Abstract

The switching behaviors of cascaded nonlinear couplers were investigated. They have nearly ideal digital-switching characteristics, and their output power levels can be adjusted by means of varying the nonlinear coupling coefficient of the final coupler. The two-input excitation nonlinear cascaded couplers can perform not only switching operations but also a series of logic operations. The logic operations depend mainly on the coupling length of the two-input coupler and its initial inputs. The power corresponding to the rising and falling ridge of the logic operating waveforms can be shifted effectively by means of varying the switching power of the reshaper. Allowable ranges of three important parameters—coupling length of the two-input coupler L 1, bias optical power P bia, and phase difference ψ between the signal and bias beams for six fundamental logic operations—were calculated. Curves for design considerations and suggestions for the best choice of parameters for stable and reliable logic operations and, or, xor, nand, nor, and nxor are also presented individually.

© 2000 Optical Society of America

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References

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  1. A. T. Pham, L. N. Binh, “Nonlinear optical directional coupler two-input operation,” Int. J. Optoelectron. 5, 367–380 (1990).
  2. A. T. Pham, L. N. Binh, “All-optical modulation and switching using a nonlinear-optical directional coupler,” J. Opt. Soc. Am. B 8, 1914–1931 (1991).
    [CrossRef]
  3. Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
    [CrossRef]
  4. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1981).
  5. Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
    [CrossRef]
  6. K. Kitayama, S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17–19 (1983).
    [CrossRef]
  7. A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
    [CrossRef]
  8. J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
    [CrossRef] [PubMed]
  9. C.-C. Yang, A. J. S. Wang, “Asymmetric nonlinear coupling and its applications to logic functions,” IEEE J. Quantum Electron. QE-28, 479–4873 (1981).
  10. T. Fukushima, T. Sakamoto, “All optical logic operations using Kerr bistability in a four-port optical fiber loop resonator,” in Proceedings of the International Laser, Lightwave and Microwave Conference (World Publishing, Shanghai, 1995), pp. 250–252.
  11. Y. Wang, J. Liu, “All-fiber logical devices based on the nonlinear directional coupler,” IEEE Photonics. Technol. Lett. 11, 72–74 (1999).
    [CrossRef]
  12. Y. Wang, “Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: analysis,” J. Lightwave Technol. 17, 292–297 (1999).
    [CrossRef]

1999 (2)

Y. Wang, J. Liu, “All-fiber logical devices based on the nonlinear directional coupler,” IEEE Photonics. Technol. Lett. 11, 72–74 (1999).
[CrossRef]

Y. Wang, “Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: analysis,” J. Lightwave Technol. 17, 292–297 (1999).
[CrossRef]

1995 (1)

1992 (2)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
[CrossRef]

1991 (1)

1990 (2)

A. T. Pham, L. N. Binh, “Nonlinear optical directional coupler two-input operation,” Int. J. Optoelectron. 5, 367–380 (1990).

Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
[CrossRef]

1983 (1)

K. Kitayama, S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17–19 (1983).
[CrossRef]

1981 (2)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1981).

C.-C. Yang, A. J. S. Wang, “Asymmetric nonlinear coupling and its applications to logic functions,” IEEE J. Quantum Electron. QE-28, 479–4873 (1981).

Aitchison, J. S.

J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Binh, L. N.

A. T. Pham, L. N. Binh, “All-optical modulation and switching using a nonlinear-optical directional coupler,” J. Opt. Soc. Am. B 8, 1914–1931 (1991).
[CrossRef]

A. T. Pham, L. N. Binh, “Nonlinear optical directional coupler two-input operation,” Int. J. Optoelectron. 5, 367–380 (1990).

Chen, Y.

Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
[CrossRef]

Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
[CrossRef]

Fukushima, T.

T. Fukushima, T. Sakamoto, “All optical logic operations using Kerr bistability in a four-port optical fiber loop resonator,” in Proceedings of the International Laser, Lightwave and Microwave Conference (World Publishing, Shanghai, 1995), pp. 250–252.

Ironside, C. N.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1981).

Kitayama, K.

K. Kitayama, S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17–19 (1983).
[CrossRef]

Liu, J.

Y. Wang, J. Liu, “All-fiber logical devices based on the nonlinear directional coupler,” IEEE Photonics. Technol. Lett. 11, 72–74 (1999).
[CrossRef]

Mitchell, D. J.

Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
[CrossRef]

Payne, D. N.

Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
[CrossRef]

Pham, A. T.

A. T. Pham, L. N. Binh, “All-optical modulation and switching using a nonlinear-optical directional coupler,” J. Opt. Soc. Am. B 8, 1914–1931 (1991).
[CrossRef]

A. T. Pham, L. N. Binh, “Nonlinear optical directional coupler two-input operation,” Int. J. Optoelectron. 5, 367–380 (1990).

Sakamoto, T.

T. Fukushima, T. Sakamoto, “All optical logic operations using Kerr bistability in a four-port optical fiber loop resonator,” in Proceedings of the International Laser, Lightwave and Microwave Conference (World Publishing, Shanghai, 1995), pp. 250–252.

Snyder, A. W.

Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
[CrossRef]

Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
[CrossRef]

Stegeman, G. I.

J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Villeneuve, A.

J. S. Aitchison, A. Villeneuve, G. I. Stegeman, “All-optical switching in two cascaded nonlinear directional couplers,” Opt. Lett. 20, 698–700 (1995).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Wang, A. J. S.

C.-C. Yang, A. J. S. Wang, “Asymmetric nonlinear coupling and its applications to logic functions,” IEEE J. Quantum Electron. QE-28, 479–4873 (1981).

Wang, S.

K. Kitayama, S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17–19 (1983).
[CrossRef]

Wang, Y.

Y. Wang, J. Liu, “All-fiber logical devices based on the nonlinear directional coupler,” IEEE Photonics. Technol. Lett. 11, 72–74 (1999).
[CrossRef]

Y. Wang, “Nonlinear optical limiter and digital optical switch by cascaded nonlinear couplers: analysis,” J. Lightwave Technol. 17, 292–297 (1999).
[CrossRef]

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Yang, C. C.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Yang, C.-C.

C.-C. Yang, A. J. S. Wang, “Asymmetric nonlinear coupling and its applications to logic functions,” IEEE J. Quantum Electron. QE-28, 479–4873 (1981).

Appl. Phys. Lett. (2)

K. Kitayama, S. Wang, “Optical pulse compression by nonlinear coupling,” Appl. Phys. Lett. 43, 17–19 (1983).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, C. N. Ironside, “Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap,” Appl. Phys. Lett. 61, 147–149 (1992).
[CrossRef]

Electron. Lett. (1)

Y. Chen, A. W. Snyder, D. J. Mitchell, “Ideal optical switching by nonlinear multiple (parasitic) core couplers,” Electron. Lett. 26, 77–78 (1990).
[CrossRef]

IEEE J. Quantum Electron. (3)

Y. Chen, A. W. Snyder, D. N. Payne, “Two core nonlinear couplers with gain and loss,” IEEE J. Quantum Electron. 28, 239–245 (1992).
[CrossRef]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 1580–1583 (1981).

C.-C. Yang, A. J. S. Wang, “Asymmetric nonlinear coupling and its applications to logic functions,” IEEE J. Quantum Electron. QE-28, 479–4873 (1981).

IEEE Photonics. Technol. Lett. (1)

Y. Wang, J. Liu, “All-fiber logical devices based on the nonlinear directional coupler,” IEEE Photonics. Technol. Lett. 11, 72–74 (1999).
[CrossRef]

Int. J. Optoelectron. (1)

A. T. Pham, L. N. Binh, “Nonlinear optical directional coupler two-input operation,” Int. J. Optoelectron. 5, 367–380 (1990).

J. Lightwave Technol. (1)

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

Opt. Lett. (1)

Other (1)

T. Fukushima, T. Sakamoto, “All optical logic operations using Kerr bistability in a four-port optical fiber loop resonator,” in Proceedings of the International Laser, Lightwave and Microwave Conference (World Publishing, Shanghai, 1995), pp. 250–252.

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Figures (15)

Fig. 1
Fig. 1

Influence of normalized coupling length on switching characteristics of one-input cascaded couplers. Both the input and output powers are normalized to P C = 4C/ Q.

Fig. 2
Fig. 2

Influence of nonlinear coupling coefficient of final coupler in cascaded couplers on normalized (to P C = 4C/ Q) input–output characteristics of one-input cascaded couplers.

