assumptions. We describe under what conditions the mathematical relation of the dielectric constant e(w)is expressed in terms of tuning or detuning between two oscillators, and under what conditions it is e(w)>1, e(w)<1, and also under what conditions e(w) becomes negative. The latter is of particular importance because if such conditions are achievable, matter has negative dielectric constant, the refractive index is purely imaginary, the group velocity meaningless, and a new chapter in photonic technology opens.