Re: [10GMMF] Polarization effects for 10GBASE-LRM
Dear John,
first of all thank you for your clarification. I fully agree that sin
and cos mode of same order must have same propagation constant and
delay. This is true, according to WGA, to all modes within the same
group. This is essentially my objection to the conclusion (David and Yu)
that Mode Group Power, MGP, should not change due to polarization and
offset variation. How does the pulse change if Mode Power Distribution,
MPD, does not? According to the above conclusion, every group will bring
constant power versus any polarization changes, and it will travel
compact, dispersionless, with all individual modes traveling with same
speed.
Thank you and best regards
Stefano
-----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: Dienstag, 26. Oktober 2004 15:34
To: STDS-802-3-10GMMF@listserv.ieee.org
Subject: Re: [10GMMF] Polarization effects for 10GBASE-LRM
Dear Stefano,
In the Laguerre-Gauss formulation (as in Snyder&Love or the G.K.
Grau reference in Archive fur Electronik & Uebertragungstechnik Vol.34
No.6 pp259 which David referenced) the modal solution has the form
Psi_mu_nu(r) cos(nu theta) &
Psi_mu_nu(r) sin(nu theta),
so that the radial dependence and the angular dependence are clearly
separated, and if nu=zero the individual mode has only radial
dependence. In the Gauss-Hermite formulation (Saijonmaa et al. Applied
Optics Vol.19 No.14 p.2442 which David referenced) the individual modes
in the higher order groups are linear combinations of the Laguerre-Gauss
modes, and none of the Gauss-Hermite modes has a pure radial dependence.
This itself is a minor observation, but the point is that
in the Laguerre-Gauss formulation if the index profile n(r) has only
radial dependence, the "cosine" and "sine" individual modes must
theoretically have the same propagation constant beta and the same mode
delay tau, so that it is quite difficult for me to understand how the
effect of polarization can result in any observable change to the output
pulse. That is, in the LaguerreGauss formulation, there is a 4-fold
degeneracy with 4 individual modes having the same radial dependence
Psi_mu_nu(r) and then differing in their azimuthal dependence and
polarization orientation. Since they all have identical betas and taus
it's hard to understand how shifting the polarization angle of the
launching beam can change the output pulse.
I'm still noodling over this, and very much appreciate Infineon &
Agilent sharing experimental observations since there is definitely an
observed polarization effect.
Regards,
John Abbott
-----Original Message-----
From: Bottacchi.external@INFINEON.COM
[mailto:Bottacchi.external@INFINEON.COM]
Sent: Monday, October 25, 2004 1:03 PM
To: STDS-802-3-10GMMF@listserv.ieee.org
Subject: Re: [10GMMF] Polarization effects for 10GBASE-LRM
Importance: High
Dear John,
Thank you for your comments. I do not understand one assertion: why do
you invoke Laguerre-Gauss mode as responsible for the symmetry of the
fundamental mode within each mode group? The fundamental mode of each
mode group is axial symmetric since it has any radial dependence,
independently of course from any mathematical approximation used. As a
consequence it will not suffer from any offset nor polarization effect.
The coupled power to every group fundamental mode will never change
versus the input polarization nor the offset coordinates. This is
implicit in the overlapping integral, because there is not mode angular
dependence. Since now we basically agreed on individual mode coupling
coefficient dependency upon input polarization, my major concern now
regards the constancy David (and Yu) calculated of every mode group
power MGP respect to polarization and offset position. Even if David
(and Yu) calculate individual mode power variation within a specific
group versus input!
polarization and offset, I find
Best regards
Stefano
-----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: Montag, 25. Oktober 2004 16:59
To: STDS-802-3-10GMMF@listserv.ieee.org
Subject: Re: [10GMMF] Polarization effects for 10GBASE-LRM
It is my impression from reading David's note and from rereading these
older references that if one looks at the modes in the Laguerre-Gauss
framework as we usually do, that the individual modes within a mode
group vary in two distinct ways. There is a radial component and in
fact a single axisymmetric mode in every other mode group, and there are
the spiral or azimuthal modes in every group after the fundamental mode.
