Abstract

The spectral region around 2μm wavelengths is of special significance for applications in optical communications, which is facing a capacity crunch at the telecommunication band. Development of CMOS-compatible on-chip photonic and optoelectronic devices operating in this spectral region is highly demanded but still at its infancy. In this paper, we present a design of graphene-on-germanium slot waveguides at the wavelength of 2μm. Due to the optical-field enhancement and poor mode confinement, light-matter interactions are enhanced in the graphene-on-germanium slot waveguide. Moreover, the influence of the refractive index contrast and the number of integrated graphene layers on the optical absorption enhancement of the slot waveguide is studied. Based on the graphene-on-slot waveguide configuration, energy-efficient and compact Mach-Zehnder interferometer and microring resonator phase modulators are designed. Our study paves the way for the development of on-chip electro-optic modulators at 2μm wavelengths.

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

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References

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2018 (3)

2017 (1)

Z. Wu, Y. Chen, T. Zhang, Z. Shao, Y. Wen, P. Xu, Y. Zhang, and S. Yu, “Design and optimization of optical modulators based on graphene-on-silicon nitride microring resonators,” J. Opt. 19(4), 045801 (2017).
[Crossref]

2016 (3)

W. Li, P. Anantha, S. Bao, K. H. Lee, X. Guo, T. Hu, L. Zhang, H. Wang, R. Soref, and C. S. Tan, “Germanium-on-silicon nitride waveguides for mid-infrared integrated photonics,” Appl. Phys. Lett. 109(24), 241101 (2016).
[Crossref]

J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8(27), 13206–13211 (2016).
[Crossref]

U. Younis, S. K. Vanga, A. E. Lim, P. G. Lo, A. A. Bettiol, and K. W. Ang, “Germanium-on-SOI waveguides for mid-infrared wavelengths,” Opt. Express 24(11), 11987–11993 (2016).
[Crossref]

2015 (5)

J. Wang, Z. Cheng, Z. Chen, J. Xu, H. K. Tsang, and C. Shu, “Graphene photodetector integrated on silicon nitride waveguide,” J. Appl. Phys. 117(14), 144504 (2015).
[Crossref]

T. Pan, C. Qiu, J. Wu, X. Jiang, B. Liu, Y. Yang, H. Zhou, R. Soref, and Y. Su, “Analysis of an electro-optic modulator based on a graphene-silicon hybrid 1D photonic crystal nanobeam cavity,” Opt. Express 23(18), 23357 (2015).
[Crossref]

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

X. Yin, T. Zhang, L. Chen, and X. Li, “Ultra-compact TE-pass polarizer with graphene multilayer embedded in a silicon slot waveguide,” Opt. Lett. 40(8), 1733 (2015).
[Crossref]

M. Nedeljkovic, J. S. Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stanković, T. D. Bucio, C. G. Littlejohns, F. Y. Gardes, and G. Z. Mashanovich, “Surface-Grating-Coupled Low-Loss Ge-on-Si Rib Waveguides and Multimode Interferometers,” IEEE Photon. Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

2014 (4)

2013 (4)

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

X. Wang, Z. Cheng, K. Xu, H. K. Tsang, and J.-B. Xu, “High-responsivity graphene/silicon-heterostructure waveguide photodetectors,” Nat. Photonics 7(11), 888–891 (2013).
[Crossref]

K. Xu, L. G. Yang, J. Y. Sung, Y. M. Chen, Z. Z. Cheng, C. W. Chow, C. H. Yeh, and H. K. Tsang, “Compatibility of Silicon Mach-Zehnder Modulators for Advanced Modulation Formats,” J. Lightwave Technol. 31(15), 2550–2554 (2013).
[Crossref]

A. Malik, M. Muneeb, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon planar concave grating wavelength (de) multiplexers in the mid-infrared,” Appl. Phys. Lett. 103(16), 161119 (2013).
[Crossref]

2012 (3)

2011 (1)

E. Desurvire, C. Kazmierski, F. Lelarge, X. Marcadet, A. Scavennec, F. A. Kish, D. F. Welch, R. Nagarajan, C. H. Joyner, R. P. Schneider, and et al., “Science and technology challenges in XXIst century optical communications,” C. R. Phys. 12(4), 387–416 (2011).
[Crossref]

2010 (4)

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[Crossref]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

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

V. C. Joris, W. M. J. Green, A. Solomon, and Y. A. Vlasov, “Integrated NiSi waveguide heaters for CMOS-compatible silicon thermo-optic devices,” Opt. Lett. 35(7), 1013–1015 (2010).
[Crossref]

2009 (1)

Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref]

2007 (2)

2006 (1)

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1618–1627 (2006).
[Crossref]

2005 (1)

2000 (2)

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

Alam, S.-U.

Anantha, P.

