## System tolerance of all-optical sampling OFDM using AWG discrete Fourier transform |

Optics Express, Vol. 19, Issue 14, pp. 13590-13597 (2011)

http://dx.doi.org/10.1364/OE.19.013590

Acrobat PDF (1310 KB)

### Abstract

The fundamental-mode arrayed waveguide grating (AWG) for all-optical discrete Fourier transformer (DFT) shows significant feasibility in the system tolerance of all-optical sampling orthogonal frequency division multiplexing (AOS-OFDM) systems. We discuss the system tolerance of AWG-based DFT designs for 100/160Gbps OFDM transmission system in comparison with coupler-based DFT designs.

© 2011 OSA

## 1. Introduction

## 2. Phase errors in all-optical DFT processors

4. K. Lee, C. T. D. Thai, and J.-K. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**(6), 4023–4028 (2008). [CrossRef] [PubMed]

*N*is defined by

*k*and

*n*are integer. Considering the mathematical expression of DFT, we can implement that a DFT processor with

*N*sampling ports introduces fixed phase changes of

*n*-th time domain sample for the

*k*-th input

*k*-th frequency domain output for the

*n*-th input

*n-*th time-domain port. Here,

*T*is the symbol period.

12. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. **12**(1), 63–65 (1987). [CrossRef] [PubMed]

6. W. Li, X. Liang, W. Ma, T. Zhou, B. Huang, and D. Liu, “A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems,” Opt. Fiber Technol. **16**(1), 5–11 (2010). [CrossRef]

*O*(

*N*log

*N*) scalability, where

*N*is the number of optical OFDM subcarriers. However, in manufacturing, every waveguide between couplers always has a certain phase error, which is indicated with a yellow marker in Fig. 1(a), caused by little difference of waveguide width and length. As the coupler-based Marhic DFT circuits utilize complex interferences in a network of couplers, phase error can break the inter-subcarrier orthogonality in an AOS-OFDM system. In the case of an

*N*x

*N*coupler-based DFT, the number of phase error impairments grows with 2

*N*log

*N*. As a result, performance evaluation shows serious penalties due to phase errors in the Marhic DFT [7

7. S. Lim and J.-K. K. Rhee, “System performance of 2x2 coupler-based all-optical OFDM System,” in *Photonics in Switching*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2

7. S. Lim and J.-K. K. Rhee, “System performance of 2x2 coupler-based all-optical OFDM System,” in *Photonics in Switching*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2

7. S. Lim and J.-K. K. Rhee, “System performance of 2x2 coupler-based all-optical OFDM System,” in *Photonics in Switching*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2

*N*arrayed waveguides for

*N*subcarrier channels between two slab waveguides which are two-dimensional free propagation regions (FPR), as shown in Fig. 1(b). A careful design of waveguide ports on a slab waveguide can achieve the DFT phase relations [15

15. G. Cincotti, N. Wad, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers,” J. Lightwave Technol. **24**(1), 103–112 (2006). [CrossRef]

17. Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express **19**(5), 4501–4512 (2011). [CrossRef] [PubMed]

*n*= 1…

*N*, to multiplex and demultiplex an OFDM symbol [18

18. K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Optical orthogonal frequency division multiplexing demultiplexer using slab star coupler-based optical discrete Fourier transform circuit,” Opt. Lett. **36**(7), 1140–1142 (2011). [CrossRef] [PubMed]

*N*subcarriers is only

*N*, so that we can expect less impact on inter-subcarrier crosstalk between subcarrier channels.

8. Y. Chu, X. O. Zheng, H. Zhang, X. Liu, and Y. Guo, “The impact of phase errors on arrayed waveguide gratings,” IEEE J. Sel. Top. Quantum Electron. **8**(6), 1122–1129 (2002). [CrossRef]

*m*-th waveguide and

*σ*is a standard deviation of Gaussian distribution. It is noted that the range of Gaussian random variable is limited to twice of standard deviation, which is assumed as a manufacturing tolerance, for practical modeling. Constant coefficient

*A*normalizes the distribution, such that

*λ*/20. The transfer function of the FM-AWG shows slight difference from the ideal case but that of the coupler-based IDFT shows significant crosstalks that are responsible for orthogonality degradation. In Fig. 2, the maximum crosstalk value of FM-AWG IDFT is −46 dB at 0 GHz, while that of coupler-based IDFT is −27 dB. This comparison motivates a study for practical implementation with FM-AWG devices. Insertion loss non-uniformity error also introduces penalties on the OFDM process in both types of DFT devices [7

