Abstract

We report a substantial increase in PMD tolerance in a single-channel ultrahigh-speed transmission using optical Nyquist pulses. We demonstrate both analytically and experimentally a large reduction in depolarization-induced crosstalk with optical Nyquist pulses, which is one of the major obstacles facing polarization-multiplexed ultrashort pulse transmission. By taking advantage of the high PMD tolerance, a low-penalty 1.28 Tbit/s/ch optical Nyquist TDM transmission at 640 Gbaud was achieved over 525 km.

© 2013 Optical Society of America

1. Introduction

The increase in the symbol rate by optical time division multiplexing (OTDM) has made it possible to achieve a single-channel bit rate of 1 Tbit/s and beyond [15]. A 1.28 Tbaud symbol rate has been realized [3], which made it possible to realize a single-channel bit rate of 10 Tbit/s with the adoption of polarization multiplexing and 16 QAM [4]. However, such an ultrafast symbol rate requires a subpicosecond optical pulse, whose spectral bandwidth easily exceeds 1 THz. Therefore, transmission of such an ultrahigh-speed signal over long distances becomes highly vulnerable to chromatic dispersion (CD) and polarization-mode dispersion (PMD). In particular, even when second-order CD or first-order PMD are fully compensated, higher-order CD and PMD need to be carefully controlled. Furthermore, it is recognized that, in a polarization-multiplexed transmission, higher-order PMD induces detrimental transmission impairments as a result of inter-polarization crosstalk, which is inevitable even with full compensation of first-order PMD [5, 6]. The only possible way to overcome this obstacle is to reduce the magnitude of the depolarization, which is practically difficult since PMD is inherent in fibers, or to decrease the spectral width of the data signal.

Recently, we proposed a novel OTDM transmission scheme using optical Nyquist pulses, which is suitable for ultrahigh-speed and spectrally efficient transmission [7]. An optical Nyquist pulse has a sinc-function-like waveform with a periodically oscillating tail and a rectangular or raised-cosine spectral profile. These profiles are precisely given by the impulse response and transfer function of a Nyquist filter [8]. By setting the zero-crossing period of the oscillating pulse tail to match the OTDM interval, individual isolated optical Nyquist pulses can be time-interleaved to a higher symbol rate without intersymbol interference (ISI) after the OTDM, in spite of the strong overlap between adjacent pulses. This is in complete contrast to conventional OTDM with Gaussian or sech optical pulses, in which adjacent optical pulses have to be separated adequately to avoid ISI. The overlapped OTDM allows us to achieve an ultrahigh data rate with a reduced signal bandwidth, and therefore we can expect the CD and PMD tolerance to be greatly increased. By taking advantage of this property, 160 Gbaud Nyquist OTDM transmission has been reported [911], demonstrating a substantial increase in CD tolerance [9]. Such a high bandwidth efficiency is also attractive for the dense spectral packing of OTDM-WDM channels and it enables efficient add-drop multiplexing operation [11]. Nyquist filtering to 1.28 Tbaud OTDM signal and its 100 km transmission has also been recently reported [12].

In this paper, we demonstrate a substantial performance improvement in 640 Gbaud polarization-multiplexed transmission over 525 km by using optical Nyquist pulses. We first present both analytically and experimentally the high PMD tolerance of optical Nyquist pulses through a large reduction of the depolarization-induced crosstalk in an ultrahigh-speed polarization-multiplexed transmission. Motivated by this advantage, a 1.28 Tbit/s polarization-multiplexed DPSK transmission of 640 Gbaud Nyquist OTDM signals is demonstrated over 525 km. Based on our previous preliminary reports [13, 14], here we elaborate our analytical and experimental description of the depolarization-induced crosstalk for optical Nyquist pulses, and focus particularly on its system impact on ultrahigh-speed Nyquist OTDM transmission.

2. PMD tolerance improvement with optical Nyquist pulses

2.1 Analysis of depolarization-induced crosstalk of optical Nyquist pulses

The amplitude waveform and frequency spectrum of the optical Nyquist pulse are defined as

r(t)=sin(πt/T)πt/Tcos(απt/T)1(2αt/T)2,R(f)={T,0|f|1α2TT2{1sin[π2α(2T|f|1)]},1α2T|f|1+α2T0,|f|1+α2T,
where T is the OTDM symbol interval (i.e., the baud rate after OTDM is given by R = 1/T), and α (0 ≤ α ≤ 1) is a roll-off factor. The pulse waveform has an oscillating tail, but it becomes zero periodically at t = nT (n: integer), and therefore the bit-interleaved OTDM signal has no ISI at any symbol interval, despite a strong overlap with neighboring pulses. This property contributes to the considerable bandwidth reduction in ultrahigh-speed OTDM transmission. Specifically, the spectral width, defined as the width of both edges of the spectrum tail (not the FWHM), is given by B = (1 + α)/T = (1 + α)R. The OTDM signal at R = 640 Gbaud, for example, can be transmitted within a bandwidth of 640(1 + α) GHz.

