## Single-PPLN-based simultaneous half-adder, half-subtracter, and OR logic gate: proposal and simulation

Optics Express, Vol. 15, Issue 4, pp. 1690-1699 (2007)

http://dx.doi.org/10.1364/OE.15.001690

Acrobat PDF (204 KB)

### Abstract

We propose and simulate all-optical simultaneous half-adder, half-subtracter, and OR logic gate at 40 Gbit/s based on the cascaded sum-and difference-frequency generation (SFG+DFG) using only one periodically poled lithium niobate (PPLN) waveguide. The SFG and DFG processes generate the Borrow and Carry outputs, respectively. The Sum/Difference and OR are obtained by properly combining the outputs from PPLN after SFG+DFG. The eye diagrams, pulse width, quality-factor (Q-factor), extinction ratio (ER), and tunability are calculated and discussed,showing impressive operation performance.

© 2007 Optical Society of America

## 1. Introduction

1. K. E. Stubkjaer, ‘Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,’ IEEE J. Sel. Top. Quantum Electron. **6**,1428–1435 (2000). [CrossRef]

2. J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, ‘All-optical multiple logic gates with XOR, NOR, OR,
and NAND functions using parallel SOA-MZI structures: theory and experiment,’ J. Lightwave Technol. **24**,3392–3399 (2006). [CrossRef]

4. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, ‘All-optical binary half-adder,’ Opt. Commun. **156**,22–26 (1998). [CrossRef]

5. J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, ‘All-optical half adder using semiconductor optical amplifier based devices,’ Opt. Commun. **218**,345–349 (2003). [CrossRef]

8. J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, ‘Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO_{3} waveguides,’ IEEE Photonics Technol. Lett. **15**,1743–1745
(2003). [CrossRef]

16. J. Wang, J. Sun, and Q. Sun, ‘Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation,’ Opt. Lett. **31**,1711–1713 (2006). [CrossRef] [PubMed]

17. J. Sun and J. Wang, ‘Simulation of optical NOT gate switching by sum-frequency generation in LiNbO_{3} waveguides,’ Opt. Commun. **267**,187–192 (2006). [CrossRef]

## 2. Concept of half-adder, half-subtracter, and OR logic gate

*A*⊕

*B*). As the XOR function can be also represented by Ā ∙

*B*+

*A*∙

*B*̄, it may be implemented by using two AND gates with inverters (‘bubbles’) at the input, and an OR gate to combine the outputs Ā∙

*B*and

*A*∙

*B*̄ from AND gates. The Carry output for half-adder is the AND operation (

*A*∙

*B*) which can be simply obtained with a single AND gate. The Borrow output for half-subtracter takes the logical operation in terms of Ā∙

*B*for A-B and

*A*∙

*B*̄ for B-A. Note that Ā∙

*B*and

*A*∙

*B*̄ are realized during the generation of XOR. Additionally, the logical OR of A and B can be expressed as

*A*+Ā∙

*B*or

*B*+

*A*∙

*B*̄, thus it may be achieved by use of an OR gate to combine

*A*and Ā∙

*B*or

*B*and

*A*∙

*B*̄. As a result, the entire implementation of simultaneous halfadder, half-subtracter, and OR logic gate requires three AND gates, two inverters, and two OR gates.

## 3. Operation principle

*λ*,

_{SA}*λ*), together with the continuous-wave (CW) pump(

_{SB}*λ*) are launched into the PPLN waveguide, in which the SFG+DFG nonlinear interactions take place under the quasi-phase matching (QPM) condition. In the SFG+DFG processes, the SFG interaction converts one photon from signal A(

_{P}*λ*) and another photon from signal B(

_{SA}*λ*) into one sum-frequency photon(

_{SB}*λ*), which is simultaneously transformed into one photon of the pump (

_{SF}*λ*) and the other photon of the new generated idler wave (

_{P}*λ*) through the subsequent DFG process. Thus, both signals A and B are depleted during the generation of the sum-frequency and idler waves. Such phenomenon has been successfully observed in our preliminary experimental work [13

_{i}13. J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, ‘Experimental observation of tunable wavelength downand
up-conversions of ultra-short pulses in a periodically poled LiNbO_{3} waveguide,’ Opt. Commun. **269**,179–187 (2006). [CrossRef]

16. J. Wang, J. Sun, and Q. Sun, ‘Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation,’ Opt. Lett. **31**,1711–1713 (2006). [CrossRef] [PubMed]

*λ*). Similarly, the output data stream A carries the logical result of A ∙ B (

_{SB}*λ*). On the other hand, only when both input A and B data bits are ‘1’, the output sum-frequency and idler waves carry the data bit of ‘1’, corresponding to the logical AND of A and B (A∙B).

