Ultra-low timing-jitter 40GHz clock recovery using EAM-MZM double ...

Ultra-low timing-jitter 40GHz clock recovery using EAM-MZM double-loop and its application in a 640Gbit/s OTDM system Deming Kong,* Hui Wang, Yan Li, Jizhao Zang, Siyuan Zhou, Xixue Jia, Jian Wu, and Jintong Lin State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, 100876, China * [email protected]

Abstract: An ultra-low timing-jitter clock recovery scheme based on EAMMZM double-loop with the ability of simultaneous time-division demultiplexing is proposed and demonstrated in a 640Gbit/s OTDM transmission system. Compared with traditional clock recovery scheme based on OEO loop, significant timing-jitter improvement of the 40GHz recovered clock is realized: from 58fs to 30fs in back-to-back configuration and from 59fs to 35fs after 400km transmission in the 100Hz to 10MHz range, without increasing the overall system complexity and cost. Enabled by the proposed clock recovery and demultiplexing scheme, error-free performance of the OTDM system is achieved after 400km transmission with an average power penalty of 4dB. ©2012 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.2360) Fiber optics links and subsystems.

References and links 1.

H. C. Mulvad, L. K. Oxenlowe, M. Galili, A. T. Clausen, L. Grüner-Nielsen, and P. Jeppesen, “1.28 Tbit/s single-polarisation serial OOK optical data generation and demultiplexing,” Electron. Lett. 45(5), 280–281 (2009). 2. H. C. H. Mulvad, M. Galili, L. K. Oxenlowe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Error-free 5.1 Tbit/s data generation on a single-wavelength channel using a 1.28 Tbaud symbol rate,” in Proceedings, Annual meeting IEEE Photonics Society, pages: PD 1.2, 2009, IEEE. 3. H. Hu, M. Galili, L. K. Oxenlowe, J. Xu, H. C. H. Mulvad, C. Peucheret, A. T. Clausen, and P. Jeppesen, “Errorfree transmission of serial 1.28 Tbaud RZ-DPSK signal,” in European Conference and Exhibition on Optical Communication (ECOC) (Optical Society of America, Washington, DC, 2010), P4.18. 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 National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPA9. 5. T. Richter, E. Palushani, C. Schmidt-Langhorst, R. Ludwig, L. Molle, M. Nölle, and C. Schubert, “Transmission of single-channel 16-QAM data signals at terabaud symbol rates,” J. Lightwave Technol. 30(4), 504–511 (2012). 6. H. Hu, H. C. H. Mulvad, C. Peucheret, M. Galili, A. T. Clausen, P. Jeppesen, and L. K. Oxenløwe, “10 GHz pulse source for 640 Gbit/s OTDM based on phase modulator and self-phase modulation,” Opt. Express 19(26), B343–B349 (2011). 7. P. Guan, T. Hirano, K. Harako, Y. Tomiyama, T. Hirooka, and M. Nakazawa, “2.56 Tbit/s/ch polarizationmultiplexed DQPSK transmission over 300 km using time-domain optical fourier transformation,” in European Conference and Exhibition on Optical Communication (ECOC) (Optical Society of America, Washington, DC, 2011), We.10.P1.80. 8. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). 9. L. Wang, N. Zhu, W. Li, and J. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach–Zehnder modulator and a chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(22), 1688–1690 (2011). 10. J. Lasri, P. Devgan, R. Tang, and P. Kumar, “Ultra-low timing jitter 40Gb/s clock recovery using a novel electroabsorption-modulator-based self-starting optoelectronic oscillator,” in the 2003 Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS’03), 2003, paper TuY6. 11. H. Tsuchida, “Simultaneous prescaled clock recovery and serial-to-parallel conversion of data signals using a polarization modulator-based optoelectronic oscillator,” J. Lightwave Technol. 27(17), 3777–3782 (2009).

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Received 7 Sep 2012; revised 25 Nov 2012; accepted 25 Nov 2012; published 7 Dec 2012

10 December 2012 / Vol. 20, No. 26 / OPTICS EXPRESS B615

12. N. Jia, T. Li, K. Zhong, J. Sun, M. Wang, and J. Li, “Simultaneous clock enhancing and demultiplexing for 160Gb/s OTDM signal using two bidirectionally operated electroabsorption modulators,” IEEE Photon. Technol. Lett. 23(21), 1615–1617 (2011). 13. Y. Ji, Y. Li, J. Wu, F. Z. Zhang, K. Xu, W. Li, X. B. Hong, and J. T. Lin, “Phase stable short pulses generator using an EAM and phase modulators for application in 160-GBaud DQPSK systems,” IEEE Photon. Technol. Lett. 24(1), 64–66 (2012).

