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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11590–11605
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Transmission of multi-polarization-multiplexed signals: another freedom to explore?

Zhiyu Chen, Lianshan Yan, Wei Pan, Bin Luo, Yinghui Guo, Hengyun Jiang, Anlin Yi, Yafei Sun, and Xiaoxia Wu  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11590-11605 (2013)
http://dx.doi.org/10.1364/OE.21.011590


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Abstract

We propose a configuration of signal multiplexing with four polarization states, and investigate its transmission performance over single-mode-fiber links. Assisted by coherent detection and digital signal processing (DSP), the demodulation of four-polarization multiplexed (4PM) on-off-keying (OOK) and phase-shift-keying (PSK) signals are achieved. We then discuss the impact of the crosstalk from polarization mode dispersion (PMD) on 4PM systems. The transmission distance is extended from ~50-km to ~80 km by employing feedback-decision-equalizers. We also compare the back-to-back characteristics of the 40-Gbit/s 4PM-OOK system and 40-Gbit/s PDM-QPSK system with the same spectral efficiency. The results show that the performance of 4PM systems is comparable to that of PDM-QPSK systems, which indicates that the proposed scheme is a potentially promising candidate for future optical networks.

© 2013 OSA

1. Introduction

In recent years, both the system capacity and the spectral efficiency (SE) have been significantly improved to meet the demands of the ever-growing data traffic [1

1. L. S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J. 3(2), 325–330 (2011). [CrossRef]

, 2

2. P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010). [CrossRef]

]. Thanks to the advanced modulation formats (i.e. orthogonal frequency-division multiplexing, phase-shift-keying (PSK) and quadrature amplitude modulation (QAM)) and coherent detection techniques, the spectral efficiency with close to 10 bit/s/Hz or even higher has been achieved [3

3. X. Liu, S. Chandrasekhar, X. Chen, P. J. Winzer, Y. Pan, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “1.12-Tb/s 32-QAM-OFDM superchannel with 8.6-b/s/Hz intrachannel spectral efficiency and space-division multiplexed transmission with 60-b/s/Hz aggregate spectral efficiency,” Opt. Express 19(26), B958–B964 (2011). [CrossRef] [PubMed]

5

5. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3. [CrossRef]

]. However, the growth of the data traffic does not appear to be leveling off any time soon, and most likely it will continue to grow in an exponential trend. Thus, many researchers focus on how to further increase the SE and overall capacity [5

5. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3. [CrossRef]

18

18. E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron. 12, 1129–1131 (2010).

]. Generally there are five major candidates, including higher-order modulation formats (i. e. 256-QAM, 512-QAM and so on) [5

5. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3. [CrossRef]

, 6

6. D. O. Captan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5-Gsloth ptically-preamplified M-PPM with 4 photonbit receiver sensitivity,” presented at Optical Fiber Communication Conference 2005 (OFC2005), paper PDP32.

], polarization-division multiplexing (PDM) [7

7. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22(15), 1129–1131 (2010). [CrossRef]

10

10. F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010). [CrossRef] [PubMed]

], frequency-division multiplexing (FDM) [11

11. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]

13

13. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM superchannel over 7200-km of ultra-large-area fiber,” in 35th European Conference on Optical Communication,2009 (ECOC '09), paper PDPB2.6.

], space-division multiplexing (SDM) [14

14. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express 20(11), 11718–11733 (2012). [CrossRef] [PubMed]

16

16. N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]

] and orbital-angular momentum [17

17. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]

]. Among these technologies, advanced higher-order modulation formats combined with PDM scheme, in which information is encoded on amplitude, phase and polarization of the light wave, seem to be more practical in the near future [19

19. X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, and R. Lingle, “32 (320×114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber,” presented at Optical Fiber Communication Conference 2009 (OFC'2009), paper PDPB4.

22

22. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PDPB2.3. [CrossRef]

].

Up to now, only two orthogonal states of polarization (SOPs) are available in traditional PDM systems due to the relatively simple demultiplexing method and manageable crosstalk between two SOPs. It would be highly desirable if we can further utilize the multidimensional polarization as it can provide infinite multiplexing freedoms in theory. However, due to the difficulty of polarization management, the demonstrated PDM systems are limited to two polarization states.

Previously, we have performed the first-step investigation about the feasibility of signal multiplexing with four SOPs for on-off-keying (OOK) signals [23

23. L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

]. Compared with traditional OOK system, the proposed scheme could quadruple the system capacity and SE directly. In this paper, a thorough analysis of the 4PM system is presented. In our scheme, the signal is generated by combining two conventional PDM signals, and demodulated using coherent detection technology combined with post digital signal processing (DSP). The angle between any two neighbor SOPs is set to be 45° (i.e. 0, 45, 90 and 135° at the transmitter). Then, the details of phase synchronization scheme are presented. Furthermore, we also analyze the impact of the crosstalk from polarization-mode dispersion (PMD) on four-polarization-multiplexing (4PM) systems. Simulation results show that the transmission distance of a 4 × 10-Gbit/s 4PM non-return-to-zero OOK (NRZ-OOK) could be extended from ~50 km to more than ~80 km using feedback-decision equalizer (FDE). The potential of 4PM-OOK system is also shown comparable performance with 40-Gbit/s PDM-QPSK systems under the same SE, which indicates that utilizing the freedom of polarization may also be another potential solution for future networks.

