Abstract

In this paper, the implementation of an all-optical logic gate based on a Mach-Zehnder interferometer (MZI) configuration is addressed with underlying nonlinear slot-waveguides. In order to reduce power consumption requirements, different ring-resonator structures are introduced in the arms of the MZI. A nonlinear Transfer Matrix Method is developed and used to analyze the response of the nonlinear MZI in order to optimize power requirements with maximum bit rates. The numerical analysis shows that a reduction in the switching power from 2.5 W to less than 5 mW can be achieved by a proper design of the ring-resonator structures introduced in the MZI arms. In addition, it is shown that the logic gate can handle bit rates higher than 60 Gbit/s.

© 2007 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics (Academic Press, 2003).
  2. G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
    [Crossref]
  3. C.A. Barrios, “High-performance all-optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
    [Crossref]
  4. P. Sanchis, et alt, “All-optical MZI XOR logic gate based on Si slot waveguides filled by Si-nc embedded in SiO2,” Proceedings of the 3rd International conference on Group IV photonics. 13–15 September 2006, Otawa (Canada).
  5. M. Soljačić, S. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).
    [Crossref]
  6. Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [Crossref] [PubMed]
  7. S. Dubovitsky and H. Steier, “Relationship Between the Slowing and Loss in Optical Delay Lines,” IEEE J. Quantum Electron. 42, 372–377 (2006).
    [Crossref]
  8. J.E. Heebner and R.W. Boyd, “Enhanced all-optical switching by use of fiber ring resonator,” Opt. Lett. 24, 847–849, (1999).
    [Crossref]
  9. J.K.S. Poon, J. Scheuer, S. Mookherjea, G.T. paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103, (2004),http://www.opticsexpress.org/abstract.cfm?id=78458
    [Crossref] [PubMed]
  10. X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
    [Crossref]
  11. A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
    [Crossref]
  12. V. Lousse and J.P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
    [Crossref]
  13. F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).
  14. J.E. Heebner, “Nonlinear Optical Whispering Gallery Microresonators for Photonics,“ (2003). Thesis available in the following link: http://www.optics.rochester.edu/workgroups/boyd/nonlinear.html
  15. P. Andrew Anderson, Bradley S. Schmidt, and Michal Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202, (2006),http://oe. osa. or g/abstract.cfm?id=114595
    [Crossref] [PubMed]
  16. B.G. Lee, B.A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31,2701–2703, (2006).
    [Crossref] [PubMed]
  17. G. P. Agrawal, Fiber-Optic Communications, (Wiley-InterSciencie, 3rd edition, 2002).

2006 (4)

S. Dubovitsky and H. Steier, “Relationship Between the Slowing and Loss in Optical Delay Lines,” IEEE J. Quantum Electron. 42, 372–377 (2006).
[Crossref]

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

B.G. Lee, B.A. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31,2701–2703, (2006).
[Crossref] [PubMed]

P. Andrew Anderson, Bradley S. Schmidt, and Michal Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202, (2006),http://oe. osa. or g/abstract.cfm?id=114595
[Crossref] [PubMed]

2004 (4)

J.K.S. Poon, J. Scheuer, S. Mookherjea, G.T. paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103, (2004),http://www.opticsexpress.org/abstract.cfm?id=78458
[Crossref] [PubMed]

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

C.A. Barrios, “High-performance all-optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
[Crossref]

2003 (1)

J.E. Heebner, “Nonlinear Optical Whispering Gallery Microresonators for Photonics,“ (2003). Thesis available in the following link: http://www.optics.rochester.edu/workgroups/boyd/nonlinear.html

2002 (2)

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

M. Soljačić, S. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).
[Crossref]

2001 (1)

V. Lousse and J.P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
[Crossref]

1999 (1)

1995 (1)

A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communications, (Wiley-InterSciencie, 3rd edition, 2002).

Almeida, Vilson R.

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Andrew Anderson, P.

Barrios, C.A.

C.A. Barrios, “High-performance all-optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
[Crossref]

Barrios, Carlos A.

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Bergman, K.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

Boyd, R.W.

Cazzanelli, M.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Cuesta-Soto, F.

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

Dubovitsky, S.

S. Dubovitsky and H. Steier, “Relationship Between the Slowing and Loss in Optical Delay Lines,” IEEE J. Quantum Electron. 42, 372–377 (2006).
[Crossref]

Fan, S.

Franzó, G.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Gaburro, Z.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

García-Baños, B.

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

Heebner, J.E.

J.E. Heebner, “Nonlinear Optical Whispering Gallery Microresonators for Photonics,“ (2003). Thesis available in the following link: http://www.optics.rochester.edu/workgroups/boyd/nonlinear.html

J.E. Heebner and R.W. Boyd, “Enhanced all-optical switching by use of fiber ring resonator,” Opt. Lett. 24, 847–849, (1999).
[Crossref]

Hong, W.

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

Huang, D.

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

Huang, Y.

Iacona, F.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Ibanescu, M.

Ippen, E.

Joannopoulos, J.

Johnson, S.

Koshiba, M.

A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
[Crossref]

Lee, B.G.

Lipson, M.

Lipson, Michal

P. Andrew Anderson, Bradley S. Schmidt, and Michal Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202, (2006),http://oe. osa. or g/abstract.cfm?id=114595
[Crossref] [PubMed]

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Lousse, V.

V. Lousse and J.P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
[Crossref]

Martí, J.

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

Martínez, A.

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

Mookherjea, S.

Niiyama, A.

A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
[Crossref]

paloczi, G.T.

Panepucci, Roberto R.

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Pavesi, L.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Poon, J.K.S.

Priolo, F.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Sanchis, P.