1. Introduction Optical time-division multiplexing (OTDM) technique is a promising candidate for future high-speed transmission system to satisfy the ever increasing bandwidth demand. Breakthrough works have been reported recently, concentrating on T-baud OTDM transmission systems [1–5]. At the transmitter side, a stable, ultra-short optical pulse source with pulse-width less than several hundred femtoseconds, followed by modulation with advanced modulation formats, is required for dense time-multiplexing to fulfill the baud-rate requirement [6,7]. At the receiver side, great challenges have been raised for the clock recovery (CR) and optical demultiplexing stage. A stable clock with ultra-low timing-jitter, either optical or electrical, is of great significance to be extracted from the received OTDM signal to offer precise sychronization for the optical demultiplexing stage. Then a stabilized base-rate signal can be further processed by the receiver, enabling a good overall performance. Clock recovery has been widely developed based on optoelectronic oscillator (OEO) feedback loops, utilizing various electro-optical devices such as Mach-Zehnder modulator (MZM) [8], dual-parallel MZM (DPMZM) [9], electro-absorption modulator (EAM) [10] and polarization modulator (PolM) [11]. These schemes feature simple structure, stabilized operation, but difficult to meet the requirement of timing-jitter for ultra-high baudrate OTDM systems. Recently a 10GHz enhanced clock recovery and demultiplexing scheme with less than 300fs timing-jitter has been proposed with two EAMs aided by an electrical phase-locked loop (PLL) [12]. But it is complex, costly, with large insertion loss and a nonnegligible timing-jitter for applications in ultra-high baud-rate OTDM system. In this paper, an ultra-low timing-jitter CR scheme with the ability of simultaneous timedivision demultiplexing based on EAM-MZM double-loop is proposed and demonstrated in a 640Gbit/s dual-polarization return-to-zero quadrature phase-shift keying (RZ-QPSK) OTDM system. The performance of the proposed double-loop CR scheme is analyzed through the comparison with traditional OEO loop based CR scheme [8]. Compared with the OEO loop based scheme, the timing-jitter of the 40GHz recovered clock is reduced through the proposed double-loop scheme from 58fs to 30fs in back-to-back configuration and from 59fs to 35fs after 400km transmission in the 100Hz to 10MHz range, without increasing the overall system complexity and cost. Enabled by the proposed scheme, error-free performance of the 640Gbit/s OTDM system is achieved after 400km transmission with an average power penalty of 4dB, while a BER floor at 10−7 is observed applying the OEO based CR. Experimental results after each transmission span provides further proof of the performance improvement. Given all the benefits, the proposed scheme has potential in ultra-high baudrate OTDM systems. 2. Principles Figure 1(a) shows the proposed CR and OTDM demultiplexing scheme based on EAM-MZM double-loop, with the comparison to traditional OEO loop based scheme [8] (Fig. 1(b)). Assume that a single polarization (after polarization demultiplexing) 4 × 40Gbaud OTDM signal features a Gaussian pulse envelop, the amplitude of the 40GHz fundamental frequency component (clock) of the electrical signal M (ω1 ) after photo-detection can be expressed as (see appendix for detailed derivation process): M (ω1 ) =

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π 3π i i 1 −2 a 2 π 2 (A 0 + A1e 2 + A 2e i π + A 3e 2 ) e T

(1)



