Novoptel. Application note 1 Error signals for polarization control. Novoptel 1 of 9 EPC1000_application_note_01_n16.doc

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1 Novoptel Application note rror signals for polarization control Revision history Version Date Remarks Author Draft version R. Noé Final version R. Noé Typo corrected R. Noé QAM, DPSK, duobinary and ASK added, minor corrections R. Noé ASK and Bessel line detection described in detail R. Noé Contents Summary Optical power of cross-polarized signal lectrical power in coherent receiver Interference detection of polarization-multiplexed DQPSK and QAM signals Interference detection of polarization-multiplexed DPSK and duobinary signals Interference detection of polarization-multiplexed ASK signals Relation between relative intensity error and feedback signal Literature Summary rror signal generation is described in many application scenarios of the PC000 family of endless polarization controllers: direct and coherent detection, single and dual polarization signals, modulation formats DQPSK, QAM, DPSK, duobinary, ASK. Novoptel GmbH IM- Warburger Str Paderborn Germany Novoptel reserves the right to change the content. Novoptel of 9 PC000_application_note_0_n6.doc

2 Optical power of cross-polarized signal FPGA-based electronic controller input LiNbO 3 polarization beam splitter output PC000-??-?-?--?-??-O Fig. : Simplified block diagram of PC000 endless polarization controller with power measurement in cross polarization The simplest way of determining polarization mismatch errors is it to measure the power behind a polarization beam splitter or polarizer. Let S be the normalized field vector of the wave behind the LiNbO 3 polarization transformer, before an ideal polarization beam splitter or polarizer with normalized transmitted eigenmode pol,. The output field behind the polarization beam splitter or polarizer is out pol, pol, S J pols. () Here J pol pol, pol, is the Jones matrix of the polarizer. The + sign means Hermitian conjugate. The output signal has the Jones vector pol,, multiplied by the scalar quantity pol, S. The relative intensity RI or normalized output power equals RI pol, S. () The relative intensity error RI, i.e. the normalized power of the cross-polarized output signal, is the complement of the RI, RI RI pol,s, (3) where pol, is the second polarizer eigenmode, orthogonal to pol,. Orthogonality means it holds pol, pol, Using normalized Stokes vectors (S instead of, with unchanged indices), we can write T T RI S pol, S S cos cos S pol, SS, (5) 0. (4) S cos sin S S T T RI S pol, S pol, S, (6) where T means the transpose and, the polarization error, is the angle between S S and S pol, on the Poincaré sphere. RI measurements are directly influenced by intensity fluctuations. It is therefore better to measure the RI. This is sketched in Fig.. From the RI we can calculate the polarization error arcsin RI RI. (7) The approximation holds for small. A standard, highly accurate characterization procedure of PC000 endless polarization controllers is it to record RI over time and to display the complementary distribution function F(RI) of the relative intensity error. Novoptel of 9 PC000_application_note_0_n6.doc

3 lectrical power in coherent receiver transmitter fiber local oscillator laser coupler electrical output, I(t) balanced or differential photoreceiver Fig. : Coherent transmission setup FPGA-based electronic controller user-supplied error signal input LiNbO 3 polarization beam splitter outputs PC000-??-?-?--?-??-N Fig. 3: Simplified block diagram of PC000 endless polarization controller, suitable for electrical power measurement in coherent receiver A very similar scenario occurs in coherent receivers (Fig. ). With signal and local oscillator fields jst j t S S, 0e j,0e (8) j and a coupler transfer matrix the photocurrent difference is obtained as j j t I RP P R RejS R Re,0S,0e IF R IF PS Here P S S P S,0 S,0 S,0,0 P IF cos t IF arg,0 IF S,0. (9) IF is the (angular) intermediate frequency (IF) and IF a phase angle. The electrical AC signal power in the coherent receiver is proportional to the relative intensity,0s,0 T RI S cos cos SS (0) S,0,0 where is the angle between signal polarization S S and local oscillator polarization S on the Poincaré sphere. Note that the field vectors are not normalized here whereas the Stokes vectors S are normalized. We see that the electrical power in a coherent receiver behaves like the power behind a polarizer. As a consequence, the error signal in the configuration of Fig. 3 can be the electrical power measured in a coherent receiver of Fig.. Novoptel 3 of 9 PC000_application_note_0_n6.doc

