Abstract

We propose and analyze a novel loadable and erasable optical memory unit based on an active microring optical integrator associated with electroabsorption modulators (EAM) on III-V material system. The gain of the active microring is characterized by the two energy band model with amplified spontaneous emission noises taken into account. Based on the light field propagation equation in the active microring waveguide and the transfer function of the EAM-MZI switch, the step function performances of the optical memory under the gain matching condition are discussed for different injection light powers. After that, the memory operation of the novel optical memory unit is analyzed in detail. Simulations show that, the step function response and memory performances are affected by the carrier consumption. However, such influence will be released, and the memory operates well for the low light power injection case. The novel optical memory unit is promising to be cascaded connected and densely integrated for high speed low power optical data stream storage and buffer.

© 2009 OSA

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  5. A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
    [CrossRef]
  6. Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
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  7. S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
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    [CrossRef]
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    [CrossRef]

2008 (7)

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008).
[CrossRef]

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).
[CrossRef]

M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33(12), 1348–1350 (2008).
[CrossRef] [PubMed]

W. D. Sacher and J. K. S. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16(20), 15741–15753 (2008).
[CrossRef] [PubMed]

2007 (6)

E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007).
[CrossRef] [PubMed]

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
[CrossRef] [PubMed]

G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007).
[CrossRef]

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[CrossRef]

2006 (5)

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
[CrossRef]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14(7), 2956–2968 (2006).
[CrossRef] [PubMed]

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
[CrossRef] [PubMed]

2005 (4)

J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22(5), 1062–1074 (2005).
[CrossRef]

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

2004 (2)

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

2003 (1)

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

2002 (1)

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002).
[CrossRef]

2001 (2)

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

2000 (2)

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000).
[CrossRef]

1999 (1)

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

1995 (1)

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995).
[CrossRef]

Azaña, J.

Beals, M.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Bernardis, S.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Bian, J.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Bichler, M.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Binh, L. N.

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995).
[CrossRef]

Binsma, H.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Boucher, Y.

Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000).
[CrossRef]

Boyd, R. W.

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002).
[CrossRef]

Cheng, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Chi, N.

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
[CrossRef]

Connelly, M. J.

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

Danckaert, J.

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

De Vries, T.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Den Besten, J. H.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Ding, Y. H.

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

Donati, S.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Dong, P.

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[CrossRef]

Dorren, H. J.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Fu, S. N.

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

Giuliani, G.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Gong, Y. D.

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Hanlim, L.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002).
[CrossRef]

Hill, M. T. D.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Ho, S. T.

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

Hou, L. P.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Huang, D. X.

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007).
[CrossRef] [PubMed]

Jaeho, H.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Jaehoon, L.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Jichai, J.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Kapsalis, A.

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

Kawakami, Y.

Kawanishi, H.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Khoe, G. D.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Khurgin, J. B.

Kim, S. S.

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

Kimerling, L. C.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Kotthaus, J. P.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Laybourn, P. J. R.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Leijtens, X. J.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Li, Y. J.

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

Lim, M. S.

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

Lipson, M.

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[CrossRef]

Liu, A. M.

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

Liu, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Michel, J.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Miglierina, R.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Mikroulis, S.

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

Mineo, N.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Murai, H.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Muriel, M. A.

Ngo, N. Q.

N. Q. Ngo, “Optical integrator for optical dark-soliton detection and pulse shaping,” Appl. Opt. 45(26), 6785–6791 (2006).
[CrossRef] [PubMed]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995).
[CrossRef]

Ning, G.

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Oei, Y. S.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Oh, T. W.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Park, J.

Park, S.

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

Pomerene, A.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Poon, J. K. S.

Preciado, M. A.

Quoc Ngo, N.

Riding, J. L.

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008).
[CrossRef]

Sacher, W. D.

Scire, A.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Sekaric, L.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Sharaiha, A.

Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000).
[CrossRef]

Shibuya, Y.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Shum, P.

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

Smalbrugge, B.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Smit, M. K.

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Sorel, M.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

Stamataki, I.

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

Sun, R.

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Syvridis, D.

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

Tucker, R. S.

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008).
[CrossRef]

Verschaffelt, G.

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

Vlasov, Y.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Wada, H.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Wang, L. F.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Wang, L. W.

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

Wang, W.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Wang, Z. R.

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
[CrossRef]

Wegscheider, W.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Wixforth, A.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Wu, C. Q.

