Abstract

Photonic crystal Fano lasers have recently been realised experimentally, showing useful properties such as pinned single-mode lasing and passive pulse generation. Here the fundamental properties of the modes of the Fano laser are analysed, showing how the laser functionality depends sensitively on the system configuration. Furthermore the laser stability is investigated and linked to the small-signal response, which shows additional dynamics that cannot be explained with a conventional rate equation model, including a damping of relaxation oscillations and a frequency modulation bandwidth that is only limited by the nanocavity response.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (1)

2017 (5)

Y. Ota, M. Kakuda, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Thresholdless quantum dot nanolaser,” Opt. Express 25, 19981–19994 (2017).
[Crossref] [PubMed]

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal fano lasers,” Laser & Photonics Rev. 11, 1700089 (2017).
[Crossref]

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

2016 (2)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

2015 (3)

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

2014 (2)

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal fano laser: Terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref] [PubMed]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

2013 (2)

A. M. Yacomotti, S. Haddadi, and S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804 (2013).
[Crossref]

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

2011 (1)

2009 (2)

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[Crossref]

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

2006 (1)

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[Crossref]

2003 (2)

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

2002 (1)

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

1987 (1)

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Agrawal, G. P.

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

Arakawa, Y.

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

Baba, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Barbay, S.

A. M. Yacomotti, S. Haddadi, and S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804 (2013).
[Crossref]

Beaudoin, G.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Bekele, D. A.

Bouchoule, S.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Chen, Y.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal fano laser: Terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref] [PubMed]

Coldren, L.

L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1st ed. (Wiley, 1995).

Combrié, S.

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[Crossref]

Corzine, S.

L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1st ed. (Wiley, 1995).

Crosnier, G.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Daniel, B. A.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

de Lasson, J. R.

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

De Rossi, A.

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[Crossref]

Fan, S.

Fukaya, N.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Galili, M.

Gregersen, N.

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

Guan, P.

Haddadi, S.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

A. M. Yacomotti, S. Haddadi, and S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804 (2013).
[Crossref]

Hamel, P.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Hasebe, K.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Heuck, M.

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal fano laser: Terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref] [PubMed]

Hsu, C. W.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

Hu, H.

D. A. Bekele, Y. Yu, H. Hu, P. Guan, L. Ottaviano, M. Galili, L. K. Oxenløwe, K. Yvind, and J. Mork, “Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal fano structures,” Opt. Lett. 43, 955–958 (2018).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Iwai, T.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Iwamoto, S.

Jang, H.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[Crossref]

Joseph, D. D.

G. Looss and D. D. Joseph, Elementary stability and bifurcation theory, 1st ed. (Springer, 1990).

Kakitsuka, T.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Kakuda, M.

Karnadi, I.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Kristensen, P. T.

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Lee, Y.-H.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Levenson, A.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Looss, G.

G. Looss and D. D. Joseph, Elementary stability and bifurcation theory, 1st ed. (Springer, 1990).

Matsuo, S.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Maywar, D. N.

Miller, D. A. B.

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Mitsugi, S.

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[Crossref]

Monnier, P.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Mork, J.

D. A. Bekele, Y. Yu, H. Hu, P. Guan, L. Ottaviano, M. Galili, L. K. Oxenløwe, K. Yvind, and J. Mork, “Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal fano structures,” Opt. Lett. 43, 955–958 (2018).
[Crossref] [PubMed]

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal fano lasers,” Laser & Photonics Rev. 11, 1700089 (2017).
[Crossref]

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal fano laser: Terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref] [PubMed]

Motegi, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

Notomi, M.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[Crossref]

Nozaki, K.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Olesen, H.

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Ota, Y.

Ottaviano, L.

D. A. Bekele, Y. Yu, H. Hu, P. Guan, L. Ottaviano, M. Galili, L. K. Oxenløwe, K. Yvind, and J. Mork, “Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal fano structures,” Opt. Lett. 43, 955–958 (2018).
[Crossref] [PubMed]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Oxenlowe, L. K.

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Oxenløwe, L. K.

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Pan, X.

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Peucheret, C.

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Pramudita, P.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Raineri, F.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Raj, R.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Rasmussen, T. S.

T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal fano lasers,” Laser & Photonics Rev. 11, 1700089 (2017).
[Crossref]

Sagnes, I.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Saito, S.

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Sakai, A.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Sanchez, D.

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Sato, T.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Semenova, E.

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Shinya, A.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Soljacic, M.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

Song, J.-H.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Soo Kim, K.

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

Suh, W.

Takeda, K.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Taniyama, H.

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

Tran, N.-V.-Q.

