Abstract

All-optical processing offers low power consumption and fast operation speed and is a promising approach to high-bit-rate communication. Realization of all-optical integrated photonics requires core materials that strongly mediate photon–photon interaction. Recently, it was shown that, in the long-wavelength limit, graphene nanoribbons (GNRs) have a very strong Kerr optical nonlinearity in the telecom wavelength range ($1.3-1.6\;\mu$m). We propose a dielectric waveguide with embedded GNRs for all-optical self-amplitude-modulation applications. By implanting a van der Waals (vdW) heterostructure consisting of GNRs and hexagonal boron nitride into a rib silicon waveguide, we maximize the optical concentration near the GNRs and enhance nonlinear optical effects. Different-width GNRs incorporated in the vdW heterostructure provide strong self-sustaining broadband modulation over the telecom frequency range, without a need for dynamical tuning. The compact footprint and self-sustaining, broad-bandwidth saturable absorption make the proposed device a suitable component for ultrafast nanophotonic applications.

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

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References

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    [Crossref]

2019 (2)

T.-H. Chen, C.-H. Cheng, Y.-H. Lin, C.-T. Tsai, Y.-C. Chi, Z. Luo, and G.-R. Lin, “Optimizing the self-amplitude modulation of different 2D saturable absorbers for ultrafast mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 25(4), 1–10 (2019).
[Crossref]

Q. Feng, H. Cong, B. Zhang, W. Wei, Y. Liang, S. Fang, T. Wang, and J. Zhang, “Enhanced optical kerr nonlinearity of graphene/si hybrid waveguide,” Appl. Phys. Lett. 114(7), 071104 (2019).
[Crossref]

2018 (6)

F. Karimi, A. Davoody, and I. Knezevic, “Nonlinear optical response in graphene nanoribbons: The critical role of electron scattering,” Phys. Rev. B 97(24), 245403 (2018).
[Crossref]

Y. Kivshar, “All-dielectric meta-optics and non-linear nanophotonics,” Natl. Sci. Rev. 5(2), 144–158 (2018).
[Crossref]

F. Sun, L. Xia, C. Nie, J. Shen, Y. Zou, G. Cheng, H. Wu, Y. Zhang, D. Wei, and S. Yin, “The all-optical modulator in dielectric-loaded waveguide with graphene-silicon heterojunction structure,” Nanotechnology 29(13), 135201 (2018).
[Crossref]

X. Sun, B. Zhang, Y. Li, X. Luo, G. Li, Y. Chen, C. Zhang, and J. He, “Tunable ultrafast nonlinear optical properties of graphene/MOs2 van der Waals heterostructures and their application in solid-state bulk lasers,” ACS Nano 12(11), 11376–11385 (2018).
[Crossref]

A. J. Way, R. M. Jacobberger, and M. S. Arnold, “Seed-initiated anisotropic growth of unidirectional armchair graphene nanoribbon arrays on germanium,” Nano Lett. 18(2), 898–906 (2018).
[Crossref]

Y. Sun, C. Tu, Z. You, J. Liao, Y. Wang, and J. Xu, “One-dimensional Bi2 Te2 nanowire based broadband saturable absorber for passively Q-switched Yb-doped and Er-doped solid state lasers,” Opt. Mater. Express 8(1), 165–174 (2018).
[Crossref]

2017 (8)

R. M. Jacobberger and M. S. Arnold, “High-performance charge transport in semiconducting armchair graphene nanoribbons grown directly on germanium,” ACS Nano 11(9), 8924–8929 (2017).
[Crossref]

F. Karimi and I. Knezevic, “Plasmons in graphene nanoribbons,” Phys. Rev. B 96(12), 125417 (2017).
[Crossref]

H. Rostami, M. I. Katsnelson, and M. Polini, “Theory of plasmonic effects in nonlinear optics: the case of graphene,” Phys. Rev. B 95(3), 035416 (2017).
[Crossref]

S. Yu, X. Wu, Y. Wang, X. Guo, and L. Tong, “2d materials for optical modulation: challenges and opportunities,” Adv. Mater. 29(14), 1606128 (2017).
[Crossref]

K. J. Ooi, P. C. Leong, L. K. Ang, and D. T. Tan, “All-optical control on a graphene-on-silicon waveguide modulator,” Sci. Rep. 7(1), 12748 (2017).
[Crossref]

Y. Shen, N. C. Harris, S. Kirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

M. R. Shcherbakov, S. Liu, V. V. Zubyuk, A. Vaskin, P. P. Vabishchevich, G. Keeler, T. Pertsch, T. V. Dolgova, I. Staude, I. Brener, and A. A. Fedyanin, “Ultrafast all-optical tuning of direct-gap semiconductor metasurfaces,” Nat. Commun. 8(1), 17 (2017).
[Crossref] [PubMed]

