Abstract

All-optical temporal integrator using phase-shifted distributed-feedback semiconductor optical amplifier (DFB-SOA) is investigated. The influences of system parameters on its energy transmittance and integration error are explored in detail. The numerical analysis shows that, enhanced energy transmittance and integration time window can be simultaneously achieved by increased injected current in the vicinity of lasing threshold. We find that the range of input pulse-width with lower integration error is highly sensitive to the injected optical power, due to gain saturation and induced detuning deviation mechanism. The initial frequency detuning should also be carefully chosen to suppress the integration deviation with ideal waveform output.

© 2014 Optical Society of America

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References

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  1. M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16(15), 11459–11469 (2008).
    [Crossref] [PubMed]
  2. R. Slavík, Y. Park, 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), paper CPDB3.
  3. R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).
    [Crossref] [PubMed]
  4. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
    [Crossref] [PubMed]
  5. M. H. Asghari, Y. Park, and J. Azaña, “New design for photonic temporal integration with combined high processing speed and long operation time window,” Opt. Express 19(2), 425–435 (2011).
    [Crossref] [PubMed]
  6. N. Huang, N. Zhu, R. Ashrafi, X. Wang, W. Li, L. Wang, J. Azana, and M. Li, “Active Fabry-Perot resonator for photonic temporal integrator,” in Asia Communications and Photonics Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper AF1B.7.
    [Crossref]
  7. N. L. Kazanskiy and P. G. Serafimovich, “Coupled-resonator optical waveguides for temporal integration of optical signals,” Opt. Express 22(11), 14004–14013 (2014).
    [Crossref] [PubMed]
  8. Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
    [Crossref] [PubMed]
  9. M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
    [Crossref] [PubMed]
  10. N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry-Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22(3), 3105–3116 (2014).
    [Crossref] [PubMed]
  11. A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
    [Crossref] [PubMed]
  12. Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
    [Crossref]
  13. Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
    [Crossref]
  14. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (New York, 1993).

2014 (2)

2012 (1)

2011 (1)

2010 (2)

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[Crossref] [PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

2008 (3)

2005 (1)

Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
[Crossref]

2000 (1)

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Ahn, T.-J.

Asghari, M. H.

Ashrafi, R.

Ayotte, N.

Azaña, J.

N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry-Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22(3), 3105–3116 (2014).
[Crossref] [PubMed]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

M. H. Asghari, Y. Park, and J. Azaña, “New design for photonic temporal integration with combined high processing speed and long operation time window,” Opt. Express 19(2), 425–435 (2011).
[Crossref] [PubMed]

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35(8), 1191–1193 (2010).
[Crossref] [PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[Crossref] [PubMed]

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16(15), 11459–11469 (2008).
[Crossref] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).
[Crossref] [PubMed]

Chu, S. T.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Dai, Y.

Doucet, S.

Ferrera, M.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Han, J.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Huang, N.

Jeong, J.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Jia, X. H.

Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
[Crossref]

Kazanskiy, N. L.

Kim, Y.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

LaRochelle, S.

Lee, H.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Lee, J.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Li, M.

Little, B. E.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Malacarne, A.

Morandotti, R.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Moss, D. J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Oh, T. W.

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Park, Y.

Razzari, L.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Serafimovich, P. G.

Slavík, R.

Wang, C.

Wang, L.

Wang, X.

Wu, Z. M.

Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
[Crossref]

Xia, G. Q.

Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
[Crossref]

Yao, J.

Zhu, N.

IEEE J. Quantum Electron. (2)

Z. M. Wu, G. Q. Xia, and X. H. Jia, “Nonuniform DFB-SOAs: dynamic characteristics of bistability and a novel configuration based on linearly variable current injection,” IEEE J. Quantum Electron. 41(3), 384–389 (2005).
[Crossref]

Y. Kim, H. Lee, J. Lee, J. Han, T. W. Oh, and J. Jeong, “Chirp characteristics of 10-Gb/s electroabsorption modulator integrated DFB lasers,” IEEE J. Quantum Electron. 36(8), 900–908 (2000).
[Crossref]

Nat Commun (1)

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat Commun 1(3), 29 (2010).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Other (3)

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers (New York, 1993).