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[Crossref]

Tromborg, B.

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Watanabe, K.

Watanabe, Y.

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

Xue, W.

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Yacomotti, A. M.

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

A. M. Yacomotti, S. Haddadi, and S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804 (2013).
[Crossref]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Yu, Y.

D. A. Bekele, Y. Yu, H. Hu, P. Guan, L. Ottaviano, M. Galili, L. K. Oxenløwe, K. Yvind, and J. Mork, “Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal fano structures,” Opt. Lett. 43, 955–958 (2018).
[Crossref] [PubMed]

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal fano lasers,” Laser & Photonics Rev. 11, 1700089 (2017).
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Yvind, K.

D. A. Bekele, Y. Yu, H. Hu, P. Guan, L. Ottaviano, M. Galili, L. K. Oxenløwe, K. Yvind, and J. Mork, “Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal fano structures,” Opt. Lett. 43, 955–958 (2018).
[Crossref] [PubMed]

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

Zhen, B.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

Appl. Phys. Lett. (1)

Y. Yu, M. Heuck, H. Hu, W. Xue, C. Peucheret, Y. Chen, L. K. Oxenlowe, K. Yvind, and J. Mork, “Fano resonance control in a photonic crystal structure and its application to ultrafast switching,” Appl. Phys. Lett. 105, 061117 (2014).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” IEEE J. Quantum Electron. 38, 743–752 (2002).
[Crossref]

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

S. Matsuo, T. Sato, K. Takeda, A. Shinya, K. Nozaki, H. Taniyama, M. Notomi, K. Hasebe, and T. Kakitsuka, “Ultralow operating energy electrically driven photonic crystal lasers,” IEEE J. Sel. Top. Quantum Electron. 19, 4900311 (2013).
[Crossref]

J. Light. Technol. (1)

P. T. Kristensen, J. R. de Lasson, M. Heuck, N. Gregersen, and J. Mork, “On the theory of coupled modes in optical cavity-waveguide structures,” J. Light. Technol. 35, 4247–4259 (2017).
[Crossref]

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

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

Laser & Photonics Rev. (2)

Y. Yu, Y. Chen, H. Hu, W. Xue, K. Yvind, and J. Mork, “Nonreciprocal transmission in a nonlinear photonic-crystal fano structure with broken symmetry,” Laser & Photonics Rev. 9, 241–247 (2015).
[Crossref]

T. S. Rasmussen, Y. Yu, and J. Mork, “Theory of self-pulsing in photonic crystal fano lasers,” Laser & Photonics Rev. 11, 1700089 (2017).
[Crossref]

Nat Photon (2)

Y. Yu, W. Xue, E. Semenova, K. Yvind, and J. Mork, “Demonstration of a self-pulsing photonic crystal fano laser,” Nat Photon 11, 81–84 (2017). Letter.
[Crossref]

P. Hamel, S. Haddadi, F. Raineri, P. Monnier, G. Beaudoin, I. Sagnes, A. Levenson, and A. M. Yacomotti, “Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers,” Nat Photon 9, 311–315 (2015). Letter.
[Crossref]

Nat. Commun. (1)

H. Jang, I. Karnadi, P. Pramudita, J.-H. Song, K. Soo Kim, and Y.-H. Lee, “Sub-microwatt threshold nanoisland lasers,” Nat. Commun. 6, 8276 (2015). Article.
[Crossref]

Nat. Photonics (1)

G. Crosnier, D. Sanchez, S. Bouchoule, P. Monnier, G. Beaudoin, I. Sagnes, R. Raj, and F. Raineri, “Hybrid indium phosphide-on-silicon nanolaser diode,” Nat. Photonics 11, 297 (2017).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016). Review Article.
[Crossref]

Nature. (1)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-q photonic nanocavity in a two-dimensional photonic crystal,” Nature. 425, 944–947 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[Crossref]

A. M. Yacomotti, S. Haddadi, and S. Barbay, “Self-pulsing nanocavity laser,” Phys. Rev. A 87, 041804 (2013).
[Crossref]

Phys. Rev. B (1)

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).
[Crossref]

Phys. Rev. Lett. (2)

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref] [PubMed]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal fano laser: Terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref] [PubMed]

Proc. IEEE (1)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Quantum Electron. IEEE J. (1)

B. Tromborg, H. Olesen, X. Pan, and S. Saito, “Transmission line description of optical feedback and injection locking for fabry-perot and dfb lasers,” Quantum Electron. IEEE J. 23, 1875–1889 (1987).
[Crossref]

Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Other (2)

