Theory of line narrowing by deep nano-trap lattice in Raman gas

Recently we demonstrated a system for light-trapping molecules and stimulated Raman scattering based on a lattice of ultra-deep traps created by spatially modulated Raman saturation, where Raman-active molecules are strongly localized in a one-dimensional array of nanometre-wide sections, resulting in a central line with a sub-recoil linewidth as low as 14 kHz. Here the theoretical modelling of such a process is presented in detail. The numerical formalism is presented on both microscopic and macroscopic scale. The field distribution in the fiber is discussed, and the predictions regarding the line narrowing, sidebands, and lattice motion are provided.