In the Laguerre-Gauss framework the radially symmetric modes are not
affected by polarization or the position of the input spot, while the
azimuthal modes are actually "two" separate modes with a sine or cosine
dependence. The Infineon calculations and also David's note show that
the relative power in the sine mode or the cosine mode depends on either
the polarization or the location of the input spot azimuthally around
the fiber, and the intensity distribution in a fixed lab coordinate
system will vary as either is changed. I disagree with David's comment
w! ! hich Stefano asks about in (2)
Within the Laguerre-Gaussian formulation the variation in mode
delays between individual modes in the mode group has to do with
different radial distributions of the individual modes. The
Gaussian-Hermite basis functions are equivalent but I think they do not
add clarity to this specific feature.
-----Original Message-----
From: Bottacchi.external@INFINEON.COM
[mailto:Bottacchi.external@INFINEON.COM]
Sent: Monday, October 25, 2004 9:38 AM
To: STDS-802-3-10GMMF@listserv.ieee.org
Subject: Re: [10GMMF] Polarization effects for 10GBASE-LRM
Importance: High
Dear David,
I appreciate your critical analysis and I am quite happy you agree on my
explanation for the observed polarization effects. I went through you
detailed calculations and I have a couple of questions:
(1) You conclude the MGP is constant respect relative angle between
the polarization and the offset direction. On the other hand, changing
the linear polarization you wrote the "coupled power is not
equi-partitioned between the individual modes within a group". As a
consequence, you concluded the measured variation of the impulse
response versus polarization orientation after 200~300 meters of MMF
were due to "delay differences between modes within same mode group". My
concern is that since a mode group is specified (within WGA) for having
the same propagation constant (asymmetries in refractive index
circularities are excluded), how do you support the measured pulse
distortion in terms of higher order beta variations? DMD should not be
included in your conclusion since DMD refers to different mode groups.
(2) The second question is more fundamental and it coincides with my
early concern on the validity of the "natural orientation" assumption
when linear polarization is included in the picture. I agree on this
picture. The basis function will be naturally oriented along the
polarization axis. If so, the mathematics will follow, but this is only
an assumption and it should be proved or at least well justified. I was
proposing first the "natural orientation assumption of the basis set",
but I am still thinking to some physical justification about it.
Thank you one more time for your excellent work.
Best regards
Stefano
> -----Original Message-----
> From: CUNNINGHAM,DAVID (A-England,ex1)
> [mailto:david_cunningham@agilent.com]
> Sent: Donnerstag, 21. Oktober 2004 20:55
> To: Bottacchi Stefano (IFFO MOD CE external); ysun@optiumcorp.com
> Cc: STDS-802-3-10GMMF@listserv.ieee.org
> Subject: RE: Polarization effects for 10GBASE-LRM
>
> Dear Stefano and Yu,
>
> I attach a PDF file which documents an analysis of SMF offset launch
> as a function of polarisation direction.
>
> Stefano: I now agree with you.
> The mathematical analysis I attach shows the effects that you describe
> and it is perfectly consistent within the references I quoted. I now
> agree that it is likely to be the launch in combination with
> incomplete mode mixing between the modes within groups that is likely
> to be causing the change in impulse response (IPR) with polarisation
> rotation. The variation in IPR will be largest when the index
> perturbations (which are cylindrically symmetric) cause delay
> splitting within groups and significant light power is launched into
> the modes with such splitting. I also agree that the scalar wave
> equation is sufficient to explain these effects.
>
> Yu: On your call on Monday I said I would provide example calculations
> for coupling into the fibre. Please accept this as my example - the
> extension to connectors is straightforward. It is school mid-term
> break here in the UK so I'm taking tomorrow off work. So this is as
> much as I can get done on this this week. I thought it best to send
> you what I had done so far.
>
> Obviously, having worked through the analysis I now agree with your
> general method for analyzing connectors too.
>
> Stefano and Yu: Please confirm that my analysis is indeed in agreement
> with the concepts you have been advocating to the group.
>
> Sorry for the stress I may have caused you during this debate, David
>
>
> << File: LaunchMPDdgc1.pdf >>
>
>
>
>
> -----Original Message-----
> From: Bottacchi Stefano (IFFO MOD CE external)
> [mailto:Bottacchi.external@infineon.com]
> Sent: 18 October 2004 11:35
> To: david_cunningham@agilent.com
> Cc: STDS-802-3-10GMMF@listserv.ieee.org
> Subject: RE: Polarization effects for 10GBASE-LRM
> Importance: High
>
> David,
>
> please find my comments in blue.