2. Principle and theoretical model for 4PM-OOK signal

Figure 1
Fig. 1 (a) Setup for four SOPs multiplexing, transmission and demodulation. (b) Receiver configuration for 4PM-OOK signal. OC: optical coupler; PC: polarization controller; VOA: variable optical attenuator; SMF: single-mode fiber; PBS: polarization beam splitter; LO: local oscillator laser; PD: photodetector; ADC: analog to digital converter; DSP: digital signal processing; CHn: channel n, (n = 1-4).
shows the generation and demultiplexing scheme for the 4PM-OOK system. The NRZ-OOK signal E1, E2, E3 and E4 (CH1-CH4) are generated from the laser1, which can be written as Ei=|Ai|exp(jωct+ϕ) (i = 1 ~4), where Ai, ωc and ϕ are the amplitudes, carrier angular frequency and phase of laser, respectively. Thus, after optical coupler2 (OC2), the multiplexed signal is expressed as follows. Note that there needs to be an additional π/2phase shift in the lower arm of the OC2.
Em=Ex+Ey=[x^(22A1+12jA312jA4)+y^(22A2+12jA3+12jA4)]exp(jωct+ϕ),
(1)
where Ex and Ey are the horizontal and vertical polarization modes, respectively.

In order to demodulate the signal, firstly the SOP of E1 should be adjusted to be aligned with the x-axis of PBS3 by a polarization control (PC7). Assuming that the angular frequency and initial phase of the local oscillator (LO) laser are ωc and θ, the LO laser can be written as ELO=|ALO|exp[j(ωct+θ)]. Next, the signals combined with a LO laser are fed into two optical hybrids, whose outputs are Ex±jELO, Ex±ELO, Ey±jELO and Ey±ELO, respectively. Here, we only use the four outputs (Ex±jELO and Ey±jELO) and obtain the expressions as follows:
{E1=22{22A1exp[j(ωct+ϕ)]+12jA3exp[j(ωct+ϕ)]12jA4exp[j(ωct+ϕ)]+jALOexp[j(ωct+θ)]}=22{22A1exp[j(ωct+ϕ)]+jB1expj(ωct)},E2=22{22A1exp[j(ωct+ϕ)]+12jA3exp[j(ωct+ϕ)]12jA4exp[j(ωct+ϕ)]jALOexp[j(ωct+θ)]}=22{22A1exp[j(ωct+ϕ)]+jB2expj(ωct)},E3=22{22A2exp[j(ωct+ϕ)]+12jA3exp[j(ωct+ϕ)]+12jA4exp[j(ωct+ϕ)]+jALOexp[j(ωct+θ)]}=22{22A2exp[j(ωct+ϕ)]+jB3expj(ωct)},E4=22{22A2exp[j(ωct+ϕ)]+12jA3exp[j(ωct+ϕ)]+12jA4exp[j(ωct+ϕ)]jALOexp[j(ωct+θ)]}=22{22A2exp[j(ωct+ϕ)]+jB4expj(ωct)},
(2)
where E’n (n = 1~4) are the outputs of the optical hybrids.

[B1B2B3B4]=[12A3exp(jϕ)12A4exp(jϕ)+ALOexp(jθ)12A3exp(jϕ)12A4exp(jϕ)ALOexp(jθ)12A3exp(jϕ)+12A4exp(jϕ)+ALOexp(jθ)12A3exp(jϕ)+12A4exp(jϕ)ALOexp(jθ)].
(3)

Afterwards, the optical fields are detected by photodetectors (PDs) with responsivity to produce the photocurrents in, which are given by

i1=2[22A1expj(ωct+ϕ)+jB1expj(ωct)][22A1expj(ωctϕ)jB1*expj(ωct)]=2[12A12+B1B1*22jA1B1*exp(jϕ)+22jA1B1exp(jϕ)],
(4)
i2=2[12A12+B2B2*22jA1B2*exp(jϕ)+22jA1B2exp(jϕ)],
(5)
i7=2[12A22+B3B3*22jA2B3*exp(jϕ)+22jA2B3exp(jϕ)],
(6)
i8=2[12A22+B4B4*22jA2B4*exp(jϕ)+22jA2B4exp(jϕ)].
(7)

For simplicity, assuming that ϕ=θ, the sum of the third and fourth terms in Eqs. (4)(7) becomes zero. Thus, in can be simplified as follows:
i1=[14A12+(24A324A4+22ALO)2],
(8)
i2=[14A12+(24A324A422ALO)2],
(9)
i7=[14A22+(24A3+24A4+22ALO)2],
(10)
i8=[14A22+(24A3+24A422ALO)2],
(11)
and

i1i2=(A3ALOA4ALO),
(12)
i7i8=(A3ALO+A4ALO).
(13)

Combining Eqs. (8)(13), the four SOPs multiplexing signal can be demodulated and the four output channels are respectively described as follows, which can be used for digital signal processing (DSP).

