Re: [10GMMF] Re feedback Polarisation effect and my HMG calculations
David, thanks for your kind note.
I would comment to the overall group that the mathematics gets burdensome in some of this and David's care is appreciated. For example, his equation (27) corrects a typographical error in the Saijonmaa reference.
I think that maybe in the observation of polarization sensitivity what is happening is that one of our assumptions about the laser launch & light propagation in FDDI links is not a sufficiently accurate approximation
These are some of the ideas which have occurred to me:
A. is the launch axis parallel to the fiber axis? I think the Grau paper in David's reference list suggests that if the launch has some tilt that there will be a polarization effect, and one explanation is that the launch is extremely sensitive to tilt (i.e. we can never eliminate tilt) so that we cannot eliminate some residual polarization sensitivity.
B. similarly, David's revival of the Hermite-Gaussian modes suggests the idea that a very small core ovality might break the symmetry presumed in much of our analysis, and that as soon as that happens polarization effects can be important. Since worst-case FDDI fibers can have a core ovality of 6%, one could definitely imagine this effect; however, Agilent and Infineon seem to see the effect on every fiber with a perturbation which they look at....
C. There is a dn/dr polarization correction term (the scalar wave equation ignores an extra term in the vector Maxwell's equations) which can help explain a polarization effect in fibers with large perturbations near the center; however, it sounds like Agilent & Infineon see effects with an offset launch if there is an index perturbation at that radial position.
Of these, it sounds like quantifying the sensitivity to ovality might be the most useful, but maybe it is worthwhile brainstorming other ideas.
John A.
-----Original Message-----
From: david_cunningham@agilent.com [mailto:david_cunningham@agilent.com]
Sent: Wednesday, November 03, 2004 11:41 AM
To: AbbottJS@corning.com; STDS-802-3-10GMMF@LISTSERV.IEEE.ORG
Subject: Re feedback Polarisation effect and my HMG calculations
John,
Per your feedback I have converted the calculations of my earlier discussion document called "Variation of the power coupled to the mode groups of a circular core square law multimode fibre from a circular single spatial mode laser" from HMG into LGG format (see attachment for amended document).
The results now agree with your feedback. Specifically:
1) The excited mode power distribution (MPD) is constant and independent of the orientation of the optical polarisation of the laser source.
2) The coupled power is not equi-partitioned between the individual modes within a group.
3) At the launch, the optical polarisation of the excited fibre modes are the same as that of the exciting laser.
4) For axial-symmetric refractive index distributions the impulse response remains constant when the angle of optical polarization is rotated.
This is because the modes within each group which exchange power when the polarisation is varied are the cosine and sine modes. As you have already said for axisymmetric index perturbations these mode have the same delay time.
I am now right back where I was about a month ago - I don't see how axisymmetric models can be used to calculate the change in impulse due to launch polarisation variation.
Thanks for the feedback,
David