where T , A n (n =0,1,2,3) represent the symbol duration and the normalized pulse amplitude of each tributary. a is a factor proportional to the 3dB pulse-width, defined in the appendix. According to Eq. (1), if the four tributaries feature the same amplitude, there will be no 40GHz component. In order to enhance the fundamental frequency clock, one easy way is to make the amplitude of the four tributaries uneven. A maximum amplitude value of 40GHz clock component can be got if two adjacent tributaries feature maximum amplitude and the other two tributaries are suppressed to minimum. But it is difficult to realize. It should be pointed out that in real optical multiplexing, the four tributaries will have slightly amplitude difference so that the fundamental frequency clock can be directly extracted by a simple OEO loop. And the greater the fundamental frequency clock, the better phase noise performance of the recovered clock. A much simpler way to enhance the fundamental frequency clock without increasing the complexity is to form a second feedback loop by connecting the output of the demultiplexing unit (EAM) to the input of the OEO loop based clock recovery unit (Fig. 1(a)). The second loop ensures that only the demultiplexed 40Gbaud base-rate tributary is injected to the OEO (e.g. A 0 =1, A1 =0, A 2 =0, A 3 =0 ), compared to the circumstance with the injection of 4 × 40Gbaud OTDM signal with slightly amplitude difference on each tributary (Fig. 1(b)). This scheme is referred to EAM-MZM double-loop in this article. The double-loop also features self-starting and simultaneous demultiplexing, without increasing the overall system complexity and cost. 3. Experimental setup

Fig. 1. (a) The proposed EAM-MZM based double-loop clock recovery and demultiplexing scheme and (b) the traditional OEO based scheme, used in the (c) 640Gbit/s OTDM transmission system.

Figure 1(c) shows the setup of the 640Gbit/s-400km OTDM system. A phase-stabilized 1.8ps ultra-short pulse source with a repetition rate of 40GHz at 1550nm [13] is QPSK modulated by two de-correlated 40Gbit/s electrical non-return-to-zero (NRZ) signal with a pattern length of 27-1, then 4 times multiplexed and polarization-multiplexed to a 640Gbit/s RZ-QPSK OTDM signal. Then the signal is launched to a 5-span optical link. Each span consists of 80km standard SMF, 10km DCF to compensate the chromatic dispersion (CD), two inline EDFAs (ILA) to compensate the insertion loss and a variable optical attenuator (VOA) to adjust the optimum injection power. Two 3nm optical BPFs are inserted after 160km and 400km to suppress the accumulated ASE noise. The average launch power of the first span is 7dBm. The received OTDM signal is processed by either the proposed EAM-MZM double-loop based CR and demultiplexing module (Fig. 1(a)) or the OEO based (Fig. 1(b)) module. The OTDM signal is first polarization-demultiplexed to a 160baud RZ-QPSK OTDM signal. Then the signal is fed to an EAM for demultiplexing. The 40GHz clock signal is extracted using an

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OEO feedback loop, which consists of a 50GHz photodetector (PIN) with a responsivity of 0.65 for optical-to-electrical conversion, a low noise amplifier (LNA) with a noise figure less than 4dB and small signal gain of 48dB, a band-pass filter (BPF) with a 3dB bandwidth of 20MHz and out-of-band suppression larger than 50dB, a power amplifier (PA) with saturation output power of 27dBm, an attenuator with a phase shifter to adjust the feedback clock signal and a power splitter to close the loop. In the proposed double-loop (Fig. 1(a)), the demultiplexed signal is split by a 3dB optical coupler and fed back into the OEO loop. While in the OEO based scheme (Fig. 1(b)), the demultiplexed 40Gbaud signal is directly fed into the demodulation stage. The average input power of the MZM and the EAM is kept to 10dBm and 4dBm for both schemes. The demultiplexed 40Gbaud RZ-QPSK signal is then launched to a 40Gbaud selfcoherent receiver for demodulation and bit-error rate (BER) testing. The differential detection is processed without precoding at the transmitter side and the BER tester is programmed to receive the expected data. 4. Results and discussions

The experimental results, including baseline test, performance of the proposed scheme with comparison to OEO based scheme, under continuous wave (CW) injection, under 40Gbaud single tributary injection, in back-to-back configuration and after 400km transmission, are shown below respectively. 4.1 Baseline test -50

E8257D OUT, raw E8257D OUT, fitted

-70

SB Phase Noise (dBc/Hz)


-50

-90 -110 -130 -150 2 10

10

3

4

5

10 10 Frequency Offset (Hz)

6

10

7

10

Filter + PA OUT, raw Filter + PA OUT, fitted

-70 -90 -110 -130 -150 2 10

10

3

4

5


6

10

7

10

Fig. 2. Measured phase noise (a) from RF source and (b) after power amplifier (PA).

