All-optical Nyquist-OTDM to Nyquist-WDM conversion for high-granular flexible optical networks

Satoshi Shimizu; Gabriella Cincotti; Naoya Wada

doi:10.1364/OE.25.003496

1. Introduction

To deal with the drastically increasing network traffic in the internet, both time and frequency division multiplexing techniques, as well as spectral efficient modulation and multiplexing techniques, are developed for the effective use of the limited spectral resources. On the other hand, flexible optical channel control is also an important technology to fully utilize the network resources in dynamically changing network traffic [1–7]. The optical Nyquist pulse coding is one of the most spectral efficient modulation techniques, because its spectral bandwidth is exactly same as the signal baud-rate frequency, and both optical time division multiplex (Nyquist-OTDM) and wavelength division multiplex (Nyquist-WDM) are investigated for spectral efficient large capacity transmission [8,9]. The Nyquist-OTDM is the better solution for an ultra-high capacity single channel transmission such as over 1 Tbit/s transport system, whereas the Nyquist-WDM is better for the high granular flexible channel control, such as add-drop operation at the network node [10–12]. For future highly flexible optical network, they are expected to co-exist in the same networks and seamless conversion between time and frequency domain is needed. As illustrated in Fig. 1, Nyquist-OTDM-based transport system and Nyquist-WDM-based add-drop system can be combined, where a part of wavelength of OTDM signal is aggregated to add-drop network as Nyquist-WDM format, by using MUX-format conversion from OTDM to WDM, and higher flexibility and effective resource management can be possible. In some approaches to OTDM-to-WDM conversion, complicated phase modulation with highly nonlinear fiber and optical Fourier transform are employed [13,14], while another approach uses a specially designed optical filter and optical time-lens effect [15].

Fig. 1 Nyquist-OTDM and Nyquist-WDM systems (a) without MUX-format conversion, and (b) with MUX-format conversion.

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In this paper, we propose and demonstrate the multiplexing(MUX)-format conversion from Nyquist-OTDM to Nyquist-WDM by using a simple phase modulator and an optical Nyquist filter [16]. A Nyquist-OTDM signal is phase-modulated by a sinusoidal wave with half frequency of the signal baud-rate. The rising and falling of the phase modulation corresponds to the blue- and red-shift of the carrier frequency. Therefore, the phase-modulated signal becomes a multiplexing of the blue- and red-shifted signals with half baud-rate, and the optical Nyquist filtering achieves the Nyquist-WDM signal. The bit-error-rate (BER) measurement revealed that the MUX-format conversion has been successfully achieved for 50 Gbaud to 2 x 25 Gbaud (50G-25G) and 25 Gbaud to 2 x 12.5 Gbaud (25G-12.5G) conversions. In addition, a 50 Gbaud Nyquist signal is converted to four channels of 12.5 Gbaud signals by cascading two stages of MUX-format converters. The optimum driving condition of the phase modulator is theoretically investigated and 0.913V_π is found to be the optimum condition to achieve the perfect separation between blue- and red-shifted signals, and it is experimentally verified.

2. Operation principle

Figure 2 shows the system configuration of the MUX-format converter. The phase modulator (PM) is a simple straight-type LiNbO₃ (LN) modulator driven by a sinusoidal wave with half frequency of the signal baud-rate. The phase modulation by a sinusoidal wave corresponds to the frequency modulation with cosine wave; the rising and falling of the phase are the blue- and red-shift of the carrier frequency, respectively. Therefore, each symbol of the signal has different carrier frequency with respect to the adjacent symbols as illustrated in Fig. 2(a), and the signal becomes a WDM of two different carrier frequency channels with half baud-rate. The driving voltage for the phase modulator should be decided to achieve the highest separation between blue- and red-shifted components, and the value can be theoretically determined. The incoming Nyquist signal x(t) can be expressed as Eq. (1),

\begin{array}{l} x (t) = \sum_{n} A_{n} h_{0} (t - n T) \\ h_{0} (t) = \frac{\sin (2 π f_{0} t)}{2 π f_{0} t}, f_{0} = \frac{1}{2 T} \end{array}

where A_n is the complex amplitude of the n_th data-bit, h₀(t) is the sinc pulse waveform for original signal baud-rate, and T is the symbol time interval of original signal. The sinc pulse waveform h₀(t) can be transformed as follows,

\begin{array}{l} h_{0} (t) = \frac{\sin (2 π f_{0} t)}{2 π f_{0} t} = \frac{\sin (2 π \frac{f_{0}}{2} t)}{2 π \frac{f_{0}}{2} t} \cos (2 π \frac{f_{0}}{2} t) \\ = h (t) \cdot \frac{1}{2} (e^{- 2 π f_{m} t} + e^{+ 2 π f_{m} t}) \\ h (t) = \frac{\sin (2 π f_{m} t)}{2 π f_{m} t} = h_{0} (\frac{t}{2}), f_{m} = \frac{f_{0}}{2} . \end{array}