W. Li, P. Anantha, S. Bao, K. H. Lee, X. Guo, T. Hu, L. Zhang, H. Wang, R. Soref, and C. S. Tan, “Germanium-on-silicon nitride waveguides for mid-infrared integrated photonics,” Appl. Phys. Lett. 109(24), 241101 (2016).
[Crossref]

Ang, K. W.

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Bao, S.

W. Li, P. Anantha, S. Bao, K. H. Lee, X. Guo, T. Hu, L. Zhang, H. Wang, R. Soref, and C. S. Tan, “Germanium-on-silicon nitride waveguides for mid-infrared integrated photonics,” Appl. Phys. Lett. 109(24), 241101 (2016).
[Crossref]

Barrios, C. A.

Ben-Ezra, S.

Bettiol, A. A.

Birks, T.

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Bucio, T. D.

M. Nedeljkovic, J. S. Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stanković, T. D. Bucio, C. G. Littlejohns, F. Y. Gardes, and G. Z. Mashanovich, “Surface-Grating-Coupled Low-Loss Ge-on-Si Rib Waveguides and Multimode Interferometers,” IEEE Photon. Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Cameron, N.

Cao, W.

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys.: Condens. Matter 19(2), 026222 (2007).
[Crossref]

Cardenas, J.

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

Casquel, R.

Chang, C.-Y.

Chang, Y. C.

Chen, L.

Chen, Y.

Z. Wu, Y. Chen, T. Zhang, Z. Shao, Y. Wen, P. Xu, Y. Zhang, and S. Yu, “Design and optimization of optical modulators based on graphene-on-silicon nitride microring resonators,” J. Opt. 19(4), 045801 (2017).
[Crossref]

Chen, Y. M.

Chen, Z.

J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8(27), 13206–13211 (2016).
[Crossref]

J. Wang, Z. Cheng, Z. Chen, J. Xu, H. K. Tsang, and C. Shu, “Graphene photodetector integrated on silicon nitride waveguide,” J. Appl. Phys. 117(14), 144504 (2015).
[Crossref]

Cheng, Z.

T.-H. Xiao, Z. Zhao, W. Zhou, C.-Y. Chang, S. Y. Set, M. Takenaka, H. K. Tsang, Z. Cheng, and K. Goda, “Mid-infrared high-Q germanium microring resonator,” Opt. Lett. 43(12), 2885–2888 (2018).
[Crossref]

J. Wang, Z. Cheng, and X. Li, “Progress on Waveguide-Integrated Graphene Optoelectronics,” Adv. Condens. Matter Phys. 2018, 1–9 (2018).
[Crossref]

J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8(27), 13206–13211 (2016).
[Crossref]

J. Wang, Z. Cheng, Z. Chen, J. Xu, H. K. Tsang, and C. Shu, “Graphene photodetector integrated on silicon nitride waveguide,” J. Appl. Phys. 117(14), 144504 (2015).
[Crossref]

Z. Cheng, H. K. Tsang, X. Wang, J.-B. Xu, and K. Xu, “Mid-infrared Suspended Membrane Waveguide and Ring Resonator on Silicon-on-Insulator,” IEEE J. Sel. Top. Quantum Electron. 20(1), 43–48 (2014).
[Crossref]

X. Wang, Z. Cheng, K. Xu, H. K. Tsang, and J.-B. Xu, “High-responsivity graphene/silicon-heterostructure waveguide photodetectors,” Nat. Photonics 7(11), 888–891 (2013).
[Crossref]

Cheng, Z. Z.

Chow, C. W.

Couny, F.

Crommie, M. F.

Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref]

Desurvire, E.

E. Desurvire, C. Kazmierski, F. Lelarge, X. Marcadet, A. Scavennec, F. A. Kish, D. F. Welch, R. Nagarajan, C. H. Joyner, R. P. Schneider, and et al., “Science and technology challenges in XXIst century optical communications,” C. R. Phys. 12(4), 387–416 (2011).
[Crossref]

Dimitropoulos, D.

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1618–1627 (2006).
[Crossref]

Dwivedi, S.

Englund, D.

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

Farr, L.

Fathpour, S.

B. Jalali, V. Raghunathan, R. Shori, S. Fathpour, D. Dimitropoulos, and O. Stafsudd, “Prospects for silicon mid-IR Raman lasers,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1618–1627 (2006).
[Crossref]

Freude, W.

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000).
[Crossref]

Gan, X.

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

Gao, Y.

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
[Crossref]

Gardes, F.

Gardes, F. Y.

M. Nedeljkovic, J. S. Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stanković, T. D. Bucio, C. G. Littlejohns, F. Y. Gardes, and G. Z. Mashanovich, “Surface-Grating-Coupled Low-Loss Ge-on-Si Rib Waveguides and Multimode Interferometers,” IEEE Photon. Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

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

Girit, C.

Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref]

Goda, K.

Green, W. M. J.