Figure 1 shows the waveform and spectrum of Gaussian and Nyquist (α = 0.5) pulses for 640 Gbaud transmission. The FWHM of the Gaussian pulse is set at 600 fs assuming a 40% duty cycle. As shown in Fig. 1(b), the 3 dB spectral width for a Gaussian pulse is 750 GHz, and the tail of the spectrum decays slowly, resulting in a spectral width as large as 2 THz at 20 dB. On the other hand, the 3 dB spectral width for a Nyquist pulse is 525 GHz and the spectrum is confined completely within a bandwidth of B = 960 GHz. This indicates the possibility of a large improvement in CD and PMD tolerance.

 figure: Fig. 1

Fig. 1 Comparison of Gaussian and Nyquist pulse waveforms (a) and spectra (b) for 640 Gbaud transmission.

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In our previous work [6], we described inter-polarization crosstalk induced by second-order PMD, which leads to a large transmission impairment in polarization-multiplexed ultrahigh-speed transmission even when first-order PMD is fully compensated. It is well known that, if the signal is coupled to the principal state of polarization (PSP) of the fiber link, which is defined as a frequency-independent state of polarization (SOP) after transmission, there is no differential group velocity (DGD) distortion. PSP coupling also enables the complete separation of the polarization-multiplexed channels with a polarization beam splitter (PBS) at the receiver. However, if PSP has a frequency dependence, which is not negligible, especially for a large spectral width such as that of subpicosecond pulses, the signal becomes depolarized and the SOP at a certain frequency component may even become orthogonal to the SOP at another frequency within its bandwidth. This inevitably leads to crosstalk between polarization-multiplexed channels.

It has been found that the crosstalk increases in proportion to the fourth power of the spectral width, Δω4, and grows by the square of the distance L2 [6]. The Δω4 dependence indicates that this crosstalk is disadvantageous especially for shorter optical pulses. Therefore, a reduced spectral width with an optical Nyquist pulse is expected to be particularly useful for mitigating this detrimental impairment.

Following the procedure described in [6], here we derive the analytical formula of the depolarization-induced crosstalk for a Nyquist pulse. We define the complex spectral amplitudes of the two channels as A˜(ω) and B˜(ω). The intensity of the crosstalk component from B˜(ω) to A˜(ω), with PSP coupling at the center frequency ω = ω0, is then obtained as

IBA(ω)=Δω416|B˜(ω)|2|dndω(ω0)Δτ(ω0)|2
where n is a unit vector in the direction of the PSP vector on the Poincaré sphere, Δτ is the DGD, and the term |(dn/dω)Δτ| represents the magnitude of depolarization. Δω = ω − ω0 is the frequency offset from ω0 and is a measure of the spectral width. From Eq. (2), the magnitude of the crosstalk is given by
η=IBA(ω)dω|B˜(ω)|2dω=116|dndω(ω0)Δτ(ω0)|2(ωω0)4|B˜(ω)|2dω|B˜(ω)|2dω.
For example, for a Gaussian pulse, B(t) = exp(−t2/2T02), whose spectrum is given by B˜(ω) = exp(−ω2/2Ω02) with Ω0 = 1/T0, Eq. (3) is calculated as
ηGauss=364Ω04|dndω(ω0)Δτ(ω0)|2,
which explicitly indicates that the crosstalk increases with the fourth power of the spectral width Ω04. For a Nyquist pulse, by substituting Eq. (1) into (4), we obtain
ηNyquist=4π4T4(4α)|dndω(ω0)Δτ(ω0)|2[(116π238π41320)α5+(24π43π2+116)α4+(316π2132)α3+(1π2+18)α2α64+180].
In particular, when α = 0 (sinc pulse), Eq. (5) is reduced to
ηsinc=π420T4|dndω(ω0)Δτ(ω0)|2.
Equations (5) and (6) also imply the fourth power dependence of the crosstalk on the spectral width (1/T)4.

2.2 Depolarization-induced crosstalk measurement

We measured the inter-polarization crosstalk during the propagation of polarization-multiplexed Nyquist pulses, and evaluated its dependence on bandwidth, transmission distance, roll-off factor α, and by comparison with Gaussian pulses. The experimental setup is shown in Fig. 2. The pulse source was a 40 GHz mode-locked fiber laser (MLFL). We employed SPM-induced spectral broadening in a highly nonlinear fiber (HNLF) as shown in Fig. 3(a). Then the spectral profile was manipulated with a pulse shaper to obtain an optical Nyquist pulse, whose transfer function is shown in Fig. 3(b). Here we set T = 1.56 ps for 640 Gbaud OTDM, and α = 0.5. Figure 3(c) and (d) show the optical spectrum and intensity profile of the generated Nyquist pulse, which were measured with an optical spectrum analyzer and a cross-correlator (sampling pulse width: 350 fs), respectively.

 figure: Fig. 2

Fig. 2 Experimental setup for inter-polarization crosstalk measurement.