By substituting Eq. (2) to Eq. (1), we get

\begin{array}{l} x (t) = \frac{1}{2} \sum_{n} A_{n} h (t - n T) \cdot (e^{- j 2 π f_{m} (t - n T)} + e^{+ j 2 π f_{m} (t - n T)}) \\ = ​ \frac{1}{2} \sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{- j 2 π f_{m} t} + \frac{1}{2} \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{+ j 2 π f_{m} t} . \end{array}

The first and second terms correspond to the lower (−f_m) and higher ( + f_m) frequency components, respectively, as illustrated in Fig. 2(b). If we apply a phase modulation on the signal, the resultant spectrum would be a convolution of the signal and multi tones generated by the phase modulation, as illustrated in Fig. 2(b). Because the Nyquist filter in Fig. 2(a) has the same bandwidth as the original Nyquist signal, we will focus only on the first-order side-bands. According to the phase modulation theory, the amplitude of the side-band can be expressed by using Bessel function of the first kind [17], and therefore the generated side-band components x₀(t), x₁(t), and x₋₁(t) can be expressed as bellow.

\begin{array}{l} x_{0} (t) = J_{0} (β) \cdot \frac{1}{2} {\sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{- j 2 π f_{m} t} + \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{+ j 2 π f_{m} t}}, \\ x_{1} (t) = J_{1} (β) \cdot \frac{1}{2} e^{+ j 2 π \cdot 2 f_{m} t} {\sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{- j 2 π f_{m} t} + \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{+ j 2 π f_{m} t}} \\ = J_{1} (β) \frac{1}{2} {\sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{+ j 2 π f_{m} t} + \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{+ j 2 π \cdot 3 f_{m} t}}, \\ x_{- 1} (t) = J_{- 1} (β) \cdot \frac{1}{2} e^{- j 2 π \cdot 2 f_{m} t} {\sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{- j 2 π f_{m} t} + \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{+ j 2 π f_{m} t}} \\ = J_{- 1} (β) \frac{1}{2} {\sum_{n} A_{n} e^{+ j \frac{π}{2} n} h (t - n T) e^{- j 2 π \cdot 3 f_{m} t} + \sum_{n} A_{n} e^{- j \frac{π}{2} n} h (t - n T) e^{- j 2 π f_{m} t}}, \end{array}

where J_n(β) is the n_th order Bessel function, β is the modulation index, and j is the imaginary unit. If we ignore the out-of-band components ( ± 3f_m) and use the relation J₋₁(β) = −J₁(β), the output signal y(t) = x₀(t) + x₁(t) + x₋₁(t) can be expressed,

\begin{array}{l} y (t) = \frac{1}{2} \sum_{n} A_{n} (J_{0} (β) e^{+ j \frac{π}{2} n} - J_{1} (β) e^{- j \frac{π}{2} n}) h (t - n T) e^{- j 2 π f_{m} t} \\ + \frac{1}{2} \sum_{n} A_{n} (J_{0} (β) e^{- j \frac{π}{2} n} + J_{1} (β) e^{+ j \frac{π}{2} n}) h (t - n T) e^{+ j 2 π f_{m} t} . \end{array}

If we choose β to satisfy J₀(β) = J₁(β), Eq. (5) becomes,

\begin{array}{l} y (t) = \frac{1}{2} J_{0} (β) {\sum_{n} A_{n} (e^{+ j \frac{π}{2} n} - e^{- j \frac{π}{2} n}) h (t - n T) e^{- j 2 π f_{m} t} \\ + \sum_{n} A_{n} (e^{- j \frac{π}{2} n} + e^{+ j \frac{π}{2} n}) h (t - n T) e^{+ j 2 π f_{m} t}} \\ = \frac{1}{2} J_{0} (β) {\sum_{m} A_{2 m + 1} h (t - (2 m + 1) T) e^{- j (2 π f_{m} t + \frac{π}{2})} + \sum_{m} A_{2 m} h (t - 2 m T) e^{+ j 2 π f_{m} t}}, \end{array}

