## Reconfigurable linear combination of phase-and-amplitude coded optical signals |

Optics Express, Vol. 22, Issue 3, pp. 2609-2619 (2014)

http://dx.doi.org/10.1364/OE.22.002609

Acrobat PDF (1688 KB)

### Abstract

We introduce an all-optical arithmetic unit operating a weighted addition and subtraction between multiple phase-and-amplitude coded signals. The scheme corresponds to calculating the field dot-product of frequency channels with a static vector of coefficients. The system is reconfigurable and format transparent. It is based on Fourier-domain processing and multiple simultaneous four-wave mixing processes inside a single nonlinear element. We demonstrate the device with up to three channels at 40 Gb/s and evaluate its efficiency by measuring the bit-error-rate of a distortion compensation operation between two signals.

© 2014 Optical Society of America

## 1. Introduction

1. P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. **24**, 4711–4728 (2006). [CrossRef]

2. K. Azadet, E. Haratsch, and H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid State Circuits **37**, 317–327 (2002). [CrossRef]

3. L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express **18**, 17075–17088 (2010). [CrossRef] [PubMed]

4. P. Bower and I. Dedic, “High speed converters and DSP for 100G and beyond,” Opt. Fiber Technol. **17**, 464–471 (2011). [CrossRef]

5. R. A. Athale, “Optical matrix algebraic processors: a survey,” in *10th International Optical Computing Conference*,S. Horvitz, ed. (International Society for Optics and Photonics, 1983), pp. 24–31. [CrossRef]

6. X. Wang, J. Peng, M. Li, Z. Shen, and O. Shan, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. **49**, 2352–2362 (2010). [CrossRef] [PubMed]

7. D. E. Tamir, N. T. Shaked, P. J. Wilson, and S. Dolev, “High-speed and low-power electro-optical DSP coprocessor,” J. Opt. Soc. Am. A **26**, 11–20 (2009). [CrossRef]

8. P. Yeh and A. E. T. Chiou, “Optical matrix-vector multiplication through four-wave mixing in photorefractive media,” Opt. Lett. **12**, 138–140 (1987). [CrossRef] [PubMed]

9. H. Ishikawa, *Ultrafast All-Optical Signal Processing Devices* (John Wiley, 2008). [CrossRef]

10. G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. **18**, 917–919 (2006). [CrossRef]

11. S. Singh and L. Lovkesh, “Ultrahigh speed optical signal processing logic based on an SOA-MZI,” IEEE J. Sel. Top. Quantum Electron. **18**, 970–977 (2012). [CrossRef]

12. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics **5**, 364–371 (2011). [CrossRef]

13. M. Freiberger, D. Templeton, and E. Mercado, “Low latency optical services,” in National Fiber Optic Engineers Conference(2012), paper NTu2E.1. [CrossRef]

14. D. Schneider, “Trading at the speed of light,” IEEE Spectrum **48**, 11–12 (2011). [CrossRef]

15. L. Yan, A. Willner, X. Wu, and A. Yi, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. **30**, 3760–3770 (2012). [CrossRef]

16. J. Kurumida and S. J. B. Yoo, “Nonlinear optical signal processing in optical packet switching systems,” IEEE J. Sel. Top. Quantum Electron. **18**, 978–987 (2012). [CrossRef]

17. H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics **4**, 261–263 (2010). [CrossRef]

18. A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. **17**, 320–332 (2011). [CrossRef]

19. Y. Paquot, J. Schröder, M. D. Pelusi, and B. J. Eggleton, “All-optical hash code generation and verification for low latency communications,” Opt. Express **21**, 23873–23884 (2013). [CrossRef] [PubMed]

## 2. Principle

**E**(

*t*) and a static vector of coefficients

**a**. Mathematically, this operation is a linear form in the complex space resulting in a scalar

*E*

_{Itot}(

*t*) = ∑

_{j}*a*(

_{j}E_{j}*t*) where

*E*(

_{j}*t*) and

*a*are the components of the two vectors. In optical terms, this would correspond to a weighted sum between orthogonal light fields

_{j}*E*(

_{j}*t*), for example signals encoded on separate WDM channels.