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 figure: Fig. 3

Fig. 3 (a) Optical spectrum of 40 GHz Gaussian pulse with SPM-induced spectral broadening, and (b) the transfer function to shape it into a Nyquist pulse (T = 1.56 ps, α = 0.5). (c) and (d): optical spectrum and waveform of a generated optical Nyquist pulse.

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The optical Nyquist pulse was then launched into a fiber link with a single polarization (e.g., // channel), where the SOP before transmission was manually adjusted to the PSP of the transmission link using a polarization controller (PC) so that the degree of polarization (DOP) was maximized after transmission. The fiber link was composed of 75 km spans of dispersion-managed fiber, where each span consisted of a 50 km standard single-mode fiber (SSMF) and a 25 km inverse-dispersion fiber (IDF) that simultaneously compensated for the GVD and dispersion slope of the SSMF. The SOP prior to the PBS was optimized so that the output power from the // port was maximum. We then switched the launched pulse to the other polarization channel (here the channel), and measured the output spectrum and its power from the same PBS port in a fixed PC setup for PSP coupling and polarization demultiplexing. The output spectrum of the channel from the // port gives the crosstalk component I//(ω), and the power ratio of // and channels, η=P/P//, measured at the // port corresponds to the magnitude of the crosstalk.

Figure 4 shows how the maximum DOP values are degraded during the propagation of a 600 fs Gaussian pulse and a Nyquist pulse with T = 1.56 ps and α = 0.5 (the same parameters as in Fig. 1). In the absence of higher-order PMD, it is possible to maintain the maximum DOP at 1 under the PSP coupling condition. However, the results in Fig. 4 indicate that the DOP decreases gradually no matter how the SOP is optimized. This indicates the existence of depolarization within the signal bandwidth induced by second-order PMD. Figure 4 also indicates that the Nyquist pulse is less susceptible to DOP degradation, implying greater PMD tolerance.

 figure: Fig. 4

Fig. 4 Maximum DOP values for Gaussian and Nyquist pulses measured at various propagation lengths.

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Figure 5 shows optical spectra of major and minor channels (red and blue curves, respectively) of Nyquist and Gaussian pulses monitored at the same PBS port after propagation over various distances. The blue curve corresponds to the crosstalk component. The dip in the crosstalk component is a consequence of the Δω4 factor in Eq. (2) [6]. The magnitude of the crosstalk as a function of the distance is plotted in Fig. 6. It can be seen that the crosstalk growth rate is much lower with a Nyquist pulse, and the crosstalk was 3.8 dB lower than that of a Gaussian pulse after propagation over 525 km.

 figure: Fig. 5

Fig. 5 Optical spectra of signal and crosstalk components when a Nyquist (a) and Gaussian (b) pulse were propagated over 75, 150, 300, and 525 km.

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 figure: Fig. 6

Fig. 6 Dependence of inter-polarization crosstalk on the fiber length measured for a 600 fs Gaussian pulse and an optical Nyquist pulse (T = 1.56 ps, α = 0.5). The dots are the experimental data, and the curves are their L2 fitting.

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We also evaluated the dependence of the crosstalk on the spectral width and the roll-off factor. Figure 7 compares the crosstalk η for Gaussian and Nyquist pulses (α = 0.5) with various 3 dB spectral widths, which were measured at 75 km. The solid curves are analytical results given by Eqs. (4) and (5), in which |(dn/dω)(ω0)Δτ(ω0)| = 0.1 ps2 was used as the measured depolarization value at 75 km. As can be seen, the crosstalk grows rapidly for a broader spectral width with a Gaussian pulse, and it reaches 0.09 (–10.5 dB) for a 1.3 THz spectral width, which corresponds to 350 fs FWHM. On the other hand, a Nyquist pulse suffers from much less crosstalk under the same spectral width, and it is still less than –17 dB even at a spectral width of 1.1 THz.

 figure: Fig. 7

Fig. 7 Dependence of depolarization-induced crosstalk on spectral width, measured at 75 km. The dots are the experimental data, and the red curve is the analytical result given by Eqs. (4) and (5).

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Figure 8 shows the measured crosstalk for Nyquist pulses with T = 1.56 ps and various α values. The crosstalk takes a minimum value when α = 0.36, but overall the α dependence of η is found to be insignificant. For example, a lower α, even with a narrower spectral width B, yields a more uniform distribution of the spectral component around the center frequency. The spectrum is therefore vulnerable to inter-polarization crosstalk uniformly over the entire bandwidth. On the other hand, a larger α leads to a broader spectral width, but the tail of the spectrum also decays rapidly, resulting in a lower susceptibility to the crosstalk. This observation becomes one of the key issues as regards optimizing polarization demultiplexing as we describe in Sec. 3.2 below.

 figure: Fig. 8

Fig. 8 Dependence of depolarization-induced crosstalk on roll-factor α for Nyquist pulses for 640 Gbaud transmission, measured at 75 km. The dots are the experimental data, and the red curve is the analytical result given by Eq. (5).

