## Design of arrayed-waveguide grating routers for use as optical OFDM demultiplexers

Optics Express, Vol. 18, Issue 13, pp. 14129-14143 (2010)

http://dx.doi.org/10.1364/OE.18.014129

Acrobat PDF (1465 KB)

### Abstract

All-optical OFDM uses optical techniques to multiplex together several modulated lightsources, to form a band of subcarriers that can be considered as one wavelength channel. The subcarriers have a frequency separation equal to their modulation rate. This means that they can be demultiplexed without any cross-talk between them, usually with a Discrete Fourier Transform (DFT), implemented optically or electronically. Previous work has proposed networks of optical couplers to implement the DFT. This work shows that the topology of an Arrayed Grating Waveguide Router (AWGR) can be used to perform the demultiplexing, and that the AWGR can be considered as a serial-to-parallel converter followed by a DFT. The simulations show that the electrical bandwidths of the transmitter and receiver are critical to orthogonal demultiplexing, and give insight into how crosstalk occurs in all-optical OFDM and coherent-WDM systems using waveforms and spectra along the system. Design specifications for the AWGR are developed, and show that non-uniformity will lead to crosstalk. The compensation of dispersion and the applications of these techniques to ‘coherent WDM’ systems using Non-Return to Zero modulation is discussed.

© 2010 OSA

## 1. Introduction

1. S. B. Weinstein, “The history of orthogonal frequency-division multiplexing [History of Communications],” IEEE Commun. Mag. **47**(11), 26–35 (2009). [CrossRef]

3. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express **14**(6), 2079–2084 (2006). [CrossRef] [PubMed]

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

7. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. **27**(16), 3705–3713 (2009). [CrossRef]

8. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. **17**(2), 504–506 (2005). [CrossRef]

9. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express **17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

8. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. **17**(2), 504–506 (2005). [CrossRef]

10. K. Yonenaga, A. Sano, E. Yamazaki, F. Inuzuka, Y. Miyamoto, A. Takada, and T. Yamada, “100 Gbit/s all-optical OFDM transmission using 4 x 25 Gbit/s optical duobinary signals with phase-controlled optical sub-carriers,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2008), paper JThA48.

11. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, R. Kudo, K. Ishihara, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, H. Yamazaki, S. Kamei, and H. Ishii, “13.4-Tb/s (134x111-Gb/s/ch) no-guard-interval coherent OFDM transmission over 3,600 km of SMF with 19-ps average PMD,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Th.3.E.1.

13. 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. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express **17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

*when no cyclic prefix nor guard bands are used*, equals the subcarrier spacing and the modulation of the subcarriers is time-aligned) gives a local optimum for received signal quality whilst maintaining a high spectral efficiency. To obtain low cross-talk between the demultiplexed subcarriers, the receiver required four-times oversampling and fractionally-spaced equalizers. A five subcarrier system was also studied, using a standard 0.5-nm optical band-pass filter for subcarrier separation. This arrangement led to a floor in the Bit Error Ratio (BER) versus Optical Signal to Noise Ratio (OSNR) characteristic.

25. C. Dragone, “An N*N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. **3**(9), 812–815 (1991). [CrossRef]

26. 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]

## 2. Theory of optical OFDM

9. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express **17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

8. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. **17**(2), 504–506 (2005). [CrossRef]

**17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

28. E. Ip, A. P. Lau, D. J. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express **16**(2), 753–791 (2008). [CrossRef] [PubMed]

29. H. Bulow, F. Buchali, and A. Klekamp, “Electronic Dispersion Compensation,” J. Lightwave Technol. **26**(1), 158–167 (2008). [CrossRef]

### Conditions for orthogonality

**17**(24), 21350–21361 (2009). [CrossRef] [PubMed]

30. Q. Yang, W. Shieh, and Y. Ma, “Guard-band influence on orthogonal-band-multiplexed coherent optical OFDM,” Opt. Lett. **33**(19), 2239–2241 (2008). [CrossRef] [PubMed]

31. S. B. Weinstein and P. M. Ebert, “Data transmission frequency-division multiplexing using the discrete Fourier transform,” IEEE Trans. Commun. Technol. **19**(5), 628–634 (1971). [CrossRef]

