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*To*: STDS-802-3-10GMMF@xxxxxxxxxxxxxxxxx*Subject*: Re: [10GMMF] Polarization effects for 10GBASE-LRM*From*: David Cunningham <david_cunningham@xxxxxxxxxxx>*Date*: Tue, 12 Oct 2004 21:44:59 +0100*Reply-To*: "IEEE P802.3aq 10GBASE-LRM"<stds-802-3-10gmmf@xxxxxxxx>*Sender*: owner-stds-802-3-10gmmf@xxxxxxxx*Thread-Index*: AcSv24HBLC21gYczQBGhuTKv6HNO7wAqNu7g*Thread-Topic*: 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. 2) Birefringence of multimode fibre of circular cross-section. 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. 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. 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 papers are wrong. 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. 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. 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. The two directions define the effective optical axis of the underlying basis modes of the fibre. 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. 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 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. 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 > -----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 >

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