[10GMMF] kink perturbations for channel modeling ad hoc, task 1 subgroup, other modeling
The task 1 subgroup supports development of mode delay sets and the related index profiles for the channel modeling ad hoc and the TP2,TP3 teams.
I have received questions about the exact form of the "kink" perturbation used in the 108 fiber example and I have forwarded *.txt and *.pdf files to Piers for posting on the FTP site.
Let me emphasize that this is just an example. It was motivated by an actual measured profile I had which produced a mode delay and DMD prediction showing a noticeable "kinkish" shift to the DMD. Therefore I feel confident that similar perturbations do occur, and I tried to find a functional form which reproduced the effect seen empirically.
There are certainly other functions would generate a similar effect of a relatively flat sequence of mode group delays "jumping" to another relatively flat sequence. Initially we thought the profile must be discontinous in its value at the point of the "kink" but what we found was that it was tied to a discontinuity in the slope or derivative of the profile, making it significantly more subtle and more likely to occur in manufacturing.
I would encourage those interested in this topic & doing modeling to look at a variety of perturbations. I looked at Gaussian perturbations, exponential perturbations, and then, generalizing, to functions of the sort as exp ( -a |x|^b) where x is the distance from the kink and b would 2 for a Gaussian and 1 for an exponential.
The example I am using here results in an index profile with a discontinuous slope at one point.
A related perturbation which this might be approximating would have the inner profile be a perfect alpha profile of the form D_inner= D1[1 - (r/a1)^1.97] and the outer profile would also have the form D_outer = D2(1-(r/a2)^1.97), but D1,a1 and D2,a2 would be such that D1<D2 and a1<a2 and at the transition radius where D_inner = D_outer the index profile stays continuous but there is a discontinuity in slope.
The particular perturbation we are using in the 108 fiber set may not be the most "efficient" in the sense of causing the largest, sharpest "kink" in the mode group delays with the smallest amplitude of perturbation; it was the best example I could construct with the time I had and again it is similar to examples I've seen. I would be quite interested in any further examples colleagues might suggest.
Thanks to all for interest & questions.
John Abbott
Advanced Modeling & Analysis
Corning Incorporated SP-PR-1-3