*N*times during each OFDM symbol, it is possible to completely distinguish between

*N*subcarriers, and also detect each subcarrier’s phase and amplitude. For example, in Fig. 2, consider four equally-spaced samples, A, B, C, D of the first symbol. These four samples form a

*sampling window*. The lower (‘red’) subcarrier would produce samples with + + − − values: the upper (‘teal’) subcarrier would produce samples with + − + − values. Thus by weighting the samples, then adding them, it is possible to differentiate between the subcarriers; for example, the sum P

_{teal}= A − B + C − D would detect the ‘teal’ subcarrier of the first symbol, completely rejecting the ‘red’ subcarrier. Looking at the second OFDM symbol in the left graph, P

_{teal}would be zero, because the samples fall on the zero-crossings of the teal waveform. Fortunately, the when the same sampling instants are applied to the quadrature (or imaginary-component) of the teal subcarrier (not shown), they produce a non-zero result, indicating a phase of 90°.

_{teal}= A − B + C − D is no longer zero when applied to the red waveform. This means that information in the red waveform has leaked into the detector for the teal waveform, so the waveforms are no longer orthogonal. This introduces the condition that: “

*the sampling window must not include a phase transition*”. This allows some drift of the sampling instants: if the phase transitions are instantaneous, this drift can be up to half the period between samples.

*phase transitions must be fast enough so as not to affect the value of the samples*(particularly samples A and D). Figure 3, Right, shows an example using our simplified waveforms, but shifted 90-degrees. The top waveform is for the red subcarrier with a fast transition: The sum P

_{teal}= A − B + C − D will produce a null output, as desired, because the magnitudes of all of the samples are equal. The bottom waveform is for a slow transition, which has lowered the magnitude of sample D. The sum P

_{teal}= A − B + C − D now produces a non-zero output, indicating leakage between channels. In this example, the transition must be substantially complete between two consecutive samples, if the sampling is instantaneous. In Fourier transform theory, it is well known that non-uniform windowing of waveforms (reducing the magnitude of some samples) will cause leakage between adjacent frequency components.

### Forming the sum of the samples

*V*. The sum of the samples is typically written as a discrete Fourier transform (DFT), giving a complex-valued output,

_{in}*V*, carrying the amplitude and phase subcarrier

_{sc,k}*k*:where:

*V*is the value of the complex input waveform at sample points

_{in}(m)*m*= 1,2…

*N*-1, where

*N*is the number of subcarriers. Because the samples are being continually updated as the input waveform arrives at the receiver, the sum of the samples, hence the estimate of

*V*, is also being updated, that is, it is a continuous waveform. If the interval between samples is Δ

_{sc,k}*T*, Eq. (1) can be rewritten as:

## 3. The AWGR as a DFT

13. 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]

26. 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]

*time delay waveguides at the single wavelength ports of an AWG WDM and a power combiner…*” neglects an important equivalence between a standard AWGR (followed by samplers) and the DFT, which is illustrated in Fig. 4 . The top of this Fig. shows an AWGR [26

26. 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]

### AWGR input slab coupler

33. K. Okamoto, K. Takahashi, M. Yasu, and Y. Hibino, “Fabrication of a wavelength-insensitive 8x8 star coupler,” IEEE Photon. Technol. Lett. **4**(1), 61–63 (1992). [CrossRef]

### AWGR grating waveguides

### AWGR output slab coupler

*m*, are presented to the output slab coupler, which implements a matrix of phase shifts, surrounded by splitters and couplers. The phase shifts implement the exponential term in Eq. (1); the couplers implement the summation for each subcarrier frequency, and present the result for each subcarrier at the outputs of the AWGR. Ideally all paths from any grating waveguide to any output have the same loss. Again, by proper design of the waveguide tapers, it is possible to make the loss reasonably uniform. Alternatively, a multimode-interference coupler could be used [35

35. L. O. Lierstuen and A. Sudbo, “8-channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. **7**(9), 1034–1036 (1995). [CrossRef]

