Polarization division multiplex (PolDM) doubles the data rate in existing trunk lines without need for additional optical bandwidth. In the presence of dispersion compensation, polarization mode dispersion (PMD) limits the achievable transmission length. PMD tolerance of standard binary intensity modulation or non-return-to-zero coding has already been published. Recently, the return-to-zero (RZ) transmission format has become of more interest; therefore we assess the PMD tolerance of PolDM by numerical simulations and a transmission experiment. For a given total data rate per wavelength PolDM supports at least as much differential group delay as standard binary intensity modulation. So, PolDM is an attractive multilevel modulation scheme to solve capacity problems with low additional effort.
©2001 Optical Society of America
Because of the increasing huge demand for optical data transmission capacity there is interest for an economic upgrade of existing optical transmission lines. Polarization division multiplex (PolDM) is particularly suited for this purpose. Two orthogonally polarized signals are transmitted to double the data throughput. Bandwidth efficiency is also doubled if both polarization channels have equal carrier frequencies, to which case we restrict ourselves. Polarization control and a polarization beamsplitter or polarizers are needed at the receiver side for polarization demultiplexing .
Especially ‘old’ fibers exhibit a lot of polarization mode dispersion (PMD) . Sensitivity and PMD tolerance of various multilevel modulation schemes have been evaluated numerically  for the non-return-to-zero (NRZ) data format. For a given total data rate per wavelength, NRZ PolDM was found to be advantageous because it supports 1.4 times as much differential group delay (DGD) as standard binary intensity modulation (2-IM). On the same basis it is slightly more sensitive (~0.5 dB) than 2-IM whereas quaternary intensity modulation is ~7 dB less sensitive. In , the results concerning PMD tolerance have also been proven experimentally.
Return-to-zero (RZ) signals are generally preferred over NRZ signals because they allow to increase the power budget . We therefore investigate the PMD tolerance of RZ PolDM signals.
2. Numerical simulation
A pseudo random bit sequence was modulated with rectangular pulses having a variable duty cycle d from 0 to 1, where the value 1 represents NRZ. It was passed through a Gaussian lowpass filter with a variable 3 dB bandwidth of 1/(dT). T is the PolDM symbol duration. The electric field was chosen to be the square root of this signal. Further calculation took place in the frequency domain using Jones vectors and matrices given in .
The output state-of-polarization (SOP) of the transmitter was 0° for 2-IM and 0° (x) and 90° (y) for PolDM, followed by a DGD section with principal states-of-polarization of ±45° which is the worst case. In order to simplify calculation, the product of DGD times optical carrier frequency was chosen to be an integer, so input and output states of polarization (SOPs) were identical.
For NRZ and maybe also RZ signal formats the polarization channels are normally clocked bit-synchronously (non-interleaved), and non-perfect polarization demultiplexing results in coherent crosstalk . However, a variant with bit-interleaved, alternate-polarization RZ pulses is possible which does not exhibit coherent crosstalk. If bandwidth is not limited the bit-interleaved, alternate-polarization RZ scheme needs just a single receiver without polarization control but this is outside the scope of this paper. Consequently, we also call a NRZ transmission with a delay of half a bit duration between both data channels interleaved.
In the receiver, simple intensity detection was used, in combination with a polarizer in front of the photodiode for the PolDM system. The 3 dB bandwidth B of the Gaussian baseband filter was adapted from 0.367/T (RZ, d=0) to 0.7/T (NRZ) to obtain a constant eye opening between 93 and 94 percent in the absence of PMD.
Then the DGD was increased for different interchannel phase differences until the eye was completely closed. The values depended on the interchannel phase difference. Worst-case values are shown in Fig. 1. For 2-IM, PMD tolerance is essentially the same for NRZ and RZ coding, with little dependence on the pulse width. Note that the eye closes already at DGD=0.5T, because one symbol carries only one bit and therefore the data rate had to be doubled. Of course the 2-IM receiver bandwidth was also doubled.
For the non-interleaved scheme, PMD tolerance increases linearly for a duty cycle d=0.1 to 0.5, reaches a maximum of 0.76T (d=0.8) and decreases negligibly for NRZ transmission. The reason is that simultaneously transmitted pulses can already interfere at a small DGD, due to mode coupling. This becomes better for wide pulses and NRZ transmission, which has been proven in . A lowpass filter with a wide fixed bandwidth of 0.7/T slightly enhances the PMD tolerance, but reduces the receiver sensitivity.
