Abstract

A measurement method that can be used to extract the relative intensity noise of a nanolaser is introduced and analyzed. The method is based on optical injection of emission from a nanolaser, serving as a master oscillator, transferring its intensity fluctuations to a low-noise semiconductor laser serving as a slave oscillator. Using the stochastic rate equation formalism, we demonstrate that the total relative intensity noise of the system is a weighted superposition of the relative intensity noise of individual lasers. We further discuss the analytical relations that can be used to extract the relative intensity noise spectrum of a nanolaser. Finally, we use mutual correlation as a mathematical tool to quantify the degree of resemblance between the injected and extracted intensity fluctuations, theoretically confirming that the spectra are at least 97% correlated within the 3-dB bandwidth when an injection strength is chosen properly.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. M. J. Heck and J. E. Bowers, “Energy efficient and energy proportional optical interconnects for multi-core processors: Driving the need for on-chip sources,” IEEE J. Sel. Top. Quantum Electron. 20, 332–343 (2014).
    [Crossref]
  2. Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
    [Crossref]
  3. H. Walther, “Experiments on cavity quantum electrodynamics,” Phys. Reports 219, 263–281 (1992).
    [Crossref]
  4. Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
    [Crossref] [PubMed]
  5. E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
    [Crossref] [PubMed]
  6. T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
    [Crossref] [PubMed]
  7. S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
    [Crossref]
  8. C.-Y. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoleds,” Opt. Express 20, 16450–16470 (2012).
    [Crossref]
  9. R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
    [Crossref]
  10. W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
    [Crossref]
  11. M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
    [Crossref] [PubMed]
  12. E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
    [Crossref]
  13. G. Ghione, Semiconductor devices for high-speed optoelectronics(Cambridge University, 2009).
    [Crossref]
  14. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode lasers and photonic integrated circuits(John Wiley & Sons, 2012).
    [Crossref]
  15. A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
    [Crossref]
  16. S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
    [Crossref]
  17. J. Ohtsubo, Semiconductor lasers: stability, instability and chaos(Springer, 2012).
  18. G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
    [Crossref]

2016 (1)

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

2015 (2)

A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
[Crossref]

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
[Crossref]

2014 (2)

M. J. Heck and J. E. Bowers, “Energy efficient and energy proportional optical interconnects for multi-core processors: Driving the need for on-chip sources,” IEEE J. Sel. Top. Quantum Electron. 20, 332–343 (2014).
[Crossref]

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
[Crossref]

2013 (1)

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

2012 (2)

C.-Y. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoleds,” Opt. Express 20, 16450–16470 (2012).
[Crossref]

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

2010 (3)

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

2009 (3)

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
[Crossref]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

1992 (1)

H. Walther, “Experiments on cavity quantum electrodynamics,” Phys. Reports 219, 263–281 (1992).
[Crossref]

Abdelhady, K.

A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
[Crossref]

Alouini, M.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

Baili, G.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

Beaudoin, G.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Beveratos, A.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Bowers, J. E.

M. J. Heck and J. E. Bowers, “Energy efficient and energy proportional optical interconnects for multi-core processors: Driving the need for on-chip sources,” IEEE J. Sel. Top. Quantum Electron. 20, 332–343 (2014).
[Crossref]

Braive, R.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Bretenaker, F.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

Chow, W. W.

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
[Crossref]

Chuang, S. L.

C.-Y. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoleds,” Opt. Express 20, 16450–16470 (2012).
[Crossref]

Coldren, L. A.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode lasers and photonic integrated circuits(John Wiley & Sons, 2012).
[Crossref]

Corzine, S. W.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode lasers and photonic integrated circuits(John Wiley & Sons, 2012).
[Crossref]

Dolfi, D.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

El Amili, A.

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Fainman, Y.

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Frateschi, N. C.

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

Ghione, G.

G. Ghione, Semiconductor devices for high-speed optoelectronics(Cambridge University, 2009).
[Crossref]

Gies, C.

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
[Crossref]

Gregersen, N.

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

Gu, Q.

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

Heck, M. J.

M. J. Heck and J. E. Bowers, “Energy efficient and energy proportional optical interconnects for multi-core processors: Driving the need for on-chip sources,” IEEE J. Sel. Top. Quantum Electron. 20, 332–343 (2014).
[Crossref]

Hostein, R.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Jahnke, F.

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
[Crossref]

Kakitsuka, T.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Katz, M.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Kawaguchi, Y.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Khajavikhan, M.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Lakhani, A.

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

Lau, E. K.

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
[Crossref]

Le Gratiet, L.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Lee, J.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Lomakin, V.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Mahmoud, A.

A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
[Crossref]

Mahmoud, S. W.

A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
[Crossref]

Malherbe, T.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

Mashanovitch, M. L.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode lasers and photonic integrated circuits(John Wiley & Sons, 2012).
[Crossref]

Matsuo, S.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Michel, J.