where m is an integer. The first term is the half baud-rate Nyquist signal with red-shifted carrier frequency (−f_m), whereas the second term is the one with blue-shifted carrier frequency ( + f_m). In this way, the Nyquist OTDM signal is converted to the WDM signal of two Nyquist channels with half baud-rate. To satisfy the condition J₀(β) = J₁(β), the modulation index β should be 1.435 and it corresponds to the driving voltage of 0.913V_π for the phase modulator. As can be seen in Eq. (6), the result does not depend on the data amplitude A_n, and it means that this technique can work for any kind of modulation format.

Fig. 2 The system configuration (a) and spectrum schematics (b).

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3. Experimental demonstration

Figure 3 shows the experimental setup for the 25G-12.5G and 50G-25G conversions. For 25G-12.5G conversion, carrier suppressed return-to-zero (CS-RZ) modulation is applied to the continuous wave (CW) laser light source with the frequency of 193.250 THz by using single Mach-Zehnder modulator (MZM) driven by a 12.5 GHz clock, and 25 Gbaud quadrature phase shift keying (QPSK) signal is directly generated by 25 Gbaud electrical data sequence and IQ-MZM. The following optical Nyquist filter with 25 GHz bandwidth is used for the Nyquist spectral shaping, which extract the 25 GHz flat-top region of the spectrum after the data-modulation [10]. The roll-off factor of the filter is 0.15. In 50G-25G conversion, two cascaded MZM driven by 12.5 GHz clocks for three tones generation were used, and 2x1 fiber-based OTDM circuit followed by a 50 GHz optical Nyquist filter with 0.075 roll-off factor, which extract 50 GHz flat-top region of the signal spectrum, generates a 50 Gbaud Nyquist QPSK signal, as illustrated in Fig. 3(b). In the MUX-format converter in Fig. 3(c), the driving voltage for the phase modulator is determined to achieve the highest separation between the blue- and red-shifted components, which is 0.913V_π of the modulator, as derived in Section 2. After the phase modulation, the signal spectrum has several extra side-bands and the following optical Nyquist filter removes these side-band components to make a Nyquist-WDM signal. In this scheme, the optical power loss is inevitable due to the reduction of extra side-band components, and it may lead to penalty to the system. In addition, a clock recovery function will be mandatory for this scheme to align the phase of sinusoidal modulation waveform, according to the theory discussed in Section2. However, in this proof-of-concept experiment, we do not implement this functionality. The converted Nyquist-WDM signal is de-multiplexed by another optical Nyquist filter with half bandwidth. Then, the signal is received by a coherent receiver to measure the bit-error-rate (BER), where duo-binary filter is applied to reduce the cross-talk effect [12].

Fig. 3 Experimental setup of (a) 25Gbaud Nyquist signal, (b) 50Gbaud Nyquist signal, and (c) MUX-format conversion and receiver system.

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Figure 4 shows the experimental spectra of 25G-12.5G and 50G-25G conversion. (i)-(iv) correspond to the input signal, output of the phase-modulator, output of MUX-format converter, and the output of de-multiplexing Nyquist filter, respectively, as indicated in Fig. 3(c). The insets are the received eye-diagrams of before and after MUX-format conversion. In both baud-rate cases, the single Nyquist signal is successfully converted to the WDM signal. Even after the de-multiplexing, the eye-diagrams show clear eye-opening, although 12.5 Gbaud signals are suffering from relatively larger cross-talk due to the larger roll-off factor of the optical Nyquist filter. These cross-talk components can be suppressed by duo-binary filter at the receiver. The output spectrum from the phase modulator in 50G-25G case is asymmetric due to the distortion of the driving sinusoidal wave for the phase modulator, and it will affect the BER performance.

Fig. 4 Experimental spectra and eye-diagrams for (a) 25G-12.5G conversion and (b) 50G-25G conversion.

