1. Introduction

Ultrahigh-speed single-carrier transmission technology will make it possible to achieve ultrahigh capacity optical networks with a simple configuration, large flexibility, and low power consumption at the switching nodes through the use of fewer wavelength channels. Optical time division multiplexing (OTDM) is expected to be a driving force for realizing a serial transport system with a Tbit/s channel capacity [1]. The first Tbit/s/ch transmission was demonstrated in 2000 by using a 640 Gbaud polarization-multiplexed on-off keying (OOK) signal [2]. Since then, the bit rate has been increased to 2.56 Tbit/s by employing differential quadrature phase-shift keying (DQPSK) [3], and to 5.12 Tbit/s with 16-quadrature amplitude modulation (QAM) [4]. Efforts have also recently been made to increase the symbol rate to 1.28 Tbaud [5], and the fastest single-carrier bit rate yet achieved is 10.2 Tbit/s [6]. However, a long-haul transmission at such a high symbol rate over several hundreds of kilometers such as in a metro or backbone network is still a major challenge. A higher symbol rate increases susceptibility to chromatic dispersion (CD) and polarization-mode dispersion (PMD), whereas a higher bit rate realized by multi-level modulation leads to reduced OSNR tolerance. Taking this trade-off into account, the adoption of polarization-multiplexed DQPSK is expected to provide optimum performance at a single-channel bit rate in the Tbit/s regime, as demonstrated by 1.07 Tbit/s-480 km [7] and 2.56 Tbit/s-160 km [3] transmissions.

We recently reported a 1.28 Tbit/s-525 km transmission using a 640 Gbaud single-polarization DQPSK signal [8]. The transmission distance was extended by employing an ultrafast time-domain optical Fourier transformation (OFT) technique, which helped to reduce the impairments caused by higher-order PMD and other linear perturbations. In this paper, we report a 2.56 Tbit/s/ch transmission over 300 km by using polarization multiplexing in the previous DQPSK experiment. In particular, we detail the influence of inter-polarization crosstalk caused by depolarization during transmission, which is a major limitation in the transmission performance.

2. Experimental setup

Figure 1 shows the experimental setup for a 2.56 Tbit/s/ch-300 km polarization-multiplexed DQPSK transmission. A 40 GHz mode-locked fiber laser (MLFL) was used as an optical pulse source, which emits a 1.6 ps pulse train at 1540 nm. The pulse was amplified to 18 dBm and launched into a 2 km-long highly nonlinear dispersion-flattened fiber (HNL-DFF), with a dispersion of – 0.2 ps/nm/km, a dispersion slope of 0.002 ps/nm²/km and a nonlinear coefficient γ = 5 W⁻¹km⁻¹, in which the pulse was compressed to 600 fs after the self-phase modulation (SPM)-induced chirp had been compensated with a single-mode fiber (SMF). The time-bandwidth product of the compressed pulse was 0.45, indicating that it was almost a transform-limited Gaussian pulse (0.44). The 600 fs pulse train was then DQPSK modulated with a 40 Gbaud (80 Gbit/s), 2⁷ − 1 PRBS using an IQ modulator. The DQPSK signals were optically time-division multiplexed to 1.28 Tbit/s with a single polarization using an optical delay-line multiplexer. Figure 2(a) shows the 1.28 Tbit/s DQPSK signal waveform, which was measured with an optical sampling oscilloscope with 800 fs time-resolution. The pulse train was well aligned with a slight power variation between different tributaries. The 1.28 Tbit/s DQPSK signal was then polarization multiplexed to 2.56 Tbit/s.

 

Fig. 1 Experimental setup for 2.56 Tbit/s polarization-multiplexed DQPSK transmission over 300 km. Abbreviations are defined in the text.

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Fig. 2 (a) 1.28 Tbit/s DQPSK signal waveform, (b) switching gate of NOLM switch.

