Dynamic Evolution of Physical Quantities in Disordered Media
UV-written intracore Fiber Bragg gratings are now routinely used for applications in optical telecommunications or as sensors in civil engineering. Most applications require a long grating lifetime. For example, in dense wavelength-division multiplexing (DWDM) optical communication systems, the grating-based devices should continue working at an agreed specification for 25 years in the temperature range −40 °C < θ < 80 °C. Accordingly, several theoretical and/or experimental studies, dealing with accelerated lifetime tests, have been carried out with a view to forecast possible degradation of the UV-induced refractive index changes.
For modeling the relaxation processes in disordered media, several approaches can be used and an extended report can be found in the reference book of Richert and Blumen. The main problem is to account for the effect of disorder on thermally activated processes. The disorder can have an impact on the various steps of the physico-chemical reaction, leading to a change in the observed quantity (e.g., index changes, radiation-induced losses, etc.). For instance, if hopping is concerned in the reaction, the disorder will appear in the hopping distance or in the waiting time, if an energy barrier is involved, the activation energy will be distributed because the transition and/or the stable state configurations are varied.
These two examples differ fundamentally on one point: the temperature will not affect, in the same way, the range limit or the temperature-activated hopping. In particular, the dependence on the stability of refractive index with the writing or the ageing temperature can be only explained by processes with distributed activation energies. Other arguments connected to changes in the structure reinforce this conclusion. However, a process like decoration of defect networks with H will not necessarily be relevant to a thermally activated process. In our studies, we consider only processes involving the distribution of activation energies as it is seen that this approach yield good results with regards to the problem of index stability.