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

Xia, F. N.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Xu, Q. F.

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[CrossRef]

Yamada, K.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Yamauchi, Y.

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Yonggyoo, K.

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

Yu, S. Y.

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007).
[CrossRef]

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
[CrossRef]

Yuan, G. H.

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007).
[CrossRef]

Zhang, X. B.

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

Zhang, X. L.

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

E. B. Zhou, X. L. Zhang, and D. X. Huang, “Analysis on dynamic characteristics of semiconductor optical amplifiers with certain facet reflection based on detailed wideband model,” Opt. Express 15(14), 9096–9106 (2007).
[CrossRef] [PubMed]

Zhou, E. B.

Zhou, F.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Zhu, H. L.

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

Zimmermann, S.

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Appl. Opt. (1)

Electron. Lett. (1)

A. M. Liu, C. Q. Wu, M. S. Lim, Y. D. Gong, and P. Shum, “Optical buffer configuration based on a 3×3 collinear fibre coupler,” Electron. Lett. 40(16), 1017 (2004).
[CrossRef]

IEEE J. Lightwave Technol. (3)

Z. R. Wang, N. Chi, and S. Y. Yu, “Time-slot assignment using optical buffer with a large variable delay range based on AVC crosspoint switch,” IEEE J. Lightwave Technol. 24(8), 2994–3001 (2006).
[CrossRef]

R. S. Tucker and J. L. Riding, “Optical ring-resonator random-access memories,” IEEE J. Lightwave Technol. 26(3), 320–328 (2008).
[CrossRef]

N. Q. Ngo and L. N. Binh, “Optical realization of Newton-Cotes-based integrators for dark soliton generation,” IEEE J. Lightwave Technol. 24(1), 563–572 (2006).
[CrossRef]

IEEE J. Quantum Electron. (6)

M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. 37(3), 439–447 (2001).
[CrossRef]

I. Stamataki, S. Mikroulis, A. Kapsalis, and D. Syvridis, “Investigation on the multimode dynamics of InGaAsP-InP microring lasers,” IEEE J. Quantum Electron. 42(12), 1266–1273 (2006).
[CrossRef]

Y. Boucher and A. Sharaiha, “Spectral properties of amplified spontaneous emission in semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(6), 708–720 (2000).
[CrossRef]

K. Yonggyoo, L. Hanlim, L. Jaehoon, H. Jaeho, T. W. Oh, and J. Jichai, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[CrossRef]

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[CrossRef]

S. Park, S. S. Kim, L. W. Wang, and S. T. Ho, “InGaAsP-InP nanoscale waveguide-coupled microring lasers with submilliampere threshold current using Cl-2-N-2-based high-density plasma etching,” IEEE J. Quantum Electron. 41(3), 351–356 (2005).
[CrossRef]

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

G. H. Yuan and S. Y. Yu, “Analysis of dynamic switching Behavior of bistable semiconductor ring lasers triggered by resonant optical pulse injection,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1227–1234 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

L. P. Hou, H. L. Zhu, F. Zhou, L. F. Wang, J. Bian, and W. Wang, “Lossless electroabsorption modulator monolithically rntegrated with a semiconductor optical amplifier and dual-wavegulde spot-size converters,” IEEE Photon. Technol. Lett. 17(8), 1635–1637 (2005).
[CrossRef]

H. Kawanishi, Y. Yamauchi, N. Mineo, Y. Shibuya, H. Murai, K. Yamada, and H. Wada, “EAM-integrated DFB laser modules with more than 40-GHz bandwidth,” IEEE Photon. Technol. Lett. 13(9), 954–956 (2001).
[CrossRef]

Z. R. Wang, G. H. Yuan, G. Verschaffelt, J. Danckaert, and S. Y. Yu, “Storing 2 bits of information in a novel single semiconductor microring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[CrossRef]

J. Mod. Opt. (1)

J. E. Heebner and R. W. Boyd, “'Slow' and 'fast' light in resonator-coupled waveguides,” J. Mod. Opt. 49(14-15), 2629–2636 (2002).
[CrossRef]

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

Nat. Photonics (2)

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[CrossRef]

Nat. Phys. (1)

Q. F. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3(6), 406–410 (2007).
[CrossRef]

Nature (2)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

M. T. D. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[CrossRef] [PubMed]

Opt. Commun. (3)

N. Q. Ngo and L. N. Binh, “Programmable incoherent Newton-Cotes optical integrator,” Opt. Commun. 119(3-4), 390–402 (1995).
[CrossRef]