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The 300 km transmission fiber link was composed of four 75 km spans of dispersion-managed fiber. Each span consisted of a 50 km-long SMF or super-large area (SLA) fiber with anomalous dispersion followed by a 25 km-long inverse-dispersion fiber (IDF) that compensated for both the dispersion and the dispersion slope. The SMF and SLA were optimally allocated to minimize the residual dispersion slope. The first-order PMD was mitigated by adjusting the polarization state of the data signal so that it was coupled to the principal state of polarization (PSP) of the link. This monitoring was carried out in advance by launching either polarization channel without polarization multiplexing and maximizing the degree of polarization (DOP) at the end of the transmission link. It should be noted that, in the polarization-multiplexed transmission of ultrashort pulses, because of the large signal bandwidth, second-order PMD causes depolarization due to the frequency dependence of PSP, n(ω), where n is the Stokes vector of PSP. This frequency dependence is expressed as a Taylor series expansion around the center frequency ω₀, i.e., n(ω₀) + (dn/dω)Δω. This indicates that the signal is depolarized gradually as Δω increases, which results in crosstalk between two polarization channels_.

At the receiver, the 2.56 Tbit/s DQPSK signal was divided into two orthogonal polarization channels with a polarization beam splitter (PBS) and demultiplexed from 1.28 Tbit/s to 80 Gbit/s using a nonlinear optical loop mirror (NOLM) switch. The NOLM was composed of a 100 m HNLF with a nonlinear coefficient γ = 17 W⁻¹km⁻¹, a dispersion slope of 0.03 ps/nm²/km, and a zero-dispersion wavelength of 1548 nm. The insertion loss was 9 dB. As a control pulse source, we used an MLFL directly emitting a 40 GHz 720 fs pulse train at 1563 nm, which was PLL-operated with a 40 GHz clock extracted from the polarization-demultiplexed 640 Gbaud data using an electro-optical PLL clock recovery unit [9]. The walk-off between the signal and control pulse was 230 fs. The optical power at the HNLF input was set at 18 dBm for the data signal and 16 dBm for the control pulse, respectively. The switching gate window of the NOLM is shown in Fig. 2(b), which was measured by launching CW light instead of the data pulse. The switching gate width was 1.0 ps with an extinction ratio of > 17 dB.

After removing the control pulses with 15 and 5 nm optical filters, we coupled the demultiplexed DQPSK signal to an ultrafast time-domain optical Fourier transform circuit (OFTC) including an LN phase modulator in a round-trip configuration and an SMF [10]. With a combination of linear chirp K and dispersion D, it is possible to transform an optical waveform between the time and frequency domains under the condition K = 1/D. Since the spectral envelope profile remains unchanged even if its time-domain waveform is distorted by linear perturbations including higher-order PMD and time-varying perturbations, OFT enables us to obtain a distortion-free pulse waveform in the time domain and thus eliminate linear transmission impairments [11]. We successfully obtained the chirp rate K = 0.71 ps⁻² by adopting the round-trip configuration, that is a sufficiently large amount of chirp required for the OFT of ultrashort pulses. As a dispersion medium, we used a 2 m-long SMF, which was chosen for minimum pulse width at the output of OFTC. The Fourier-transformed DQPSK signal was then preamplified and demodulated with a one-bit delay interferometer, which was biased at + π/4 or – π/4 depending on the phase component being measured. Finally, the bit error rate (BER) was measured after detection with a balanced photo-detector (PD).