**2**(2), 236–250 (1996). [CrossRef]

36. H. G. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. **35**(5), 311–350 (1945). [CrossRef]

*R*, while the output waveguides terminate on a circular boundary of radius

*R*/2 (the Rowland Circle). The RC circle is co-tangential with the large circle at the centre of the arrayed waveguides, called the ‘pole’. The distance between any input (from the arrayed waveguides) and output,

*AP*, is given by a rather complex expression (Eq. (9) of [36

36. H. G. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. **35**(5), 311–350 (1945). [CrossRef]

*F*

_{1}] of [36

36. H. G. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. **35**(5), 311–350 (1945). [CrossRef]

*is small compared with*

_{,}w,*R*:where

*θ*is the angle from the pole to the output waveguide and

*r*is the distance from the pole to the chosen output waveguide. This path length introduces a phase delay dependent on the originating arrayed waveguide and the receiving output waveguide. Because

*r*and θ are fixed for any chosen output guide, and

*d*increments from one arrayed waveguide to the next, it is possible to implement a set of linearly-decreasing phase shifts between any arrayed waveguide and any output. Poguntke and Soole [37

37. K. R. Poguntke and J. B. D. Soole, “Design of a multistripe array grating integrated cavity (MAGIC) laser,” J. Lightwave Technol. **11**(12), 2191–2200 (1993). [CrossRef]

**35**(5), 311–350 (1945). [CrossRef]

*m*) and the outputs of the AWGR (label

*n*, which carries the signal of a subcarrier,

*k*). A similar expression is also provided by Gholipour and Faraji-Dana [38

38. A. Gholipour and R. Faraji-Dana, “Nonuniform arrayed waveguide gratings for flat-top passband transfer function,” J. Lightwave Technol. **25**(12), 3678–3685 (2007). [CrossRef]

*n*is the effective index of the slab,

_{s}*d*is the spacing (pitch) of the grating waveguides as they enter the output slab,

*λ*is the centre wavelength of the system,

*R*is the focal length of the grating array as used in the RC derivation (e.g. from the output of any grating waveguide to the central output waveguide),

*d*

_{o}is the pitch of the output waveguides at the output-side of the output slab.

*d*=

*d*= 25 μm, the focal length should be around 2.5 mm in Silica.

_{o}### Samplers

## 4. System example

*Q*, value from which the Bit Error Ratio (BER) can be estimated.

### Optical spectra along the system

### Eye diagrams at the outputs of the coherent receivers

### Sampling of the outputs of the coherent receivers

*q*, where

*q*= mean-value-squared/variance in either the x- or the y-coordinate. The samplers are then followed by thresholders, to produce digital bits representing the I and Q signals. These can then be decoded into 2-bits per channel per OFDM symbol, typically using a Gray code to minimize errors from a single threshold error. If the spread along one axis is Gaussian, the Bit Error Ratio (BER) after thresholding can be estimated from BER = (0.5)erfc(

*q*/√2). More often a dB quality value is used, where

*Q*(dB) = 20.log

_{10}(

*q*) using these definitions. For example, when

*Q*= 9.8 dB the BER will be 10

^{−3}.

*Q*value is >40 dB, indicating negligible cross-talk between subcarriers and an extremely-low BER. For comparison, the

*Q*obtained when only one channel was transmitted was 60 dB. As a

*Q*of greater than 40 dB would also require an optical signal to noise ratio of the same order, the crosstalk in these systems would have a negligible impact on systems performance in all but the shortest of systems. Such systems could support a very-high QAM constellation, allowing at least 8-bits per symbol to be transmitted. The constellation on the right is for a system with 40-GHz 4th-order Bessel filters before the modulator and after the photodiodes. The new optimum sample time is changed by the delay of the filters: the optimum was found by sweeping the sampling instant across the eye. The

*Q*-value has dropped to 13 dB for the outer channels. This would only just support an 8-QAM system with 3-bits/symbol, but realistically, added amplifier noise would reduce the

*Q*further.