*a*to the fields. Mixing of the modified fields with pump fields in a Kerr medium operates frequency-conversion of the WDM channels to a unique idler frequency where they add or subtract coherently. We show for up to three signals that this scheme implements the dot-product operation of the analogue values contained in the complex optical fields of phasors

_{j}*E*

_{S}_{1},

*E*

_{S}_{2}and

*E*

_{S}_{3}with a vector of complex coefficients (

*a*

_{1},

*a*

_{2},

*a*

_{3}) normalized so that |

*a*≤ 1 ∀

_{j}|*j*= 1, 2, 3. The following equations are written for the case of three signals, but can be extended to any number of channels. With the coefficients expressed with their modules |

*a*| and arguments

_{j}*ϕ*, this corresponds to the phasor in Eq. (2).

_{j}*ν*. The dot-product device sets them with custom attenuation levels and relative phases before combining them with pump signals having half their spectral separation

**E**

_{S}_{1}(

*t*),

**E**

_{S}_{2}(

*t*) and

**E**

_{S}_{3}(

*t*) are phase locked due to the fact that they originate from the same frequency comb source. The pump signals

**E**

_{P}_{1}(

*t*),

**E**

_{P}_{2}(

*t*) and

**E**

_{P}_{3}(

*t*) are also phase locked together, however they do not need to be locked to the signals. Their electric field is expressed in Eqs. (3) to (8). In these expressions,

*E*

_{S}_{1},

*E*

_{S}_{2},

*E*

_{S}_{3},

*E*

_{P}_{1},

*E*

_{P}_{2}and

*E*

_{P}_{3}are the phasors of the fields. In the following development, we consider that their amplitudes, defined by

*A*= |

_{Sj}*E*| and

_{Sj}*A*= |

_{Pj}*E*|, are respectively

_{Pj}*A*

_{S}_{1},

*A*

_{S}_{2},

*A*

_{S}_{3},

*A*

_{P}_{1}=

*A*

_{P}_{2}=

*A*

_{P}_{3}=

*A*and wave vectors

_{P}*k*

_{S}_{1},

*k*

_{S}_{2},

*k*

_{S}_{3},

*k*

_{P}_{1},

*k*

_{P}_{2}and

*k*

_{P}_{3}. The first order FWM idlers generated from these waves have phasors

*E*

_{I}_{1}=

*A*

_{I}_{1}

*e*

^{iϕI1},

*E*

_{I}_{2}=

*A*

_{I}_{2}

*e*

^{iϕI2}and

*E*

_{I}_{3}=

*A*

_{I}_{3}

*e*

^{iϕI3}. The wave vectors of the generated idlers are determined by the phase matching condition of the FWM processes [20]: From these relations and considering that signals are phase locked and pumps are phase locked, the explicit phase relations of the idlers can be written [21

21. J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express **17**, 12555–12563 (2009). [CrossRef] [PubMed]

*ϕ*

_{S}_{1},

*ϕ*

_{S}_{2}and

*ϕ*

_{S}_{3}and the pump phase is set so that

*ϕ*

_{P}_{1}=

*ϕ*

_{P}_{2}=

*ϕ*

_{P}_{3}=

*ϕ*. We consider the phase of the incoming phase-locked signals as a reference and shift their relative phases respectively by

_{P}*ϕ*→

_{Sj}*ϕ*+

_{Sj}*ϕ*∀

_{j}*j*= 1, 2, 3 in order to implement the argument of the coefficients in the dot-product. In case that (

*a*

_{1},

*a*

_{2},

*a*

_{3}) are real, these phases are 0 (addition) or

*π*(subtraction). The coherent idlers add or subtract accordingly due to interference. In Fig. 1, we consider real coefficients (

*a*

_{1},

*a*

_{2},

*a*

_{3}). Signals with opposite phases are symbolized by arrows pointing in opposite directions.

*a*

_{1}|

^{2}, |

*a*

_{2}|

^{2}, |

*a*

_{3}|

^{2}), which are applied to the signal waves. In terms of field amplitude, this results in Eqs. (15) to (17).