A1=12(i1+i2)(i1i2)22ALO22ALO2,
(14)
A2=12(i7+i8)(i7i8)22ALO22ALO2,
(15)
A3=i1i2+i7i82ALO,
(16)
A4=i1i2(i7i8)2ALO.
(17)

3. Phase synchronization

In the practical systems, the assumption of ϕ=θ is difficult to be implemented. Thus, when ϕθ, the photocurrents i1 and i2 become

i1=2[12A12+14A32+14A42+ALO212A3A4+A3ALOcos(ϕθ)A4ALOcos(ϕθ)+2A1ALOsin(ϕθ)],
(18)
i2=2[12A12+14A32+14A42+ALO212A3A4A3ALOcos(ϕθ)+A4ALOcos(ϕθ)2A1ALOsin(ϕθ)].
(19)

In this case, the difference of i1 and i2 becomes

i1i2=[A3ALOcos(ϕθ)A4ALOcos(ϕθ)+2A1ALOsin(ϕθ)].
(20)

It is different from the Eq. (12), which leads to the large error when demodulating the channels. Thus, an algorithm is required to synchronize the phase of the local oscillator with the transmitter laser. If we assume that the phases of carrier and LO drift slowly, one solution is shown in Fig. 2
Fig. 2 Phase synchronization scheme for 4PM-OOK signal. Re{X}: real part of X.
, where i3 and i4 are given by (Ex + ELO) × (Ex-ELO)* and (Ex + ELO) × (Ex-ELO)*, respectively.

i3=2[12A12+14A32+14A42+ALO212A3A4A3ALOsin(ϕθ)+A4ALOsin(ϕθ)+2A1ALOcos(ϕθ)],
(21)
i4=2[12A12+14A32+14A42+ALO212A3A4+A3ALOsin(ϕθ)A4ALOsin(ϕθ)2A1ALOcos(ϕθ)].
(22)

By subtracting i3 from i4, we can obtain the expression as follow

i3i4=[A3ALOsin(ϕθ)A4ALOsin(ϕθ)2A1ALOcos(ϕθ)].
(23)

Afterwards, the expression of point A (i.e. Figure 2) is given by

EA=[A3ALOexpj(ϕθ)A4ALOexpj(ϕθ)2A1ALOexpj(ϕθ+π2)].
(24)

The relative phase difference between LO and transmitter laser can be estimated according to the Eq. (24). To cancelled the phase asynchronization, the EA should be shifted by ϕθ, and the output of B can be written as

EB=EAexp[j(ϕθ)]=[A3ALOA4ALOj2A1ALO].
(25)

Finally, by retrieving the real part of the EB, we can obtain the output of phase synchronization as

iout=(A3ALOA4ALO).
(26)

Compared the Eq. (26) with Eq. (12), the phase asynchronization between LO and transmitter laser is successfully compensated. In addition, the frequency offset between LO laser and input signals also need to be compensated in the DSP unit.

4. Demodulation for 4PM-PSK signal

The PSK modulation format has recently attracted increasing interests due to the 3-dB receiver sensitivity enhancement and better tolerance to nonlinear effects [24

24. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]

, 25

25. J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett. 12(12), 1627–1629 (2000). [CrossRef]

]. Thus, we also investigate the demodulation scheme for 4PM-PSK signal. In this case, the inputs are given by Ei=|A|exp(jωct+ϕi), where ϕi is the phase information of the i-th channel. After OC2, the multiplexing signal can be expressed as

Em=Aexp(jωct){x^[22exp(jϕ1)+12jexp(jϕ3)12jexp(jϕ4)]+y^[22exp(jϕ2)+12jexp(jϕ3)+12jexp(jϕ4)]}.
(27)

As shown in Fig. 3
Fig. 3 Demodulation scheme for PSK signal. BPD: balance photodetector.
, similar to the demodulation scheme for 4PM-OOK signal, the divided signals (Ex & Ey) are combined with a LO laser into the corresponding optical hybrid, whose the outputs are Ex ± jELO, Ex ± ELO, Ey ± jELO and Ey ± ELO, respectively. Here, ELO is given by ELO=|A|exp(jωct+ϕLO), where ϕLO is the initial phase of the LO laser. After photoelectric conversion, eight signals can be expressed as

{i1(1)=(Ex+jELO)(Ex+jELO)*=|A|2[22sin(ϕ1ϕ3)+22sin(ϕ4ϕ1)+2sin(ϕ1ϕLO)12cos(ϕ3ϕ4)+cos(ϕ3ϕLO)cos(ϕLOϕ4)+2]i1(2)=(ExjELO)(ExjELO)*=|A|2[22sin(ϕ1ϕ3)+22sin(ϕ4ϕ1)2sin(ϕ1ϕLO)12cos(ϕ3ϕ4)cos(ϕ3ϕLO)+cos(ϕLOϕ4)+2],
(28)
{i2(1)=(Ex+ELO)(Ex+ELO)*=|A|2[22sin(ϕ1ϕ3)+22sin(ϕ4ϕ1)+2cos(ϕ1ϕLO)12cos(ϕ3ϕ4)sin(ϕ3ϕLO)+sin(ϕ4ϕLO)+2]i2(2)=(ExELO)(ExELO)*=|A|2[22sin(ϕ1ϕ3)+22sin(ϕ4ϕ1)2cos(ϕ1ϕLO)12cos(ϕ3ϕ4)+sin(ϕ3ϕLO)sin(ϕ4ϕLO)+2],
(29)
{i3(1)=(Ey+ELO)(Ey+ELO)*=|A|2[22sin(ϕ2ϕ3)+22sin(ϕ2ϕ4)+2cos(ϕ2ϕLO)+12cos(ϕ3ϕ4)sin(ϕ3ϕLO)sin(ϕ4ϕLO)+2]i3(2)=(EyELO)(EyELO)*=|A|2[22sin(ϕ2ϕ3)+22sin(ϕ2ϕ4)2cos(ϕ2ϕLO)+12cos(ϕ3ϕ4)+sin(ϕ3ϕLO)+sin(ϕ4ϕLO)+2],
(30)
{i4(1)=(Ey+jELO)(Ey+jELO)*=|A|2[22sin(ϕ2ϕ3)+22sin(ϕ2ϕ4)+2sin(ϕ2ϕLO)+12cos(ϕ3ϕ4)+cos(ϕ3ϕLO)+cos(ϕ4ϕLO)+2]i4(2)=(EyjELO)(EyjELO)*=|A|2[22sin(ϕ2ϕ3)+22sin(ϕ2ϕ4)2sin(ϕ2ϕLO)+12cos(ϕ3ϕ4)cos(ϕ3ϕLO)cos(ϕ4ϕLO)+2].
(31)