Figure 2(a) shows the phase noise performance of the radio frequency (RF) source at 40GHz. Figure 2(b) gives the results when the RF signal is amplified by the power amplifier. The results explain that, the 4kHz side-mode component on all the phase noise results, comes from the electrical power amplifier. 4.2 CW and 40Gbaud single tributary data injection

Figure 3(a) gives the results when CW light is injected into the two schemes for comparison. The phase noise results indicate that both CR modules are not locked. But it can be concluded that the EAM-MZM double-loop based CR has a better noise suppression. Figure 3(b) shows the results when only one 40Gbaud tributary is injected into the clock recovery modules. Both schemes feature almost identical phase noise performance. The calculated timing-jitter values of the recovered clock are 31.7fs and 30.5fs, integrated from the raw data of the phase noise in the 100Hz to 10MHz range results using trapezoidal interpolation (same for the following of this article), for OEO based CR module and EAMMZM double-loop based CR module respectively. The test, compared to following results, in some degree confirms that for both of the two schemes, the 40GHz fundamental frequency

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component is great enough for a good clock recovery performance under single tributary injection. -50 OEO, CW in, RAW OEO, CW in, fitted EAM-MZM DP, CW in, RAW EAM-MZM DP, CW in, fitted

-40 -60



-20

-80 -100 -120 -140 -150 2 10

3

10

4

5


10

6

10

7

OEO loop, 40G IN, RAW OEO loop, 40G IN, fitted EAM-MZM DP, 40G IN, RAW EAM-MZM DP, 40G IN, fitted

-70 -90 -110 -130 -150 2 10

3

4

10

5


10

6

10

7

Fig. 3. Phase noise performance of the proposed EAM-MZM double-loop and the OEO on (a) under CW injection and (b) under 40Gbaud single tributary injection.

4.3 Results in back-to-back configuration

-70

-111dBc/Hz @ 1MHz

-90 -110

Jitter: 58-fs

3

4

5


(a)

0

320Gbaud dual-pol.

-10

Pol.1

-20

25ps

-30

-20

-40

20dB

-50

-40

160Gbaud single-pol.

-60

Pol.2

-70 1545 1547

(a)

1549 1551 1553 1555 Wavelength (nm)

(b)

-60

Jitter: 30-fs 10

EAM-OEO DL, B2B OEO, B2B

25ps

0

-129dBc/Hz @ 1MHz

-130 -150 2 10

20

OEO, B2B, RAW OEO, B2B, fitted EAM-MZM DP, B2B, RAW EAM-MZM DP, B2B, fitted

Power (dBm)


-50

10

6

10

7

-80 -5

-4

-3

-2 -1 0 1 2 Offset Frequency (Hz)

3

(b)

4 x 10

5 4

Fig. 4. (a) Phase noise results of the two schemes in back-to-back configuration. (b) The corresponding electrical spectrums of the recovered 40GHz clock with insets show (a) optical eye-diagrams of the 640Gbit/s OTDM signal; (b) optical spectrums of single-polarization and dual-polarization OTDM signals.

Figure 4(a) gives the phase noise performance in back-to-back configuration of the proposed EAM-MZM double-loop and the OEO schemes with injection of the 640Gbit/s OTDM signal. A great improvement of the phase noise from 100kHz to 10MHz range is observed. A timing-jitter of as low as 30fs can be calculated from the raw data for the EAM-MZM doubleloop. While for the OEO based CR, the timing-jitter is calculated to be 58fs. It could be concluded that EAM-MZM double-loop better tolerates the signal with weak fundamental frequency component. The results can be well explained according to Eq. (1) as it becomes 2

2

M (ω1 ) =(A / T )e −2a π when the feedback provides only 40Gbaud signal to the MZM-EAM double-loop which has a much stronger fundamental frequency component than the OTDM signal (see appendix for more information). Figure 4(b) shows the corresponding electrical spectrums of recovered clock. Inset (a) shows OTDM signal on two orthogonal polarizations. Inset (b) gives the optical spectrums of the OTDM signal, for both single-polarization and dual-polarization.