>
> -----Original Message-----
> From: CUNNINGHAM,DAVID (A-England,ex1)
> [<mailto:david_cunningham@agilent.com>]
> Sent: Dienstag, 12. Oktober 2004 22:45
> To: Bottacchi Stefano (IFFO MOD CE external);
> david_cunningham@agilent.com
> Cc: STDS-802-3-10GMMF@listserv.ieee.org
> Subject: RE: Polarization effects for 10GBASE-LRM
>
> Stefano,
>
> RE: I appreciated your comments and I understand you
> disagree on almost any polarization-dependent effect in MMF
> transmission, at least assuming circular symmetric refractive index
> without any birefringence.
>
> Ans: This is not quite correct. My concern is about how
> the task group proposes to model the following:
>
> 1) The excitation of the modes of multimode fibre of
> circular cross section with a monomode, monochromatic source.
> [Stefano Bottacchi] Please specify, since it not clear
> to me the reason for your concern.
>
> 2) Birefringence of multimode fibre of circular
> cross-section.
> [Stefano Bottacchi] I agree with you, birefringence of
> normal circular cross section fiber is not responsible for the
> polarization effects we experienced. To clean any doubt, Joerg
> disassembled the spool to lay down the fiber in order to cancel out
> any potentially stressed condition. The measured polarization effects
> were exactly the same of the wounded fiber.
>
> I am not satisfied with the sketchy models that have
> been briefly outlined so far. Since no detailed mathematics has been
> presented I cannot check if this is simply a miss-understanding.
>
> But from what I have understood so far I am compelled to
> say I do not agree with what has been outlined.
>
> RE: The exciting electric field is linearly polarized.
> Let us choose the Cartesian reference system to represent the vector
> field components Ex, Ey and Ez and let us choose the cylindrical
> (r,phi,z) coordinate system for representing the position. Let us
> define the x-axis along the polarization axis. Modes are the
> eigensolution of the scalar wave equation (Helmoltz equation)
>
> ANS: The scalar wave equation contains no information
> about polarization. Polarization effects must be added by some other
> means for example the polarization of the modal fields must be set by
> inspection or other knowledge - it is not an output of the scalar wave
> equation. Also, as far as propagation constants are concerned if the
> scalar wave equation is solved then small corrections could be applied
> to account for polarization - but at a fundamental level scalar wave
> solvers do not include polarization effects.
> [Stefano Bottacchi] The solution of the scalar wave
> equation represents the complete set of bound modes allowable by that
> waveguide geometry. The choice for x and y axis is arbitrary assuming
> the refractive index is a scalar with no birefringence components. If
> the exciting electric field is linearly polarized along some direction
> in the cross section, we can conveniently choose that direction as one
> coordinate axis (x-axis). Of course, we could also choose x and y axis
> independently from any polarization assumption. In that case we will
> deal with two orthogonal field components acting along respective
> coordinate axis. This gauge just makes mathematics more complicated
> but does not change the physical solution. Now, rotating the linear
> polarized field respect a fixed observer makes the whole mode set
> rotating in the same way respect the fixed reference system. Let us
> assume the fixed spatial orientation is the direction defined by the
> offset coordinate respect the center of the fiber. This is the picture
> we have in mind to justify how polarization takes place in multimode
> fiber when a fixed offset direction is involved. If the refractive
> index is a scalar and the fiber exhibits no asymmetries nor stress,
> there is no reason for any polarization effect, even negligible small.
> Even in single mode fiber, PMD arise just because the fundamental mode
> degeneration breaks into two very slightly different modes due to
> birefringence. This is not the case we are considering. In our basic
> model the multimode fiber is ideal, circular with a true scalar
> refractive index. Polarization effect arise just during the coupling
> between an offset fiber and a given linear polarization.
>
> If the vector wave equation is solved then there are
> small (very, very small) differences in the propagation constants even
> for modes within the same group due to the optical polarization of the
> modes.
>
> I would recommend reading Snyder&Love, Optical Waveguide
> Theory, Chapman & Hall 1983 sections:
> 11-15, 13-6,13-7,13-11 for more information.
> [Stefano Bottacchi] I have that book (very nice and
> complete) and I red it as my first reference on fiber optic. I will
> reconsider the sections you mentioned anywise.
>
> Therefore, I accept polarization effects can exist even
> in circular fibres. But, this is unlikely to be the cause of the
> larger birefringence we observe in the lab.
>
> RE: What happens now if we compute the overlapping
> integral with a small and exocentric (some offset) Gaussian spot? The
> basic conclusion is that the axial symmetry will be definitely broken.