*Photonics in Switching*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2

16. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express **18**(13), 14129–14143 (2010). [CrossRef] [PubMed]

10. C. R. Doerr and K. Okamoto, “Advances in silica planar lightwave circuits,” J. Lightwave Technol. **24**(12), 4763–4789 (2006). [CrossRef]

11. M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. **2**(2), 236–250 (1996). [CrossRef]

## 3. Comparison of system performance between fundamental mode AWG and coupler-based AOS-OFDM system

*cw*) laser and a pulse carver produce a return-to-zero (RZ) pulse train, which is split into 4 of 25Gbps modulators. The pulse train forms a comb spectrum with a 3-dB full width bandwidth of 80 GHz as shown in the upper part of Fig. 3(c). Individually modulated optical RZ on-off data are fed to an all-optical IDFT circuit which is either a coupler-based Marhic circuit or an FM-AWG (Fig. 3(d)). The all-optical IDFT circuit transforms each modulated RZ data into the corresponding OFDM subcarrier and all subcarrier components are superpositioned to form an optical OFDM symbol. The lower plot of Fig. 3(c) shows the power spectrum density of transmitter output of AOS-OFDM using FM-AWG. In this system, the subcarrier frequencies are situated at every 25 GHz from the optical center frequency. The 50-GHz channel is divided into ± 50 GHz channels due to the aliasing effect of IDFT. In practical application, the OFDM symbol can be transmitted over a fiber link. However, in this paper, as our performance investigation is limited to the DFT circuit feasibility, we assumed an ideal transmission fiber link with no dispersion and nonlinearity impairments. Finally, at the receiver side, an optical bandpass filter is used to eliminate out-of-band optical amplifier noise, namely, amplified spontaneous emission (ASE). Subsequently, the OFDM symbol can be de-multiplexed by DFT process. The left side of Fig. 3(b) shows the output waveforms of the DFT process. In turn, the RZ optical data of each subcarrier channel is retrieved at every 40ps by sampling using an electro-absorption modulator pulse carver as shown in the right side of Fig. 3(b) by following the operation principle discussed in [4

4. K. Lee, C. T. D. Thai, and J.-K. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**(6), 4023–4028 (2008). [CrossRef] [PubMed]

4. K. Lee, C. T. D. Thai, and J.-K. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express **16**(6), 4023–4028 (2008). [CrossRef] [PubMed]

9. T. Goh, S. Suzuki, and A. Sugita, “Estimation of waveguide phase error in silica-based waveguides,” J. Lightwave Technol. **15**(11), 2107–2113 (1997). [CrossRef]

_{10}Q) by adjusting the OSNR levels. This reference provides a reasonable OSNR requirement. In Fig. 5(a) , we have plotted the average Q-factor as a function of the standard deviation of phase error distribution in radian. Initially, Q values of all cases decrease slowly as the phase errors increase, but when phase errors are large, the Q penalty becomes more sensitive to phase error, Besides, in the case of an 8-channel coupler-based OFDM, Q value is about 2.1dB less than an 8-channel FM-AWG-based OFDM system at a phase error standard deviation of λ/20 as compared in the figure. In this result, an FM-AWG-based AOS-OFDM system shows lower sensitivity to phase error compared with a coupler-based system.

*N*, which is less than that of a coupler-based DFT circuit,

*N*log

_{2}

*N*. The second reason comes from the differences in designs and operation principles of the DFT processes. In the case of coupler-based DFT, it utilizes the lightwave interference between two waveguides and the corresponding interferences are nested [7

*Photonics in Switching*, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2

## 4. Conclusion

## Acknowledgment

## References and links

1. | J. Armstrong, “OFDM for optical communication,” J. Lightwave Technol. |

2. | Y. Benlachtar, P. M. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. C. Hoe, M. Püschel, M. Glick, and R. I. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express |

3. | A. Sano, H. Masuda, E. Yoshida, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30x100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in |

4. | K. Lee, C. T. D. Thai, and J.-K. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express |

5. | H. Chen, M. Chen, and S. Xie, “All-optical sampling orthogonal frequency-division multiplexing Scheme for High-Speed Transmission System,” J. Lightwave Technol. |

6. | W. Li, X. Liang, W. Ma, T. Zhou, B. Huang, and D. Liu, “A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems,” Opt. Fiber Technol. |

7. | S. Lim and J.-K. K. Rhee, “System performance of 2x2 coupler-based all-optical OFDM System,” in |