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4.4 Results after 400km transmission

Figure 5(a) illustrates the phase noise performance of the two CR schemes with the injection of the OTDM signal transmitted 400km. The results are barely changed compared to the back-to-back configuration (Fig. 4(a)). The timing-jitter calculated for schemes based on EAM-MZM double-loop and OEO loop are 35fs and 59fs respectively. Figure 5(b) shows the electrical spectrums of recovered clock after 400km transmission. Inset (a) shows the eye-diagrams of polarization-demultiplexed OTDM signal after 400km transmission. Insets (b) and (c) give the eye-diagrams of demultiplexed 40Gbaud RZ-QPSK signal using OEO and EAM-MZM double-loop respectively, in which much more clear eyediagrams of the demultiplexed signal are achieved using the proposed scheme, indicating the demultiplexed signal has a much smaller timing-jitter. Inset (d) gives the optical spectrums of the received OTDM signal on two orthogonal polarizations. 20

OEO, 400km, RAW OEO, 400km, fitted EAM-MZM DP, 400km, RAW EAM-MZM DP, 400km, fitted

-90 -110

-20 -40 -60

-130 -150 2 10

EAM-MZM DL, 400km OEO loop, 400km

0 Optical Power (dBm)

-70

Power (dBm)


-50

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3

4

5


6

10

10

7

-80 -5

-4

-3

-2 -1 0 1 2 Offset Frequency (Hz)

3

4

5 4

x 10

Fig. 5. (a) Phase noise results of the two schemes after 400km transmission. (b) Spectrums of recovered clock after 400km transmission, with insets show (a) received OTDM signal (depolarized); (b) demultiplexed 40Gbaud RZ-QPSK signal using OEO based scheme; (c) demultiplexed 40Gbaud RZ-QPSK signal using EAM-MZM double-loop based scheme (d) optical spectrums of the received OTDM on two polarizations.

Timing Jitter (ps)

70

OEO loop EAM-MZM double loop E8257D

60 50 40 30 0

80

160

240

320

Transmission Distance (km)

400

Fig. 6. Calculated timing-jitter after each transmission span (80km), suggesting EAM-MZM based CR has a better and stable performance along the whole transmission spans.

Figure 6 gives the calculated timing-jitter of the two CR schemes from phase noise measured after each transmission span. It suggests that the proposed CR scheme based on EAM-MZM double loop has a better and stable performance during the whole transmission spans. Figure 7(a) illustrates the BER performance of both schemes with comparison to the performance of a 40Gbaud RZ-QPSK signal in back-to-back configuration. The power penalty is 3dB and 2dB for OEO and EAM-MZM double-loop based schemes respectively in #175582 - $15.00 USD

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40G QPSK I 40G QPSK Q OEO, B2B, I OEO, B2B, Q OEO, 400km, I OEO, 400km, Q EAM-MZM DL, B2B, I EAM-MZM DL, B2B, Q EAM-MZM DL, 400km, I EAM-MZM DL, 400km, Q

2

-log(BER)

3 4 5 6 7 8 9 10 11 -11 -10 -9

-8

-7

-6

-5

-4

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-1

0

1

Sensitivity @BER=1e-9 (dBm)

back-to-back configuration. BER floor is observed at a BER value of 10−7 after 400km transmission with OEO based scheme while error-free performance is achieved with a power penalty of 4dB with the EAM-MZM double-loop based scheme. It could be concluded that the EAM-MZM double-loop has greatly improved the overall system performance, enabled 400km error-free transmission of the 640Gbit/s OTDM signal. Figure 7(b) gives the measured system sensitivity using EAM-MZM double-loop as CR. The optical power is measured before the optical delay interferometer. Both the in-phase tributary and the quadrature tributary are measured. -6.0 EAM-MZM DL, I Trib EAM-MZM DL, Q Trib

-5.5 -5.0 -4.5 -4.0 -3.5

Received Power (dBm)

0

80

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400

Fig. 7. (a) BER results show BER floor is eliminated by utilizing EAM-MZM double-loop based CR and demultiplexing scheme, enabling error-free performance of 640Gbit/s OTDM signal after 400km transmission. (b) Measured system sensitivity as a function of transmission distance (5 spans).

5. Conclusion

An EAM-MZM double-loop based clock recovery scheme with the ability of simultaneous demultiplexing is proposed, analyzed and experimentally demonstrated compared to traditional OEO based scheme. A detailed principle is firstly introduced. Then a baseline test is carried out before the proposed scheme being applied in a 640Gbit/s dual-polarization RZQPSK OTDM system. The proposed double-loop scheme could greatly reduce the timingjitter of the 40GHz recovered clock from 58fs to 30fs in back-to-back configuration and from 59fs to 35fs after 400km transmission in the 100Hz to 10MHz range, compared with OEO loop, without increasing system complexity and cost. Employing the proposed scheme, errorfree performance of the OTDM system is achieved after 400km transmission with an average power penalty of 4dB. Given all these benefits, our scheme has potential in ultra-high-speed OTDM systems. Appendix