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
[Crossref]

Mizrahi, A.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Mørk, J.

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

Nezhad, M. P.

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

Ni, C.-Y. A.

C.-Y. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoleds,” Opt. Express 20, 16450–16470 (2012).
[Crossref]

Notomi, M.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Nozaki, K.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Ohtsubo, J.

J. Ohtsubo, Semiconductor lasers: stability, instability and chaos(Springer, 2012).

Pan, S. H.

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Robert-Philip, I.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Sagnes, I.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

Sato, T.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Segawa, T.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Shinya, A.

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Simic, A.

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Slutsky, B.

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Smalley, J. S.

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

Suhr, T.

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

Talneau, A.

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Tucker, R. S.

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

Vallini, F.

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

Walther, H.

H. Walther, “Experiments on cavity quantum electrodynamics,” Phys. Reports 219, 263–281 (1992).
[Crossref]

Wong, L. J.

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
[Crossref]

Wu, M. C.

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
[Crossref]

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

Yin, B.

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
[Crossref]

Yvind, K.

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

Zhou, Z.

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
[Crossref]

Beni-Suef Univ. J. Basic Appl. Sci. (1)

A. Mahmoud, S. W. Mahmoud, and K. Abdelhady, “Modeling and simulation of dynamics and noise of semiconductor lasers under ntsc modulation for use in the catv technology,” Beni-Suef Univ. J. Basic Appl. Sci. 4, 99–108 (2015).
[Crossref]

EPL (1)

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-b to class-a transition in the dynamical behavior of a semiconductor laser,” EPL 87, 44005 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15, 618–633 (2009).
[Crossref]

M. J. Heck and J. E. Bowers, “Energy efficient and energy proportional optical interconnects for multi-core processors: Driving the need for on-chip sources,” IEEE J. Sel. Top. Quantum Electron. 20, 332–343 (2014).
[Crossref]

Light. Sci. & Appl. (2)

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light. Sci. & Appl. 4, e358 (2015).
[Crossref]

W. W. Chow, F. Jahnke, and C. Gies, “Emission properties of nanolasers during the transition to lasing,” Light. Sci. & Appl. 3, e201 (2014).
[Crossref]

Nat. Photonics (1)

S. Matsuo, A. Shinya, T. Kakitsuka, K. Nozaki, T. Segawa, T. Sato, Y. Kawaguchi, and M. Notomi, “High-speed ultracompact buried heterostructure photonic-crystal laser with 13 fj of energy consumed per bit transmitted,” Nat. Photonics 4, 648–654 (2010).
[Crossref]

Nature (1)

M. Khajavikhan, A. Simic, M. Katz, J. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

Opt. Express (4)

C.-Y. A. Ni and S. L. Chuang, “Theory of high-speed nanolasers and nanoleds,” Opt. Express 20, 16450–16470 (2012).
[Crossref]

Q. Gu, B. Slutsky, F. Vallini, J. S. Smalley, M. P. Nezhad, N. C. Frateschi, and Y. Fainman, “Purcell effect in sub-wavelength semiconductor lasers,” Opt. Express 21, 15603–15617 (2013).
[Crossref] [PubMed]

E. K. Lau, A. Lakhani, R. S. Tucker, and M. C. Wu, “Enhanced modulation bandwidth of nanocavity light emitting devices,” Opt. Express 17, 7790–7799 (2009).
[Crossref] [PubMed]

T. Suhr, N. Gregersen, K. Yvind, and J. Mørk, “Modulation response of nanoleds and nanolasers exploiting purcell enhanced spontaneous emission,” Opt. Express 18, 11230–11241 (2010).
[Crossref] [PubMed]

Opt. Lett. (1)

R. Hostein, R. Braive, L. Le Gratiet, A. Talneau, G. Beaudoin, I. Robert-Philip, I. Sagnes, and A. Beveratos, “Demonstration of coherent emission from high-β photonic crystal nanolasers at room temperature,” Opt. Lett. 35, 1154–1156 (2010).
[Crossref]

Optica (1)

S. H. Pan, Q. Gu, A. El Amili, F. Vallini, and Y. Fainman, “Dynamic hysteresis in a coherent high-β nanolaser,” Optica 3, 1260–1265 (2016).
[Crossref]

Phys. Reports (1)

H. Walther, “Experiments on cavity quantum electrodynamics,” Phys. Reports 219, 263–281 (1992).
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Other (3)

