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

Yvan Paquot; Jochen Schröder; Benjamin J. Eggleton

doi:10.1364/OE.22.002609

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

Yvan Paquot, Jochen Schröder, and Benjamin J. Eggleton

Optics Express
Vol. 22,
Issue 3,
pp. 2609-2619
(2014)
•https://doi.org/10.1364/OE.22.002609

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

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Related Topics
Table of Contents Category
- Optics in Computing
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- All-optical networks (060.1155)
- Nonlinear optics, four-wave mixing (190.4380)

About this Article
History
- Original Manuscript: October 16, 2013
- Revised Manuscript: December 14, 2013
- Manuscript Accepted: January 22, 2014
- Published: January 30, 2014

Accessible

Open Access

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.

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References

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Year
|
Author
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Publication

P. J. Winzer and R.-J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. 24, 4711–4728 (2006).
[Crossref]
K. Azadet, E. Haratsch, and H. Kim, “Equalization and FEC techniques for optical transceivers,” IEEE J. Solid State Circuits 37, 317–327 (2002).
[Crossref]
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]
P. Bower and 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, and 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, and S. Dolev, “High-speed and low-power electro-optical DSP coprocessor,” J. Opt. Soc. Am. A 26, 11–20 (2009).
[Crossref]
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]
H. Ishikawa, Ultrafast All-Optical Signal Processing Devices (John Wiley, 2008).
[Crossref]
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]
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]
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]
M. Freiberger, D. Templeton, and 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, and A. Yi, “All-optical signal processing for ultrahigh speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
[Crossref]
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]
H. J. Caulfield and 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, and 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, and 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, 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]
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]
A. Hill and 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, and S. Walker, “Analysis of optical crosstalk effects in multi-wavelength switched networks,” IEEE Photonics Technol. Lett. 6, 302–305 (1994).
[Crossref]

2013 (2)

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]

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]

2012 (3)

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]

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]

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]

2011 (4)

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]

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]

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

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

2010 (3)

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

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]

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]

2009 (2)

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]

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]

2006 (2)

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]

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

2002 (1)

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

1994 (1)

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]

1987 (1)

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]

1985 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Athale, R. A.

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]

Azadet, K.

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

Becker, J.

Ben Ezra, S.

Berrettini, G.

Bogoni, A.

Bonk, R.

Bower, P.

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

Caulfield, H. J.

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

Chiou, A. E. T.

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]

Dedic, I.

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

Dolev, S.

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

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]

Dreschmann, M.

Du, L. B.

Eggleton, B. J.

Ellermeyer, T.

Essiambre, R.-J.

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

Freiberger, M.

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

Freude, W.

Frey, F.

Frisken, S.

Haratsch, E.

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

Hill, A.

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

Hillerkuss, D.

Hoh, M.

Huber, G.

Huebner, M.

Ishikawa, H.

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

Jordan, M.

Kim, H.

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

Kleinow, P.

Koenig, S.

Koos, C.

Kurumida, J.

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]

Leuthold, J.

Li, J.

Li, M.

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]

Lovkesh, L.

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]

Lowery, A. J.

Ludwig, A.

Lutz, J.

Malacarne, A.

Marculescu, A.

Mercado, E.

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

Meyer, J.

Moeller, M.

Narkiss, N.

Nebendahl, B.

Nuccio, S. R.

O’Mahony, M.

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]

Oehler, A.

Paquot, Y.

Parmigiani, F.

Payne, D.

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

Pelusi, M. D.

Peng, J.

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]

Petropoulos, P.

Potí, L.

Resan, B.

Roeger, M.

Roelens, M. A. F.

Schellinger, T.

Schmogrow, R.

Schneider, D.

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

Schröder, J.

Shaked, N. T.

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]

Shan, O.

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]

Shen, Z.

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]

Simi, A.

Singh, S.

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]

Sun, J.

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]

Sun, Q.

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]

Tamir, D. E.

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]

Templeton, D.

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

Vallaitis, T.

Walker, S.

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]

Wang, J.

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]

Wang, X.

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]

Weingarten, K.

Willner, A.

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]

Wilson, P. J.

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]

Winter, M.

Yilmaz, O.

Yoo, S. J. B.

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]

Zhang, L.

Zhou, J.

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]

Appl. Opt. (1)

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]

IEEE J. Sel. Top. Quantum Electron. (3)

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]

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]

IEEE J. Solid State Circuits (1)

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

IEEE Photonics Technol. Lett. (2)

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]

IEEE Spectrum (1)

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

J. Lightwave Technol. (3)

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

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]

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

J. Opt. Soc. Am. A (1)

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]

Nat. Photonics (2)

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

Opt. Express (4)

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]

Opt. Fiber Technol. (1)

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

Opt. Lett. (1)

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]

Other (4)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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

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

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Fig. 1 Principle of the all-optical dot-product. Relative phase and magnitude coefficients are applied to three WDM signals before propagating through a Kerr nonlinear medium for generation of idlers at a same frequency. Signals with opposite phases (represented with opposite arrows), lead to idlers canceling each other.

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Fig. 2 Experimental diagram. A comb source is split into a pump pulse train and a data signal encoded using a Mach-Zehnder modulator. Spectral carving and selective delaying of the data signal creates three distinct bit streams. After following different path, pumps and signals are recombined and controlled in phase and intensity by a Fourier domain programmable optical processor (FD-POP) and generate an idler in a highly nonlinear fibre.