R. Slavík, Y. Park, 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), paper CPDB3.

N. Huang, N. Zhu, R. Ashrafi, X. Wang, W. Li, L. Wang, J. Azana, and M. Li, “Active Fabry-Perot resonator for photonic temporal integrator,” in Asia Communications and Photonics Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper AF1B.7.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Unsaturated gain (a) and phase (b) spectrums under different current injection.
Fig. 2
Fig. 2 Input (a),(c),(e) and output (b),(d),(f) waveforms of phase-shifted DFB-SOA for different cases.(a),(b): integrator; (c),(d):counter;(e),(f):flip-flop.
Fig. 3
Fig. 3 Real (solid) and ideal (dotted) output waveforms for different input pulse-width. The input waveform is the derivative of Gaussion pulse.
Fig. 4
Fig. 4 Energy transmittance (left) and integration error (right) as a function of normalized input pulse-width for different current injection.red: I/Ith = 0.999; green: I/Ith = 0.995; blue: I/Ith = 0.990.The detuning ΔL = 0.
Fig. 5
Fig. 5 Energy transmittance (left) and integration error (right) as a function of normalized pulse-width for different input peak power (Ps).red: Ps = −30dBm; green: Ps = −32.5dBm; blue: Ps = −35dBm. The detuning ΔL = 0.
Fig. 6
Fig. 6 Energy transmittance (left) and integration error (right) as a function of normalized input pulse-width for different current injection.red: I/Ith = 0.999; green: I/Ith = 0.995; blue: I/Ith = 0.990.The detuning ΔL = 0.1.

Tables (1)

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Table 1 Device Structure and Material Parameters Used in Simulation

Equations (14)

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h ( t ) u ( t ) = { 1 f o r t 0 0 f o r t < 0
H ( ϖ ) 1 i ( ϖ ϖ 0 ) + π δ ( ϖ )
A f z + 1 v g A f t = i [ σ A f + κ A b ]
A b z 1 v g A b t = i [ σ A b + κ A f ]
σ = Δ i g ' / 2
Δ = δ Γ g 2 α = ( n e f f ϖ c π Λ ) Γ g 2 α , g ' = Γ g α int ,
g t = g 0 g τ c g P τ c P s a t
g 0 = a N 0 ( I I 0 1 ) , P s a t = A c r o s s h ν Γ a τ c ,
[ A f ( L ) A b ( L ) ] = T Σ [ A f ( 0 ) A b ( 0 ) ] = T 2 T ϕ T 1 [ A f ( 0 ) A b ( 0 ) ]
T 1 = T 2 = [ T 11 T 12 T 21 T 22 ] = [ cos h ( γ l ) + i σ γ sin h ( γ l ) i k γ sin h ( γ l ) i k γ sin h ( γ l ) cos h ( γ l ) i σ γ sin h ( γ l ) ]
T ϕ = [ ϕ 11 0 0 ϕ 11 * ] = [ exp ( i ϕ s h / 2 ) 0 0 exp ( i ϕ s h / 2 ) ]
T Σ = [ T Σ , 1 , 1 T Σ , 1 , 2 T Σ , 2 , 1 T Σ , 2 , 2 ] = [ T 11 2 ϕ 11 + T 12 T 21 ϕ 11 T 11 T 12 ϕ 11 + T 12 T 22 ϕ 11 T 11 T 21 ϕ 11 + T 21 T 22 ϕ 11 T 21 T 12 ϕ 11 + T 22 2 ϕ 11 ]
H ( ϖ ) = 1 T Σ 2 , 2 ( ϖ ) = 1 i k 2 γ 2 sin h 2 ( γ l ) i [ cos h ( γ l ) i σ γ sin h ( γ l ) ] 2
H ( ϖ ) 1 T Σ 2 , 2 ( ϖ t h ) + T Σ 2 , 2 ' ( ϖ t h ) ( ϖ ϖ t h ) 1 ϖ ϖ t h

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