8. | Y. Chu, X. O. Zheng, H. Zhang, X. Liu, and Y. Guo, “The impact of phase errors on arrayed waveguide gratings,” IEEE J. Sel. Top. Quantum Electron. |

9. | T. Goh, S. Suzuki, and A. Sugita, “Estimation of waveguide phase error in silica-based waveguides,” J. Lightwave Technol. |

10. | C. R. Doerr and K. Okamoto, “Advances in silica planar lightwave circuits,” J. Lightwave Technol. |

11. | M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. |

12. | M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. |

13. | A. E. Siegman, “Fiber Fourier optics,” Opt. Lett. |

14. | Y.-K. Huang, R. Saperstein, and T. Wang, “All-optical OFDM transmission with coupler-based IFFT/FFT and pulse interleaving,” in |

15. | G. Cincotti, N. Wad, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers,” J. Lightwave Technol. |

16. | A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express |

17. | Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express |

18. | K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Optical orthogonal frequency division multiplexing demultiplexer using slab star coupler-based optical discrete Fourier transform circuit,” Opt. Lett. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4230) Fiber optics and optical communications : Multiplexing

(070.7145) Fourier optics and signal processing : Ultrafast processing

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 17, 2011

Revised Manuscript: June 18, 2011

Manuscript Accepted: June 18, 2011

Published: June 29, 2011

**Citation**

Seong-Jin Lim and June-Koo Kevin Rhee, "System tolerance of all-optical sampling OFDM using AWG discrete Fourier transform," Opt. Express **19**, 13590-13597 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13590

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### References

- J. Armstrong, “OFDM for optical communication,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
- Y. Benlachtar, P. M. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. C. Hoe, M. Püschel, M. Glick, and R. I. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17(20), 17658–17668 (2009). [CrossRef] [PubMed]
- A. Sano, H. Masuda, E. Yoshida, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30x100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in Proceedings of IEEE Conference on 33th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Berlin, 2007), Paper PDS1.7.
- K. Lee, C. T. D. Thai, and J.-K. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16(6), 4023–4028 (2008). [CrossRef] [PubMed]
- H. Chen, M. Chen, and S. Xie, “All-optical sampling orthogonal frequency-division multiplexing Scheme for High-Speed Transmission System,” J. Lightwave Technol. 27(21), 4848–4854 (2009). [CrossRef]
- W. Li, X. Liang, W. Ma, T. Zhou, B. Huang, and D. Liu, “A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems,” Opt. Fiber Technol. 16(1), 5–11 (2010). [CrossRef]
- S. Lim and J.-K. K. Rhee, “System performance of 2x2 coupler-based all-optical OFDM System,” in Photonics in Switching, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PWF2. http://www.opticsinfobase.org/abstract.cfm?URI=PS-2010-PWF2
- Y. Chu, X. O. Zheng, H. Zhang, X. Liu, and Y. Guo, “The impact of phase errors on arrayed waveguide gratings,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1122–1129 (2002). [CrossRef]
- T. Goh, S. Suzuki, and A. Sugita, “Estimation of waveguide phase error in silica-based waveguides,” J. Lightwave Technol. 15(11), 2107–2113 (1997). [CrossRef]
- C. R. Doerr and K. Okamoto, “Advances in silica planar lightwave circuits,” J. Lightwave Technol. 24(12), 4763–4789 (2006). [CrossRef]
- M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996). [CrossRef]
- M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987). [CrossRef] [PubMed]
- A. E. Siegman, “Fiber Fourier optics,” Opt. Lett. 26(16), 1215–1217 (2001). [CrossRef] [PubMed]
- Y.-K. Huang, R. Saperstein, and T. Wang, “All-optical OFDM transmission with coupler-based IFFT/FFT and pulse interleaving,” in proceedings of IEEE conference on Lasers and Electro-Optics Society (Institute of Electrical and Electronics Engineers, Acapulco, 2008), pp.408–409.
- G. Cincotti, N. Wad, and K. Kitayama, “Characterization of a full encoder/decoder in the AWG configuration for code-based photonic routers,” J. Lightwave Technol. 24(1), 103–112 (2006). [CrossRef]
- A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]
- Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express 19(5), 4501–4512 (2011). [CrossRef] [PubMed]
- K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Optical orthogonal frequency division multiplexing demultiplexer using slab star coupler-based optical discrete Fourier transform circuit,” Opt. Lett. 36(7), 1140–1142 (2011). [CrossRef] [PubMed]

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