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Figure 5 shows the measured BERs for both conversion cases as functions of optical signal-to-noise ratio (OSNR), and the insets are the constellations of the received signals after the duo-binary filter, which is the reason of nine-point constellation. The data-sequences applied to I- and Q-channels are 2²³−1 and 2¹⁵−1 pseudo random binary sequences (PRBSs), respectively. In 50G-25G conversion case, BER of Back-to-Back (B-to-B) is measured for the original 25 Gbaud signal before OTDM, due to the bandwidth limitation of the receiver: an oscilloscope with 13 GHz bandwidth. In both cases, MUX-format conversions have been successfully achieved with low OSNR penalties, although 0.5 dB penalty was observed in 50G-25G case at the BER = 10⁻⁵. This is due to the distorted sinusoidal waveform for the modulator, whose effect can be seen in Fig. 4(b)-(ii), and the effect of the optical power loss in the phase modulation and filtering was quite small.

Fig. 5 BER and constellation of (a) 25G-12.5G, (b) 50G-25G.

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To verify the theory discussed in Section 2, we measured the error-vector-magnitude (EVM) for different modulation amplitude for the phase-modulator. In Fig. 6(a), the measured EVM for blue- and red-shifted signals are plotted as functions modulation voltage amplitude in 25G-12.5G conversion. The graph shows the minimum EVM at the modulation voltage of 4.95 V. Figure 6(b) shows the optical spectrum of the phase-modulated CW laser light source with 4.95 V modulation voltages. As can be seen in the spectrum, the center three tones have the same magnitude, which means that the operation condition is exactly same as the theory discussion in Section 2, where J₀(β) = J₁(β) is satisfied.

Fig. 6 (a) The measured EVMs as functions of the driving voltage for the phase modulator, and (b) spectrum of phase-modulated CW laser with the driving voltage of minimum EVM condition, in 25G-12.5G conversion.

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Finally, we tried cascaded MUX-format conversion: 50G-25G-12.5G conversion. Figure 7 shows the system setup. The 50 Gbaud Nyquist signal is first converted to 25 Gbaud x 2 Nyquist WDM signal, and each de-multiplexed 25 Gbaud signal is converted to 12.5 Gbaud x 2 Nyquist WDM signal. The BERs for all the converted channels are measured. In Fig. 8, all the converted channels show almost same performances and very low OSNR penalties compared to the original signal, whose BER is shown in Fig. 5.

Fig. 7 Experimental setup for the cascaded MUX-format conversion.

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Fig. 8 BERs and constellations for the cascaded MUX-format converter.

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In principle, the direct conversion from 50G to 4x12.5G (or more channels) will be possible. To achieve such operation, LN-PM should be replaced by IQ-MZM for complex modulation and the driving signal should be a complex analog waveform instead of a simple sinusoidal wave, which generate many tones spectrum. The main limitation factor will be the accuracy of the modulation waveform and the roll-off factor of the original signal. The modulation waveform accuracy will directly affect the separation of converted WDM channels, and the roll-off factor will affect the cross-talk between WDM channels.

4. Summary

We have proposed and experimentally demonstrated all-optical MUX-format conversion from Nyquist OTDM to Nyquist WDM. The system is simply configured with straight-type phase modulator and optical Nyquist filter. In the theoretical investigation, it is proved that the single Nyquist signal can be completely converted to Nyquist WDM signal which contains two channels of half-baud-rate signals. The modulation voltage for the phase modulator is slightly lower than V_π of the modulator: 0.913 V_π, where J₀(β) = J₁(β) is satisfied.

In the experimental demonstrations, 50G-25G and 25G-12.5G conversions were successfully demonstrated and the OSNR penalties were quite low (<0.5dB). The theoretical operation condition was experimentally verified and the optical spectrum of CW laser proved that the operation condition satisfy J₀(β) = J₁(β). Finally, cascaded MUX-format conversion was also demonstrated; 50 Gbaud Nyquist signal was converted to four channels of 12.5 Gbaud Nyquist signals with negligible OSNR penalties.

References and links

1. O. Gerstel, M. Jinno, A. Lord, and S. J. Ben Yoo, “Elastic optical networking: A new dawn for the optical layer?,” IEEE Communications Magazine, S12–S20, February (2012).

