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Re: [10GMMF] Re feedback Polarisation effect and my HMG calculations

Dear John,

Thank you very much for your comments.

For a perfect radial symmetric waveguide, the change of input polarization
varies the energy of the degenerate modes (the sin mode and cos mode) in one
mode. The total power of the mode is a constant. The root of the
polarization effect is the imperfection of the fibers, the asymmetric fiber
core, the perturbation of the index profile, as well as the external stress.
These imperfections introduce the modal selective loss, mode coupling and
power diffusion in the multimode fibers. The exact mathematic expression of
these behaviors is complicated. However, the common point of these behaviors
is that the energy in the modes is redistributed and how the energy is
redistributed depends on the spatial distribution of the modes and their
initial power partition. Empirically, the combination of polarization
induced energy transfer among the degenerate modes and modal selective lose,
such as an offset at the connector or detector, resembles the experimental

I hope this make some sense. I would appreciate your comments.

Best regards,


-----Original Message-----
From: owner-stds-802-3-10gmmf@IEEE.ORG
[mailto:owner-stds-802-3-10gmmf@IEEE.ORG] On Behalf Of Abbott, John S Dr
Sent: Thursday, November 04, 2004 1:40 PM
Subject: Re: [10GMMF] Re feedback Polarisation effect and my HMG

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
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: []
Sent: Wednesday, November 03, 2004 11:41 AM
Subject: Re feedback Polarisation effect and my HMG calculations


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

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,