Propagation and absorption of light in planar dielectric waveguides with two-dimensional semiconductors

Yuri N. Gartstein; Anton V. Malko

doi:10.1364/OE.25.023128

Propagation and absorption of light in planar dielectric waveguides with two-dimensional semiconductors

Yuri N. Gartstein and Anton V. Malko

Optics Express
Vol. 25,
Issue 19,
pp. 23128-23136
(2017)
•https://doi.org/10.1364/OE.25.023128

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Yuri N. Gartstein and Anton V. Malko, "Propagation and absorption of light in planar dielectric waveguides with two-dimensional semiconductors," Opt. Express 25, 23128-23136 (2017)

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Related Topics
Table of Contents Category
- Atomic and Molecular Physics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Guided waves (130.2790)
- Semiconductor materials (160.6000)
- Polaritons (240.5420)
- Subwavelength structures, nanostructures (310.6628)

About this Article
History
- Original Manuscript: August 14, 2017
- Revised Manuscript: September 6, 2017
- Manuscript Accepted: September 8, 2017
- Published: September 12, 2017

Accessible

Open Access

Abstract

Strong optical responses of atomically thin two-dimensional (2D) semiconductors make them attractive candidates for integration into various photonic and optoelectronic structures. We discuss some fundamental effects of such integration into planar dielectric waveguides by demonstrating that a substantial modification of the spectrum of waveguide modes can occur due to high in-plane polarizability of 2D layers. Our calculations illustrate both the conceptual possibilities associated with sharp excitonic resonances as well as the results obtained with the experimentally assessed polarizability of monolayer MoS₂ over a broad spectral range. We point out that waveguide structures could also enable the tunable absorption by 2D semiconductors of the light that propagates along them, a modality quite different from the traditional light harvesting geometry.