> The overlapping integrals deal with the mode fields, not intensities.
> The coupling coefficient will depend on the cylindrical coordinates on
> the fibre cross section, including both the radial and the angular
> one. For each given mode LP(l,m) the overlapping integral leads to two
> different values for each of the two intrinsic degenerate solutions
> (sine and cosine). The "weight" of the sine and cosine terms will be
> no more the same due to the broken circular symmetry and when the
> intensity of LP(l,m) is computed it will be no more a constant. It
> will be dependent on both cylindrical coordinates, r and phi. In other
> words, the amount of field coupled depends on the relative orientation
> of the offset and the light polarization.
>
> ANS: I do not agree. Suggest you read the following
> papers:
>
> 1) Saijonmaa et al., Applied Optics Vol. 19 No.14
> (15Jul1980)p.2442-2452.
>
> 2) Grau et al., " Mode Excitation in Parabolic Index
> Fibres by Gaussian Beams" AEU, Band 34, 1980, Heft 6 pages 259-265.
> see Appendix 2: Connection between the power coupling coefficients and
> polarization.
>
> In words these references show that the input optical
> beam polarization can be decomposed into two equivalent orthogonal
> components (reference 2 is much more explicit here):
>
> A first one parallel to the line from the centre of the
> exciting laser spot to the optical centre of the fibre.
> A second parallel a line through the centre of the
> exciting laser spot parallel to the tangent to the core/cladding
> interface of the fibre.
>
> Furthermore, it is shown that the normalized coupling
> strength to each mode of the fibre is the same for each polarization
> component of the beam.
>
> The two directions, which are defined by the geometry of
> the excitation, define the relevant optical axis for the underlying
> basis modes of the fibre.
>
> Changing the orientation of the polarization of the
> input beam changes the relative power in each of the underlying
> orthogonal components of the beam. This leads to an asymmetry in the
> power coupled to the basis modes of the fibre. That is the same modes
> are always excited in each basis set but the relative excitation of
> each basis set is dependent on the angle of polarization.
>
> Hence the mode power distribution (MPD) is constant -
> the same modes are always excited.
>
> There is no rotation of modes at any point in this
> process - only a change in orientation of the polarization of the
> input beam.
>
> I don't expect you to believe my words but if I am to
> accept another model I need to know where these
> [Stefano Bottacchi] The basic difference is that now we
> have to consider THE POLARIZATION RESPECT TO THE OFFSET DIRECTION. It
> is this angle which is responsible for breaking circular symmetry
> originating polarization dependent coupling coefficients.
>
>
> RE: We nned only one more brick to close the wall: since
> the fiber is assumed highly dispersive compared to the bit-rate, with
> a not optimized refractive index profile (multiple alpha, kinks,...),
> the different power contributions to the launched pulse will travel at
> different speeds reaching the final section at different time instants
> and leading to pulse broadening.
>
> ANS: Perturbations which break symmetry are very likely
> to induce polarization splitting of mode groups that have large
> amounts of power in the region of the perturbation.
> [Stefano Bottacchi] Why do you introduce perturbations?
> Offset and polarization state are not perturbations.
>
> If the vector wave equation is solved, with the
> asymmetric perturbation included, this splitting will arise as part of
> the model. If the scalar wave equation is solved correction terms
> need to be calculated.
>
> BUT IN OUR MODELS THE UNDERLYING REFRACTIVE INDEX
> PROFILES ARE RADIALLY SYMMETRIC. THEREFORE, EVEN IF THE VECTOR WAVE
> EQUATION IS SOLVED THERE ARE NO SIGNIFICANT POLARIZATION EFFECTS.
>
> I agree that real fibres are exhibiting significant
> birefringence.
>
> I DISAGREE THAT THESE EFFECTS CAN BE MODELLED WITH THE
> CURRENT RADIALLY SYMMETRIC REFRACTIVE INDEX PROFILES.
> [Stefano Bottacchi] David, I guess there is some
> misunderstanding. I am not assuming any perturbation here. I just
> repeated above the fiber model is pretty ideal, basic like in standard
> textbooks. In order to simplify mathematics we could reach same
> qualitative polarization sensitivity even working with the simpler
> step index fiber.
>
>
> RE: For a given refractive index profile and fibre
> length, the amount of pulse broadening is therefore a function of the
> coupling coefficient distribution (overlapping integrals) and
> definitely of the relative angle between the offset position and the
> light orientation.