Interleaved pulses behave worse than non-interleaved ones at large d and better at small d: For d<0.27 in conjunction with the untypically large receiver bandwidth 0.7/T interleaved pulses are preferred, and result in a nearly constant PMD tolerance of 0.5T. This is quite clear because a sufficient receiver bandwidth allows the separation of pulses emerging from both data channels as long as DGD is less than half a bit duration. If the filter bandwidth is adapted, the cross-over between the two schemes occurs at d=0.275.
Eye diagrams were generated for various DGDs using a duty cycle d=0.34 and a typical filter bandwidth of 0.35/T (Fig. 2). Non-interleaved (a-c) yield slightly better eye diagrams than interleaved pulses (d-e) because overshoot appears between, not at the eye openings. For a DGD of 0.375T the eye is completely closed if interleaved pulses are chosen.
For convenience cosine-roll-off pulses as sent symbols and impulse response of the low pass filter (B=0.42/T) in the receiver were chosen in the following. The lowest and highest signal levels for 00 and 01 as well as 11, 10 transitions were recorded, respectively. From these values eye closure penalty (EOP) and system penalty for a bit error ratio of 10-9 was calculated, assuming an optical to electrical filter bandwidth ratio of 8 and χ2 distributed photocurrents (Fig. 3). It was found that the system penalty expressed as the required additional signal to noise ratio (SNR)/dB is at least twice the EOP/dB.
The left half shows that PolDM with interleaved pulses tolerates roughly half as much DGD as 2-IM at this pulse width, and non-interleaving is advantageous. The dependence on the interleave time t between the two PolDM channels was assessed for several fixed DGD values in the right part of Fig. 3. Partly overlapping pulses give rise to a strong penalty in one channel. Finally, the bit error ratio was calculated for a fixed SNR and converted into Q-factor, BER=0.5 erfc(Q/√2) (left part of Fig. 6). For non-interleaved PolDM and 2-IM the eye closes at the same DGD of 0.5T, whereas the runs of the curves are different.
A 2×20 Gb/s transmission experiment was conducted. RZ pulses were generated with commercial 40 Gb/s equipment with every other bit being zero similar to the method described in . Light from a laser was then modulated externally and split into two branches. One path was delayed and the nearly decorrelated data streams were combined with orthogonal polarizations in a polarization beam splitter (PBS) using manual polarization controllers (not shown in Fig. 4).
The transmission line consisted of 33 km of dispersion-shifted fiber, EDFAs and an optical band pass filter. Using an electro-optic polarization controller and a polarizer in the receiver, one PolDM channel can be selected. A small frequency modulation of the laser which caused interchannel phase modulation due to the delay line, is detected in the receiver and used to minimize crosstalk between the PolDM channels (not shown).
In order to evaluate PMD tolerance, different lengths of polarization maintaining fiber (PMF) were inserted with worst-case orientation. Fig. 5 (b) shows resulting eye patterns on a 50 GHz monitor receiver for different DGDs. Results of an additional wide band simulation are also shown (a); theory and measurement agree well.
Q-factors were measured by scanning the threshold of the decision circuit in the receiver (right half of Fig. 6). The tendency of the simulation was well reproduced. A DGD×total bit rate product of 0.25 is supported (Q≥9); this is twice as much as in a WDM system with orthogonal polarizations in adjacent channels .
4. Discussion and conclusions
PMD tolerance of RZ PolDM transmission has been evaluated in comparison with 2-IM. The most attractive scheme uses >0.63T wide, non-interleaved pulses and is >1.4 times as PMD tolerant as 2-IM for a given total data rate per wavelength. This permits even a higher bit rate×length product than for 2-IM because the average DGD scales with the square root of fiber length.
If short pulses are chosen interleaving is preferred. If the receiver bandwidth is at least 0.7 times the bit rate the eye closes no earlier than in the 2-IM case. So, PolDM supports the same DGD×bit rate product or lowers the required bandwidth for system components like modulator driver or photoreceiver.
Generally, interleaving is advantageous only for short pulses, whereas the non-interleaved case is better for long pulses and the NRZ format. If new fiber with low PMD or a PMD compensator is installed, benefit can be taken from capacity doubling with PolDM without need for additional optical bandwidth or complicated terminal equipment.
The authors would like to thank Siemens ICN and Deutsche Forschungsgemeinschaft for their support.
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