*E*

_{Itot}as a function of the characteristics of the incoming fields and the attenuation and phase shifts applied. The latter expression matches the result expected in Eq. (1). Note that

*ϕ*results in an absolute phase offset of the total idler, which is not relevant, and hence no phase relation is required between signals and pumps. Although other first-order cross products are generated from the pumps and signals, these appear at other frequencies than the idler of interest and can be removed by bandpass filtering. The method can be generalized to a dot-product between more than three channels by using more wavelength channels and pump waves.

_{P}*a*|

_{j}^{2}and phase shift |

*ϕ*| are applied via attenuation and phase control using a FD-POP device schematically represented in the inset of Fig. 1.

_{j}## 3. Experiment

^{31}– 1 pseudo random bit sequence (PRBS) via a Mach-Zehnder modulator (M-Z).

22. J. Schröder, M. A. F. Roelens, L. B. Du, A. J. Lowery, S. Frisken, and B. J. Eggleton, “An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing,” Opt. Express **21**, 690–697 (2013). [CrossRef] [PubMed]

*S*

_{1}and

*S*

_{2}or

*S*

_{2}and

*S*

_{3}that were used for calibration of the relative phases. When the pair of signals had the same bit pattern and were set with opposite phases, a dip appeared in the spectrum of the idler as a signature of the destructive interference. The power contrast due to interference between identical signals in the cases of addition and subtraction exceeded 20 dB. The solid trace features the dot-product operating with all three signals with a given set of phase and amplitude coefficients.

## 4. Results

### 4.1. Dot-product with 3 signals

*S*was a 64 bits on-off keying (OOK) pattern.

*S*

_{1},

*S*

_{2}and

*S*

_{3}were obtained by delaying

*S*respectively by −1, 0 and 1 bit-delay (25 ps). The results are given for four different configurations of coefficients (

*a*

_{1},

*a*

_{2},

*a*

_{3}). From left to right and top to bottom, these take the values (1, −0.4, 0), (0.3, −1, 0.7), (0.3, −1, 0.3) and (0.5, −1, −0.5).

### 4.2. BER performance with 2 signals

**X**. Basic algebra shows that this distortion can be undone by multiplication with the corresponding inverse matrix

**X**

^{−1}. Reverting the transformation was applied to one channel via the all-optical dot-product device. After cancellation of the impairment, the resulting recovered channel was analyzed through BER and eye diagram measurement.

*Distortion generation:*The linear transformation of the two signals by multiplication with the matrix

**X**was operated inside the first FD-POP represented on Fig. 2. The operation can be represented mathematically by a matrix product

**D**=

**XS**where

**S**is an array of the signals before modification (for example optical fields),

**D**represents the distorted signals, and

**X**is the transformation matrix. Distortion can therefore be canceled by applying the inverse transfer matrix

**X**

^{−1}to the degraded signals

**S**=

**X**

^{−1}

**D**, supposing that the adjacent channels are known. Here the matrices are normalized to verify conservation of energy and expressed with their coefficients. The expression of

**X**

^{−1}is given for the particular case of 2-by-2 matrices. Note that the application of the matrix

**X**is similar to the introduction of linear crosstalk between the two signals. Such linear crosstalk can appear in optical networks due to imperfect filtering in optical add-drop multiplexers (OADM) combining WDM channels from different origins [23

23. A. Hill and D. Payne, “Linear crosstalk in wavelength-division-multiplexed optical-fiber transmission systems,” J. Lightwave Technol. **3**, 643–651 (1985). [CrossRef]

24. J. Zhou, M. O’Mahony, and S. Walker, “Analysis of optical crosstalk effects in multi-wavelength switched networks,” IEEE Photonics Technol. Lett. **6**, 302–305 (1994). [CrossRef]

**X**was applied by an interferometric technique inside the FD-POP. The method emulates the effect without applying an actual power transfer between the channels. This is allowed by the manner used to generate the incoming signals by delaying a single initial bit-pattern. Considering that both channels are identical replicas delayed by one bit-length Δ

*L*, the extra-diagonal coefficient

*b*corresponding to a leak from channel 2 into channel 1 can be synthesized by adding a fraction

*b*of each symbol into the next one in the manner of a delay line interferometer (DLI) illustrated in Fig. 6 (right). Power and phase transfer functions of such DLI are derived for a signal of phasor

