Abstract

A general multilevel carrier kinetics model is explored to simulate the saturation of absorption in the time-domain. Contrarily to approaches relying upon phenomenological descriptions, in this study, we deal with the saturation through a physics-based model that can predict the realistic temporal dynamics of the entire system. Additionally, the proposed method allows high flexibility and generality for the problems under consideration as it is built on a full-wave three-dimensional time-domain solver that can include nonlinear material dispersion, optical activity, and other effects within a joint multiphysics framework. We discretize all the equations using finite-differences combined with the auxiliary differential equation technique which allows adding polarizations driven by diverse underlying physical mechanisms accounting for multiple material dynamics. With our framework, a plethora of time-resolved spatially-dependent numerical data, which are not attainable otherwise, is becoming accessible, hence enabling a comprehensive understanding of the foundations of the materials physics and empowering accurate optimization of new nonlinear photonic devices.

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

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References

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  1. E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
    [Crossref]
  2. J. A. Morris and C. R. Pollock, “Passive Q switching of a diode-pumped Nd:YAG laser with a saturable absorber,” Opt. Lett. 15(8), 440–442 (1990).
    [Crossref] [PubMed]
  3. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
    [Crossref]
  4. S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibers and their application to mode-locked fiber lasers,” Opt. Lett. 29(14), 1581–1583 (2004).
    [Crossref] [PubMed]
  5. C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
    [Crossref]
  6. H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).
  7. D. Wu, J. Peng, Z. Cai, J. Weng, Z. Luo, N. Chen, and H. Xu, “Gold nanoparticles as a saturable absorber for visible 635 nm Q-switched pulse generation,” Opt. Express 23(18), 24071–24076 (2015).
    [Crossref] [PubMed]
  8. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method(Artech house, 2005), chapter 9.
  9. S. C. Hill, G. Videen, W. Sun, and Q. Fu, “Scattering and internal fields of a microsphere that contains a saturable absorber: finite-difference time-domain simulations,” Appl. Opt. 40(30), 5487–5494 (2001).
    [Crossref]
  10. Y. Feng, N. Dong, G. Wang, Y. Li, S. Zhang, K. Wang, L. Zhang, W. J. Blau, and J. Wang, “Saturable absorption behavior of free-standing graphene polymer composite films over broad wavelength and time ranges,” Opt. Express 23(1), 559–569 (2015).
    [Crossref] [PubMed]
  11. C. Varin, G. Bart, R. Emms, and T. Brabec, “Saturable lorentz model for fully explicit three-dimensional modeling of nonlinear optics,” Opt. Express 23(3), 2686–2695 (2015).
    [Crossref] [PubMed]
  12. C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
    [Crossref]
  13. A. Mock, “Modeling passive mode-locking via saturable absorption in graphene using the finite-difference time-domain method,” IEEE J. Quantum Electron. 53(5), 1–10 (2017).
    [Crossref]
  14. Lumerical Inc. http://www.lumerical.com/tcad-products/fdtd/ .
  15. COMSOL, Inc. https://www.comsol.com/wave-optics-module .
  16. S. H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12(16), 3827–3833 (2004).
    [Crossref] [PubMed]

2018 (1)

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

2017 (1)

A. Mock, “Modeling passive mode-locking via saturable absorption in graphene using the finite-difference time-domain method,” IEEE J. Quantum Electron. 53(5), 1–10 (2017).
[Crossref]

2016 (1)

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

2015 (3)

2012 (1)

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

2009 (1)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

2004 (2)

2001 (1)

1990 (1)

1972 (1)

E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
[Crossref]

Ahmad, H.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Ali, Z.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Bao, Q.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Bart, G.

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

C. Varin, G. Bart, R. Emms, and T. Brabec, “Saturable lorentz model for fully explicit three-dimensional modeling of nonlinear optics,” Opt. Express 23(3), 2686–2695 (2015).
[Crossref] [PubMed]

Blau, W. J.

Brabec, T.

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

C. Varin, G. Bart, R. Emms, and T. Brabec, “Saturable lorentz model for fully explicit three-dimensional modeling of nonlinear optics,” Opt. Express 23(3), 2686–2695 (2015).
[Crossref] [PubMed]

Cai, Z.

Chang, S. H.

Chen, N.

Chen, Y.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Dienes, A.

E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
[Crossref]

Dong, N.

Emms, R.

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

C. Varin, G. Bart, R. Emms, and T. Brabec, “Saturable lorentz model for fully explicit three-dimensional modeling of nonlinear optics,” Opt. Express 23(3), 2686–2695 (2015).
[Crossref] [PubMed]

Feng, Y.

Fennel, T.

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

Fu, Q.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method(Artech house, 2005), chapter 9.

Harun, S.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Hill, S. C.

Inoue, Y.

Ippen, E.

E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
[Crossref]

Ismail, M.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Jablonski, M.

Lee, C.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Li, Y.