_{SA}*B*(

*λ*) is combined with input A(

_{SB}*λ*) through a coupler acting as an OR gate, because of which

_{SA}*A*+ Ā∙ B is achieved,representing the logical OR of A and B. Meanwhile, by combing

*A*∙

*B*̄(

*λ*) with input B (

_{SA}*λ*), the logical OR can be also obtained as

_{SB}*B*+

*A*∙

*B*̄. Note that the combination of output Ā∙B (

*λ*) and

_{SB}*A*∙

*B*̄ (

*λ*) results in Ā ∙

_{SA}*B*+

*A*∙

*B*̄, i.e. logical XOR corresponding to the Sum/Difference of the half-adder and half-subtracter. The output Ā∙

*B*(

*λ*or

_{SF}*λ*) is the Carry of the half-adder. The output Ā∙

_{i}*B*(

*λ*) and

_{SB}*A*∙

*B*(

*λ*) are the Borrows of the half-subtracter A-B and B-A, respectively. As shown in Fig. 2, we use tunable filters (TFs) to isolate the required signals, employ variable optical attenuators (VOAs) to equalize the power level of two data streams before entering into the coupler, and utilize tunable delay lines (TDLs) to align the data bits.

_{SA}## 4. Results and discussions

13. J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, ‘Experimental observation of tunable wavelength downand
up-conversions of ultra-short pulses in a periodically poled LiNbO_{3} waveguide,’ Opt. Commun. **269**,179–187 (2006). [CrossRef]

*A*,

_{SA}*A*,

_{SB}*A*,

_{SF}*A*and

_{P}*A*, as functions of the distance

_{i}*z*and time

*t*, represent the complex amplitudes of the signal A, signal B, sum-frequency, pump, and idler waves,respectively.

*β*

_{1j}and

*β*

_{2j}are the first and second derivatives of the propagation constant

*k*with respect to the angular frequency ω, evaluated at ω

_{j}_{j}(

*j*=

*SA*,

*SB*,

*SF*,

*P*,

*i*).

*κ*and

_{SFG}*κ*are coupling coefficients for the SFG and DFG processes.

_{DFG}*d*is the effective nonlinear coefficient.

_{eff}*A*is the effective interaction area.

_{eff}*n*(

_{j}*j*=

*SA*,

*SB*,

*SF*,

*P*,

*i*) are the refractive indexes for different optical waves. The parameter μ

_{0}is the permeability and

*c*is the light velocity in vacuum. Δ

*k*

_{SFG}and Δ

*k*

_{DFG}refer to the phase mismatching in the SFG and DFG processes, and Λ is the microdomain period of the periodically poled structure in the PPLN waveguide. The above coupled-mode Eqs. (1)-(5) can be numerically solved using the finite difference beam propagation method (FD-BPM) [9

9. J. Sun, Z. Ma, D. Liu, and D. Huang, ‘Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO_{3} waveguides,’ Opt. Quantum Electron. **37**443–456 (2005). [CrossRef]

10. J. Sun, D. Huang, and D. Liu, ‘Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO_{3} waveguides,’ Opt. Commun. **259**,321–327 (2006). [CrossRef]

^{7}-1, 40 Gbit/s pseudorandom bit sequence (PRBS) return-to-zero (RZ) data signals (A, B) with hyperbolicsecant type and 5-ps pulse width are assumed. A continuous-wave pump is considered. The PPLN waveguide is 30 mm long with a waveguide effective area of 50μm

^{2}, and its microdomain period is assumed to be 18.8 μm to meet the SFG QPM condition for sumfrequency wavelength at 772.0 nm. The nonlinear coefficient

*d*

_{33}of the PPLN waveguide is about 27 pm/V and thus the effective nonlinear coefficient (

*d*=

_{eff}*d*

_{33}∙ 2/π) is approximately 17.2 pm/V. The central wavelengths of signals A and B are set at 1550.0 and 1538.0 nm, respectively, producing the sum-frequency wave at 772.0 nm via SFG. The pump wavelength is tuned at 1555.0 nm, thus the idler wavelength is generated at about 1533.2 nm by DFG. The peak powers of signals A, B and the pump power launched into the PPLN waveguide are assumed to be 1000,1000 ∙ λ