2. M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Communications Magazine, 138–145, August (2010).

3. M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, T. Yoshimatsu, T. Kobayashi, Y. Miyamoto, K. Yonenaga, A. Takada, O. Ishida, and S. Matsuoka, “Demonstration of novel spectrum-efficient elastic optical path network with per-channel variable capacity of 40 Gb/s to over 400 Gb/s,” in Proceedings of European Conference on Optical Communication2008 (ECOC2008), Th.3.F.6. [CrossRef]

4. Y. Yin, K. Wen, D. J. Geisler, R. Liu, and S. J. B. Yoo, “Dynamic on-demand defragmentation in flexible bandwidth elastic optical networks,” Opt. Express 20(2), 1798–1804 (2012). [CrossRef] [PubMed]

5. N. Amaya, M. Irfan, G. Zervas, K. Banias, M. Garrich, I. Henning, D. Simeonidou, Y. R. Zhou, A. Lord, K. Smith, V. J. F. Rancano, S. Liu, P. Petropoulos, and D. J. Richardson, “Gridless optical networking field trial: flexible spectrum switching, defragmentation and transport of 10G/40G/100G/555G over 620-km field fiber,” in Proceedings of European Conference on Optical Communication2011 (ECOC2011), Th.13.K.1. [CrossRef]

6. K. Sone, X. Wang, S. Oda, G. Nakagawa, Y. Aoki, I. Kim, P. Palacharla, T. Hoshida, M. Sekiya, and J. C. Rasmussen, “First demonstration of hitless spectrum defragmentation using real-time coherent receivers in flexible grid optical networks,” European Conference on Optical Communication 2012 (ECOC2012), Th.3.D.1. [CrossRef]

7. H. N. Tan, T. Inoue, K. Tanizawa, T. Kurosu, and S. Namiki, “All-optical Nyquist filtering for elastic OTDM signals and their spectral defragmentation for inter-datacenter networks,” in Proceedings of European Conference on Optical Communication2014 (ECOC2014), Tu.3.6.1. [CrossRef]

8. 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]

9. J. Yu, Z. Dong, H. Chien, Z. Jia, X. Li, D. Huo, M. Gunkel, P. Wagner, H. Mayer, and A. Schippel, “Transmission of 200 G PDM-CSRZ-QPSK and PDM-16 QAM with a SE of 4 b/s/Hz,” J. Lightwave Technol. 31(4), 515–522 (2013). [CrossRef]

10. S. Shimizu, G. Cincotti, and N. Wada, “Demonstration of no-guard-interval 6 x 25 Gbit/s all-optical Nyquist WDM system for flexible optical networks by using CS-RZ signal and optical Nyquist filtering,” in Proceedings of OptoElectronics and Communication Conference (OECC, 2014), MO1B–1.

11. S. Shimizu, G. Cincotti, and N. Wada, “High frequency-granularity and format independent optical channel defragmentation for flexible optical networks,” in Proceedings of European Conference on Optical Communication (ECOC, 2014), paper We.1.5.1. [CrossRef]

12. S. Shimizu, G. Cincotti, and N. Wada, “Demonstration of multi-hop optical add-drop network with high frequency granular optical channel defragmentation nodes,” in Proceedings of Optical Fiber Communication Conference (OFC, 2015), paper M2I.4. [CrossRef]

13. E. Palushani, C. H. M. Hans, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM Conversion Based on Time-to-Frequency Mapping by Time-Domain Optical Fourier Transformation,” IEEE J. Sel. Top. Quantum Electron. 18(2), 681–688 (2012). [CrossRef]

14. K. G. Petrillo and M. A. Foster, “Full 160-Gb/s OTDM to 16x10-Gb/s WDM conversion with a single nonlinear interaction,” Opt. Express 21(1), 508–518 (2013). [CrossRef] [PubMed]

15. G. Cincotti, S. Shimizu, T. Murakawa, T. Kodama, K. Hattori, M. Okuno, S. Mino, A. Himeno, T. Nagashima, M. Hasegawa, N. Wada, H. Uenohara, and T. Konishi, “Flexible Power-efficient Nyquist-OTDM transmitter, using a WSS and time-lens effect,” in Proceedings of Optical Fiber Communication Conference2015 (OFC2015), W3C.5. [CrossRef]

16. S. Shimizu, G. Cincotti, and N. Wada, “All-Optical Nyquist-OTDM to Nyquist-WDM conversion for Highly Flexible Optical Networks,” in Proceedings of Optical Fiber Communication Conference2016 (OFC2016), W3D.1. [CrossRef]

17. S. Haykin, Communication Systems (John Wiley & Sons Inc., 2001).

All-optical Nyquist-OTDM to Nyquist-WDM conversion for high-granular flexible optical networks

Abstract

1. Introduction

2. Operation principle

3. Experimental demonstration

4. Summary

References and links

Cited By

Figures (8)

Equations (6)

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