*E*

_{S}_{1}=

*A*

_{S}_{1}

*e*

^{iϕS1}. Constructive interference after recombination of the arms

*a*and

*b*results in a total field equivalent to

*E*

_{S}_{1}distorted by a leak from

*E*

_{S}_{2}=

*A*

_{S}_{2}

*e*

^{iϕS2}. The latter signal can be written as a function of

*S*1 thanks to the link that exists between the two pseudo-independent channels:

*ν*is the frequency. Configuration of the FD-POP so as to apply these spectral transfer functions to the two channels is equivalent to distortion by the matrix

**X**.

*Distortion compensation:*The dot-product device was used on the distorted signal to undo the linear impairment. The attenuation level of the channels translated the absolute value of the matrix coefficients of

**X**

^{−1}, while their relative phase (either 0 or

*π*) set the signs. The FD-POP is configured so that both channels are

*π*out of phase and the channel to be subtracted is attenuated by

*b*

^{2}. The idler wavelength is then filtered using a bandpass filter and measured using a 40 Gb/s bit-error rate tester and a sampling oscilloscope.

*b*

^{2}= 0.185 = −7.3

*dB*and flipped by a

*π*phase shift. Note that the spectral shape of the signals changes slightly when the distortion is applied, due to the FD-POP spectral shaping operation.

## 5. Discussion

## 6. Conclusion

## Acknowledgments

## References and links

1. | P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. |

2. | K. Azadet, E. Haratsch, and H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid State Circuits |

3. | L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express |

4. | P. Bower and I. Dedic, “High speed converters and DSP for 100G and beyond,” Opt. Fiber Technol. |

5. | R. A. Athale, “Optical matrix algebraic processors: a survey,” in |

6. | X. Wang, J. Peng, M. Li, Z. Shen, and O. Shan, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. |

7. | D. E. Tamir, N. T. Shaked, P. J. Wilson, and S. Dolev, “High-speed and low-power electro-optical DSP coprocessor,” J. Opt. Soc. Am. A |

8. | P. Yeh and A. E. T. Chiou, “Optical matrix-vector multiplication through four-wave mixing in photorefractive media,” Opt. Lett. |

9. | H. Ishikawa, |

10. | G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, and L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. |

11. | S. Singh and L. Lovkesh, “Ultrahigh speed optical signal processing logic based on an SOA-MZI,” IEEE J. Sel. Top. Quantum Electron. |

12. | D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit/s line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics |

13. | M. Freiberger, D. Templeton, and E. Mercado, “Low latency optical services,” in National Fiber Optic Engineers Conference(2012), paper NTu2E.1. [CrossRef] |

14. | D. Schneider, “Trading at the speed of light,” IEEE Spectrum |

15. | L. Yan, A. Willner, X. Wu, and A. Yi, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. |

16. | J. Kurumida and S. J. B. Yoo, “Nonlinear optical signal processing in optical packet switching systems,” IEEE J. Sel. Top. Quantum Electron. |

17. | H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics |

18. | A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, and S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. |

19. | Y. Paquot, J. Schröder, M. D. Pelusi, and B. J. Eggleton, “All-optical hash code generation and verification for low latency communications,” Opt. Express |

20. | G. P. Agrawal, |

21. | J. Wang, Q. Sun, and J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express |

22. | J. Schröder, M. A. F. Roelens, L. B. Du, A. J. Lowery, S. Frisken, and B. J. Eggleton, “An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing,” Opt. Express |

23. | A. Hill and D. Payne, “Linear crosstalk in wavelength-division-multiplexed optical-fiber transmission systems,” J. Lightwave Technol. |

24. | J. Zhou, M. O’Mahony, and S. Walker, “Analysis of optical crosstalk effects in multi-wavelength switched networks,” IEEE Photonics Technol. Lett. |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(060.1155) Fiber optics and optical communications : All-optical networks

**ToC Category:**

Optics in Computing

**History**

Original Manuscript: October 16, 2013

Revised Manuscript: December 14, 2013

Manuscript Accepted: January 22, 2014

Published: January 30, 2014

**Citation**

Yvan Paquot, Jochen Schröder, and Benjamin J. Eggleton, "Reconfigurable linear combination of phase-and-amplitude coded optical signals," Opt. Express **22**, 2609-2619 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2609

