## New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer

Optics Express, Vol. 16, Issue 1, pp. 248-257 (2008)

http://dx.doi.org/10.1364/OE.16.000248

Acrobat PDF (286 KB)

### Abstract

We propose new all-optical logic gates containing a local nonlinear Mach-Zehnder interferometer waveguide structure. The light-induced index changes in the Mach-Zehnder waveguide structure make the output signal beam propagate through different nonlinear output waveguides. Based on the output signal beam propagating property, various all-optical logic gates by using the local nonlinear Mach-Zehnder waveguide interferometer structure with two straight control waveguides have been proposed to perform XOR/NXOR, AND/NAND, and OR/NOR logic functions.

© 2008 Optical Society of America

## 1. Introduction

9. C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE J. Quantum Electron. **21**, 774–783 (1985). [CrossRef]

15. A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. **22**, 319–324 (1986). [CrossRef]

19. C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, “Analyzing multilayer optical waveguide with all nonlinear layers,” Optics Express **15**, 2499–2516 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-5-2499 [CrossRef] [PubMed]

24. A. M. Kan’an and P. Likam wa, “Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer,” J. Opt. Soc. Am. B. **14**, 3217–3223 (1997). [CrossRef]

26. Y. Chung and N. Dagli, “As assessment of finite difference beam propagation method,” IEEE Journal of Quantum Electronics. **26**, 1335–1339 (1994). [CrossRef]

## 2. Analysis

*θ*,

_{1}*w*the width of control waveguide,

_{1}*w*the width of Mach-Zehnder waveguide,

_{2}*L*the length of Mach-Zehnder waveguide,

_{1}*L*the length of nonlinear output waveguides, and

_{2}*L*the length of local nonlinear waveguides. The distance between the local control waveguide and the nearest signal waveguide is

_{3}*l*and the branching angle between the output guides is

*θ*.

_{2}*m*=3,5,7,…). The cladding and substrate layers are assumed to extend to infinity in the +x and −x direction, respectively. The major significance of this assumption is that there are no reflections in the x direction to be concerned with, except for those occurring at interfaces.

*ω*is the angular frequency,

*k*

_{0}is the wave number in the free space, and

**β**is the effective refractive index. For a Kerr-type nonlinear medium, the square of the refractive index of the guiding film can be expressed as[27–28]:

*n*

_{0i}and

*α*are the linear refractive index and the nonlinear coefficient of the

_{i}*i*-th layer nonlinear guiding film, respectively. The transverse electric field in each layer can be

*d*and

*w*are the widths of the guiding film and the interaction layer, respectively.

*p*,

_{i}*b*,

_{i}*A*,

_{i}*l*,

_{i}*b*′

_{i},

*A*′

_{i}, and

*l*′

_{i}can be expressed as

*a*,

_{i}*a*′

_{i},

*q*,

_{i}*Q*,

_{i}*K*,

_{i}*x*

_{0i}, and

*x*′

_{0i}are all constants which can be determined by a numerical method on a computer.

## 3. Numerical Results

*µm*. The numerical data have been calculated with the value: the total propagation distance

*z*=12500

*µm*,

*θ*=0.5°,

_{1}*θ*=0.25°,

_{2}*l*=3.5

*µm*,

*w*=1

_{1}*µm*,

*w*=2

_{2}*µm*,

*L*=10000

_{1}*µm*,

*L*=2500

_{2}*µm*,

*L*=4100

_{3}*µm*, α=6.3786µm

^{2}/V

^{2},

*n*=1.55,

_{f0}*n*=1.545, the free space wavelength

_{c0}*λ*=1.55

*µm*. We first examine the XOR/NXOR logic functions, as shown in Fig. 3(a)–(d). Figure 3 shows the typical evolutions of the input light waves propagating along the structure with the input control power P

_{c}=23.7 W/m and the input signal power P

_{s}=79 W/m. When there is no control straight through the central output guide C, as shown in Fig. 3(a). When only the right control guide B is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 3(b). When only the left control guide A is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 3(c). When both of the control guides A and B are excited simultaneously, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 3(d). As the results shown above, the output port C functions as an NXOR Gate and the output port D functions as an XOR gate. All logic states of the XOR and NXOR gates are shown in Table 1.