L. Coldren and S. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1st ed. (Wiley, 1995).

G. Looss and D. D. Joseph, Elementary stability and bifurcation theory, 1st ed. (Springer, 1990).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the Fano laser structure. The white circles indicate air holes etched into the dielectric membrane, and the red dots indicate quantum dot active material, the arrows show possible decay channels and the dashed black lines define the effective laser mirror planes. (b) Fano mirror reflection and phase as function of frequency detuning for γc/γint = 16, where the nanocavity is in close proximity to the waveguide (see schematic inset), leading to a large peak reflectivity. (c) Fano mirror reflection and phase for the case where the nanocavity is far from the waveguide, as illustrated by the schematic inset, leading to weak coupling (γc/γint = 1) and low reflectivity.
Fig. 2
Fig. 2 (a) Dependence of cavity quality factor on length of laser cavity for the two cases of Fig. 1, showing how the Q factor depends sensitively on the length. This is because a longitudinal mode must align with the nanocavity resonance in order to obtain a large Fano reflection coefficient. Inset shows a zoom in for a specific mode. (b) Modal threshold gain as function of laser cavity length for the two cases of Fig. 1. Inset shows a zoom in near the gain minima, showing how the minimum threshold gain decreases with increasing length, due to the smaller distributed mirror losses.
Fig. 3
Fig. 3 (a) Modal threshold gain as function of nanocavity resonance frequency shift, displaying α-induced asymmetry and periodicity. (b) Effective detuning (ωcωL) as function of nanocavity resonance shift near zero detuning, showcasing the linear regime of Eq. (10) near each gain minimum. Inset shows the global behaviour, which is periodic.
Fig. 4
Fig. 4 (a) 3 dB bandwidth as function of bias current for zero detuning. Here the FP curve is identical for all 3 cases, and the system converges towards the FP curve as the nanocavity Q decreases towards zero. (b) Absolute difference in relaxation resonance frequency between Fano laser and equivalent FP laser as function of effective detuning and pump current showing significant differences. Here QT = 736.
Fig. 5
Fig. 5 (a) FM response (left axis) for A+ (full red) and Ac (dashed red) for 3γT detuning of ωc (effective detuning is 0.22γT ), with the accompanying IM response (right axis) as quantified by the modulation index in the through-port (TP, blue) and cross-port (CP, dashed green). The dashed black line indicates the relaxation resonance predicted by the eigenvalue analysis. (b) FM response at zero detuning for the throughport (TP, blue), cross-port (CP, red) and A+. Here the resonance vanishes, because the reflectivity slope is zero.

Equations (18)

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

γ T = γ c + γ i n t = γ c + γ i + γ p
r 2 ( ω c , ω L ) = i γ c i ( ω c ω L ) + γ T
| r max | 2 = | r 2 ( ω L , ω L ) | 2 = γ c 2 γ T 2 = Q T 2 Q c 2 = ( 1 Q Q i n t ) 2
r 1 ( ω L ) r 2 ( ω c , ω L ) exp ( 2 i L [ ω L c n ( ω L , N ) i 2 ( Γ g ( ω L , N ) α i ) ] ) = 1
g ( ω , N ) g N ( N N 0 )
ω c n ( ω , N ) ω r c n ( ω r , N r ) + ω ω r c n g Γ α 2 g N ( N N r )
Q = ω L τ p = ω L Γ v g g t h
Γ g t h = α i + 1 2 L ln ( 1 R 1 R 2 ( ω L , ω c ) )
( Δ L max λ ) 2 = 1 16 π 2 n 2 [ ln ( 1 R 1 R 2 ) + 2 α i L ]
Δ ω L = ( 1 1 + τ i n γ T ) Δ ω c
d A + ( t ) d t = 1 2 ( 1 i α ) ( Γ v g g N ( N N 0 ) 1 τ p ) A + ( t ) + γ L [ γ c A c ( t ) r 2 ( ω L , ω c ) A + ( t ) ]
d A c ( t ) d t = ( i Δ ω γ T ) A c ( t ) + i γ c A + ( t )
d N ( t ) d t = η p J e V L C R ( N ) Γ v g g N ( N ( t ) N 0 ) σ ( ω L , ω C ) | A + ( t ) | 2 V L C
P t ( t ) = 2 ϵ 0 n c | γ c A c ( t ) i A + ( t ) | 2
P x ( t ) = 2 ϵ 0 n c γ p | A c ( t ) | 2
x ˙ ( t ) = A x ( t ) + F x = [ δ | A + | , δ | A c | , δ ϕ + , δ ϕ c , δ N ] T
λ F P = γ 2 ± γ 2 4 ω r e l 2
γ = 1 τ s + v g g N N p ω r e l 2 = v g g N N p τ p