Sort: Year | Journal | Reset

### References

- P. J. Winzer, R.-J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. 24, 4711–4728 (2006). [CrossRef]
- K. Azadet, E. Haratsch, H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid State Circuits 37, 317–327 (2002). [CrossRef]
- L. B. Du, A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18, 17075–17088 (2010). [CrossRef] [PubMed]
- P. Bower, I. Dedic, “High speed converters and DSP for 100G and beyond,” Opt. Fiber Technol. 17, 464–471 (2011). [CrossRef]
- R. A. Athale, “Optical matrix algebraic processors: a survey,” in 10th International Optical Computing Conference,S. Horvitz, ed. (International Society for Optics and Photonics, 1983), pp. 24–31. [CrossRef]
- X. Wang, J. Peng, M. Li, Z. Shen, O. Shan, “Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platform,” Appl. Opt. 49, 2352–2362 (2010). [CrossRef] [PubMed]
- D. E. Tamir, N. T. Shaked, P. J. Wilson, S. Dolev, “High-speed and low-power electro-optical DSP coprocessor,” J. Opt. Soc. Am. A 26, 11–20 (2009). [CrossRef]
- P. Yeh, A. E. T. Chiou, “Optical matrix-vector multiplication through four-wave mixing in photorefractive media,” Opt. Lett. 12, 138–140 (1987). [CrossRef] [PubMed]
- H. Ishikawa, Ultrafast All-Optical Signal Processing Devices (John Wiley, 2008). [CrossRef]
- G. Berrettini, A. Simi, A. Malacarne, A. Bogoni, L. Potí, “Ultrafast integrable and reconfigurable XNOR, AND, NOR, and NOT photonic logic gate,” IEEE Photonics Technol. Lett. 18, 917–919 (2006). [CrossRef]
- S. Singh, L. Lovkesh, “Ultrahigh speed optical signal processing logic based on an SOA-MZI,” IEEE J. Sel. Top. Quantum Electron. 18, 970–977 (2012). [CrossRef]
- D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, J. Leuthold, “26 Tbit/s line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5, 364–371 (2011). [CrossRef]
- M. Freiberger, D. Templeton, E. Mercado, “Low latency optical services,” in National Fiber Optic Engineers Conference(2012), paper NTu2E.1. [CrossRef]
- D. Schneider, “Trading at the speed of light,” IEEE Spectrum 48, 11–12 (2011). [CrossRef]
- L. Yan, A. Willner, X. Wu, A. Yi, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012). [CrossRef]
- J. Kurumida, S. J. B. Yoo, “Nonlinear optical signal processing in optical packet switching systems,” IEEE J. Sel. Top. Quantum Electron. 18, 978–987 (2012). [CrossRef]
- H. J. Caulfield, S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4, 261–263 (2010). [CrossRef]
- A. Willner, O. Yilmaz, J. Wang, X. Wu, A. Bogoni, L. Zhang, S. R. Nuccio, “Optically efficient nonlinear signal processing,” IEEE J. Sel. Top. Quantum Electron. 17, 320–332 (2011). [CrossRef]
- Y. Paquot, J. Schröder, M. D. Pelusi, B. J. Eggleton, “All-optical hash code generation and verification for low latency communications,” Opt. Express 21, 23873–23884 (2013). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
- J. Wang, Q. Sun, J. Sun, “All-optical 40 Gbit/s CSRZ-DPSK logic XOR gate and format conversion using four-wave mixing,” Opt. Express 17, 12555–12563 (2009). [CrossRef] [PubMed]
- J. Schröder, M. A. F. Roelens, L. B. Du, A. J. Lowery, S. Frisken, B. J. Eggleton, “An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing,” Opt. Express 21, 690–697 (2013). [CrossRef] [PubMed]
- A. Hill, D. Payne, “Linear crosstalk in wavelength-division-multiplexed optical-fiber transmission systems,” J. Lightwave Technol. 3, 643–651 (1985). [CrossRef]
- J. Zhou, M. O’Mahony, S. Walker, “Analysis of optical crosstalk effects in multi-wavelength switched networks,” IEEE Photonics Technol. Lett. 6, 302–305 (1994). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.