_{SA}/

*λ*[17

_{SB}17. J. Sun and J. Wang, ‘Simulation of optical NOT gate switching by sum-frequency generation in LiNbO_{3} waveguides,’ Opt. Commun. **267**,187–192 (2006). [CrossRef]

13. J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, ‘Experimental observation of tunable wavelength downand
up-conversions of ultra-short pulses in a periodically poled LiNbO_{3} waveguide,’ Opt. Commun. **269**,179–187 (2006). [CrossRef]

17. J. Sun and J. Wang, ‘Simulation of optical NOT gate switching by sum-frequency generation in LiNbO_{3} waveguides,’ Opt. Commun. **267**,187–192 (2006). [CrossRef]

_{10}[(μ

_{1}-μ

_{0})/(σ

_{1}+σ

_{0})] and ER=10log

_{10}

^{(μ1/μ0)}are used to evaluate the operation performance, where μ

_{1}and μ

_{0}are the average power of logical ‘1’ and ‘0’ of the eye diagrams at the sampling time, while σ

_{1}and σ

_{0}are the corresponding standard deviations. Note that the performance degradation of Sum/Difference and Borrows shown in Fig. 4(c), Fig. 4(f), and Fig. 4(g) can be explained with the fact that signals A and B are not depleted completely when their data bits are both ‘1’. Such phenomenon can be also clearly seen from Fig. 3(c), Fig. 3(f), and Fig. 3(g). As shown in Fig. 4(d), the Carry of sum-frequency wave (3.1 ps) is compressed compared with the input signal (5 ps). However, due to walk-off effects [13

_{3} waveguide,’ Opt. Commun. **269**,179–187 (2006). [CrossRef]

_{3} waveguides,’ Opt. Commun. **267**,187–192 (2006). [CrossRef]

_{3} waveguide,’ Opt. Commun. **269**,179–187 (2006). [CrossRef]

_{3} waveguides,’ Opt. Commun. **267**,187–192 (2006). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and Links

1. | K. E. Stubkjaer, ‘Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,’ IEEE J. Sel. Top. Quantum Electron. |

2. | J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, ‘All-optical multiple logic gates with XOR, NOR, OR,
and NAND functions using parallel SOA-MZI structures: theory and experiment,’ J. Lightwave Technol. |

3. | S. Kim, S. Lee, B. Kang, S. Lee, and J. Park, ‘All-optical binary half adder using SLALOMs,’ CLEO/Pacific Rim 2001,2, II-254-II-255 (2001). |

4. | A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, ‘All-optical binary half-adder,’ Opt. Commun. |

5. | J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, ‘All-optical half adder using semiconductor optical amplifier based devices,’ Opt. Commun. |

6. | S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, ‘All-optical half adder using a PPLN waveguide and an SOA,’ OFC 2004, February, |

7. | J. E. McGeehan, S. Kumar, and A. E. Willner, ‘All-optical digital half-subtracter/adder using semiconductor optical amplifiers and a PPLN waveguide,’ CLEO 2005, May, |

8. | J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, ‘Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO |

9. | J. Sun, Z. Ma, D. Liu, and D. Huang, ‘Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO |

10. | J. Sun, D. Huang, and D. Liu, ‘Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO |

11. | J. Wang, J. Sun, C. Luo, and Q. Sun, ‘Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum-and difference frequency generation (cSFG/DFG) in a PPLN waveguide,’ Appl. Phys. B |

12. | J. Wang, J. Sun, C. Luo, and Q. Sun, ‘Experimental demonstration of wavelength conversion between pspulses based on cascaded sum-and difference frequency generation (SFG+DFG) in LiNbO |

13. | J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, ‘Experimental observation of tunable wavelength downand
up-conversions of ultra-short pulses in a periodically poled LiNbO |

14. | J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, ‘Tunable wavelength conversion of ps-pulses exploiting
cascaded sum-and difference frequency generation in a PPLN-fiber ring laser,’ IEEE Photonics Technol. Lett. |

15. | J. E. McGeehan, M. Giltrelli, and A. E. Willner, ‘All-optical digital 3-input AND gate using sum-and difference-frequency generation in a PPLN waveguide,’ LEOS 2005, July,179–180 (2005). |

16. | J. Wang, J. Sun, and Q. Sun, ‘Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation,’ Opt. Lett. |

17. | J. Sun and J. Wang, ‘Simulation of optical NOT gate switching by sum-frequency generation in LiNbO |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(070.4560) Fourier optics and signal processing : Data processing by optical means