>
> ANS: I disagree, you are almost right. The following is
> what standard theory would say:
>
> For a multimode fibre excited with an offset single
> mode beam
>
> The input beam can be decomposed into two equivalent
> orthogonal components:
> A first one parallel to the line from the centre of the
> exciting laser spot to the optical centre of the fibre.
> A second parallel a line through the centre of the
> exciting laser spot parallel to the tangent to the core of the fibre.
> [Stefano Bottacchi] OK, it is an assumption.
>
> The two directions define the effective optical axis of
> the underlying basis modes of the fibre.
> [Stefano Bottacchi] What are more explicitly those
> "effective optical axis"? The exciting electric field is oscillating
> along its polarization axis. Of course I can decompose it along the
> two direction you mentioned above but why should I do this if the
> fiber is circular symmetric?
>
> The normalized coupling strength to each equivalently
> polarized mode of the fibre is the same for each of the two equivalent
> orthogonal components of the beam.
> [Stefano Bottacchi] OK, the fiber is isotropic.
>
> Changing the orientation of the polarization of the
> input beam changes the relative power in each of the underlying
> orthogonal components of the beam.
> [Stefano Bottacchi] OK
> This leads to an asymmetry in the power coupled to the
> basis modes of the fibre.
> [Stefano Bottacchi] OK, the source power distribution
> between the two axis is changing accordingly.
> That is the same mode groups are always excited with
> the same mode power distribution in each basis set but the excitation
> of one basis set relative to the other is dependent on the angle of
> polarization.
> [Stefano Bottacchi] This is not clear to me. Do you
> assert each mode group receive the SAME power independently from the
> polarization? What do you mean with "one basis set relative to the
> other..." Which would be the "other" basis set?
>
> Therefore, the total normalized MPD remains constant but
> the relative power in each basis mode set varies with the orientation
> of the polarization.
>
> Therefore, since the MPD remains constant, in models
> that have radial symmetric refractive index profiles, since the
> propagation constants for the two underlying modal polarizations are
> the same (to very, very high precision) there is no polarization
> splitting.
>
> But, if non symmetric refractive index perturbations are
> included in the model and either the vector wave equation is solved or
> polarization corrections are used then birefringence will result.
> Modes with light in the area of the perturbation will be "split" the
> most.
>
> RE: Of course, fixing the offset position and rotating
> the light polarization leads to the same conclusion and we are facing
> with the polarization induced pulse broadening under offset launching
> condition. This does not deal at all with modal noise. No connector
> was never been involved into all the abovementioned discussion.
>
> ANS: I assume you mean artificially rotating the
> underlying basis modes in order to change the coupling coefficients
> and hence compute a different MPD. If this is what you mean then this
> is exactly what I disagree with. I do not agree it is a valid model or
> even a valid approximation. The MPD does not change.
>
> Once again, I don't expect you to believe my words but
> if I am to accept another model I need to know where these papers are
> wrong.
>
> Regards,
> David
> [Stefano Bottacchi]
> In conclusion I identify two basic points in our
> discussion:
> * Is the modal field solution rotating according to the input
> linear polarization orientation? Paper from Saijonmaa et al., Applied
> Optics Vol. 19, No.14 (15Jul1980)p.2442-2452, refers to x-polarized
> light and it does not specify any polarization changing effect.
> * Once the overlapping integral have been computed, the intensity
> for each mode group is independent from the polarization orientation
> respect to the offset axis?
>
> Best regards
>
> Stefano
>
> -----Original Message-----
> From: Bottacchi Stefano (IFFO MOD CE external)
> [<mailto:Bottacchi.external@infineon.com>]
> Sent: 12 October 2004 08:46
> To: david_cunningham@agilent.com
> Cc: STDS-802-3-10GMMF@listserv.ieee.org
> Subject: Polarization effects for
> 10GBASE-LRM
> Importance: High
>
> David,
>
> following the long and interesting conference
> call held this afternoon on Task 4, I would like to clarify the
> background theory I shortly sketched during the discussion. I
> appreciated your comments and I understand you disagree on almost any
> polarization-dependent effect in MMF transmission, at least assuming
> circular symmetric refractive index without any birefringence.
> Nevertheless, since I am fully convinced of its relevance, at least
> starting from our experimental evidence, please find below some more
> detailed reasoning.
