Abstract

A novel concept of unidirectional optical interference is presented, inspired by a non-Hermitian formulation of quantum mechanics via Maxwell-Schrödinger equation analogy. This model is employed for the design of photonic devices controlling strong fields by weak ones, suitable for large-scale optical logic. Implementations of very low-power photonic logic based on linear unidirectional optical gratings are presented. A linear photonic inverter is demonstrated and its performance is optimized by numerical calculations. The simulations are performed by full-vectorial beam propagation methods showing high signal to noise ratios.

©2009 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Cascadable and reconfigurable photonic logic gates based on linear lightwave interference and non-linear phase erasure

Bar Larom, Moshe Nazarathy, Arkady Rudnitsky, Amir Nevet, and Zeev Zalevsky
Opt. Express 18(13) 13600-13607 (2010)

All-optical linear reconfigurable logic with nonlinear phase erasure

Moshe Nazarathy, Zeev Zalevsky, Arkady Rudnitsky, Bar Larom, Amir Nevet, Meir Orenstein, and Baruch Fischer
J. Opt. Soc. Am. A 26(8) A21-A39 (2009)

All-optical switches, unidirectional flow, and logic gates with discrete solitons in waveguide arrays

U. Al Khawaja, S. M. Al-Marzoug, and H. Bahlouli
Opt. Express 24(10) 11062-11074 (2016)

References

  • View by:
  • |
  • |
  • |

  1. Z. Li and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341–1343 (2006).
    [Crossref]
  2. E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
    [Crossref]
  3. 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]
  4. T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
    [Crossref]
  5. X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, “All-optical AND gate at 10 Gb/s based on cascaded single-port-couple SOAs,” Opt. Express 12, 361–366 (2004).
    [Crossref] [PubMed]
  6. Y. J. Jung, J. Park, and N. Park, “Wavelength-transparent nonlinear optical gate based on self-seeded gain modulation in folded tandem-SOA,” Opt. Express 15, 4929–4934 (2007).
    [Crossref] [PubMed]
  7. P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
    [Crossref] [PubMed]
  8. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
    [Crossref]
  9. M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
    [Crossref] [PubMed]
  10. C. M Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018, (2007).
    [Crossref]
  11. C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
    [Crossref]
  12. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).
    [Crossref] [PubMed]
  13. S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
    [Crossref] [PubMed]
  14. M. O. Scully and M. Fleischhauer, “Lasers Without Inversion,” Science 263, 337 (1994).
    [Crossref] [PubMed]
  15. A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
    [Crossref]
  16. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).
  17. M. Greenberg and M. Orenstein, ”Optical Unidirectional devices by Complex Spatial Single Sideband Perturbation,” IEEE J. of Quantum Electron. 41, 1013–1023 (2005).
    [Crossref]
  18. M. Greenberg and M. Orienstein, “Irreversible coupling by use of dissipative optics,” Optics Lett. 29, 451–453, (2004).
    [Crossref]
  19. W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
    [Crossref]

2008 (2)

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
[Crossref] [PubMed]

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

2007 (3)

2006 (5)

C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
[Crossref]

P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
[Crossref] [PubMed]

Z. Li and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341–1343 (2006).
[Crossref]

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]

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

2005 (1)

M. Greenberg and M. Orenstein, ”Optical Unidirectional devices by Complex Spatial Single Sideband Perturbation,” IEEE J. of Quantum Electron. 41, 1013–1023 (2005).
[Crossref]

2004 (4)

M. Greenberg and M. Orienstein, “Irreversible coupling by use of dissipative optics,” Optics Lett. 29, 451–453, (2004).
[Crossref]

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[Crossref] [PubMed]

X. Zhang, Y. Wang, J. Sun, D. Liu, and D. Huang, “All-optical AND gate at 10 Gb/s based on cascaded single-port-couple SOAs,” Opt. Express 12, 361–366 (2004).
[Crossref] [PubMed]

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[Crossref]

1994 (1)

M. O. Scully and M. Fleischhauer, “Lasers Without Inversion,” Science 263, 337 (1994).
[Crossref] [PubMed]

1992 (1)

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

Abedin, K.S.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Baets, R.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Bender, C. M

C. M Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018, (2007).
[Crossref]

Bender, C. M.

C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
[Crossref]

Bogaerts, W.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Chaudhuri, S.

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

Chen, J.-H.

C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
[Crossref]

Christodoulides, D. N.

Chu, S.

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

Dumon, P.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Eisenstein, G.

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

El-Ganainy, R.

Elor, Y.

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

Fleischhauer, M.

M. O. Scully and M. Fleischhauer, “Lasers Without Inversion,” Science 263, 337 (1994).
[Crossref] [PubMed]

Freimain, A.

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

Ginzburg, P.

Greenberg, M.

M. Greenberg and M. Orenstein, ”Optical Unidirectional devices by Complex Spatial Single Sideband Perturbation,” IEEE J. of Quantum Electron. 41, 1013–1023 (2005).
[Crossref]

M. Greenberg and M. Orienstein, “Irreversible coupling by use of dissipative optics,” Optics Lett. 29, 451–453, (2004).
[Crossref]

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[Crossref] [PubMed]

Gunther, U.

