Nerd Rage

Impair­ments in Polarization-Multiplexed DWDM Chan­nels due to Cross-Polarization Mod­u­la­tion

21th Annual Meet­ing of the IEEE Lasers and Electro-Optics Soci­ety 2008

Abstract: We derive the sta­tis­tics of cross-polarization modulation-induced non­lin­ear crosstalk in polarization-multiplexed DWDM chan­nels and an approx­i­mate rela­tion between the degree of polar­iza­tion and the asso­ci­ated noise terms.

Ref­er­ence:

M. Win­ter, C.-A. Bunge, K. Peter­mann, D. Setti, “Impair­ments in Polarization-Multiplexed DWDM Chan­nels due to Cross-Polarization Mod­u­la­tion,” The 21th Annual Meet­ing of the IEEE Lasers and Electro-Optics Soci­ety, 2008. LEOS 2008, paper WH3, 9-13 Nov. 2008

2008-Nov-26: cor­rected slides uploaded (no 3 dB “base­line” penalty for PolDM)

Notes:

A few notes on the sys­tem sim­u­la­tion slides, as these results were obtained after the paper was sub­mit­ted and are not con­tained therein. There orig­i­nally appeared an addi­tional 3 dB penalty for all PolDM points. This would only be cor­rect when cal­cu­lat­ing the PolDM OSNR penalty against the single-channel back-to-back OSNR value, as PolDM has this 3 dB penalty over SC. How­ever, the penalty should be cal­cu­lated ver­sus the back-to-back PolDM OSNR value, so that this extra penalty does not appear. Thanks to M. O’Sullivan for point­ing this out to me.

More gen­eral, the blue points in the graph show the OSNR penal­ties for CW-only probe chan­nels when inter­pret­ing the out­put as an all-zero DQPSK sig­nal (ini­tially con­stant phase), one point for each iter­a­tion of the sim­u­la­tion (ran­dom ini­tial polar­iza­tions of all chan­nels, ran­dom bit pat­terns, phases and tim­ings, ran­dom bire­frin­gence; all other para­me­ters held con­stant between iter­a­tions). The power in the inter­fer­ing chan­nels was cho­sen so that the aver­age penalty @ BER 10^-4 is 1 dB. The penal­ties are not depen­dent on the DOP of the probe in the par­tic­u­lar iter­a­tion (x-axis). There­fore, the rea­son for the penalty must be polarization-independent, which would point to XPM (in the Man­akov sense of the NLSE).

The red points show the OSNR penal­ties when a (D)QPSK chan­nel is added orthog­o­nal to the probe at the same wave­length (PolDM) to each sim­u­lated sys­tem. The DOP shown on the x-axis, which makes no sense for a PolDM sys­tem, is the DOP of the cor­re­spond­ing CW-only sys­tem (see above). The increase in penal­ties is due to the crosstalk from the orthog­o­nal chan­nel. If this crosstalk were Gauss­ian in each iter­a­tion, all the red dots would lie along the dot­ted line (plus some vari­a­tion sim­i­lar to that due to XPM). But it is only Gauss­ian in the ensem­ble mean sense and may devi­ate con­sid­er­ably for each of the iter­a­tions — sim­i­lar to the vari­a­tions in XPM; how­ever, not only depen­dent on the power of the inter­fer­ing chan­nels, but also on their polar­iza­tion.
In gen­eral, the OSNR penalty does depend on the DOP (which is a mea­sure of XPolM degra­da­tion of that par­tic­u­lar iter­a­tion), but not in a deter­min­is­tic way.

At this point it is not pos­si­ble to pre­dict the indi­vid­ual crosstalk (or, equiv­a­lently, SOP) dis­tri­b­u­tions, or even the dis­tri­b­u­tion of the DOPs for any par­tic­u­lar sys­tem (com­pris­ing the set of fiber para­me­ters and lengths of all spans). We can only pre­dict the mean DOP of the polarization/PMD ensem­ble (see this pub­li­ca­tion). The DOP dis­tri­b­u­tion around this mean depends much on the par­tic­u­lar dis­per­sion map used. With great sim­u­la­tion effort, it would be pos­si­ble to give out­age prob­a­bil­i­ties depen­dent on this mean DOP. These would, how­ever, be valid only for a sys­tem, mod­u­la­tion for­mat, and power val­ues.