J. L. Zheng, X. Tang, Z. H. Yang, Z. M. Liang, Y. X. Chen, K. Wang, Y. F. Song, Y. Zhang, J. H. Ji, Y. Liu, D. Y. Fan, and H. Zhang, “Few-Layer Phosphorene-Decorated Microfiber for All-Optical Thresholding and Optical Modulation,” Adv. Opt. Mater. 5(9), 1700026 (2017).
[Crossref]

2016 (7)

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D materials and van der Waals heterostructures,” Science 353(6298), aac9439 (2016).
[Crossref]

V. Shautsova, A. M. Gilbertson, N. C. G. Black, S. A. Maier, and L. F. Cohen, “Hexagonal boron nitride assisted transfer and encapsulation of large area cvd graphene,” Sci. Rep. 6(1), 30210 (2016).
[Crossref]

J. D. Cox, I. Silveiro, and F. J. García de Abajo, “Quantum effects in the nonlinear response of graphene plasmons,” ACS Nano 10(2), 1995–2003 (2016).
[Crossref]

F. Karimi, A. Davoody, and I. Knezevic, “Dielectric function and plasmons in graphene: A self-consistent-field calculation within a markovian master equation formalism,” Phys. Rev. B 93(20), 205421 (2016).
[Crossref]

R. K. Yadav, R. Sharma, J. Aneesh, P. Abhiramnath, and K. Adarsh, “Saturable absorption in one-dimensional Sb2 Se2nanowires in the visible to near-infrared region,” Opt. Lett. 41(9), 2049–2052 (2016).
[Crossref]

S. Yu, X. Wu, K. Chen, B. Chen, X. Guo, D. Dai, L. Tong, W. Liu, and Y. R. Shen, “All-optical graphene modulator based on optical kerr phase shift,” Optica 3(5), 541–544 (2016).
[Crossref]

2015 (2)

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

2014 (3)

2013 (1)

A. K. Geim and I. V. Grigorieva, “Van der waals heterostructures,” Nature 499(7459), 419–425 (2013).
[Crossref]

2012 (1)

S. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D. Elias, K. Novoselov, L. Ponomarenko, A. Geim, and R. Gorbachev, “Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices,” Nat. Mater. 11(9), 764–767 (2012).
[Crossref]

2011 (2)

S. Mikhailov, “Theory of the giant plasmon-enhanced second-harmonic generation in graphene and semiconductor two-dimensional electron systems,” Phys. Rev. B 84(4), 045432 (2011).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

2010 (3)

G. T. Reed, G. Mashanovich, F. Gardes, and D. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
[Crossref]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref]

2009 (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]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–polymer composites for ultrafast photonics,” Adv. Mater. 21(38-39), 3874–3899 (2009).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

2007 (2)

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of cdse quantum dots,” Nat. Photonics 1(7), 402–406 (2007).
[Crossref]

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
[Crossref]

2006 (1)

Y.-W. Son, M. L. Cohen, and S. G. Louie, “Energy gaps in graphene nanoribbons,” Phys. Rev. Lett. 97(21), 216803 (2006).
[Crossref]

2004 (2)

R. Del Coso and J. Solis, “Relation between nonlinear refractive index and third-order susceptibility in absorbing media,” J. Opt. Soc. Am. B 21(3), 640–644 (2004).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

Abhiramnath, P.

Adarsh, K.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

Aneesh, J.

Ang, L. K.

K. J. Ooi, P. C. Leong, L. K. Ang, and D. T. Tan, “All-optical control on a graphene-on-silicon waveguide modulator,” Sci. Rep. 7(1), 12748 (2017).
[Crossref]

Arnold, M. S.

A. J. Way, R. M. Jacobberger, and M. S. Arnold, “Seed-initiated anisotropic growth of unidirectional armchair graphene nanoribbon arrays on germanium,” Nano Lett. 18(2), 898–906 (2018).
[Crossref]

R. M. Jacobberger and M. S. Arnold, “High-performance charge transport in semiconducting armchair graphene nanoribbons grown directly on germanium,” ACS Nano 11(9), 8924–8929 (2017).
[Crossref]

M. S. Arnold, A. J. Way, and R. M. Jacobberger, “Seed-mediated growth of patterned graphene nanoribbon arrays,” (2017). US Patent 9,761,669.

Atwater, H. A.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of cdse quantum dots,” Nat. Photonics 1(7), 402–406 (2007).
[Crossref]

Baehr-Jones, T.