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3. 1.28 Tbit/s/ch-525 km polarization-multiplexed optical Nyquist pulse transmission

3.1 Experimental setup

By taking advantage of the large PMD tolerance, we carried out a 1.28 Tbit/s/ch-525 km polarization-multiplexed transmission using 640 Gbaud optical Nyquist pulses. The experimental setup is shown in Fig. 9. The 40 GHz optical Nyquist pulses were DPSK modulated at 40 Gbit/s, 215–1 PRBS, and multiplexed to 640 Gbaud using a delay-line bit interleaver, followed by polarization multiplexing with a polarization beam combiner (PBC). The waveform of the 640 Gbaud Nyquist OTDM signal, measured with an optical sampling oscilloscope, is shown in Fig. 10. It can be clearly seen that no ISI occurs and a constant level is maintained at every symbol interval, in spite of a strong overlap between adjacent bits.

 figure: Fig. 9

Fig. 9 Experimental setup for 1.28 Tbit/s/ch Nyquist pulse OTDM transmission over 525 km. Abbreviations are defined in the text.

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 figure: Fig. 10

Fig. 10 Waveform of a 640 Gbaud Nyquist OTDM signal before transmission.

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The 1.28 Tbit/s signal was launched into a 525 km dispersion-managed transmission link composed of 75 km spans of dispersion-managed fiber, in which the SOP of the input signal was coupled to the PSP in the same way as in Sec. 2.2. The loss of each span was compensated for with EDFAs. The transmission power launched into each span was optimally set at + 11 dBm per polarization.

At the end of the fiber link, we installed a second pulse shaper, which we employed for the following two purposes. First, the residual dispersion slope of the dispersion-managed link, Δβ3L (Δβ3: third-order dispersion coefficient and L: fiber length), was compensated for by multiplying the phase shift exp(−iΔβ3ω3L/6) in the frequency domain with a pulse shaper. In spite of the simultaneous compensation of the GVD and dispersion slope by combining SSMF and IDF, there was a residual dispersion slope Δβ3L of approximately 0.8 ps3, which was found to be non-negligible for 640 Gbaud transmission. An optical Nyquist pulse waveform before and after the dispersion slope compensation at 525 km is shown in Fig. 11. The dispersion slope-induced ripples in the trailing edge are greatly reduced after compensation with a pulse shaper. The periodic oscillation in the pulse tail is not clearly resolved in Fig. 11(b) due to the insufficient bandwidth of the optical sampling oscilloscope.

 figure: Fig. 11

Fig. 11 Transmitted optical Nyquist pulse waveforms. (a) Before dispersion slope compensation, and (b) after dispersion slope compensation.

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The second role of pulse shaping after transmission is to regain the precise spectral profile of the Nyquist pulse, so that an ideal Nyquist pulse waveform can be recovered for accurate detection of ISI-free points. Figure 12(a) shows the Nyquist pulse spectrum and waveform after a 525 km transmission and dispersion slope compensation. The spectrum is plotted on a linear scale unlike in the previous figures. We note that the top of the spectrum, which was originally entirely flat, is not rigorously maintained and suffers from distortion. In addition, the decay of the trailing edge of the spectrum to the zero level is not completely smooth. These distortions are likely to originate from the incompletely flat gain profile of the EDFA that accumulated over multiple amplifications. The distortions led to a deviation from the ideal Nyquist waveform in the time domain, making it difficult to maintain the ISI-free property. Indeed, it can be observed that the tail of the pulse shown in Fig. 12(a) is still somewhat asymmetric between the leading and trailing edge even after dispersion slope compensation. We therefore designed the intensity profile of the pulse shaper so that the original ideal Nyquist spectrum can be recovered at the output. The result of the spectral reshaping is shown in Fig. 12(b). The small remaining distortions at the top of the spectrum result from the limited accuracy when setting the intensity profile. As a result, the tail of the waveform was slightly improved, and it enabled accurate OTDM demultiplexing and signal detection.

 figure: Fig. 12

Fig. 12 Transmitted optical Nyquist pulse spectrum and waveform. (a) Before spectral reshaping on the receiver side, and (b) after spectral reshaping on the receiver side.