Afterwards, the outputs of four balance detectors are

[i1i2i3i4]=[i1(1)i1(2)i2(1)i2(2)i3(1)i3(2)i4(1)i4(2)]=[2|A|2[2sin(ϕ1ϕLO)+cos(ϕ3ϕLO)cos(ϕ4ϕLO)]2|A|2[2cos(ϕ1ϕLO)sin(ϕ3ϕLO)+sin(ϕ4ϕLO)]2|A|2[2cos(ϕ2ϕLO)sin(ϕ3ϕLO)sin(ϕ4ϕLO)]2|A|2[2sin(ϕ2ϕLO)+cos(ϕ3ϕLO)+cos(ϕ4ϕLO)]].
(32)

5. Crosstalk due to PMD

Generally, PMD is considered to be one of the major impairments in PDM systems [26

26. L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001). [CrossRef]

, 27

27. L. E. Nelson and H. Kogelnik, “Coherent crosstalk impairments in polarization multiplexed transmission due to polarization mode dispersion,” Opt. Express 7(10), 350–361 (2000). [CrossRef] [PubMed]

]. It causes the output SOP of a fully polarized input signal to vary with frequency. Due to the limited bandwidth of the signal, the orthogonal SOPs cannot be completely separated by using a PC and a PBS, which results in coherent crosstalk because of PMD. It is obvious that PMD is still one of the major obstacles in MPM systems. Thus, to analyze the impact of crosstalk due to the PMD on our 4PM system, the demodulated model is simplified as shown in Fig. 4
Fig. 4 Demodulated model of a 4PM system. PC1 and PC2 control the launch angle into fiber and PBS, respectively. CHx: channel x; CHy: channel y.
.

The 4PM-OOK signal is described by Eq. (1). The demodulated model in this paper is similar to the conventional PDM system (PC & PBS). Thus, the spectral power density coupled from Ey channel to Ex can be expressed as [26

26. L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001). [CrossRef]

]
Iyx(ω)=A˜yA˜y*(ωτ×s^Ey(0)2)2,
(33)
where the output spectral amplitude A˜y is the Fourier transform of Ay (Ay = |Ey|). ω, τ and s^Ey are the angular frequency deviation from the carrier, PMD vector, and the Stokes vector of channel y (CHy).

Considering the case of launching the signal at 45° to the principal state of polarization-maintaining fiber (PMF), we can obtain [τ×s^Ey(0)]2=(Δτ)2, where Δτ is the differential group delay (DGD). According to the definition of Iyx(ω)=A˜yx(ω)A˜yx*(ω), one can recover the spectral amplitude of crosstalk from CHy as A˜yx=j(ωΔτ/2)A˜y. Thus, by neglecting the depletion of the channel x (CHx), the output spectrum of CHx becomes A˜x(ω)=A˜x(ω)+j(ωΔτ/2)A˜y(ω). Afterwards, the Fourier transform of the spectral amplitude A˜x(ω) can be written as [26

26. L. E. Nelson, T. N. Nielsen, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Technol. Lett. 13(7), 738–740 (2001). [CrossRef]

] Ax(t)=Ax(t)+Δτ2A˙y(t), where Ax(t)Ex is the degraded signal induced by PMD, and A˙y=dAydt is the time derivative. Thus, we can obtain the expressions after PBS:

{Ex=[(22A1+12jA312jA4)+jΔτωc2(22A˙2+12jA˙3+12jA˙4)]exp[j(ωc+ϕ)]Ey=[(22A2+12jA3+12jA4)+jΔτωc2(22A˙1+12jA˙312jA˙4)]exp[j(ωc+ϕ)].
(34)

Substituting Eq. (34) into Eqs. (1)(17) and ignoring the term of Δτ2, the new expressions for the four outputs are given as

A1=A1222Δτωc(A1A˙3+A1A˙4),
(35)
A2=A2222Δτωc(A2A˙3+A2A˙4),
(36)
A3=A3+24Δτωc(A˙1+A˙2),
(37)
A4=A4+24Δτωc(A˙1+A˙2).
(38)

In these equations, the second term is the crosstalk induced by the PMD impairment. Taking channel 4 as an example, the time derivative of the interfering terms A˙1 and A˙2 imply the crosstalk only occurs at the edges of the pulse instead of during the whole pulse period. In addition, the crosstalk mainly comes from the neighboring polarization channels, while the impact from the orthogonal polarization channel can be mitigated by using signal processing algorithms.