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Fig. 3 Optical spectrum after the HNLF. (dashed trace) Signal 1 and Signal 2 are equal, ϕ_S₁ = ϕ_S₂ + π; (dotted trace) Signal 2 and Signal 3 are equal, ϕ_S₂ = ϕ_S₃ + π; (solid trace) dot-product with three signals involved. (Right) Spectrum of the corresponding idlers superimposed and filtering setup.

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Fig. 4 Sampling scope traces showing the modulus squared of the dot-product output signal. The blue traces are simulations of the expected intensity levels.

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Fig. 5 Two WDM signals with controlled amount of distortion are generated. The dot-product device is configured to revert the distortion so as to restore the initial binary signal.

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Fig. 6 Attenuation and phase profiles implemented inside the FD-POP to distort channel 1 (left) and equivalent delay line interferometer (right).

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Fig. 7 Optical spectrum after the HNLF. (black) Signal 1 and Signal 2 are equal, ϕ_S₁ = ϕ_S₂ ; (blue) Signal 1 and Signal 2 are equal, ϕ_S₁ = ϕ_S₂ + π; (green) Signal 1 and Signal 2 are different and affected by a power transfer of 30%, ϕ_S₁ = ϕ_S₂ + π.

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Fig. 8 Bit-error rate testing of the compensator. Back-to-back (B2B) and compensated curves are measured respectively at the wavelength of the signal and of the converted idler.

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Equations (28)

Equations on this page are rendered with MathJax. Learn more.

E_{I_{tot}} = a_{1} E_{S 1} + a_{2} E_{S 2} + a_{3} E_{S 3}

= | a_{1} | e^{i ϕ_{1}} E_{S 1} + | a_{2} | e^{i ϕ_{2}} E_{S 2} + | a_{3} | e^{i ϕ_{3}} E_{S 3}

E_{S 1} (t) = E_{S 1} e^{i 2 π ν_{S 1} t}

E_{S 2} (t) = E_{S 2} e^{i 2 π (ν_{S 1} + Δ ν) t}

E_{S 3} (t) = E_{S 3} e^{i 2 π (ν_{S 1} + 2 Δ ν) t}

E_{P 1} (t) = E_{P 1} e^{i 2 π ν_{P 1} t}

E_{P 2} (t) = E_{P 2} e^{i 2 π (ν_{P 1} + \frac{Δ ν}{2}) t}

E_{P 3} (t) = E_{P 3} e^{i 2 π (ν_{P 1} + Δ ν) t}

k_{I 1} = - k_{S 1} + 2 k_{P 1}

k_{I 2} = - k_{S 2} + 2 k_{P 2}

k_{I 3} = - k_{S 3} + 2 k_{P 3}

ϕ_{I 1} = - ϕ_{S 1} + 2 ϕ_{P 1} = - ϕ_{S 1} + 2 ϕ_{P}

ϕ_{I 2} = - ϕ_{S 2} + 2 ϕ_{P 2} = - ϕ_{S 2} + 2 ϕ_{P}

ϕ_{I 2} = - ϕ_{S 3} + 2 ϕ_{P 3} = - ϕ_{S 3} + 2 ϕ_{P}

A_{I 1} \propto | a_{1} | A_{S 1} A_{P 1}^{2}

A_{I 2} \propto | a_{2} | A_{S 2} A_{P 2}^{2}

A_{I 3} \propto | a_{3} | A_{S 3} A_{P 3}^{2}

E_{I_{tot}} = A_{I 1} e^{i ϕ_{I 1}} + A_{I 2} e^{i ϕ_{I 2}} + A_{I 3} e^{i ϕ_{I 3}}

\propto (| a_{1} | A_{S 1} e^{- i (ϕ_{S 1} + ϕ_{1})} + | a_{2} | A_{S 2} e^{- i (ϕ_{S 2} + ϕ_{2})} + | a_{3} | A_{S 3} e^{- i (ϕ_{S 3} + ϕ_{3})}) \underset{absolute phase offset}{\underset{︸}{\times e^{i . 2 ϕ_{P}}}}

= a_{1} E_{S 1} + a_{2} E_{S 2} + a_{3} E_{S 3}

X = (\begin{matrix} a & b \\ c & d \end{matrix})

X^{- 1} = α (\begin{matrix} d & - b \\ - c & a \end{matrix})

E_{tot} = a E_{S 1} + b E_{S 2} = A_{S 1} e^{i ϕ_{S 1}} (a e^{- i k \frac{Δ L}{2}} + b e^{+ i k \frac{Δ L}{2}})

= A_{S 1} e^{i ϕ_{S 1}} ((a + b) \cos (k \frac{Δ L}{2}) + i (b - a) \sin (k \frac{Δ L}{2}))

ℋ_{1} = \frac{{| E_{tot} |}^{2}}{{| A_{S 1} |}^{2}} = (a + b^{2}) \cos^{2} (k \frac{Δ L}{2}) + {(b - a)}^{2} \sin^{2} (k \frac{Δ L}{2})

Φ_{1} = angle (E_{tot}) = a \tan (\frac{(b - a) \sin (k \frac{Δ L}{2})}{(a + b) \cos (k \frac{Δ L}{2})})

X_{0.2} = (\begin{matrix} 0.8 & 0.2 \\ 0.2 & 0.8 \end{matrix})

X_{0.3} = (\begin{matrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{matrix})