Y. Shen, N. C. Harris, S. Kirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14, 955–959 (2014).
[Crossref]

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]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref]

Bhaskaran, H.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
[Crossref]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

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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).
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A. J. Way, R. M. Jacobberger, and M. S. Arnold, “Seed-initiated anisotropic growth of unidirectional armchair graphene nanoribbon arrays on germanium,” Nano Lett. 18(2), 898–906 (2018).
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M. S. Arnold, A. J. Way, and R. M. Jacobberger, “Seed-mediated growth of patterned graphene nanoribbon arrays,” (2017). US Patent 9,761,669.

Wei, D.

F. Sun, L. Xia, C. Nie, J. Shen, Y. Zou, G. Cheng, H. Wu, Y. Zhang, D. Wei, and S. Yin, “The all-optical modulator in dielectric-loaded waveguide with graphene-silicon heterojunction structure,” Nanotechnology 29(13), 135201 (2018).
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Wei, W.

Q. Feng, H. Cong, B. Zhang, W. Wei, Y. Liang, S. Fang, T. Wang, and J. Zhang, “Enhanced optical kerr nonlinearity of graphene/si hybrid waveguide,” Appl. Phys. Lett. 114(7), 071104 (2019).
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Wen, S.

Wright, C. D.

C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C. D. Wright, H. Bhaskaran, and W. H. Pernice, “Integrated all-photonic non-volatile multi-level memory,” Nat. Photonics 9(11), 725–732 (2015).
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F. Sun, L. Xia, C. Nie, J. Shen, Y. Zou, G. Cheng, H. Wu, Y. Zhang, D. Wei, and S. Yin, “The all-optical modulator in dielectric-loaded waveguide with graphene-silicon heterojunction structure,” Nanotechnology 29(13), 135201 (2018).
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S. Yu, X. Wu, Y. Wang, X. Guo, and L. Tong, “2d materials for optical modulation: challenges and opportunities,” Adv. Mater. 29(14), 1606128 (2017).
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F. Sun, L. Xia, C. Nie, J. Shen, Y. Zou, G. Cheng, H. Wu, Y. Zhang, D. Wei, and S. Yin, “The all-optical modulator in dielectric-loaded waveguide with graphene-silicon heterojunction structure,” Nanotechnology 29(13), 135201 (2018).
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Figures (3)

Fig. 1.
Fig. 1. The real part ($n_2$) and imaginary part ($k_2$) of the nonlinear refractive indices of undoped aGNRs. The width of aGNRs is in the range of 8–12 nm. The numbers denote the number of dimers in the aGNR’s unit cell. The aGNRs are assumed to be sandwiched between two hBN films. The nonlinear refractive index of aGNRs can be as large as $10^{-8} \textrm {m}^2 \textrm {W}^{-1}$.
Fig. 2.
Fig. 2. (a) Schematic of a GBNH-embedded rib silicon waveguide. The zoomed-in heterostructure consists of graphene nanoribbons (gray) encased in hBN (pink). (b) The cross-section view of the waveguide. (c) $E_{\textrm {GBNH}}/E_{\textrm {max}}$ as a function of the silicon strip thickness, $T_s$. $E_{\textrm {GBNH}}$ denotes the electric field at the center of the GBNH and $E_{\textrm {max}}$ is the maximal electric field across the device. The closer the ratio is to unity, the more concentrated the optical field is near the GBNH. $T_s \approx 45$ nm yields optimal optical confinement. The insets show the electric-field profile across the waveguide for narrow ($T_s = 20$ nm), optimal ($T_s = 45$ nm), and thick ($T_s = 100$ nm) silicon strips at 950 meV.
Fig. 3.
Fig. 3. (a) The average attenuation constant as a function of normalized optical intensity. The shaded area represents the range of attenuation constants calculated for the frequencies $0.75-0.95$ eV. (Within the shaded area, the curves associated with a single frequency are nonmonotonic.) (b) The modulation depth as a function of frequency for three values of $\delta W$. Increasing $\delta W$ flattens the modulation depth and broadens the BW. (c) The saturation optical intensity as a function of frequency and $\delta W$. For large $\delta W$, the saturation optical intensity varies less with frequency. (d) The modulation depth as a function of frequency for three values of $\rho$. Increasing $\rho$ enhances the modulation strength. For $\rho = 20\%$, a self-sustaining broadband modulation depth of at least $\sim$ 0.03 dB$\mu$m$^{-1}$ is achieved over the frequency range.

Equations (2)

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n 2 = n 0 Re { χ ( 3 ) } + k 0 Im { χ ( 3 ) } ε 0 ε r v p ( n 0 2 + k 0 2 ) , k 2 = n 0 Im { χ ( 3 ) } k 0 Re { χ ( 3 ) } ε 0 ε r v p ( n 0 2 + k 0 2 ) ,
χ GBNH ( E ) = ( 1 ρ 100 ) χ hBN + ρ 100 χ G,AM ( 1 ) ( 1 E 2 E sat,HM 2 ) 1 ,