4 Interference detection of polarization-multiplexed DQPSK and QAM signals input FPGA-based electronic controller LiNbO 3 PC000-??-?-?--?-??-P PC000-??-?-?--?-??-A polarization beam splitter tap couplers RF power detector outputs DQPSK interference detector Fig. 4: Simplified block diagram of PC000 endless polarization controller with interference detection of polarization-multiplexed DQPSK signals The foregoing possibilities are applicable for single-polarization signals. In contrast, the present scenario is for polarization-multiplexed (= dual-polarization) DQPSK signals which form an unpolarized sum signal S S, S, c S,,0 cs,,0. () All the same the polarization channel signals S, c S,, 0, S, cs,, 0 can be separated. The polarization channels should be orthogonal to each other, S, S, 0. S,, 0, S,, 0 are unmodulated carriers, usually from the same source. The modulated polarization j channel signals have no carriers because the complex modulation symbols c e j, j c e j have zero means c 0, c 0. They also are uncorrelated, * c c 0. The brackets mean expectation value, the star denotes the complex conjugate, and, are individual phases of the polarization channels. Behind the polarization beam splitter or polarizer the signal is fully polarized with an amplitude proportional to pol, S. Its power equals P pol, S pol, S, Re * pol, S, For simplicity we again assume orthonormal pol,, pol, constant, identical channel powers PS, PS, PS pol, S, pol, S,. () S, i P S, ( i, ) are P.. Terms i, each equal to half the total signal power S The expectation value of P is P pol, S, pol, S, PS. We substitute j arg pol, S, i pol, S, i PS, i e cos i. The angles i on the Poincaré sphere between the transmitted polarizer eigenstate and the polarization channel signals obey. The AC part of the power is now P, AC PS,PS, cos cos cos PS sin cos (3) with * arg pol, S, pol, S,. At the other polarization beam splitter output the signal amplitude is proportional to pol, S, and the AC part of the respective power equals P, AC P, AC. (4) Novoptel 4 of 9 PC000_application_note_0_n6.doc

5 This is evident because the total power is constant, P P PS, PS, PS S. It is P in two photoreceivers. The AC part of the possible to detect P, P or their difference P measured photocurrent or photocurrent difference is always proportional to sin. The expectation value of the electrical power is proportional to sin cos sin. This is due to the uncorrelated DQPSK modulation symbols. We can therefore define the relative intensity error as RI sin. (5) This is similar to (6) but a certain level of RI requires only half as large a polarization mismatch angle ( )! While we have tacitly assumed NRZ signal format the same holds also for time-aligned RZ signals. The only difference is that there is a strong clock signal component in the photocurrents. It is usually outside the bandwidth of the photoreceivers used for this interference detection. RZ signals hence yield a better interference extinction ratio than NRZ signals. QAM signals with independent zero-mean modulation in both quadratures, such as 6-QAM signals, can also be polarization-demultiplexed the same way. The difference to DQPSK signals is that there are more amplitude levels. The interference extinction ratio is therefore decreased compared to DQPSK signals. For time-interleaved RZ signal the interference becomes much weaker. Fortunately, the receiver is also much less subject to interference. Interference detection of polarization-multiplexed DPSK and duobinary signals TX laser frequency modulation delay line Modulator Modulator polarization beamsplitter output with polarization multiplex Fig. 5: Randomization of polarization channel interference by frequency modulation of the transmitter laser combined with a differential delay between the two polarization branches in the transmitter DPSK and duobinary signals are modulated in only one quadrature, like standard ASK signals. So the polarization channels interfere only when the phase difference between the polarization channels is sufficiently close to 0 or. Interference must therefore be adequately randomized. The electrical interference amplitude is proportional to cos, the interference power proportional to cos. A phase jump by does not change the term cos cos. Hence we neglect from now on the DPSK or duobinary modulation and look upon as if it contained only much slower phase variations due to effects in waveguides. Although the actual function is more complicated one may define something that could be called an equivalent averaging time in the PC000 endless polarization controller. Currently it is on the order of T = 80 ns * AT where AT is the averaging time exponent (SPI register 00h). Since the mean value of the interference phase is not controlled one must obviously modulate cos t 0 holds, where the overbar means averaging over T. t so that A straightforward way to achieve this is a frequency shift by /T of one polarization channel signal at the transmitter. In order to avoid a lossy and expensive frequency shifter one may instead simply utilize the combination of a differential delay between the two polarization channels and a transmitter (TX) laser frequency modulation, see Fig. 5. Laser FM is often permissible and possible, in particular for SBS suppression. Let the modulation frequency be f = /T and the peak-to-peak frequency deviation F pp. This results in Novoptel 5 of 9 PC000_application_note_0_n6.doc