Loh, K. P.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Luo, Z.

Maruyama, S.

Mock, A.

A. Mock, “Modeling passive mode-locking via saturable absorption in graphene using the finite-difference time-domain method,” IEEE J. Quantum Electron. 53(5), 1–10 (2017).
[Crossref]

Morris, J. A.

Murakami, Y.

Ni, Z.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Peng, J.

Pollock, C. R.

Qi, X.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Reduan, S.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Ruslan, N.

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Set, S.

Shank, C.

E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
[Crossref]

Shen, Z. X.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Sun, W.

Taflove, A.

S. H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12(16), 3827–3833 (2004).
[Crossref] [PubMed]

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method(Artech house, 2005), chapter 9.

Tang, D.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Tang, D. Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Varin, C.

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

C. Varin, G. Bart, R. Emms, and T. Brabec, “Saturable lorentz model for fully explicit three-dimensional modeling of nonlinear optics,” Opt. Express 23(3), 2686–2695 (2015).
[Crossref] [PubMed]

Videen, G.

Wang, G.

Wang, J.

Wang, K.

Wang, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Wang, Z.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Wen, S.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Weng, J.

Wu, D.

Xu, H.

Yaguchi, H.

Yamashita, S.

Yan, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Zhang, H.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Zhang, L.

Zhang, S.

Zhao, C.

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

E. Ippen, C. Shank, and A. Dienes, “Passive mode locking of the CW dye laser,” Appl. Phys. Lett. 21(8), 348–350 (1972).
[Crossref]

C. Zhao, H. Zhang, X. Qi, Y. Chen, Z. Wang, S. Wen, and D. Tang, “Ultra-short pulse generation by a topological insulator based saturable absorber,” Appl. Phys. Lett. 101(21), 211106 (2012).
[Crossref]

Comput. Phys. Commun. (1)

C. Varin, R. Emms, G. Bart, T. Fennel, and T. Brabec, “Explicit formulation of second and third order optical nonlinearity in the FDTD framework,” Comput. Phys. Commun. 222, 70–83 (2018).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Mock, “Modeling passive mode-locking via saturable absorption in graphene using the finite-difference time-domain method,” IEEE J. Quantum Electron. 53(5), 1–10 (2017).
[Crossref]

Opt. Commun. (1)

H. Ahmad, C. Lee, M. Ismail, Z. Ali, S. Reduan, N. Ruslan, M. Ismail, and S. Harun, “Zinc oxide (ZnO) nanoparticles as saturable absorber in passively q-switched fiber laser,” Opt. Commun. 381, 72–76 (2016).

Opt. Express (4)

Opt. Lett. (2)

Other (3)

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method(Artech house, 2005), chapter 9.

Lumerical Inc. http://www.lumerical.com/tcad-products/fdtd/ .

COMSOL, Inc. https://www.comsol.com/wave-optics-module .

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Figures (5)

Fig. 1
Fig. 1 Saturable absorption in a dielectric thin film modeled by a two-level system at: (a) low input fluence and (b) high input fluence where the ground state carriers are depleted and the excited-state lifetime is too long to allow for reabsorption.
Fig. 2
Fig. 2 Jablonski diagrams of (a) two-level and (b) four-level atomic systems showing the allowed transitions and the corresponding lifetimes.
Fig. 3
Fig. 3 Dynamics of a dielectric SA modeled using the two-level system. (a) Absorption vs. input fluence showing the saturation of absorption. (b) Time-dependent normalized macroscopic polarization P10 in both linear and nonlinear cases. Time evolution of carrier population density in (c) linear (6 µJ/cm2) and (d) nonlinear (94 µJ/cm2) regimes.
Fig. 4
Fig. 4 Dependence of the absorption on the (a) film thickness and (b) carriers’ concentrations.
Fig. 5
Fig. 5 An SA dielectric film modeled using the four-level system. (a) The absorption spectrum shows three peaks at the selected wavelengths. Time-dependent (b) carrier population densities and (c) normalized polarizations at an input fluence of 1 µJ/cm2

Equations (6)

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

α ( I ) = α 0 1 + I I s
d N 1 d t = N 1 τ + 1 ω 0 E d P d t
d 2 P 10 d t 2 + γ 10 d P 10 d t + ω 0 2 P 10 = κ ( N 0 N 1 ) E
D = ϵ 0 ϵ h E + m P m
d N 3 d t = N 3 τ 30 N 3 τ 31 N 3 τ 32 + 1 ω 30 E d P 30 d t d N 2 d t = N 2 τ 20 N 2 τ 21 + N 3 τ 32 + 1 ω 20 E d P 20 d t d N 1 d t = N 1 τ 10 + N 2 τ 21 + N 3 τ 31 + 1 ω 10 E d P 10 d t
d 2 P i j d t 2 + γ 1 i j d P i j d t + ω i j 2 P i j = κ i j ( N j N i ) E

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