_{c}=30 W/m and the input signal power P

_{s}=60 W/m. When there is no control beam, the output signal beam will propagate through the right output guide D, as shown in Fig. 4(a). When only the right control guide B is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 4(b). When only the left control guide A is excited, the output signal beam will propagate through the right output guide D, as shown in Fig. 4(c). When both of the control guides A and B are excited simultaneously, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 4(d). As the results shown above, the output port C functions as an AND gate and the output port D functions as a NAND gate. All logic states of the AND and NAND gates are shown in Table2.

_{c}=31.2 W/m and the input signal power P

_{s}=78 W/m. When there is no control beam, the output signal beam will propagate through the right output guide D, as shown in Fig. 5(a). When only the right control guide B is excited, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(b). When only the left control guide A is excited, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(c). When both of the control guides A and B are excited simultaneously, the output signal beam will propagate straight through the central output guide C, as shown in Fig. 5(d). As the results shown above, the output port C functions as an OR gate and the output port D functions as a XOR gate. All logic states of the OR and NOR gates are shown in Table3.

## 4. Conclusions

## Acknowledgement

## References and links

1. | Y. D. Wu, M. H. Chen, and C. H. Chu, “All-Optical Logic Device Using Bent Nonlinear Taperred Y-Junction Waveguide Structure,” Fiber and Integrated Optics. |

2. | Y. D. Wu, M. H. Chen, and R. Z. Tasy, “A new all-optical Switching Device by using the nonlinear Mach-Zehnder interferometer with a control waveguides,” Proceedings CLEO/Pacific Rim Conference on Laser and Electro-Optics. |

3. | Y. D. Wu, M. H. Chen, and H. J. Tasi, “Novel All-optical Switching Device with Localized Nonlinearity,” Optical Society of America, Optics in Computing Devices.297–299 (2002). |

4. | Y. D. Wu, “Nonlinear All-Optical Switching Device by Using the Spatial Soliton Collision,” Fiber and Integrated Optics. |

5. | F. Garzia and M. Bertolotti, “All-optical security coded key,” Optical Quantum Electronics. |

6. | Y. H. Pramono and Endarko, “Nonlinear Waveguides for Optical Logic and Computation,” Journal of Nonlinear Optical Physics & Materials. |

7. | Y. H. Pramono, M. Geshiro, T. Kitamura, and S. Sawa, “Optical Logic OR-AND-NOT and NOR Gates in Waveguides Consisting of Nonlinear Material,” IEICE Trans. Electron. |

8. | Y. D. Wu, M. L. Whang, M. H. Chen, and R. Z. Tasy, “All-optical Switch Based on the Local Nonlinear Mach-Zehnder Interferometer,” Optics Express |

9. | C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, “Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media,” IEEE J. Quantum Electron. |

10. | L. Leine, C. Wacher, U. Langbein, and F. Lederer, “Evolution of nonlinear guided optical fields down a dielectric film with nonlinear cladding,” J. Opt. Soc. Amer. B. |

11. | S. She and S. Zhang, “Analysis of nonlinear TE waves in a periodic refractive index waveguide with nonlinear cladding,” Opt. Comm. |

12. | Y. D. Wu, M. H. Chen, and H. J. Tasi, “A General Method for Analyzing the Multilayer Optical Waveguide with Nonlinear Cladding and Substrate”, SPIE Design, Fabrication, and Characterization of Photonic Device II. |

13. | Y. D. Wu and M. H. Chen, “Analyzing multiplayer optical waveguides with nonlinear cladding and substrates,” J. Opt. Soc. Am. B. |

14. | Y. D. Wu and M. H. Chen, “The fundamental theory of the symmetric three layer nonlinear optical waveguide structures and the numerical simulation,” J. Nat. Kao. Uni. of App. Sci. |

15. | A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. |

16. | H. Murata, M. Izutsu, and T. Sueta, “Optical bistability and all-optical switching in novel waveguide functions with localized optical nonlinearity,” J. Lightwave Technol. |

17. | Y. D. Wu and Y. C. Jang, “Analyzing and Numerical study of Seven-Layer Optical Waveguide with Localized Nonlinear Central guiding Film,” Proceedings Electrical and Information Engineering Symposium.24–28 (2003). |