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References

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Publication

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref] [PubMed]
B. Peng, P. K. Ang, and K. P. Loh, “Two-dimensional dichalcogenides for light-harvesting applications,” Nano Today 10, 128–137 (2015).
[Crossref]
K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Phot. 10, 216–226 (2016).
[Crossref]
A. Castellanos-Gomez, “Why all the fuss about 2D semiconductors?” Nat. Phot. 10, 202–204 (2016).
[Crossref]
T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182–194 (2017).
[Crossref]
K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]
H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]
A. Carvalho, R. M. Ribeiro, and A. H. Castro Neto, “Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides,” Phys. Rev. B 88, 115205 (2013).
[Crossref]
D. Kozawa, R. Kumar, A. Carvalho, K. K. Amara, W. Zhao, S. Wang, M. Toh, R. M. Ribeiro, A. H. Castro Neto, K. Matsuda, and G. Eda, “Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides,” Nat. Commun. 5, 4543 (2014).
[Crossref] [PubMed]
A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]
A. Chernikov, C. Ruppert, H. M. Hill, A. F. Rigosi, and T. F. Heinz, “Population inversion and giant bandgap renormalization in atomically thin WS2 layers,” Nat. Phot. 9, 466–471 (2015).
[Crossref]
N. Kinsey, M. Ferrera, V. M. Shalaev, and A. Boltasseva, “Examining nanophotonics for integrated hybrid systems: a review of plasmonic interconnects and modulators using traditional and alternative materials,” J. Opt. Soc. Am. B 32, 121–142 (2015).
[Crossref]
H. Haug and S. W. Koch, Quantum theory of the optical and electronic properties of semiconductors (World Scientific, Singapore, 2004).
[Crossref]
X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]
S. Dufferwiel, S. Schwarz, F. Withers, A. A. P. Trichet, F. Li, M. Sich, O. D. Pozo-Zamudio, C. Clark, A. Nalitov, D. D. Solnyshkov, G. Malpuech, K. Novoselov, J. Smith, M. S. Skolnick, D. N. Krizhanovskii, and A. I. Tartakovskii, “Exciton-polaritons in van der Waals heterostructures embedded in tunable microcavities,” Nat. Commun. 6, 8579 (2015).
[Crossref] [PubMed]
Y. N. Gartstein, X. Li, and C. Zhang, “Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer,” Phys. Rev. B 92, 075445 (2015).
[Crossref]
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, Hoboken, NJ, 2007).
H. M. Nguyen, O. Seitz, W. Peng, Y. N. Gartstein, Y. J. Chabal, and A. V. Malko, “Efficient radiative and nonradiative energy transfer from proximal CdSe/ZnS nanocrystals into silicon nanomembranes,” ACS Nano 6, 5574–5582 (2012).
[Crossref] [PubMed]
L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, Cambridge, 2012).
[Crossref]
V. M. Agranovich, Surface Polaritons (North Holland, Amsterdam, 1982), pp. 187–238.
S. Sampat, T. Guo, K. Zhang, J. A. Robinson, Y. Ghosh, K. P. Acharya, H. Htoon, J. A. Hollingsworth, Y. N. Gartstein, and A. V. Malko, “Exciton and trion energy transfer from giant semiconductor nanocrystals to MoS2 monolayers,” ACS Photon. 3, 708–715 (2016).
[Crossref]
T. Guo, S. Sampat, K. Zhang, J. A. Robinson, S. M. Rupich, Y. J. Chabal, Y. N. Gartstein, and A. V. Malko, “Order of magnitude enhancement of monolayer MoS2 photoluminescence due to near-field energy influx from nanocrystal films,” Sci. Rep. 7, 41967 (2017).
[Crossref]
V. M. Agranovich, Excitations in Organic Solids (Oxford University, 2009).
K. S. Thygesen, “Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures,” 2D Materials 4, 022004 (2017).
[Crossref]
H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]
G. Moody, C. Kavir Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Bergauser, E. Malic, A. Knorr, and X. Li, “Intrinsic Exciton Linewidth in Monolayer Transition Metal Dichalcogenides,” in Bulletin of the American Physical Society 60 (2015).
P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, Bristol, 2005).
M. Amani, D. H. Lien, D. Kiriya, J. Xiao, A. Azcatl, J. Noh, S. R. Madhvapathy, R. Addou, K. C. Santosh, M. Dubey, K. Cho, R. M. Wallace, S. C. Lee, J. H. He, J. W. Ager, X. Zhang, E. Yablonovitch, and A. Javey, “Near-unity photoluminescence quantum yield in MoS2,” Science 350, 1065–1068 (2015).
[Crossref] [PubMed]

2017 (3)

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182–194 (2017).
[Crossref]

T. Guo, S. Sampat, K. Zhang, J. A. Robinson, S. M. Rupich, Y. J. Chabal, Y. N. Gartstein, and A. V. Malko, “Order of magnitude enhancement of monolayer MoS2 photoluminescence due to near-field energy influx from nanocrystal films,” Sci. Rep. 7, 41967 (2017).
[Crossref]

K. S. Thygesen, “Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures,” 2D Materials 4, 022004 (2017).
[Crossref]

2016 (3)

S. Sampat, T. Guo, K. Zhang, J. A. Robinson, Y. Ghosh, K. P. Acharya, H. Htoon, J. A. Hollingsworth, Y. N. Gartstein, and A. V. Malko, “Exciton and trion energy transfer from giant semiconductor nanocrystals to MoS2 monolayers,” ACS Photon. 3, 708–715 (2016).
[Crossref]

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Phot. 10, 216–226 (2016).
[Crossref]

A. Castellanos-Gomez, “Why all the fuss about 2D semiconductors?” Nat. Phot. 10, 202–204 (2016).
[Crossref]

2015 (9)

B. Peng, P. K. Ang, and K. P. Loh, “Two-dimensional dichalcogenides for light-harvesting applications,” Nano Today 10, 128–137 (2015).
[Crossref]

H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

A. Chernikov, C. Ruppert, H. M. Hill, A. F. Rigosi, and T. F. Heinz, “Population inversion and giant bandgap renormalization in atomically thin WS2 layers,” Nat. Phot. 9, 466–471 (2015).
[Crossref]