*Q*of 13 dB. The eight-vertical mini-eyes between the main eyes indicate that the interference is deterministic; that is, it is caused by the cross-talk between the channels. Noise-driven eye closure would not have this distinct feature. The information in the mini-eyes also suggests that the main eye could be opened by electronic signal processing including sampling of the mini-eyes, which is well known in communications engineering. Increasing the electrical bandwidth to 30-GHz opens up the main eye, giving a

*Q*of >35 dB if the sampling is instantaneous. Interestingly, the higher-bandwidth also allows sharper and higher peaks between the open eyes. It is these peaks that are smeared into the eye for the lower-bandwidth system. Electrical bandwidths of 20-GHz give a respectable

*Q*of 20 dB. Chen

*et al.*[17

17. 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]

*et al.*[22

22. D. Hillerkuss, A. Marculescu, J. Li, M. Teschke, G. Sigurdsson, K. Worms, S. Ben-Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Novel optical fast Fourier transform scheme enabling real-time OFDM at 392 Gbit/s and beyond,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2010), paper OWW3.

### Effect of AWGR non-uniformity

*Q*of the outer and inner channels, due to crosstalk (a reduction in orthogonality).

*Q’*s for the four channels against AWGR power non-uniformity for 3 electrical bandwidths. Each bandwidth produces two sets of lines, corresponding to the inner (2, 3) and outer (1, 4) channels. The inner channels generally suffer the most crosstalk, whether caused by reduced electrical bandwidths or AWGR non-uniformity. From this plot, a non-uniformity of 1 dB would be acceptable for all but the highest constellation sizes. To confirm that crosstalk is the main cause of signal degradation when the grating is not uniform, the simulations were re-run with only one transmitter active. The

*Q*was extremely high (>60 dB) for all values of grating non-uniformity.

### Effect of limiting the total optical bandwidth

*Q*is reduced overall. The results in Fig. 11 indicate that a system with high-bandwidth transmitters and receivers would give good performance with cascades of wavelength-selective switches, which typically have an optical bandwidth of around 35 GHz.

## 5. Discussion

### Compensation of dispersion

7. A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. **27**(16), 3705–3713 (2009). [CrossRef]

### Application to NRZ formats

**17**(2), 504–506 (2005). [CrossRef]

10. K. Yonenaga, A. Sano, E. Yamazaki, F. Inuzuka, Y. Miyamoto, A. Takada, and T. Yamada, “100 Gbit/s all-optical OFDM transmission using 4 x 25 Gbit/s optical duobinary signals with phase-controlled optical sub-carriers,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2008), paper JThA48.

^{7}) and NRZ systems (“Coherent WDM” [41]). This is that phase-control of each subcarrier is critical for the performance of NRZ systems, whereas the phase of each subcarrier is modulated in the QPSK systems, so cannot be optimized, except within a 90° range. Simulations using NRZ modulation showed that inter-subcarrier interference produces intensity peaks that can be moved from close to the region of the open eye, to between the open eyes, by adjusting the subcarriers’ phases. In systems with reduced electrical bandwidths, it is desirable to advance these interference peaks in time, so that even after the spreading of their energy due to the transient response of the electrical filters, their energy will not encroach on the open part of the eye. Thus there will be an optimum relative phase between the subcarriers as demonstrated by Ellis and Gunning [8

**17**(2), 504–506 (2005). [CrossRef]

## 6. Conclusion

## Acknowledgements

## References and links

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3. | A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express |

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6. | I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express |

7. | A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-guard-interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. |

8. | A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. |

9. | S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express |

10. | K. Yonenaga, A. Sano, E. Yamazaki, F. Inuzuka, Y. Miyamoto, A. Takada, and T. Yamada, “100 Gbit/s all-optical OFDM transmission using 4 x 25 Gbit/s optical duobinary signals with phase-controlled optical sub-carriers,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2008), paper JThA48. |

11. | A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, S. Matsuoka, R. Kudo, K. Ishihara, Y. Takatori, M. Mizoguchi, K. Okada, K. Hagimoto, H. Yamazaki, S. Kamei, and H. Ishii, “13.4-Tb/s (134x111-Gb/s/ch) no-guard-interval coherent OFDM transmission over 3,600 km of SMF with 19-ps average PMD,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Th.3.E.1. |