3. Experimental results

We first measured the PMD characteristics of the 300 km transmission line that we used in this work. Figure 3(a) and 3(b), respectively, show the differential group delay (DGD) versus wavelength characteristics, Δτ(λ), and the evolution of the PSP vector on a Poincaré sphere with respect to the wavelength, n(λ), which were measured with the Jones matrix eigenanalysis [12]. The DGD value was 0.33 ps at 1540 nm, and the PSP axis rotated more than 180 deg. between 1530 and 1550 nm. The second-order PMD characteristics can be obtained by taking the derivative of the DGD and the PSP vector with respect to wavelength. The magnitude of the depolarization $\left|(\partial n/\partial \omega )\Delta \tau ({\omega }_0)\right|$ is plotted as a function of wavelength in Fig. 3(c). As the depolarization value at 1540 nm was 0.13 ps², the PSP direction changes on a Poincaré sphere at a rate $\left|\partial n/\partial f\right|$ = 0.79 π rad/THz with respect to frequency, or 0.09 π rad/nm with respect to wavelength. This result indicates that the PSP vector is rotated by 180 deg. within a wavelength of 11 nm.

 

Fig. 3 PMD characteristics of the 300 km transmission link. (a) DGD, (b) PSP vector on a Poincaré sphere, (c) depolarization.

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Next we evaluated the inter-polarization crosstalk by launching a 40 GHz, 600 fs pulse with individual polarization under PSP coupling. Figure 4(a) shows the optical spectra of the // and $\perp$polarization channels after a 300 km transmission, which were measured at the // output port of the PBS in the receiver. It can be seen that the spectrum leaked from the $\perp$channel has a low intensity near the center wavelength, but this increases for wavelengths away from the center. This profile clearly identifies the consequence of second-order PMD. We also evaluated the evolution of the crosstalk as a function of transmission distance L, as shown in Fig. 4(b). The crosstalk increases to 0.039 (–14 dB) at 300 km and further increases to 0.074 (– 11.3 dB) at 525 km. It can also be seen that the crosstalk increase scales as L² as shown by the solid curve in Fig. 4(b). As the crosstalk occurs mainly at the outer wavelength region as shown in Fig. 4(a), it can be reduced by using a narrowband optical filter. We installed a 2 nm filter after the preamplifier as shown in Fig. 1, whose optimum bandwidthwas chosen with a view to reducing the crosstalk as well as avoiding waveform distortions and intersymbol interference.

 

Fig. 4 Inter-polarization crosstalk in polarization-multiplexed transmission of 600 fs pulses. (a) Optical spectra of the signal and crosstalk components after a 300 km transmission, (b) magnitude of crosstalk along the transmission distance.

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The BER characteristics after a 300 km transmission are shown in Fig. 5 . The result with single polarization (1.28 Tbit/s) [8] is also shown for comparison. Because of higher OSNR requirement for DQPSK signals, an error floor already exists under the back-to-back condition. The BER performance was mainly limited by OSNR in single polarization transmission. A large error floor exists at a BER of 10⁻⁵, which is more than two orders of magnitude worse than that for the single polarization. The BER improvement with OFT was less significant in the polarization-multiplexed transmission. The pulse waveform obtained after employing the OFT is shown in Fig. 6(b) . Compared with the waveform without OFT shown in Fig. 6(a), the pulse width was shortened and the timing jitter was reduced by OFT, but the impairment around the peak was not completely eliminated. This is because an OFT is only applicable to the distortion of its own signal, but cannot be applied to distortions induced by crosstalk from different signals. Comparing the BER curves with that of single-polarization transmission in Fig. 5, the performance improvement was almost the same. This indicates that the polarization-multiplexed transmission is limited not only by the crosstalk but also by the distortions within the single-polarization, and the OFT is beneficial for the latter distortions.

 

Fig. 5 2.56 Tbit/s/ch-300 km transmission results. Squares and triangles show different polarization-component, and I and Q components are plotted with closed and open symbols, respectively.

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Fig. 6 Waveforms of demultiplexed DQPSK signals after a 300 km (a) Without OFT, (b) with OFT.

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4. Conclusion

We have demonstrated a 2.56 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km. Ultrafast OFT was used to reduce waveform distortions. We found that the performance was mainly limited by the polarization crosstalk induced by second-order PMD. PMD control and management techniques that include such higher-order effects are indispensable for exploring the feasibility of Tbit/s/ch transmission systems.