6 F F pp t sinf t F f pp t cosf t t t t ft F pp sincf momentary frequency excursion, (6) momentary angle excursion, (7) sin phase difference, (8) angular modulation index of. (9) Note that the polarization multiplexer not only introduces the time delay but, together with transmission fiber and polarization tracker, also a mean phase delay. Usually, can not be predicted and may vary over time. While the phase difference has the angular modulation index we must work with the relevant doubled phase difference and associated angular modulation index! We obtain cos t cos cos sinft J 0 cos t 0 we need to set 0. (0) To fulfill J 0. For. 405 the lowest possible frequency deviation results,.0 F pp. sinc f () To give an example: We work with PC000 at AT =, T = 60 ns and with a delay time = 0 ns (~ m of fiber). The calculated TX modulation frequency is f = /T = 6.5 MHz. Initial tuning of f for optimum control performance is highly recommended, especially at low AT values. At that high frequency f there is almost no thermally, only carrier-induced laser FM. The modulation steepness may for instance be 00 MHz/mA. The peak-to-peak frequency deviation is calculated as F pp = 39 MHz. Only a small laser modulation current of 0.39 mapp is needed to achieve it. The parasitic intensity modulation is negligible, and the frequency modulation itself is negligible for interferometric DPSK demodulation. The TX laser frequency modulation need not be sinusoidal. Other shapes likewise allow suppressing the mean of cos t, for instance a sawtooth. The described differential phase modulation with J 0 0 need not necessarily be brought about by the combination of TX laser frequency modulation and differential time delay. Instead, it may be directly applied by a phase modulator which is placed before or behind one of the data modulators in Fig. 5. Interference detection of polarization-multiplexed ASK signals Like DPSK and duobinary signals, ASK signals of NRZ, RZ and CSRZ type are modulated in only one quadrature. But the phase relation between the two polarization channels does not depend on modulation. The interference phase must again be randomized. (i) A first interference detection approach is identical to the above-described for DPSK and duobinary, including sinusoidal differential phase modulation with Only capacitive coupling is required to remove the DC component from the photodetected polarization channel signals and to assure that the electrical power is an RF power. The PC000 supports this approach with error signal generation type P (= PIN photoreceiver(s) and RF power detector). (ii) A second interference detection approach is supported by the PC000 with error signal generation type O (= ) combined with a detection of Bessel lines (consult Novoptel). This is explained in the following: The broadband RF power measurement is an asynchronous detection with heavy subsequent lowpass filtering. The baseband width is more than 3 orders lower than the pre-detection (RF) bandwidth. Sensitivity can be improved if the (quasi-)dc components of the ASK signal interference are evaluated with a low pre-detection bandwidth. The procedure was first reported in []. Novoptel 6 of 9 PC000_application_note_0_n6.doc

7 With respect to (), () we may set c * P c j e PS, cos PS, cos j, j, c, e, which leads to c 0, e,. From (), (3) the mean detected power is P P cos cos cos P sin cos S S, S, with where is polarization-dependent. Other than in (3), does not vary with modulation. Furthermore it holds S P P PS sin cos (). (3) This is the non-normalized horizontal/vertical Stokes parameter. To estimate the interference we need a differential phase modulation between the polarization channels, for example of sinusoidal type and as sketched in Fig. 5. We expand the interference term cos cos sin sinftsin t cos sinft sinft cos J 0 k k J k k J coskft cos sink ftsin. (4) The even and odd Bessel lines appear and vanish as a function of the unpredictable mean phase difference. So, at least one even and one odd Bessel line must be detected, and their electrical powers P e, 0 ~ J0 cos, P e, k ~ Jk cos and P e, k ~ Jk sin, respectively, must be added with suitable weighting. Assume that the powers of both demultiplexed polarization channels are measured and subtracted to form (3) S. ven though, the DC term P e, 0 is not usable in practice because the channel powers can not be balanced reliably to such a degree as is needed for measuring small interferences. If a small laser pump current modulation, say %, is applied like in Fig. 5 then the st harmonic is likewise corrupted by the resulting parasitic amplitude modulation. However, even a non-perfect balancing of the polarization channel powers suffices to suppress it to a negligible value, <0.% or so. So we consider using st harmonic P e, and nd harmonic P e,. Going from 0 to should not change the interference signal, even if deviates in the course of time. Hence, a good dj choice is the point dj where relative changes of, with opposite J d J d effects on J and J, have the least relative influence on the error signal for all. This requires. 37. Total interference can be calculated by J P tot P e, P e, 0.66 Pe, Pe,. The relative sensitivity on for all is bounded by J d.85. d If this sensitivity is considered too high one can work with at the maximum of J where it holds dp e, d 0 and Pe, Pe, 3 (due to dj n d Jn Jn ). We set Novoptel 7 of 9 PC000_application_note_0_n6.doc