18. | Y. D. Wu, “Analyzing Multilayer Optical Waveguides with a Localized Arbitrary Nonlinear Guiding Film,” IEEE J. Quantum. Electron. |

19. | C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, “Analyzing multilayer optical waveguide with all nonlinear layers,” Optics Express |

20. | X. F. Liu, M.L. Ke, B.C. Qiu, A.C. Bryce, and J.H. Marsh, “Fabrication of monolithically integrated Mach-Zehnder asymmetric interferometer switch,” Indium Phosphide and Related Materials, 2000. Conference Proceedings. 2000 International Conference on. 412–414 (2000). |

21. | H. Ehlers, M. Schlak, and U.H.P. Fischer, “Multi-fiber-chip-coupling modules for monolithically integrated Mach-Zehnder interferometers for TDM/WDM communication systems,” Optical Fiber Communication Conference and Exhibit. |

22. | L. Pavelescu, “Simplified design relationships for silicon integrated optical pressure sensors based on Mach-Zehnder interferometry with antiresonant reflecting optical waveguides,” Semiconductor Conference, 2001. CAS 2001 Proceedings. International. |

23. | T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, “All-optical logic gates containing a two-mode nonlinear waveguide,” IEEE Journal of Quantum Electronics. |

24. | A. M. Kan’an and P. Likam wa, “Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer,” J. Opt. Soc. Am. B. |

25. | Y. H. Pramono and Endarko, “Nonlinear waveguides for optical logic and computation,” Journal of Nonlinear Optical Physics & Materials. |

26. | Y. Chung and N. Dagli, “As assessment of finite difference beam propagation method,” IEEE Journal of Quantum Electronics. |

27. | C. T. Seaton, X. Mai, G. I. Stegeman, and N. G. Winful, “Nonlinear guided wave applications,” Opt. Eng. |

28. | H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, “Experimental observation of nonlinear guided waves,” Opt. Lett. |

**OCIS Codes**

(130.3750) Integrated optics : Optical logic devices

(190.0190) Nonlinear optics : Nonlinear optics

(190.3270) Nonlinear optics : Kerr effect

(190.4360) Nonlinear optics : Nonlinear optics, devices

(230.1150) Optical devices : All-optical devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 8, 2007

Revised Manuscript: December 14, 2007

Manuscript Accepted: December 18, 2007

Published: January 3, 2008

**Citation**

Yaw-Dong Wu, Tien-Tsorng Shih, and Mao-Hsiung Chen, "New all-optical logic gates based on the local nonlinear Mach-Zehnder interferometer," Opt. Express **16**, 248-257 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-248