(130.3730) Integrated optics : Lithium niobate

(190.0190) Nonlinear optics : Nonlinear optics

(200.3760) Optics in computing : Logic-based optical processing

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 13, 2006

Revised Manuscript: December 17, 2006

Manuscript Accepted: January 7, 2007

Published: February 19, 2007

**Citation**

Jian Wang, Junqiang Sun, and Qizhen Sun, "Single-PPLN-based simultaneous half-adder, half-subtracter, and OR logic gate: proposal and simulation," Opt. Express **15**, 1690-1699 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1690

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### References

- K. E. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Top. Quantum Electron. 6, 1428-1435 (2000). [CrossRef]
- J. Y. Kim, J. M. Kang, T. Y. Kim, and S. K. Han, "All-optical multiple logic gates with XOR, NOR, OR, and NAND functions using parallel SOA-MZI structures: theory and experiment," J. Lightwave Technol. 24, 3392-3399 (2006). [CrossRef]
- S. Kim, S. Lee, B. Kang, S. Lee, and J. Park, "All-optical binary half adder using SLALOMs," CLEO/Pacific Rim 2001, 2, II-254-II-255 (2001).
- A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, "All-optical binary half-adder," Opt. Commun. 156, 22-26 (1998). [CrossRef]
- J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, and S. H. Kim, "All-optical half adder using semiconductor optical amplifier based devices," Opt. Commun. 218, 345-349 (2003). [CrossRef]
- S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, "All-optical half adder using a PPLN waveguide and an SOA," OFC 2004, February, 1, 23-27 (2004).
- J. E. McGeehan, S. Kumar, and A. E. Willner, "All-optical digital half-subtracter/adder using semiconductor optical amplifiers and a PPLN waveguide," CLEO 2005, May, 2, 1061-1063 (2005).
- J. Sun, W. Liu, J. Tian, J. R. Kurz, and M. M. Fejer, "Multichannel wavelength conversion exploiting cascaded second-order nonlinearity in LiNbO3 waveguides," IEEE Photonics Technol. Lett. 15, 1743-1745 (2003). [CrossRef]
- J. Sun, Z. Ma, D. Liu, and D. Huang, "Wavelength conversion between picosecond pulses using cascaded second-order nonlinearity in LiNbO3 waveguides," Opt. Quantum Electron. 37443-456 (2005). [CrossRef]
- J. Sun, D. Huang, and D. Liu, "Simultaneous wavelength conversion and pulse compression exploiting cascaded second-order nonlinear processes in LiNbO3 waveguides," Opt. Commun. 259, 321-327 (2006). [CrossRef]
- J. Wang, J. Sun, C. Luo, and Q. Sun, "Flexible all-optical wavelength conversions of 1.57-ps pulses exploiting cascaded sum- and difference frequency generation (cSFG/DFG) in a PPLN waveguide," Appl. Phys. B 83, 543-548 (2006). [CrossRef]
- J. Wang, J. Sun, C. Luo, and Q. Sun, "Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides," Opt. Express 13, 7405-7414 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7405 [CrossRef] [PubMed]
- J. Wang, J. Sun, X. Zhang, X. Yuan, and D. Huang, "Experimental observation of tunable wavelength down- and up-conversions of ultra-short pulses in a periodically poled LiNbO3 waveguide," Opt. Commun. 269, 179-187 (2006). [CrossRef]
- J. Wang, J. Sun, J. R. Kurz, and M. M. Fejer, "Tunable wavelength conversion of ps-pulses exploiting cascaded sum- and difference frequency generation in a PPLN-fiber ring laser," IEEE Photonics Technol. Lett. 18, 2093-2095 (2006). [CrossRef]
- J. E. McGeehan, M. Giltrelli, and A. E. Willner, "All-optical digital 3-input AND gate using sum- and difference-frequency generation in a PPLN waveguide," LEOS 2005, July, 179-180 (2005).
- J. Wang, J. Sun, and Q. Sun, "Experimental observation of a 1.5 μm band wavelength conversion and logic NOT gate at 40 Gbit/s based on sum-frequency generation," Opt. Lett. 31, 1711-1713 (2006). [CrossRef] [PubMed]
- J. Sun, and J. Wang, "Simulation of optical NOT gate switching by sum-frequency generation in LiNbO3 waveguides," Opt. Commun. 267, 187-192 (2006). [CrossRef]

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