Kinetics of Thermally Activated Physical Processes in Disordered Media

Abstract

Abstract:We describe a framework for modeling the writing and erasure of thermally-distributed activated processes that we can specifically apply to UV-induced refractive index change, particularly in fibers. From experimental measurements (isochrons and/or isotherms), this framework allows to find the distribution function of the activation energy by providing only a constant, which can be determined by a simple variable change when a few assumptions are fulfilled. From this modeling, it is possible to know the complete evolution in time of the system. It is also possible to determine the annealing conditions for extending a lifetime. This approach can also be used for other physical quantities, such as photodarkening, stress relaxation, and luminescence decay, provided that it can be described by a distribution function.

Femtosecond laser direct writing in SiO2‐Al2O3 binary glasses and thermal stability of Type II permanent modifications

“…This corresponds to full erasure after a 30min thermal treatment at 650°C in Borofloat® 33 and 1025°C in ULE® glass. These values are quite close to their respective annealing points T a : 652°C for Borofloat® 33 and 1000°C for ULE®.Note the temperatures mentioned here are dependent on the duration of the isochronal plateau and a longer duration will shift down this "full erasure" temperature, which is somehow at the image of the glass transition temperature range, and revealing in such a way that the erasure mechanisms are in fact distributed36 .On the contrary, the R norm of both GeO 2 -doped SiO 2 and 70SiO 2 -30Al 2 O 3 exhibit a higher thermal stability and quite similar trends. The decay starts slowly at 650°C leading to 10% erasure at 850°C in 70SiO 2 -30Al 2 O 3 .…”

A Comparison between Nanogratings-Based and Stress-Engineered Waveplates Written by Femtosecond Laser in Silica

“…Consequently, in Figure 5a is displayed a comparison of the thermal stability of the waveplates, studied through an annealing experiment of isochronal (∆t = 30 min) annealing steps (∆T = 50 • C). It is worth pointing out that the curves in Figure 5 represents the "stability curve" provided that the criterion (δtk 0 ) -(∆T/Tmax) 1 is fulfilled [49] and where k 0 is the pre-exponential factor in the Arrhenius rate constant of the erasure reaction. For nanogratings written in silica, k 0 has been estimated to be around de 5.10 5 -5.10 7 s −1 [50] depending on the laser writing parameters.…”

Reliable Lifetime Prediction for Passivated Fiber Bragg Gratings for Telecommunication Applications

“…In various references [1,11,12], a framework for lifetime and passivation determination of standard type I FBG has been presented. The formalism is based on demarcation energy approximation and the existence of a master curve.…”

“…In the opposite situation, there may be several parallel or serial limiting reactions with different k 0 and different distributions. The analysis is thus more complex for achieving lifetime prediction but it is still possible to perform a VAREPA approach [1,11]. However, no MC exists anymore.…”

“…Indeed it can be shown that if one assumption is not verified in the investigated range of (t, T) and for the expression of E d that has been previously defined, no collapse is possible. In addition, a key assumption in using these MCs is that the decay in the change of refractive index is just defined by E d [11]. To check quickly this hypothesis at high temperature, one has to carry out isochronal and isothermal measurements for one quantity (here NICC) and secondly to plot data versus k B .T.ln(Δt isoc ) for the first set and k B .T isot .ln(t) for the second set.…”