S. N. Fu, P. Shum, G. Ning, C. Q. Wu, and Y. J. Li, “Theoretical investigation of dual-wavelength packet signal storage with SOA-based dual loop optical buffer,” Opt. Commun. 279(2), 255–261 (2007).
[CrossRef]

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Proposal for loadable and erasable optical memory unit based on dual active microring optical integrators,” Opt. Commun. 281(21), 5315–5321 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Science (1)

S. Zimmermann, A. Wixforth, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “A Semiconductor-Based Photonic Memory Cell,” Science 283(5406), 1292–1295 (1999).
[CrossRef] [PubMed]

Other (2)

Y. P. R. Slavík, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic Temporal Integrator,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), CPDB3 http://www.opticsinfobase.org/abstract.cfm?URI=URI=CLEO-2008-CPDB2003 .

Y. H. Ding, X. B. Zhang, X. L. Zhang, and D. X. Huang, “Raman based silicon photonic integrator,” to be presented at the 8th Pacific Rim Conference on Lasers and Electro-Optics (CLEO®/Pacific Rim 2009), Shanghai, China, 30 August - 3 September, 2009.

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Figures (7)

Fig. 1
Fig. 1

Scheme of the novel optical memory unit.

Fig. 2
Fig. 2

Lasing modes spectra at threshold of the memory unit. The integral operation wavelength is at λ0=1.55μm .

Fig. 3
Fig. 3

A 25ps FWHM Gaussian optical pulse is injected into the novel memory unit. (a), (b), (c) Roundtrip net gain dynamics for input peak power of 0.01mW, 0.1mW and 1mW respectively. (d), (e), (f) Step function response performances of the memory unit for input peak power of 0.01mW, 0.1mW and 1mW respectively. The dashed lines are ideal step function response, and solid lines are simulated results.

Fig. 4
Fig. 4

Memory operation of a 25ps FWHM Gaussian light pulse with different peak power Ppeak .

Fig. 5
Fig. 5

Output peak power Poutpeak versus input peak power Ppeak .

Fig. 6
Fig. 6

(a) The normalized read out power at different read time of read operation for different Ppeak . (b) The effective storage time versus different input peak power Ppeak .

Fig. 7
Fig. 7

(a) Normalized read out power for different coupling coefficient κ0 . (b) Threshold current versus different power coupling coefficient κ02 .

Tables (1)

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Table 1 Parameters used in the simulation.

Equations (11)

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E2signal=jκ0τ0[e12ΓEAMau(1jαu)LEAM+e12ΓEAMad(Vread)(1jαd(Vread))LEAM]E1signal         =rEAMMZI(Vread)E1signal
Eout=[κ02e12ΓEAMau(1jαu)LEAM+τ02e12ΓEAMad(Vread)(1jαd(Vread))LEAM]E1signal      =κEAMMZI(Vread)E1signal
H(ω)=E1signal(ω)Ein(ω)=jκexp(jβL1)exp(12aRL1)1[G(1κ2)exp(ΓEAMa0LEAM)exp(aRLR)]1/2exp(jωT)
G=1(1κ2)exp(ΓEAMa0LEAM)exp(aRLR)
|rEAMMZI(Vread)|=12e12ΓEAMa0LEAM|1+e12ΓEAM[ad(Vread)a0]LEAMejΓEAM[ad(Vread)αd(Vread)a0α0]LEAM|                      <e12ΓEAMa0LEAM=|rEAMMZI(0)|
1vgEpCW,CCWt±EpCW,CCWz={j2πλpΔn+12(Γg(z,t,N,λp)αs)}×EpCW,CCW+spCW,CCW
s(CW,CCW)(z,t,λk)s*(CW,CCW)(z,t,λk)=γRsp(z,t,λk)dzvgδ(zz')δ(tt')δ(λkλk')
g(ωp)=c22n12ωp2τ(2memhh(me+mhh))3/2×(ωpEg)1/2[fc(ωp)fv(ωp)]
Rsp(ωp)=Δυπτ(2memhh(me+mhh))3/2×(ωpEg)1/2fc(ωp)[1fv(ωp)]
dN(z,t)dt=IeV[Rrad(N)+Rnrad(N)]k=1NdΓvgg(z,t,λk)|ECW(z,t,λk)+ECCW(z,t,λk)|2
[ER2Et]=[τjκjκτ][ER1Ein]

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