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At the receiver, the 1.28 Tbit/s Nyquist OTDM signal was first divided into two 640 Gbit/s signals with a polarization-beam splitter, and then demultiplexed to 40 Gbit/s using a nonlinear optical loop mirror (NOLM). Here, the NOLM functions as an ultrashort optical sampler to extract data from the overlapped sequence only at the ISI-free point [8]. The switching gate width has to be optimally chosen in terms of both residual ISI and OSNR in the demultiplexed signal. This is because too narrow a switching gate causes excessive loss, while an insufficiently narrow gate allows the penetration of ISI components. Figure 13 shows the result of switching gate optimization, which was carried out for a single-polarization 640 Gbaud Nyquist OTDM signal under a back-to-back condition. Figure 13(a) plots the relationship between the bit error rate (BER) and the pulse width of the sampling pulse. Here, the sampling pulse was emitted from a 40 GHz PLL-operated MLFL (800 fs, 1563 nm), which was synchronized with a 40 GHz clock extracted from the transmitted data, and to obtain a pulse width narrower than 800 fs, it was externally compressed with an HNLF. The NOLM was composed of a 100 m highly nonlinear fiber (HNLF) with γ = 17 W−1 km−1, a dispersion slope of 0.03 ps/nm2/km, and a zero-dispersion wavelength of 1548 nm, so that the walk-off between the signal and control pulses was 230 fs. As shown in Fig. 13(a), the BER is at its minimum value when the control pulse width is 700 fs. The corresponding switching gate window is shown in Fig. 13(b), which was measured by injecting CW light at the data wavelength instead of the OTDM signal. Under this optimum condition, the gate width was 830 fs. The demultiplexed 40 Gbaud signal waveform under the optimum condition is plotted in Fig. 13(c). After OTDM demultiplexing, the 40 Gbit/s DPSK signal was separated from the sampling pulse with optical filters, and received with a preamplifier, a one-bit delay interferometer (DI), and a balanced photo diode (PD).

 figure: Fig. 13

Fig. 13 Optimization of NOLM switching gate for 640 Gbaud Nyquist OTDM demultiplexing. (a) BER vs. control pulse width. (b) The switching gate window under optimum condition. (c) a 40 Gbaud waveform demultiplexed from a 640 Gbaud Nyquist OTDM signal.

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3.2 Experimental results

We evaluated the transmission impairment caused by the depolarization-induced crosstalk that we described in Sec. 2. As we observed in Fig. 5, the depolarization-induced crosstalk is manifested as a spectral component with a dip near the center wavelength but accompanied by a larger intensity for wavelengths away from the center. This can be identified as a consequence of Δω4 dependence in the intensity IB→A(ω) as shown in Eq. (2), which was derived under the assumption of PSP coupling around the center frequency ω0. This condition was realized by installing a narrowband optical filter before the DOP monitor in our previous 640 Gbaud transmission experiment with Gaussian pulses [6], so that the DOP around the center wavelength can be preferentially maximized.

However, the same approach for SOP optimization may not be applicable for a Nyquist pulse. Figure 14(a) shows the optical spectra measured for the major and minor polarization channels (red and blue curves, respectively) after a 525 km transmission, and the waveform of the polarization- and OTDM-demultiplexed 40 Gbaud signal, when the previous SOP optimization procedure was employed. As seen in the waveform, the signal suffers from a large intensity fluctuation around the pulse peak. This unexpected large impairment can be explained from the difference in the spectral shapes of the Gaussian and Nyquist pulses. The present SOP optimization causes the crosstalk to occur intentionally in the outer wavelength region. This is highly beneficial for Gaussian pulses, since the spectrum of the major channel decays exponentially for wavelengths away from the center, and thus the impact of the crosstalk on the major channel is less significant. On the other hand, this approach can be rather disadvantageous for a Nyquist pulse, as the spectrum has a flat top unlike Gaussian pulses and therefore the deliberate increase in crosstalk components at the outer wavelength results in larger impairments overall.

 figure: Fig. 14

Fig. 14 Optical spectra of signal (red) and crosstalk components (blue) after 525 km propagation (left) and polarization- and OTDM-demultiplexed 40 Gbaud signal waveform (right). (a) SOP optimization with a maximized DOP around the center frequency, and (b) SOP optimization with a maximized DOP over the entire bandwidth.

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An alternative way to optimize the SOP for a Nyquist pulse is to distribute the crosstalk component uniformly over the entire bandwidth. This is realized by removing the narrowband optical filter in front of the DOP monitor, and maximizing the DOP value over the whole signal bandwidth. The results thus obtained are shown in Fig. 14(b). Compared with Fig. 14(a), the intensity fluctuation is greatly reduced.