Fig. 3
Fig. 3

Configuration of cascaded nonlinear coupler device. L i (1–4) denotes the coupling length of the ith coupler.

Fig. 4
Fig. 4

Influence of nonlinear coefficient of final coupler in cascaded couplers on logic operating waveforms. (a) and, (b) or.

Fig. 5
Fig. 5

(a) Influence of nonlinear coupling coefficient on switching power of reshaper. (b) Influence of switching power of reshaper on logic operating waveforms.

Fig. 6
Fig. 6

Influence of number of couplers in reshaper on (a) and, and (b) nxor logic operating waveforms. Curves 1, 2, and 3 correspond to one, two, and three couplers with identical coupling length L i = π + 0.5(i = 2, 3, 4).

Fig. 7
Fig. 7

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 of coupler 1 of Fig. 3 to perform nxor logic operation.

Fig. 8
Fig. 8

Range of normalized bias power P bia and normalized coupling length L 1 of coupler 1 in Fig. 3 to perform nor logic operation for given phase difference.

Fig. 9
Fig. 9

Range of normalized bias power P bia and normalized coupling length L 1 to perform nand logic operation for given phase difference.

Fig. 10
Fig. 10

Range of normalized bias power P bia and normalized coupling length L 1 to perform and logic operation in the case of bias power P bia launching into port A of cascaded couplers of Fig. 3 for given phase difference.

Fig. 11
Fig. 11

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 to perform and logic operation in the case of bias power P bia launching into port B of cascaded couplers of Fig. 3.

Fig. 12
Fig. 12

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 to perform or logic operation in the case of bias power P bia launching into port A of cascaded couplers of Fig. 3.

Fig. 13
Fig. 13

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 to perform or logic operation in the case of bias power P bia launching into port B of cascaded couplers of Fig. 3.

Fig. 14
Fig. 14

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 to perform xor logic operation in the case of bias power P bia launching into port A of cascaded couplers of Fig. 3.

Fig. 15
Fig. 15

For given phase difference the range of normalized bias power P bia and normalized coupling length L 1 to perform xor logic operation in the case of bias power P bia launching into port B of cascaded couplers shown in Fig. 3.

Equations (17)

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P1Z=Pt2+b0dndn-1η, k±2b0ZPc, kfor P10>Pt2,  2Pt2>A1,
P1Z=Pt2-b0dndn-1-η, k±2b0ZPc, kfor P10<Pt2,  2Pt2>A1,
P1Z=Pt2+b0cncn-1η, k1±2a02+b02Z1/2Pc, k1for A22Pt2A1,
a0=|Pt2-A1/2|1/22,  b0=Pt2-A2/21/22,k=1-a02/b021/2,  Z=2Cz, η=P10-Pt/2/b0,  k1=b02/a02+b021/2, A1,2=PC2-PCΓ±PCPC2-2PCΓ1/2, Γ=4P1ZP2Z1/2 cos ψZ-8P1ZP2Z/Pc,
P2Z=P2021+dnZP20/Pc, Pc/P20 for P20>Pc,
P2Z=P2021+cnZ, P20/Pc for P20Pc.
LPns=n+1K1/Pns,
1.67P1Z, PS=01.14,
P1Z, PS=0=Pbia/21-dnZPbia, 1/Pbia,Pbia>1=Pbia/21-cnZ, Pbia,Pbia1.
1-1/Pbia21/2dnZPbia, 1/Pbia1.
P1Z, PS=0=Pbia/21+dnZPbia, 1/Pbia,Pbia>1=Pbia/21+cnZ, Pbia,Pbia1.
1.14P1Z, PS0.051.67,P1Z, 0.475PS0.55<1.1,1.14P1Z, 0.95PS1.051.67.
1.14P1Z, PS0.051.67,P1Z, 0.475PS1.05<1.1.
1.14P1Z, PS0.551.67,P1Z, 0.95PS1.05<1.1.
P1Z, PS0.55<1.1,1.14P1Z, 0.95PS1.051.67.
P1Z, PS0.05<1.1,1.14P1Z, 0.475PS1.051.67.
P1Z, PS0.05<1.1,1.14P1Z, 0.45PS0.551.67,P1Z, 0.95PS1.05<1.1.

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