On the other hand, when PMD-induced impairments are well compensated, polarization dependent loss (PDL) becomes a primary source of the system degradation, which has been carefully studied in PDM systems [28

28. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]

, 29

29. Z. Wang, C. Xie, and X. Ren, “PMD and PDL impairments in polarization division multiplexing signals with direct detection,” Opt. Express 17(10), 7993–8004 (2009). [CrossRef] [PubMed]

]. It is obvious that PDL degrades the signals more seriously in MPM systems. It serves to cause the power imbalance during the four polarization states, which leads to the different optical signal-to-noise (OSNR) to the tributaries. Without PMD compensation, the combining effects of PMD and PDL may lead more severe performance fluctuations or degradations [30

30. L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett. 14(2), 224–226 (2002). [CrossRef]

].

6. Setup and simulation results

The simulation setup of 4PM-OOK system as shown in Fig. 1 is performed by using OptiSim simulation platform, whose credibility has been validated in many published literatures [31

31. G. S. Kanter, A. K. Samal, O. Coskun, and A. Gandhi, “Electronic equalization for enabling communications at OC-192 rates using OC-48 components,” Opt. Express 11(17), 2019–2029 (2003). [CrossRef] [PubMed]

, 32

32. K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Temperature control of the gain spectrum of fiber optical parametric amplifiers,” Opt. Express 13(12), 4666–4673 (2005). [CrossRef] [PubMed]

]. The 10-Gbit/s NRZ-OOK signal with the wavelength of 1550-nm is generated by a Mach-Zehnder modulator with a 27-1 pseudorandom bit sequence. The signal is then split into four streams by a coupler and polarization multiplexed to generate two traditional PDM signals using PBS1 and PBS2, respectively. Here, three spools of 1-km SMF (SMF1, SMF2 and SMF3) are inserted in corresponding branches to decorrelate the data stream; and variable optical attenuators (VOAs) are applied in four channels to balance the optical power among them. In order to obtain the four SOPs multiplexing signal, two PDM signals are combined through two PCs (PC5 & PC6) and a coupler (OC2). The multiplexed signal is then launched into the SMF. Two issues should be mentioned about such multiplexing configuration: (i) the principal axis of the PBS1 is adjusted to be 45° with respect of that of PBS2; (ii) there needs to be an additional π/2phase shift in the lower arm of OC2, which can be realized by using a phase modulator (PM) or a phase shifter.

After the transmission, the multiplexed signal is divided into two orthogonal streams by PBS3 as shown in Fig. 1(b). Here, PC7 is used to align the SOP of E1 with the one of the principal axis of PBS3. Then, these two streams are respectively mixed in the 90°optical hybrid with a local oscillator laser. The outputs are detected by eight photodetectors, and digitized by analog to digital converters (ADCs), respectively. Afterwards, the phase of LO is synchronized with the transmitter laser (Fig. 2), and four polarization-channels are demodulated through a DSP unit incorporating our algorithms. In addition, the performance of demodulated signal would be degraded due to the dispersion. Thus, a feedback decision equalizer (FDE) is also required to compensate the dispersion as shown in Fig. 1(b).

Figure 5
Fig. 5 Back-to-back eye-diagrams for one typical input and four demodulated outputs.
shows the back-to-back performance of the proposed demodulator. According to the Eqs. (14)(17), all the four channels are successfully demultiplexed assisted by the digital signal processing. The eye-diagrams for all outputs are clearly open, but they exhibit different performance. It is because the expressions of Eqs. (14) and (16) (or Eqs. (15) and (17)) are different. Actually, due to the terms of (i1-i2) and (i5-i6) in Eqs. (16) and (17), four corresponding PDs (i.e. Fig. 1) can be replaced by two balance detectors (BPDs), which could significantly improve the signal performance. Thus, as expected, the signal qualities of CH3 and CH4 are better than other two channels as shown in Fig. 5.

In order to investigate the PMD crosstalk, a section of polarization-maintaining fiber with the DGD of 10.2-ps is inserted before the demodulator. As an illustration, the crosstalks coupled from CHn (n = 1~3) to CH4 are shown in Fig. 6(a)
Fig. 6 Crosstalk coupled form CH1 (a), CH2 (b) or CH3(c) to CH4 in the absence of CH4. Dash line in (a)-(c) is the bit patterns of the channel 1, 2 and 3; solid line is the bit patterns of channel 4 when there is only one input (CH1 (a), CH2 (b) or CH3 (c)). (d) Coupled spectral power density from CH1 to CH4 in absence of CH2, CH3 and CH4.
6(c), respectively. If there is only one input (E1 or E2), the crosstalk from CH1 (or CH2) is serious (solid line), while that from CH3 is slight (Fig. 6(c)). Furthermore, the interference terms A˙1 and A˙2 have opposite sign at the leading (or trailing) edge of the corresponding channel, which agrees well with the Eq. (38). In addition, the spectral power density coupled from CH1 to CH4 is also obtained when the DGD value is 10.2-ps, as shown in Fig. 6(d). The BER performance are shown in Fig. 7
Fig. 7 Back-to-back BER versus received power before PBS3.
, there is ~3-dB power difference between CH1 (or CH2) and CH3 (or CH4) at the BER of 10−9. It is the major disadvantage of this demodulation technology.