Figure 15 shows the BER characteristics for a 1.28 Tbit/s-525 km polarization-multiplexed transmission, based on SOP optimization corresponding to Fig. 14(b). The result with a 600 fs Gaussian pulse is shown in Fig. 15(a). Here, the switching gate width in the NOLM was optimally chosen as 1.0 ps, which was broader than that for a Nyquist pulse. This offers better back-to-back performance for a Gaussian pulse because there is less OSNR degradation due to broader switching gate. The result of a 640 Gbit/s single-polarization transmission is also plotted for comparison. As shown in Fig. 15(a), with a Gaussian pulse, the BER for a 1.28 Tbit/s polarization-multiplexed transmission was greatly degraded compared with the single-polarization result. This is a consequence of the PMD-induced crosstalk as we have seen. On the other hand, the BER degradation associated with polarization multiplexing was much smaller with a Nyquist pulse as shown in Fig. 15(b), and a BER of ~10−7 was achieved after a 525 km transmission with a much lower power penalty and a reduced error floor. These results indicate that the use of Nyquist pulses is very promising for ultrahigh-speed transmission.

 figure: Fig. 15

Fig. 15 BER characteristics for 640 Gbaud Nyquist (a) and Gaussian (b) pulse transmission over 525 km. Blue curves show the BER for 640 Gbit/s single-polarization transmission, and red curves show the result of a 1.28 Tbit/s polarization-multiplexed transmission. The circles and squares correspond to the two polarization channels.

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4. Conclusion

We demonstrated a large PMD tolerance in a polarization-multiplexed 640 Gbaud transmission by using an optical Nyquist pulse. By virtue of the lower inter-polarization crosstalk, a low-penalty 1.28 Tbit/s/ch transmission was successfully achieved over 525 km. This scheme is potentially scalable to a higher symbol rate per channel such as 1 Tbaud, and also offers the possibility of achieving a high spectral efficiency at such an ultrahigh symbol rate by employing coherent QAM.

References and links

1. M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000). [CrossRef]  

2. H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006). [CrossRef]  

3. H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010). [CrossRef]   [PubMed]  

4. T. Richter, E. Palushani, C. Schmidt-Langhorst, M. Nölle, R. Ludwig, and C. Schubert, “Single wavelength channel 10.2 Tb/s TDM-data capacity using 16-QAM and coherent detection,” in Optical Fiber Communication Conference (OFC 2011), paper PDPA9.

5. P. Guan, T. Hirano, K. Harako, Y. Tomiyama, T. Hirooka, and M. Nakazawa, “2.56 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km using time-domain optical Fourier transformation,” Opt. Express 19(26), B567–B573 (2011). [CrossRef]   [PubMed]  

6. T. Hirooka, K. Harako, P. Guan, and M. Nakazawa, “Second-order PMD-induced crosstalk between polarization-multiplexed signals and its impact on ultrashort optical pulse transmission,” J. Lightwave Technol. 31(5), 809–814 (2013). [CrossRef]  

7. M. Nakazawa, T. Hirooka, P. Ruan, and P. Guan, “Ultrahigh-speed “orthogonal” TDM transmission with an optical Nyquist pulse train,” Opt. Express 20(2), 1129–1140 (2012). [CrossRef]   [PubMed]  

8. H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617–644 (1928).

9. T. Hirooka, P. Ruan, P. Guan, and M. Nakazawa, “Highly dispersion-tolerant 160 Gbaud optical Nyquist pulse TDM transmission over 525 km,” Opt. Express 20(14), 15001–15007 (2012). [CrossRef]   [PubMed]  

10. H. Hu, J. Wang, H. Ji, E. Palushani, M. Galili, H. C. Hansen Mulvad, P. Jeppesen, and L. K. Oxenløwe, “Nyquist filtering of 160 GBaud NRZ-like DPSK signal,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.61. [CrossRef]  

11. H. N. Tan, T. Inoue, and S. Namiki, “Pass-drop operations of 4x172Gb/s Nyquist OTDM-WDM over cascade of WSSs using distributed matched filtering,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.50.

12. H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sørensen, M. Galili, H. C. H. Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using time-domain optical Fourier transformation based receiver,” in Conference on Lasers and Electro-Optics (CLEO 2013), paper CTh5D.5. [CrossRef]  

13. K. Harako, P. Ruan, T. Hirooka, and M. Nakazawa, “Large PMD tolerant 1.28 Tbit/s/ch transmission over 525 km with 640 Gbaud optical Nyquist pulses,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.38. [CrossRef]  

14. K. Harako, T. Hirooka, and M. Nakazawa, “Marked reduction of depolarization-induced crosstalk in ultrahigh-speed Pol-MUX transmission with an optical Nyquist pulse,” in Opto-Electronics and Communication Conference (OECC 2013), paper WR4–5