8 d dj ape, Pe, a3pe, 3 with a3 ab. We choose b to achieve dj d 3 J, 3,3 d a Pe a Pe d 0 and a to make P tot independent of. J bj3 Consequently it holds 0 dp tot d for all. The calculated weighting is 0.73 Pe, Pe,. 6 Pe, 3. Choosing slighly lower a and associated a3 ab can be beneficial if varies, due to opposite curvatures dj d 0, d a J a3j3 d 0. If only one channel power () is measured then the unknown and fluctuating mean power P S must but practically cannot be subtracted and even the st harmonic is too much disturbed by parasitic amplitude modulation. So the nd harmonic is the lowest usable. Analog to the above we obtain either 0.76 Pe, Pe, 3 at 3. 55, with relative sensitivity bounded by.7, or 0.64 Pe, Pe,3. 3 Pe, 4 at 4.. Fig. 6 illustrates the various spectral powers and their weighting for the four discussed operation modes. Usage of low harmonics with associated small maximizes the tolerance of relative changes of J J J J J.6 J J.3 J J J3 J 4 J Fig. 6. Interference powers as a function of differential phase modulation index. Suggested operation points are marked by circles. Left: Usage of st and nd harmonic at.37, or st nd and 3rd harmonic at Right: Usage of nd and 3rd harmonic at 3.55, or nd, 3rd and 4th harmonic at 4.. The optional Bessel line detection of the PC000 supports all these four operation modes. Generally speaking, total interference power is calculated according to P tot a i ipe, i. The weights a i can be set for either i,, 3 or i,3, 4. If only two spectral lines are to be detected then one of the weights is set to zero. We define the individual normalized averaged powers P ave, i to be the respective averaged P e, i divided by the averaged sum i P e, i of the three powers. The PC000 makes the P ave, i available via SPI, USB and GUI. It also outputs a PWM signal (CMOS 3.3V) with the mean voltage P, P, 3.3 V or 3.3 V, depending on chosen spectral lines. There is one P ave, avep ave,3 P ave, avep ave,4 logic low and one logic high interval per PWM period. The period is 6 ( P ave, P ave,3) 0 ns or 6 ( P ave, P ave,4) 0 ns long, i.e. not longer than.3 ms. The PWM signal represents the average power distribution between the two outer harmonics and can serve for an automatic control of the modulation index. Novoptel 8 of 9 PC000_application_note_0_n6.doc

9 Relation between relative intensity error and feedback signal Ideally there should be a linear relation between the above-defined relative intensity error RI and the feedback signal of PC000 endless polarization controllers. This is fairly much the case. The relation is particularly linear for error signal generation type O, i.e., power measurement of the cross-polarized signal in configuration PC000-??-?-?--?-?-O, where a PIN diode measures power. The feedback signal minimum (= zero RI) varies minimally with temperature and due to finite polarizer extinction. The feedback signal maximum depends on input power. PC000 endless polarization controller performance is always tested with error signal generation type O before possibly changing to another type. The relation may be assumed to be less linear for error signal generation types P and A, i.e., interference detection of polarization-multiplexed DQPSK signals in configurations PC000-??-?-?--?-?-P and PC000-??-?-?--?-?-A. This is due to noise and due to the fact that the RF power detector presumably exhibits a not exactly quadratic behavior. xperimentally, the possible deviations from a linear mapping between RI and feedback signal are unproblematic, as extended dualpolarization DQPSK transmission tests have shown. The feedback signal minimum (= zero RI) may lie at about 30% of the full range. Like the feedback signal maximum it depends on the applied power, symbol rate and signal format (RZ or NRZ). Literature. R. Noé, ssentials of Modern Optical Fiber Communication, Springer Berlin Heidelberg, March 00, ISBN (Print) (Online), DOI 0.007/ Noé, R. et al., Crosstalk detection schemes for polarization division multiplex transmission. I J. Lightwave Techn. 9(00)0, pp , 3. B. Koch et al., Record 59-krad/s Polarization Tracking in -Gb/s 640-km PDM-RZ-DQPSK Transmission, I Photonics Technology Letters, Vol., No. 9, pp ,. Oct. 00, 4. Publications listed in Novoptel 9 of 9 PC000_application_note_0_n6.doc