>
> Let us review first few basic assumptions of
> optical fiber modal theory:
>
> * The fiber has circular symmetry, a circular cross section and
> straight line geometry. No bending effect nor birefringence, neither
> core ovality. I am considering the "classical" MMF model of every
> textbook assuming the refractive index is a scalar quantity depending
> on the radial coordinate only.
> * The exciting electric field is linearly polarized. Let us choose
> the Cartesian reference system to represent the vector field
> components Ex, Ey and Ez and let us choose the cylindrical (r,phi,z)
> coordinate system for representing the position. Let us define the
> x-axis along the polarization axis. Modes are the eigensolution of the
> scalar wave equation (Helmoltz equation)
> * The modal field can be separated into the product R(r)F(phi) of
> the radial component R(r) by the harmonic term F(phi) (sine and
> cosine). The latter dependence is only due to the circular symmetry.
> The radial dependence of the refractive index infer only on the radial
> component of the field.
> * The whole bound modes set constitutes a complete orthonormal
> basis for representing any bound energy propagation. Each LP(l,m) mode
> presents a degeneracy of order 2 according to the two allowable "sine"
> and "cosine" solutions. I would prefer to avoid confusion in
> identifying them as two orthogonal polarizations. For the assumed
> polarization (x-axis oriented), the axial symmetry produces an
> intrinsic degeneration of factor 2 according to the exchanging role of
> the Ex and Ey respect their azimuthal dependence (sine or cosine
> dependence). This degeneration is a consequence of the circular
> symmetry only.
> * Assuming the weakly guiding approximation WGA still valid, a
> second degeneration holds, namely originating the mode group concept.
> Different mode solutions belongs to the "same" propagation constant
> (Beta) and they propagate with the "same" group velocity (Quotation
> marks refers to the WGA assumption). Since the radial component of the
> two intrinsically degenerate mode solutions (sine and cosine) is the
> same, the intensity of each LP(l,m) must have circular symmetry, no
> matter how large or small mode numbers could be.
> * Since mode are orthogonal, results in addition that each mode
> group must have still circular symmetry. As already stated, each mode
> group propagates at a fixed and characteristic velocity. Two different
> mode groups will propagate with different velocities.
>
> Up to this point I guess you agree on those
> basic assumptions of the modal analysis. In order to compute the
> amount of modal field excitation due to a Gaussian beam incident on
> the launching cross-section we have to introduce the overlapping
> integral. Those integrals represent proper field coupling coefficients
> by virtue of the abovementioned mode orthogonality.
>
> What happens now if we compute the overlapping
> integral with a small and exocentric (some offset) Gaussian spot? The
> basic conclusion is that the axial symmetry will be definitely broken.
> The overlapping integrals deal with the mode fields, not intensities.
> The coupling coefficient will depend on the cylindrical coordinates on
> the fiber cross section, including both the radial and the angular
> one. For each given mode LP(l,m) the overlapping integral leads to two
> different values for each of the two intrinsic degenerate solutions
> (sine and cosine). The "weight" of the sine and cosine terms will be
> no more the same due to the broken circular symmetry and when the
> intensity of LP(l,m) is computed it will be no more a constant. It
> will be dependent on both cylindrical coordinates, r and phi. In other
> words, the amount of field coupled depends on the relative orientation
> of the offset and the light polarization.
>
> We nned only one more brick to close the wall:
> since the fiber is assumed highly dispersive compared to the bit-rate,
> with a not optimized refractive index profile (multiple alpha,
> kinks,...), the different power contributions to the launched pulse
> will travel at different speeds reaching the final section at
> different time instants and leading to pulse broadening.
>
> For a given refractive index profile and fiber
> length, the amount of pulse broadening is therefore a function of the
> coupling coefficient distribution (overlapping integrals) and
> definitely of the relative angle between the offset position and the
> light orientation.
>
> Of course, fixing the offset position and
> rotating the light polarization leads to the same conclusion and we
> are facing with the polarization induced pulse broadening under offset
> launching condition. This does not deal at all with modal noise. No
> connector was never been involved into all the abovementioned
> discussion.
>
> Please, letr me know you feedback. Hopefully,
> formal theory could follow in few weeks...
>
> Best regards
>
> Stefano
>
>
>
>
> Dr. Ing. Stefano Bottacchi
> Senior Technical Consultant
> Concept Engineering
> Infineon Technologies Fiber Optics GmbH
> Wernerwerkdamm 16, 13623 Berlin
> Phone +49 (0)30 85400 1930
> Mobile: +49 (0)160 8 81 20 94
>