V. C. Joris, W. M. J. Green, A. Solomon, and Y. A. Vlasov, “Integrated NiSi waveguide heaters for CMOS-compatible silicon thermo-optic devices,” Opt. Lett. 35(7), 1013–1015 (2010).
[Crossref]

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Z. Wu, Y. Chen, T. Zhang, Z. Shao, Y. Wen, P. Xu, Y. Zhang, and S. Yu, “Design and optimization of optical modulators based on graphene-on-silicon nitride microring resonators,” J. Opt. 19(4), 045801 (2017).
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Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
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Zhao, Z.

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J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8(27), 13206–13211 (2016).
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Adv. Condens. Matter Phys. (1)

J. Wang, Z. Cheng, and X. Li, “Progress on Waveguide-Integrated Graphene Optoelectronics,” Adv. Condens. Matter Phys. 2018, 1–9 (2018).
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Appl. Phys. Lett. (2)

A. Malik, M. Muneeb, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon planar concave grating wavelength (de) multiplexers in the mid-infrared,” Appl. Phys. Lett. 103(16), 161119 (2013).
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C. R. Phys. (1)

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Electron. Lett. (1)

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IEEE Photon. Technol. Lett. (1)

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J. Lightwave Technol. (2)

J. Opt. (1)

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Nano Lett. (1)

X. Gan, R. J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D. Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13(2), 691–696 (2013).
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Nanoscale (1)

J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8(27), 13206–13211 (2016).
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Nat. Photonics (5)

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X. Wang, Z. Cheng, K. Xu, H. K. Tsang, and J.-B. Xu, “High-responsivity graphene/silicon-heterostructure waveguide photodetectors,” Nat. Photonics 7(11), 888–891 (2013).
[Crossref]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
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Nature (1)

Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
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Opt. Express (6)

Opt. Lett. (4)

Optica (1)

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Figures (7)

Fig. 1.
Fig. 1. Calculated graphene permittivity as a function of Fermi level at the wavelength of 2μm.
Fig. 2.
Fig. 2. Schematics of the proposed dual-layer graphene-on-Ge slot waveguide modulator. (a) 3-dimensional schematic of the dual-layer graphene-on-slot waveguide modulator. (b) Cross-section of the dual-layer graphene-on-slot waveguide modulator. The electrodes are set on the surfaces of the two graphene layers, respectively.
Fig. 3.
Fig. 3. Calculation of graphene-on-waveguide loss factors with different waveguide configurations. Inset is the schematic of mode distributions of TE mode dual-layer graphene-on-slot waveguide and dual-layer graphene-on-channel waveguide, respectively.
Fig. 4.
Fig. 4. Calculated mode parameters for different dual-layer graphene-on-waveguide structures. (a) Real parts of effective RIs as a function of Fermi level for TE mode dual-layer graphene-on-slot waveguide and dual-layer graphene-on-channel waveguide. (b) Waveguide loss factors as a function of Fermi level for different waveguide configurations.
Fig. 5.
Fig. 5. Influence of the integrated graphene layers on the waveguide loss factor. (a) Calculated waveguide loss factor as a function of the number of graphene layers. Inset is the schematic of the multiple layers of graphene sandwiched by insulator layers on the surface of the slot waveguide. (b) The normalized derivative of the waveguide loss factor as a function of the number of graphene layers. (c) The effective RI as a function of the number of graphene layers.
Fig. 6.
Fig. 6. Design of dual-layer graphene-on-waveguide MZI phase modulators. (a) Schematic of the dual-layer graphene-on-MZI modulator structure based on the slot waveguide configuration. (b), (c) Calculated transmissions of MZI phase modulators as a function of Fermi levels of arm B for graphene-on-slot waveguide and graphene-on-channel waveguide configurations, respectively.
Fig. 7.
Fig. 7. Design of dual-layer graphene-on-microring resonator phase modulators. (a) Schematic of the microring resonator phase modulator based on the dual-layer graphene-on-slot waveguide configuration. (b), (c) Calculated transmissions of microring resonator phase modulators as a function of Fermi level with the slot waveguide and channel waveguide configurations, respectively.

Tables (1)

Tables Icon

Table 1. Real parts of effective RIs and waveguide loss factors of dual-layer graphene-on-slot waveguides and graphene-on-channel waveguides of different materials.

Equations (4)

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σ = 2 i e 2 ( Ω + 2 i Γ ) h [ 1 ( Ω + 2 i Γ ) 2 Δ ω 2 + Δ 2 ω ( δ n F ( ω ) δ ω δ n F ( ω ) δ ω ) d ω Δ ω 2 + Δ 2 ω ( n F ( ω ) n F ( ω ) ( Ω + 2 i Γ ) 2 4 ω 2 ) d ω ] ,
ε e f f = 1 + i σ ω ε 0 d ,
T ( λ ) = 1 4 × [ exp ( α 1 L ) + exp ( α 2 L ) + 2 exp ( α 1 L + α 2 L 2 ) cos ) ( Δ φ ) ] ,
B ( λ ) = a 2 + t 2 2 a t cos θ 1 + a 2 t 2 2 a t cos θ ,

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