P. Sanchis, et alt, “All-optical MZI XOR logic gate based on Si slot waveguides filled by Si-nc embedded in SiO2,” Proceedings of the 3rd International conference on Group IV photonics. 13–15 September 2006, Otawa (Canada).

Scheuer, J.

Schmidt, Bradley S.

Small, B.A.

Soljacic, M.

Steier, H.

S. Dubovitsky and H. Steier, “Relationship Between the Slowing and Loss in Optical Delay Lines,” IEEE J. Quantum Electron. 42, 372–377 (2006).
[Crossref]

Tsuji, Y.

A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
[Crossref]

Vigneron, J.P.

V. Lousse and J.P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
[Crossref]

Vijaya Prakash, G.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

Xu, Q.

Yariv, A.

Zhang, X.

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

Electron. Lett. (2)

C.A. Barrios, “High-performance all-optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
[Crossref]

X. Zhang, X. Zhang, W. Hong, and D. Huang, “Simple method for spectral response simulation of micro-ring resonators by combining transfer matrix method with FDTD method,” Electron. Lett. 42, 1095–1096, (2006)
[Crossref]

IEEE J. Quantum Electron. (1)

S. Dubovitsky and H. Steier, “Relationship Between the Slowing and Loss in Optical Delay Lines,” IEEE J. Quantum Electron. 42, 372–377 (2006).
[Crossref]

IEEE J. Sel. Top. Quantum Electron (1)

F. Cuesta-Soto, A. Martínez, B. García-Baños, and J. Martí, “Numerical Analysis of All-Optical Switching Based on a 2-D Nonlinear Photonic Crystal Directional Coupler,” IEEE J. Sel. Top. Quantum Electron 10, (2004).

J. Lightwave Technol. (1)

A. Niiyama, M. Koshiba, and Y. Tsuji, “An efficient scalar finite element formulation for nonlinear optical channel waveguides,” J. Lightwave Technol. 13, 1919–1925, (1995).
[Crossref]

J. Mod. Opt. (1)

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzó, and F. Priolo, “Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals,” J. Mod. Opt. 49, 719–730, (2002).
[Crossref]

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

Nature (1)

Vilson R. Almeida, Carlos A. Barrios, Roberto R. Panepucci, and Michal Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

V. Lousse and J.P. Vigneron, “Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials,” Phys. Rev. E 63, 027602 (2001).
[Crossref]

Other (4)

J.E. Heebner, “Nonlinear Optical Whispering Gallery Microresonators for Photonics,“ (2003). Thesis available in the following link: http://www.optics.rochester.edu/workgroups/boyd/nonlinear.html

G. P. Agrawal, Fiber-Optic Communications, (Wiley-InterSciencie, 3rd edition, 2002).

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

P. Sanchis, et alt, “All-optical MZI XOR logic gate based on Si slot waveguides filled by Si-nc embedded in SiO2,” Proceedings of the 3rd International conference on Group IV photonics. 13–15 September 2006, Otawa (Canada).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the slot waveguide employed to build the all-optical logic gate. The transverse electric field profile is drawn in blue line. A strong confinement of the electric field inside the slot is clearly observed.

Fig. 2.
Fig. 2.

Schemes of the MZI-based XOR logic gates studied in this work. The RR structures employed to enhance the nonlinear effects are surrounded by a dotted line: a) Type I and b) Type II.

Fig. 3.
Fig. 3.

Basic building blocks of a RR structure: Transmission line of length L and propagating constant γ and directional coupler; k: coupling coefficient and t transmission coefficient.

Fig. 4.
Fig. 4.

Effective nonlinear phase shift induced by the RR structure shown in the inset.

Fig. 5.
Fig. 5.

Nonlinearly induced effective phase shift in the Control signal in a single MZI arm as a function of the pumping Data A/B light power. a) Type I structure and b) Type II structure. The Data signal is centered at the resonant frequency (blue) and detuned to longer wavelengths (red). Propagation losses of 20 dB/cm are also considered in the dashed line responses.

Fig. 6.
Fig. 6.

Nonlinear induced variation in the transmitted amplitude of the Control signal in a single MZI arm as a function of the pumping Data A/B light power. a) Type I structure and b) Type II structure. The Data signal is centered at the resonant frequency of the RR (blue) and detuned to longer wavelengths (green) when losses of 20 dB/cm are considered.

Fig. 7.
Fig. 7.

Transmission of the Control signal of the whole MZI-based logic gate as a function of the Data A/B power with and without losses. a) Type I b) Type II.

Fig. 8.
Fig. 8.

Maximum Transmission of the Control signal through the whole MZI structure as a function of the Data power and Data wavelength. a) Contourmap; b) and c) height-coded maps.

Fig. 9.
Fig. 9.

Normalized time delay as a function of wavelength for the first 2 RR structure (blue line) and for the last 3 RR structure (green line) of Table 2. The ideal wavelength response (solid lines) is distorted in the nonlinear regime (dashed lines).

Fig. 10.
Fig. 10.

Bit rate as a function of wavelength for the first 2 RR structure (blue line) and the last 3 RR structure (green line) of Table 2. The ideal wavelength response (solid lines) is distorted in the nonlinear regime (dashed lines).

Tables (2)

Tables Icon

Table 1. Optimum Data-signal power for Type I structures with 1 RR.

Tables Icon

Table 2. Optimum Data-signal power for Type I structures with more than 1 RR.

Equations (3)

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H n + 1 ( λ ) = f ( λ , R , n ef , I n )
h ( t ) = ( t ) k 2 m = 1 t m 1 exp { j n = 1 m θ n } δ ( t mT R )
σ = σ 0 2 + ( τ d ω 2 σ 0 ) 2 + ( 2 τ d ω 2 4 2 σ 0 2 ) 2 1 4 B

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