References

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  1. M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
    [Crossref]
  2. H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
    [Crossref]
  3. H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
    [Crossref] [PubMed]
  4. T. Richter, E. Palushani, C. Schmidt-Langhorst, M. Nölle, R. Ludwig, and C. Schubert, “Single wavelength channel 10.2 Tb/s TDM-data capacity using 16-QAM and coherent detection,” in Optical Fiber Communication Conference (OFC 2011), paper PDPA9.
  5. P. Guan, T. Hirano, K. Harako, Y. Tomiyama, T. Hirooka, and M. Nakazawa, “2.56 Tbit/s/ch polarization-multiplexed DQPSK transmission over 300 km using time-domain optical Fourier transformation,” Opt. Express 19(26), B567–B573 (2011).
    [Crossref] [PubMed]
  6. T. Hirooka, K. Harako, P. Guan, and M. Nakazawa, “Second-order PMD-induced crosstalk between polarization-multiplexed signals and its impact on ultrashort optical pulse transmission,” J. Lightwave Technol. 31(5), 809–814 (2013).
    [Crossref]
  7. M. Nakazawa, T. Hirooka, P. Ruan, and P. Guan, “Ultrahigh-speed “orthogonal” TDM transmission with an optical Nyquist pulse train,” Opt. Express 20(2), 1129–1140 (2012).
    [Crossref] [PubMed]
  8. H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617–644 (1928).
  9. T. Hirooka, P. Ruan, P. Guan, and M. Nakazawa, “Highly dispersion-tolerant 160 Gbaud optical Nyquist pulse TDM transmission over 525 km,” Opt. Express 20(14), 15001–15007 (2012).
    [Crossref] [PubMed]
  10. H. Hu, J. Wang, H. Ji, E. Palushani, M. Galili, H. C. Hansen Mulvad, P. Jeppesen, and L. K. Oxenløwe, “Nyquist filtering of 160 GBaud NRZ-like DPSK signal,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.61.
    [Crossref]
  11. H. N. Tan, T. Inoue, and S. Namiki, “Pass-drop operations of 4x172Gb/s Nyquist OTDM-WDM over cascade of WSSs using distributed matched filtering,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.50.
  12. H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sørensen, M. Galili, H. C. H. Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using time-domain optical Fourier transformation based receiver,” in Conference on Lasers and Electro-Optics (CLEO 2013), paper CTh5D.5.
    [Crossref]
  13. K. Harako, P. Ruan, T. Hirooka, and M. Nakazawa, “Large PMD tolerant 1.28 Tbit/s/ch transmission over 525 km with 640 Gbaud optical Nyquist pulses,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.38.
    [Crossref]
  14. K. Harako, T. Hirooka, and M. Nakazawa, “Marked reduction of depolarization-induced crosstalk in ultrahigh-speed Pol-MUX transmission with an optical Nyquist pulse,” in Opto-Electronics and Communication Conference (OECC 2013), paper WR4–5

2013 (1)

2012 (2)

2011 (1)

2010 (1)

2006 (1)

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

2000 (1)

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617–644 (1928).

Boerner, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Clausen, A. T.

Ferber, S.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Futami, F.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Galili, M.

Guan, P.

Harako, K.

Hirano, T.

Hirooka, T.

Hu, H.

Jensen, J. B.

Jeppesen, P.

Kroh, M.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Ludwig, R.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Marembert, V.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Mulvad, H. C. H.

Nakazawa, M.

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617–644 (1928).

Oxenløwe, L. K.

Peucheret, C.

Ruan, P.

Schmidt-Langhorst, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Schubert, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Tamura, K. R.

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

Tomiyama, Y.

Watanabe, S.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Weber, H. G.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Yamamoto, T.

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

Electron. Lett. (2)

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (4)

Trans. Am. Inst. Electr. Eng. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617–644 (1928).

Other (6)

H. Hu, J. Wang, H. Ji, E. Palushani, M. Galili, H. C. Hansen Mulvad, P. Jeppesen, and L. K. Oxenløwe, “Nyquist filtering of 160 GBaud NRZ-like DPSK signal,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.61.
[Crossref]

H. N. Tan, T. Inoue, and S. Namiki, “Pass-drop operations of 4x172Gb/s Nyquist OTDM-WDM over cascade of WSSs using distributed matched filtering,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.50.

H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sørensen, M. Galili, H. C. H. Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using time-domain optical Fourier transformation based receiver,” in Conference on Lasers and Electro-Optics (CLEO 2013), paper CTh5D.5.
[Crossref]

K. Harako, P. Ruan, T. Hirooka, and M. Nakazawa, “Large PMD tolerant 1.28 Tbit/s/ch transmission over 525 km with 640 Gbaud optical Nyquist pulses,” in Optical Fiber Communication Conference (OFC 2013), paper J2WA.38.
[Crossref]

K. Harako, T. Hirooka, and M. Nakazawa, “Marked reduction of depolarization-induced crosstalk in ultrahigh-speed Pol-MUX transmission with an optical Nyquist pulse,” in Opto-Electronics and Communication Conference (OECC 2013), paper WR4–5

T. Richter, E. Palushani, C. Schmidt-Langhorst, M. Nölle, R. Ludwig, and C. Schubert, “Single wavelength channel 10.2 Tb/s TDM-data capacity using 16-QAM and coherent detection,” in Optical Fiber Communication Conference (OFC 2011), paper PDPA9.

