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*To*: STDS-802-3-10GMMF@xxxxxxxxxxxxxxxxx*Subject*: Re: [10GMMF] Polarization effects for 10GBASE-LRM*From*: "Abbott, John S Dr" <AbbottJS@xxxxxxxxxxx>*Date*: Tue, 26 Oct 2004 16:41:52 -0400*Reply-To*: "IEEE P802.3aq 10GBASE-LRM"<stds-802-3-10gmmf@xxxxxxxx>*Sender*: owner-stds-802-3-10gmmf@xxxxxxxx

At the 10/25 Task 4 Meeting David asked for comments on his notes. A. I've attached a *.pdf rather than a long email. I am curious about plotting figure 3b in a different way to see if the two Hermite Gauss modes HMG(2,0)+HMG(0,2) show up as having a constant total power. This is curiously related to discussions we have had in Task4 on coherent and incoherent modes: HMG(2,0)^2 + HMG(0,2)^2 does not stay constant with polarization; (HMG(2,0)+HMG(0,2))^2 does stay constant, because it is proportional {I think} to the nu=0 radial mode for the group in the Laguerre-Gauss formulation. B. I worry about some of the conclusions because I think the degenerate modes all have the same propagation constant & mode delays if the profile is axisymmetric and one uses the scalar wave equation -- so there can be no effect upon the impulse response by changing the polarization angle, since it would seem to merely shift power between the degenerate modes. I continue to be very curious about the experimental results. John A. > -----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 >

Polarization_effects_JSA_1026.pdf

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