Adiabatic frequency conversion in epsilon near zero materials: it is all about group velocity.

We investigate adiabatic frequency conversion using epsilon near zero (ENZ) materials and show that while the maximum frequency conversion for a given change of permittivity does not exhibit increase in the vicinity of {\epsilon}=0 condition. However, that change can be achieved in a shorter length, and if the pump is also in the ENZ vicinity, at a lower pump intensity. This slow propagation effect makes the conversion efficiency in the ENZ material comparable to that in microresonators and other structured slow light schemes, but unlike the latter no nanofabrication is required for ENZ materials which constitutes their major advantage over alternative frequency conversion approaches.