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Figures (15)

Fig. 1
Fig. 1 Comparison of Gaussian and Nyquist pulse waveforms (a) and spectra (b) for 640 Gbaud transmission.
Fig. 2
Fig. 2 Experimental setup for inter-polarization crosstalk measurement.
Fig. 3
Fig. 3 (a) Optical spectrum of 40 GHz Gaussian pulse with SPM-induced spectral broadening, and (b) the transfer function to shape it into a Nyquist pulse (T = 1.56 ps, α = 0.5). (c) and (d): optical spectrum and waveform of a generated optical Nyquist pulse.
Fig. 4
Fig. 4 Maximum DOP values for Gaussian and Nyquist pulses measured at various propagation lengths.
Fig. 5
Fig. 5 Optical spectra of signal and crosstalk components when a Nyquist (a) and Gaussian (b) pulse were propagated over 75, 150, 300, and 525 km.
Fig. 6
Fig. 6 Dependence of inter-polarization crosstalk on the fiber length measured for a 600 fs Gaussian pulse and an optical Nyquist pulse (T = 1.56 ps, α = 0.5). The dots are the experimental data, and the curves are their L2 fitting.
Fig. 7
Fig. 7 Dependence of depolarization-induced crosstalk on spectral width, measured at 75 km. The dots are the experimental data, and the red curve is the analytical result given by Eqs. (4) and (5).
Fig. 8
Fig. 8 Dependence of depolarization-induced crosstalk on roll-factor α for Nyquist pulses for 640 Gbaud transmission, measured at 75 km. The dots are the experimental data, and the red curve is the analytical result given by Eq. (5).
Fig. 9
Fig. 9 Experimental setup for 1.28 Tbit/s/ch Nyquist pulse OTDM transmission over 525 km. Abbreviations are defined in the text.
Fig. 10
Fig. 10 Waveform of a 640 Gbaud Nyquist OTDM signal before transmission.
Fig. 11
Fig. 11 Transmitted optical Nyquist pulse waveforms. (a) Before dispersion slope compensation, and (b) after dispersion slope compensation.
Fig. 12
Fig. 12 Transmitted optical Nyquist pulse spectrum and waveform. (a) Before spectral reshaping on the receiver side, and (b) after spectral reshaping on the receiver side.
Fig. 13
Fig. 13 Optimization of NOLM switching gate for 640 Gbaud Nyquist OTDM demultiplexing. (a) BER vs. control pulse width. (b) The switching gate window under optimum condition. (c) a 40 Gbaud waveform demultiplexed from a 640 Gbaud Nyquist OTDM signal.
Fig. 14
Fig. 14 Optical spectra of signal (red) and crosstalk components (blue) after 525 km propagation (left) and polarization- and OTDM-demultiplexed 40 Gbaud signal waveform (right). (a) SOP optimization with a maximized DOP around the center frequency, and (b) SOP optimization with a maximized DOP over the entire bandwidth.
Fig. 15
Fig. 15 BER characteristics for 640 Gbaud Nyquist (a) and Gaussian (b) pulse transmission over 525 km. Blue curves show the BER for 640 Gbit/s single-polarization transmission, and red curves show the result of a 1.28 Tbit/s polarization-multiplexed transmission. The circles and squares correspond to the two polarization channels.

Equations (6)

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r(t)= sin(πt/T) πt/T cos(απt/T) 1 (2αt/T) 2 ,R(f)={ T,0|f| 1α 2T T 2 { 1sin[ π 2α (2T|f|1) ] }, 1α 2T |f| 1+α 2T 0,|f| 1+α 2T ,
I BA (ω)= Δ ω 4 16 | B ˜ (ω) | 2 | dn dω ( ω 0 )Δτ( ω 0 ) | 2
η= I BA (ω)dω | B ˜ (ω) | 2 dω = 1 16 | dn dω ( ω 0 )Δτ( ω 0 ) | 2 (ω ω 0 ) 4 | B ˜ (ω) | 2 dω | B ˜ (ω) | 2 dω .
η Gauss = 3 64 Ω 0 4 | dn dω ( ω 0 )Δτ( ω 0 ) | 2 ,
η Nyquist = 4 π 4 T 4 (4α) | dn dω ( ω 0 )Δτ( ω 0 ) | 2 [ ( 1 16 π 2 3 8 π 4 1 320 ) α 5 +( 24 π 4 3 π 2 + 1 16 ) α 4 +( 3 16 π 2 1 32 ) α 3 +( 1 π 2 + 1 8 ) α 2 α 64 + 1 80 ].
η sinc = π 4 20 T 4 | dn dω ( ω 0 )Δτ( ω 0 ) | 2 .

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