In order to overcome this shortage, the second demodulated scheme (named as 4PM-OOK-2) has been proposed as shown in Fig. 8
Fig. 8 Second demodulated scheme for 4PM-OOK systems (4PM-OOK-2).
. The OC3 is inserted before the demodulator, and split the multiplexed signal into two streams. PC7 is used to adjust the input polarization to be 45° with respect to the principal state of polarization (PSP) of PBS3, while PC8 is used to align with the input SOP and the PSP of PBS4. Following two PBSs, four streams Exx, Eyy, Ex and Ey with different polarization states are obtained, where

Exx=x^x^(22jA3+12A1+12A2)exp(jωct+ϕ),
(39)
Eyy=y^y^(22jA412A1+12A2)exp(jωct+ϕ).
(40)

Next, the signals combined with a local oscillator laser are fed into four optical hybrids, whose outputs areExx±ELO, Eyy±ELO, Ex±jELO and Ey±jELO, respectively. Then, four BPDs are used to produce the photocurrents in, which are given by

i1=2[(Exx+ELO)(Exx+ELO)*(ExxELO)(ExxELO)*]=(A1+A2)ALO,
(41)
i2=2[(Eyy+ELO)(Eyy+ELO)*(EyyELO)(EyyELO)*]=(A2A1)ALO,
(42)
i3=2[(Ex+jELO)(Ex+jELO)*(ExjELO)(ExjELO)*]=(A3A4)ALO,
(43)
i4=2[(Ey+jELO)(Ey+ELO)*(EyELO)(EyELO)*]=(A3+A4)ALO.
(44)

Therefore, the expressions of the demodulation outputs are

A1=i1i22ALO,
(45)
A2=i1+i22ALO,
(46)
A3=i3+i42ALO,
(47)
A4=i3i42ALO.
(48)

Figure 9
Fig. 9 Back-to-back eye-diagrams for the second demodulation scheme for OOK signal (4PM-OOK-2).
shows the back-to-back eye-diagrams for four demodulated outputs, which indicates that the performance of CH1 and CH2 are greatly enhanced by using the second demodulation scheme (4PM-OOK-2). The eye-diagrams for all outputs are clearly open and the demodulated performances for all channels are quite similar (i.e. the difference is negligible).

Next, to investigate the practical usage of the MPM system, we compare the back to back performance of 4 × 10Gb/s 4PM-OOK system with that of 2 × 20Gb/s PDM-QPSK system under the same spectral efficiency. Here the QPSK signal is demodulated by differential detection. As shown in Fig. 12
Fig. 12 Back to back BER of the 4PM-OOK-2 systems and the PDM-QPSK systems.
, the power penalty difference is less than 0.5-dB at the BER of 10−3 under the same bit rate. It indicates that the proposed scheme can be used as an alternative to PDM-QPSK in a flexible-rate coherent system, which demonstrates the potential of utilizing the freedom of polarization for future optical networks to further increase the system capacity and spectral efficiency. On the other hand, compared to the well-established modulation schemes, there are still lots of problems (not limitations), such as increasing transmission distance, feasibility of advanced modulation formats, and so on. However, all of these remaining issues are worth being investigated further.

Finally, we also investigate the demodulation performance when the inputs are 4 × 40Gb/s (160-Gib/s) 4PM-OOK signals. Figure 13(a)
Fig. 13 (a) Back-to-back eye-diagrams (5-ps/div) and (b) BER performance for 4 × 40Gbit/s 4PM-OOK signals when using the second demodulation scheme.
shows the back-to-back eye-diagrams for demodulated outputs. As expected, the performance of system is degraded as the bit rate increasing. The BER performance is shown in Fig. 13(b). Compared with the 40-Gb/s 4PM-OOK system, ~6-dB power penalty at the BER of 10−3 has been obtained.

7. Discussion and conclusion

We have proposed a novel configuration of signal multiplexing with four polarization states, and investigated its transmission performance over SMF. Based on coherent detection and DSP, the demodulated schemes for 4PM-OOK and 4PM-PSK were presented. We further investigated the impact of the crosstalk induced by PMD on the 4PM-OOK system. Thanks to the FDE, the dispersion could be compensated and the transmission distance was extended from ~50 km to 80 km. The performance of proposed systems was comparable to that of PDM-QPSK systems with the same spectral efficiency by comparing the back-to-back transmission. Such scheme may stimulate the explore of new freedom in high-capacity optical communication system in addition to the wavelength (WDM), the time (TDM), the space or mode (SDM) as well as multi-level modulation. While we have to admit that there are too many issues worthwhile pursuing about the new freedom, including simplifying the MUX/DEMUX configurations, accommodating advanced modulation formats, utilizing cost-effective signal processing algorithms, exploring the effects of degrading effects, etc..

Acknowledgments

This research is supported by the National Basic Research Program of China (2012CB315704), the Natural Science Foundation of China (No. 61275068, 61111140390), the Key Grant Project of Chinese Ministry of Education under Grant 313049, the 2013 Doctoral Innovation funds of Southwest Jiaotong University and the Fundamental Research Funds for the Central Universities. The authors would like thank for valuable discussions with Dr. Xiang Liu from Bell Labs, Alcatel-Lucent, and Prof. William Shieh from University of Melbourne.