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
[Crossref] [PubMed]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[Crossref]

Hayat, A.

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

Huang, D.

Huang, W.

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

J.,

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

Jung, Y. J.

Klaiman, S.

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
[Crossref] [PubMed]

Li, G.

Z. Li and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341–1343 (2006).
[Crossref]

Li, Z.

Z. Li and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341–1343 (2006).
[Crossref]

Liang, T.K.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Liu, D.

Makris, K. G.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

Milton, K. A.

C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
[Crossref]

Miyazaki, T.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Moiseyev, N.

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
[Crossref] [PubMed]

Musslimani, Z. H.

Nazarathy, M.

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

Nunes, L.R.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Orenstein, M.

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
[Crossref] [PubMed]

M. Greenberg and M. Orenstein, ”Optical Unidirectional devices by Complex Spatial Single Sideband Perturbation,” IEEE J. of Quantum Electron. 41, 1013–1023 (2005).
[Crossref]

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[Crossref] [PubMed]

Orienstein, M.

M. Greenberg and M. Orienstein, “Irreversible coupling by use of dissipative optics,” Optics Lett. 29, 451–453, (2004).
[Crossref]

Park, J.

Park, N.

Scully, M. O.

M. O. Scully and M. Fleischhauer, “Lasers Without Inversion,” Science 263, 337 (1994).
[Crossref] [PubMed]

Shumakher, E.

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

Small, E.

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

Sun, J.

Sun, Q.

Thourhout, D. V.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Tsang, H.K.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Tsuchiya, M.

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Wang, J.

Wang, Y.

Xu, C.

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

Zhang, X.

Appl. Phys. Lett. (1)

A. Hayat, E. Small, Y. Elor, and M. Orenstein, “Phasematching in Semiconductor Nonlinear Optics by Linear Long-Period Gratings,” Appl. Phys. Lett. 92, 181110 (2008).
[Crossref]

IEEE J. of Quantum Electron. (1)

M. Greenberg and M. Orenstein, ”Optical Unidirectional devices by Complex Spatial Single Sideband Perturbation,” IEEE J. of Quantum Electron. 41, 1013–1023 (2005).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Z. Li and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341–1343 (2006).
[Crossref]

E. Shumakher, A. Hayat, A. Freimain, M. Nazarathy, and G. Eisenstein, “Timing Extraction of a 10-gb/s NRZ Signal Using an Electro-Optic Multiplication Scheme,” IEEE Photon. Technol. Lett.,  16, 2353 (2004).
[Crossref]

J. Lightwave Technol. (1)

W. Huang, C. Xu, S. Chu, S. Chaudhuri, and J., “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. 10, 295–305 (1992).
[Crossref]

J. Phys. A: Mathematical and General (1)

C. M. Bender, J.-H. Chen, and K. A. Milton, “PT-Symmetric Versus Hermitian Formulation of Quantum Mechanics,” J. Phys. A: Mathematical and General 39, 1657–1668 (2006).
[Crossref]

Opt. Commun. (1)

T.K. Liang, L.R. Nunes, M. Tsuchiya, K.S. Abedin, T. Miyazaki, D. V. Thourhout, W. Bogaerts, P. Dumon, R. Baets, and H.K. Tsang, “High speed logic gate using two-photon absorption in silicon waveguides, “ Opt. Commun. 265, 171–174 (2006).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Optics Lett. (1)

M. Greenberg and M. Orienstein, “Irreversible coupling by use of dissipative optics,” Optics Lett. 29, 451–453, (2004).
[Crossref]

Phys. Rev. Lett. (1)

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of Branch Points in PT-Symmetric Waveguides,” Phys. Rev. Lett. 101, 080402 (2008).
[Crossref] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997).
[Crossref]

Rep. Prog. Phys. (1)

C. M Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018, (2007).
[Crossref]

Science (1)

M. O. Scully and M. Fleischhauer, “Lasers Without Inversion,” Science 263, 337 (1994).
[Crossref] [PubMed]

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Unidirectional EIT ?-scheme. The forbidden transitions are crossed.
Fig. 2.
Fig. 2. Optical Inverter (a) Mode diagram with appropriate unidirectional gratings and their strength m and k. (b) Block diagram of the inverter (c) Inverter's implementation schematics.
Fig. 3.
Fig. 3. Optical NAND (a) logic table (b) Mode diagram with unidirectional gratings and their strength k/2 and k.
Fig. 4.
Fig. 4. Device implementation proposal (a) Top view (b) Side View
Fig. 5.
Fig. 5. Simulation results (a) Schematic top view of the simulated device; Total electric field amplitude and the power at the three modes are depicted for (b) “1->0” - Input signal, no Output signal.(c) “0->1” -no Input signal, Output signal
Fig. 6.
Fig. 6. Normalized output power as a function of normalized input power. Noise margin limits are marked (a) Device length 500μm, fan-out ~2-3 (b) Device length 1000μm, fan-out ~5-6.

Equations (3)

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

zA = 0 zB = 0 zC = jkA + jmB
A ( 0 ) = A 0 B ( 0 ) = B 0 C ( 0 ) = 0
A ( z ) = A 0 B ( z ) = B 0 C ( z ) = jk A 0 z + jm B 0 z

Metrics