J. Ohtsubo, Semiconductor lasers: stability, instability and chaos(Springer, 2012).

G. Ghione, Semiconductor devices for high-speed optoelectronics(Cambridge University, 2009).
[Crossref]

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode lasers and photonic integrated circuits(John Wiley & Sons, 2012).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 The block diagram of an optical injection scheme. RIN: the intrinsic relative intensity noise; κ: the injection strength; f [·]: an arbitrary function that is under investigation.
Fig. 2
Fig. 2 Total RIN at two selected injection strength (a) κ = 0.01 and (b) κ = 0.25. The master and the slave are pumped at thrice and twice of their respective threshold levels. In determining the threshold of the nanolaser, the carrier density is first calculated as a function of pump rate. The threshold is then determined graphically by extrapolating two regions around the kink in the carrier density. This prediction can be translated into an experimental measurement through its corresponding light-in-light-out curve.
Fig. 3
Fig. 3 (a) Correlation strength and (b) phase of the complex mutual correlation function. The 3-dB points correspond to the 3-dB bandwidth of the total RIN spectra. The pump levels are identical to that of Fig. 2.
Fig. 4
Fig. 4 (a) Minimally required power emitted by the nanolaser at selected values of m (b) parameters that yield a high correlation strength (≥ 97%) within the 3-dB bandwidth appear in the gray region. The pump rate and photon density are converted to power as suggested in [14].

Tables (1)

Tables Icon

Table 1 Laser parameters

Equations (26)

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d S s ( t ) d t = Γ s S s ( t ) { g 0 , s [ N s ( t ) N 0 , s ] 1 τ p , s } + Γ s F s β s N s ( t ) τ r , s + κ S n ( t ) τ r t , s + L S , s ( t ) ,
d N s ( t ) d t = P s g 0 , s [ N s ( t ) N 0 , s ] S s ( t ) [ F s β s ( 1 β s ) τ r , s + 1 τ n r , s ] N s ( t ) + L S , s ( t ) ,
L i ( t ) L j * ( t τ ) = W i j δ ( τ ) .
[ δ N ˜ s ( ω ) δ S ˜ s ( ω ) ] = 1 D s ( ω ) [ i ω + γ S S , s γ N S , s γ S N , s i ω + γ N N , s ] [ L ˜ N , s ( ω ) L ˜ N , s ( ω ) + κ τ r t , s δ S ˜ n ( ω ) ] ,
D s ( ω ) = ( ω 0 , s 2 ω 2 ) + i ω ξ s .
H s ( ω ) δ S ˜ s δ S ˜ n = κ τ r t , s i ω + γ N N , s D s ( ω ) .
ω R , s = ω 0 , s 1 ξ s 2 2 ω 0 , s 2 .
R I N ( ω ) P S D ( ω ) S ¯ 2 = δ S ˜ ( ω ) δ S ˜ * ( ω ) S ¯ 2 .
R I N t   o t ( ω ) = H f ( ω ) R I N n ( ω ) + R I N s ( ω )
H f ( ω ) = S ¯ n 2 S ¯ s 2 | H s ( ω ) | 2 .
R I N t   o t ( ω ) H f ( ω ) R I N n ( ω )
ω 0 , s 2 g 0 , s S ¯ s τ p , s + 1 τ p , s τ r , s + Γ s g 0 , s ( N ¯ s N 0 , s ) τ r , s ,
S ¯ s = 1 1 / τ p , s Γ s g 0 , s ( N ¯ s N 0 , s ) κ S ¯ n τ r t , s
C ( ω ) = δ S ˜ s ( ω ) δ S ˜ n * ( ω ) δ S ˜ s ( ω ) δ S ˜ s * ( ω ) δ S ˜ n ( ω ) δ S ˜ n * ( ω )
ξ s γ N N , s > ω 0 , s 2 .
ξ s γ N N , s = ( ω 0 , s m ) 2
γ N N , = g 0 , S ¯ + β F + ( 1 β ) τ r , ,
γ S S , = 1 τ p , Γ g 0 , ( N ¯ N 0 , ) ,
γ N S , = g 0 , ( N ¯ N 0 , ) ,
γ S N , = Γ g 0 , S ¯ + Γ F β τ r , ,
ω 0 , 2 = γ N N , γ S S , + γ N S , γ S N , ,
ξ = γ N N , + γ S S , .
R I N ( ω ) = γ S N , 2 L ˜ N , L ˜ N , * | D ( ω ) | 2 S ¯ 2 + ( γ N N , 2 + ω 2 ) L ˜ S , L ˜ S , * | D ( ω ) | 2 S ¯ 2 + 2 γ S N , γ N N , L ˜ S , L ˜ N , * | D ( ω ) | 2 S ¯ 2 ,
L ˜ S , s L ˜ N , s * = L N , s L ˜ S , s * = Γ s V s [ g 0 , s ( N ¯ s N 0 , s ) S ¯ s + F s β s N ¯ s τ r , s ] ,
L ˜ N , s L N , s * = P ¯ s V s + [ F s β s + ( 1 β s ) τ r s + 1 τ n r , s ] N ¯ s V s + g 0 , s V s ( N ¯ s + N 0 , s ) S ¯ s ,
L ˜ S , s L ˜ S , s * = S ¯ s τ p , s V s V s V p , s L ˜ S , s L N , s * + κ S ¯ n τ r t , s V p , s .

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