A detailed derivation process of Eq. (1) is given in this section. Discussions of this equation are also provided. The electrical signal after photo-detection inherits the optical intensity profile and could be seen as periodic signals which according to the Fourier series could be expressed as: m (t ) =

+∞

 M (k ω ) ⋅ e

k =-∞

1

jk ω1t

(2)

k and ω1 represent the order of the frequency components and the fundamental frequency. The Fourier coefficients are:

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M (k ω1 ) =

1 T



t 0 +T

t0

f (t ) ⋅ e - jk ω1t dt ,

(3)

which provides amplitude-frequency characteristic ( M (k ω1 ) ) and phase-frequency characteristic. Assume that the four tributaries of the OTDM signal features a Gaussian-shaped pulse profile, evenly distributed in time, with normalized amplitudes of A 0 ,A1 ,A 2 ,A 3 , then the photo-detected signal can be expressed as: +∞

m (t )=  [f (t )+f (t n =-∞

nT 2 nT 3nT )+f (t )+f (t )]. 4 4 4

The Gaussian-shaped pulse can be written as f (t )=

1

σ ⋅ 2π

exp (-

(4)

t2 ), then we have: 2σ 2

nT 2 (t ) t2 4 m (t ) = A A [ exp () exp () +  0 1 2σ 2 2σ 2 σ ⋅ 2π n = - ∞ 2nT 2 3nT 2 (t ) (t ) 4 4 ) exp ()]. A + A 2 exp (+ 3 2σ 2 2σ 2 +∞

1

(5)

T T ,T - ]. Assume that 8 8 each pulse is narrow enough, then only four pulses (one OTDM period) need to be considered:

For convenience, the integration range of Eq. (3) can be changed to [-

T (t - ) 2 t2 4 ) m (t ) = [A 0 exp (- 2 ) + A1 exp (2σ 2σ 2 σ ⋅ 2π 2T 2 3T 2 (t ) (t ) 4 4 )]. + A 2 exp (+ ) A exp (3 2σ 2 2σ 2 1

(6)

T T ,T - ] approaches zero 8 8 according to Eq. (6), so the integration range of Eq. (3) could be expanded to [-∞,+∞].

In Eq. (3), the integral value outside the integration range [-

Assume σ =aT , then the 3dB pulse-width FW HM = 2 aT ⋅ 2 ln 2. By substitute Eq. (6) to Eq. (3), T (t - ) 2 t2 4 M (k ω1 ) =  [A0 exp (- 2a 2T 2 ) + A1 exp (- 2a 2T 2 ) 2π ⋅aT 2 - ∞ 2T 2 3T 2 (t ) (t ) 4 4 )]e - jk ω1t dt . + A 2 exp (+ ) exp (A 3 2a 2T 2 2a 2T 2 1

+∞

(7)

The integration can be easily done by a computer program:

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M (k ω1 ) =

kπ 3k π i i 1 −2a 2 k 2π 2 e (A 0 + A1e 2 + A 2e ik π + A3e 2 ). T

(8)

The fundamental frequency component can be expressed as: π 3π i i 1 −2 a 2 π 2 e (9) (A 0 + A1e 2 + A 2e i π + A 3e 2 ). T If A 0 =A1 =A 2 =A 3 =A , according to Eq. (8), M (ω1 ) = M (2ω1 ) = M (3ω1 ) =0 and

M (ω1 ) =

4 −32a 2π 2 e A , which means only 160GHz component exists. The signal can be T seen as a single 160Gbaud signal. To maximize M (ω1 ) , the amplitudes of two adjacent OTDM tributaries must feature M (4ω1 ) =

2 −2 a 2 π 2 e A . The T OTDM signal now can be seen as a 40Gbaud signal with two pulses on each symbol-slot. If only one tributary takes the maximum amplitude and the others take minimum (or the opposite condition), which can be realized after time-division demultiplexing, then 2 2 1 M (ω1 ) = e −2a π A . T

maximum and the other two feature minimum (zero). In this case, M (ω1 ) =

Acknowledgment

This work was supported in part by the 863 program 2012AA011303, in part by the 973 Program 2011CB301702, in part by NSFC, under program 61001121, program 60932004, and program 61006041, and in part by the Fundamental Research Funds for the Central Universities.

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