References and links

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2.

P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag. 48(7), 26–30 (2010). [CrossRef]

3.

X. Liu, S. Chandrasekhar, X. Chen, P. J. Winzer, Y. Pan, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “1.12-Tb/s 32-QAM-OFDM superchannel with 8.6-b/s/Hz intrachannel spectral efficiency and space-division multiplexed transmission with 60-b/s/Hz aggregate spectral efficiency,” Opt. Express 19(26), B958–B964 (2011). [CrossRef] [PubMed]

4.

W. Shieh, “High spectral efficiency coherent optical OFDM for 1 Tb/s Ethernet transport,” presented at Optical Fiber Communication Conference 2009 (OFC2009), paper OWW1. [CrossRef]

5.

S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3. [CrossRef]

6.

D. O. Captan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5-Gsloth ptically-preamplified M-PPM with 4 photonbit receiver sensitivity,” presented at Optical Fiber Communication Conference 2005 (OFC2005), paper PDP32.

7.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22(15), 1129–1131 (2010). [CrossRef]

8.

A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432×171-Gb/s) C- and extended L-band transmission over 240 km using PDM-16-QAM,” presented at Optical Fiber Communication Conference 2010 (OFC2010), paper PDPB7.

9.

D. Y. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Q. Hu, and T. Wang, “High capacity/spectral efficiency 101.7-Tb/s WDM transmission using PDM-128QAM-OFDM over 165-km SSMF within C- and L-bands,” J. Lightwave Technol. 30(10), 1540–1548 (2012). [CrossRef]

10.

F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express 18(20), 21342–21349 (2010). [CrossRef] [PubMed]

11.

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]

12.

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

13.

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM superchannel over 7200-km of ultra-large-area fiber,” in 35th European Conference on Optical Communication,2009 (ECOC '09), paper PDPB2.6.

14.

C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express 20(11), 11718–11733 (2012). [CrossRef] [PubMed]

15.

B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19(17), 16665–16671 (2011). [CrossRef] [PubMed]

16.

N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20(3), 2668–2680 (2012). [CrossRef] [PubMed]

17.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]

18.

E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron. 12, 1129–1131 (2010).

19.

X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, and R. Lingle, “32 (320×114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber,” presented at Optical Fiber Communication Conference 2009 (OFC'2009), paper PDPB4.

20.

X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, P. Magill, M. Cvijetic, L. Nelson, M. Birk, G. Zhang, S. Ten, H. B. Mishra, and K. Snigdharaj, “64-Tb/s (640×107-Gb/s) PDM-36QAM transmission over 320km using both pre- and post-transmission digital equalization,” presented at Optical Fiber Communication Conference 2010 (OFC'2010), paper PDPB9.

21.

F. Grassi, J. Mora, B. Ortega, and J. Capmany, “Centralized light-source optical access network based on polarization multiplexing,” Opt. Express 18(5), 4240–4245 (2010). [CrossRef] [PubMed]

22.

S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PDPB2.3. [CrossRef]

23.

L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).

24.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]

25.

J. K. Rhee, D. Chowdhury, K. S. Cheng, and U. Gliese, “DPSK 32×10 Gb/s transmission modeling on 5×90 km terrestrial system,” IEEE Photon. Technol. Lett. 12(12), 1627–1629 (2000). [CrossRef]

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M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]

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Z. Wang, C. Xie, and X. Ren, “PMD and PDL impairments in polarization division multiplexing signals with direct detection,” Opt. Express 17(10), 7993–8004 (2009). [CrossRef] [PubMed]

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L.-S. Yan, Q. Yu, Y. Xie, and A. E. Willner, “Experimental demonstration of the system performance degradation due to the combined effect of polarization dependent loss with polarization mode dispersion,” IEEE Photon. Technol. Lett. 14(2), 224–226 (2002). [CrossRef]

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G. S. Kanter, A. K. Samal, O. Coskun, and A. Gandhi, “Electronic equalization for enabling communications at OC-192 rates using OC-48 components,” Opt. Express 11(17), 2019–2029 (2003). [CrossRef] [PubMed]

32.

K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “Temperature control of the gain spectrum of fiber optical parametric amplifiers,” Opt. Express 13(12), 4666–4673 (2005). [CrossRef] [PubMed]

33.

D. George, R. Bowen, and J. Storey, “An adaptive decision feedback equalizer,” IEEE Trans. Commun. Technol. 19(3), 281–293 (1971). [CrossRef]

34.

S. Chen, B. Mulgrew, and S. Mclaughlin, “Adaptive Bayesian equalizer with decision feedback,” IEEE Trans. Signal Process. 41(9), 2918–2927 (1993). [CrossRef]

35.

R. Noe, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schopflin, C. Gungener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, “Polarization mode dispersion compensation at 10, 20, and 40 Gb/s with various optical equalizers,” J. Lightwave Technol. 17(9), 1602–1616 (1999). [CrossRef]

36.