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### References

- Y. D. Wu, M. H. Chen, and C. H. Chu, "All-optical logic device using bent nonlinear tapered Y-junction waveguide structure," Fiber Integr. Opt. 20, 517-524 (2001).
- Y. D. Wu, M. H. Chen, and R. Z. Tasy, "A new all-optical switching device by using the nonlinear Mach-Zehnder interferometer with a control waveguides," Proceedings CLEO/Pacific Rim Conference on Laser and Electro-Optics. I, 292 (2003).
- Y. D. Wu, M. H. Chen, and H. J. Tasi, "Novel all-optical switching device with localized nonlinearity," Optical Society of America, Optics in Computing Devices, 297-299 (2002).
- Y. D. Wu, "Nonlinear all-optical switching device by using the Spatial Soliton Collision," Fiber Integr Opt. 23, 387-404 (2004). [CrossRef]
- F. Garzia and M. Bertolotti, "All-optical security coded key," Opt. Quantum Electron. 33, 527-540 (2001). [CrossRef]
- Y. H. Pramono and Endarko, "Nonlinear waveguides for optical logic and computation," J. Nonlinear Opt. Phys. Mater. 10, 209-222 (2001). [CrossRef]
- Y. H. Pramono, M. Geshiro, T. Kitamura, and S. Sawa, "Optical logic OR-AND-NOT and NOR gates in waveguides consisting of nonlinear material," IEICE Trans. Electron. E 83-C, 1755-1762 (2000).
- Y. D. Wu, M. L. Whang, M. H. Chen, and R. Z. Tasy, "All-optical switch based on the local Nonlinear Mach-Zehnder Interferometer," Opt. Express 15, 9883-9892 (2007). [CrossRef] [PubMed]
- C. T. Steaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. 21, 774-783 (1985). [CrossRef]
- L. Leine, C. Wacher, U. Langbein, and F. Lederer, "Evolution of nonlinear guided optical fields down a dielectric film with nonlinear cladding," J. Opt. Soc. Am B. 5, 547-558 (1988). [CrossRef]
- S. She and S. Zhang, "Analysis of nonlinear TE waves in a periodic refractive index waveguide with nonlinear cladding," Opt. Commun. 161, 141-148 (1999). [CrossRef]
- Y. D. Wu, M. H. Chen, and H. J. Tasi, "A General Method for Analyzing the Multilayer Optical Waveguide with Nonlinear Cladding and Substrate," SPIE Design, Fabrication, and Characterization of Photonic Device II 4594, 323-331 (2001).
- Y. D. Wu and M. H. Chen, "Analyzing multiplayer optical waveguides with nonlinear cladding and substrates," J. Opt. Soc. Am. B. 19, 1737-1745 (2002). [CrossRef]
- Y. D. Wu and M. H. Chen, "The fundamental theory of the symmetric three layer nonlinear optical waveguide structures and the numerical simulation," J. Nat. Kao. Uni. App. Sci. 32, 7982-7996 (2002).
- A. D. Boardman and P. Egan, "Optically nonlinear waves in thin films," IEEE J. Quantum Electron. 22, 319-324 (1986). [CrossRef]
- H. Murata, M. Izutsu, and T. Sueta, "Optical bistability and all-optical switching in novel waveguide functions with localized optical nonlinearity," J. Lightwave Technol. 16, 833-840 (1998). [CrossRef]
- Y. D. Wu and Y. C. Jang, "Analyzing and numerical study of seven-layer optical waveguide with localized nonlinear central guiding film," Proceedings Electrical and Information Engineering Symposium 24-28 (2003).
- Y. D. Wu, "Analyzing multilayer optical waveguides with a localized arbitrary nonlinear guiding film," IEEE J. Quantum. Electron. 40, 529-540 (2004). [CrossRef]
- C. W. Kuo, S. Y. Chen, M. H. Chen, C. F. Chang, and Y. D. Wu, "Analyzing multilayer optical waveguide with all nonlinear layers," Opt. Express 15, 2499-2516 (2007). [CrossRef] [PubMed]
- X. F. Liu, M. L. Ke, B. C. Qiu, A. C. Bryce, and J. H. Marsh, "Fabrication of monolithically integrated Mach-Zehnder asymmetric interferometer switch," Indium Phosphide and Related Materials, 2000. Conference Proceedings 2000 International Conference 412-414 (2000).
- H. Ehlers, M. Schlak, and U. H. P. Fischer, "Multi-fiber-chip-coupling modules for monolithically integrated Mach-Zehnder interferometers for TDM/WDM communication systems," Optical Fiber Communication Conference and Exhibit. 3, WDD66-1~66-3 (2001).
- L. Pavelescu, "Simplified design relationships for silicon integrated optical pressure sensors based on Mach-Zehnder interferometry with antiresonant reflecting optical waveguides," Semiconductor Conference, 2001. CAS 2001 Proceedings. International 1, 201-204 (2001). [CrossRef]
- T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron 38, 37-46 (2002). [CrossRef]
- A. M. Kan’an and P. Likamwa, "Ultrafast all-optical switching not limited by the carrier lifetime in an integrated multiple-quantum-well Mach-Zehnder interferometer," J. Opt. Soc. Am. B. 14, 3217-3223 (1997). [CrossRef]
- Y. H. Pramono and Endarko, "Nonlinear waveguides for optical logic and computation," J. Nonlinear Opt. Phys. Mater. 10, 209-222 (2001). [CrossRef]
- Y. Chung and N. Dagli, "As assessment of finite difference beam propagation method," IEEE J. Quantum Electron. 26, 1335-1339 (1994). [CrossRef]
- C. T. Seaton, X. Mai, G. I. Stegeman, and N. G. Winful, "Nonlinear guided wave applications," Opt. Eng. 24, 593-599 (1985).
- H. Vach, G. I. Stegeman, C. T. Seaton, and I. C. Khoo, "Experimental observation of nonlinear guided waves," Opt. Lett. 9, 238-240 (1984). [CrossRef] [PubMed]

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