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14. | H. Sanjoh, E. Yamada, and Y. Yoshikuni, “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to 1 bit/s/Hz,” in Conference on Optical Fiber Communication, OFC, (Anaheim, CA, 2002), paper ThD1, pp. 401–402. |

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22. | D. Hillerkuss, A. Marculescu, J. Li, M. Teschke, G. Sigurdsson, K. Worms, S. Ben-Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Novel optical fast Fourier transform scheme enabling real-time OFDM at 392 Gbit/s and beyond,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2010), paper OWW3. |

23. | D. Hillerkuss, T. Schellinger, R. Schmogrow, M. Winter, T. Vallaitis, R. Bonk, A. Marculescu, J. Li, M. Dreschmann, J. Meyer, S. B. Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Single source optical OFDM transmitter and optical FFT receiver demonstrated at line rates of 5.4 and 10.8 Tbit/s,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2010), paper PDPC1. |

24. | D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express |

25. | C. Dragone, “An N*N optical multiplexer using a planar arrangement of two star couplers,” IEEE Photon. Technol. Lett. |

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

27. | A. D. Ellis, F. C. G. Gunning, B. Cuenot, T. C. Healy, and E. Pincemin, “Towards 1TbE using Coherent WDM,” in Opto-Electronics and Communications Conference, 2008 and the 2008 Australian Conference on Optical Fibre Technology, OECC/ACOFT, (2008), pp. 1–4. |

28. | E. Ip, A. P. Lau, D. J. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express |

29. | H. Bulow, F. Buchali, and A. Klekamp, “Electronic Dispersion Compensation,” J. Lightwave Technol. |

30. | Q. Yang, W. Shieh, and Y. Ma, “Guard-band influence on orthogonal-band-multiplexed coherent optical OFDM,” Opt. Lett. |

31. | S. B. Weinstein and P. M. Ebert, “Data transmission frequency-division multiplexing using the discrete Fourier transform,” IEEE Trans. Commun. Technol. |

32. | C. K. Madsen, and J. H. Zhao, |

33. | K. Okamoto, K. Takahashi, M. Yasu, and Y. Hibino, “Fabrication of a wavelength-insensitive 8x8 star coupler,” IEEE Photon. Technol. Lett. |

34. | L. Soldano, F. Veerman, M. K. Smit, B. Verbeek, and E. Pennings, “Multimode interference couplers,” in Integrated Photonics Research, (Monteray, CA, 1991), paper TuD1. |

35. | L. O. Lierstuen and A. Sudbo, “8-channel wavelength division multiplexer based on multimode interference couplers,” IEEE Photon. Technol. Lett. |

36. | H. G. Beutler, “The theory of the concave grating,” J. Opt. Soc. Am. |

37. | K. R. Poguntke and J. B. D. Soole, “Design of a multistripe array grating integrated cavity (MAGIC) laser,” J. Lightwave Technol. |

38. | A. Gholipour and R. Faraji-Dana, “Nonuniform arrayed waveguide gratings for flat-top passband transfer function,” J. Lightwave Technol. |

39. | S. L. Jansen, I. Morita, and H. Tanaka, “16x52.5-Gb/s, 50-GHz spaced, POLMUX-CO-OFDM transmission over 4,160 km of SSMF enabled by MIMO processing,” in ECOC 2007, (Berlin, 2007), paper PD 1.3. |

40. | A. D. Ellis, “Modulation formats which approach the Shannon limit,” in Conference on Optical Fiber Communication, OFC, (San Diego, CA, 2009), paper OMM4. |

41. | A. D. Ellis, F. C. G. Gunning, and T. Healy, “Coherent WDM: the achievement of high information spectral density through phase control within the transmitter,” in Conference on Optical Fiber Communication, OFC, (Anaheim, CA, 2006), paper OThR4. |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: April 29, 2010

Revised Manuscript: June 8, 2010

Manuscript Accepted: June 9, 2010

Published: June 16, 2010

**Citation**

Arthur James Lowery, "Design of arrayed-waveguide grating routers for use as optical OFDM demultiplexers," Opt. Express **18**, 14129-14143 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-14129

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### References

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