C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4230) Fiber optics and optical communications : Multiplexing
(260.5430) Physical optics : Polarization

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 1, 2013
Revised Manuscript: April 25, 2013
Manuscript Accepted: April 26, 2013
Published: May 3, 2013

Citation
Zhiyu Chen, Lianshan Yan, Wei Pan, Bin Luo, Yinghui Guo, Hengyun Jiang, Anlin Yi, Yafei Sun, and Xiaoxia Wu, "Transmission of multi-polarization-multiplexed signals: another freedom to explore?," Opt. Express 21, 11590-11605 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11590


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References

  1. L. S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J.3(2), 325–330 (2011). [CrossRef]
  2. P. J. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010). [CrossRef]
  3. X. Liu, S. Chandrasekhar, X. Chen, P. J. Winzer, Y. Pan, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “1.12-Tb/s 32-QAM-OFDM superchannel with 8.6-b/s/Hz intrachannel spectral efficiency and space-division multiplexed transmission with 60-b/s/Hz aggregate spectral efficiency,” Opt. Express19(26), B958–B964 (2011). [CrossRef] [PubMed]
  4. W. Shieh, “High spectral efficiency coherent optical OFDM for 1 Tb/s Ethernet transport,” presented at Optical Fiber Communication Conference 2009 (OFC’2009), paper OWW1. [CrossRef]
  5. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PD2.3. [CrossRef]
  6. D. O. Captan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5-Gsloth ptically-preamplified M-PPM with 4 photonbit receiver sensitivity,” presented at Optical Fiber Communication Conference 2005 (OFC’2005), paper PDP32.
  7. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett.22(15), 1129–1131 (2010). [CrossRef]
  8. A. Sano, H. Masuda, T. Kobayashi, M. Fujiwara, K. Horikoshi, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432×171-Gb/s) C- and extended L-band transmission over 240 km using PDM-16-QAM,” presented at Optical Fiber Communication Conference 2010 (OFC’2010), paper PDPB7.
  9. D. Y. Qian, M. F. Huang, E. Ip, Y. K. Huang, Y. Shao, J. Q. Hu, and T. Wang, “High capacity/spectral efficiency 101.7-Tb/s WDM transmission using PDM-128QAM-OFDM over 165-km SSMF within C- and L-bands,” J. Lightwave Technol.30(10), 1540–1548 (2012). [CrossRef]
  10. F. Yaman, N. Bai, Y. K. Huang, M. F. Huang, B. Zhu, T. Wang, and G. Li, “10 x 112Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers,” Opt. Express18(20), 21342–21349 (2010). [CrossRef] [PubMed]
  11. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express14(9), 3767–3775 (2006). [CrossRef] [PubMed]
  12. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol.26(1), 6–15 (2008). [CrossRef]
  13. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval CO-OFDM superchannel over 7200-km of ultra-large-area fiber,” in 35th European Conference on Optical Communication,2009 (ECOC '09), paper PDPB2.6.
  14. C. Antonelli, A. Mecozzi, M. Shtaif, and P. J. Winzer, “Stokes-space analysis of modal dispersion in fibers with multiple mode transmission,” Opt. Express20(11), 11718–11733 (2012). [CrossRef] [PubMed]
  15. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express19(17), 16665–16671 (2011). [CrossRef] [PubMed]
  16. N. Bai, E. Ip, Y. K. Huang, E. Mateo, F. Yaman, M. J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, V. Tse, K. Man Chung, A. P. Lau, H. Y. Tam, C. Lu, Y. Luo, G. D. Peng, G. Li, and T. Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express20(3), 2668–2680 (2012). [CrossRef] [PubMed]
  17. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics6(7), 488–496 (2012). [CrossRef]
  18. E. B. Basch, R. Egorov, S. Gringeri, and S. Elby, “Architectural tradeoffs for reconfigurable dense wavelength-division multiplexing systems,” IEEE J. Sel. Top. Quantum Electron.12, 1129–1131 (2010).
  19. X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, and R. Lingle, “32 (320×114Gb/s) PDM-RZ-8QAM transmission over 580km of SMF-28 ultra-low-loss fiber,” presented at Optical Fiber Communication Conference 2009 (OFC'2009), paper PDPB4.
  20. X. Zhou, J. J. Yu, M. F. Huang, Y. Shao, T. Wang, P. Magill, M. Cvijetic, L. Nelson, M. Birk, G. Zhang, S. Ten, H. B. Mishra, and K. Snigdharaj, “64-Tb/s (640×107-Gb/s) PDM-36QAM transmission over 320km using both pre- and post-transmission digital equalization,” presented at Optical Fiber Communication Conference 2010 (OFC'2010), paper PDPB9.
  21. F. Grassi, J. Mora, B. Ortega, and J. Capmany, “Centralized light-source optical access network based on polarization multiplexing,” Opt. Express18(5), 4240–4245 (2010). [CrossRef] [PubMed]
  22. S. Okamoto, K. Toyoda, T. Omiya, K. Kasai, M. Yoshida, and M. Nakazawa, “512 QAM (54 Gbit/s) coherent optical transmission over 150 km with an optical bandwidth of 4.1 GHz,” presented at European Conference on Optical Communication 2010 (ECOC'2010), paper PDPB2.3. [CrossRef]
  23. L. S. Yan, Z. Y. Chen, W. Pan, B. Luo, Y. H. Guo, H. Y. Jiang, A. L. Yi, X. X. Wu, W. Li, and J. G. Liu, “Transmission and demodulation of multi-polarization-multiplexed signals,” Chin. Sci. Bull. (accepted).
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