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

S. Dufferwiel, S. Schwarz, F. Withers, A. A. P. Trichet, F. Li, M. Sich, O. D. Pozo-Zamudio, C. Clark, A. Nalitov, D. D. Solnyshkov, G. Malpuech, K. Novoselov, J. Smith, M. S. Skolnick, D. N. Krizhanovskii, and A. I. Tartakovskii, “Exciton-polaritons in van der Waals heterostructures embedded in tunable microcavities,” Nat. Commun. 6, 8579 (2015).
[Crossref] [PubMed]

Y. N. Gartstein, X. Li, and C. Zhang, “Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer,” Phys. Rev. B 92, 075445 (2015).
[Crossref]

M. Amani, D. H. Lien, D. Kiriya, J. Xiao, A. Azcatl, J. Noh, S. R. Madhvapathy, R. Addou, K. C. Santosh, M. Dubey, K. Cho, R. M. Wallace, S. C. Lee, J. H. He, J. W. Ager, X. Zhang, E. Yablonovitch, and A. Javey, “Near-unity photoluminescence quantum yield in MoS2,” Science 350, 1065–1068 (2015).
[Crossref] [PubMed]

N. Kinsey, M. Ferrera, V. M. Shalaev, and A. Boltasseva, “Examining nanophotonics for integrated hybrid systems: a review of plasmonic interconnects and modulators using traditional and alternative materials,” J. Opt. Soc. Am. B 32, 121–142 (2015).
[Crossref]

2014 (2)

D. Kozawa, R. Kumar, A. Carvalho, K. K. Amara, W. Zhao, S. Wang, M. Toh, R. M. Ribeiro, A. H. Castro Neto, K. Matsuda, and G. Eda, “Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides,” Nat. Commun. 5, 4543 (2014).
[Crossref] [PubMed]

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]

2013 (1)

A. Carvalho, R. M. Ribeiro, and A. H. Castro Neto, “Band nesting and the optical response of two-dimensional semiconducting transition metal dichalcogenides,” Phys. Rev. B 88, 115205 (2013).
[Crossref]

2012 (2)

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref] [PubMed]

H. M. Nguyen, O. Seitz, W. Peng, Y. N. Gartstein, Y. J. Chabal, and A. V. Malko, “Efficient radiative and nonradiative energy transfer from proximal CdSe/ZnS nanocrystals into silicon nanomembranes,” ACS Nano 6, 5574–5582 (2012).
[Crossref] [PubMed]

2010 (1)

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Acharya, K. P.

Addou, R.

Ager, J. W.

Agranovich, V. M.

V. M. Agranovich, Surface Polaritons (North Holland, Amsterdam, 1982), pp. 187–238.

V. M. Agranovich, Excitations in Organic Solids (Oxford University, 2009).

Amani, M.

Amara, K. K.

Ang, P. K.

B. Peng, P. K. Ang, and K. P. Loh, “Two-dimensional dichalcogenides for light-harvesting applications,” Nano Today 10, 128–137 (2015).
[Crossref]

Avouris, P.

Azcatl, A.

Bergauser, G.

G. Moody, C. Kavir Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Bergauser, E. Malic, A. Knorr, and X. Li, “Intrinsic Exciton Linewidth in Monolayer Transition Metal Dichalcogenides,” in Bulletin of the American Physical Society 60 (2015).

Boltasseva, A.

Caldwell, J. D.

Carvalho, A.

Castellanos-Gomez, A.

A. Castellanos-Gomez, “Why all the fuss about 2D semiconductors?” Nat. Phot. 10, 202–204 (2016).
[Crossref]

Castro Neto, A. H.

Chabal, Y. J.

Chaves, A.

Chen, C.-H.

Chernikov, A.

Cho, K.

Clark, C.

Clark, G.

Coleman, J. N.

Cui, X.

H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]

Dubey, M.

Dufferwiel, S.

Eda, G.

Fang, N. X.

Ferrera, M.

Galfsky, T.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Gartstein, Y. N.

Y. N. Gartstein, X. Li, and C. Zhang, “Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer,” Phys. Rev. B 92, 075445 (2015).
[Crossref]

Ghosh, Y.

Gies, C.

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

Gong, P.

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]

Guinea, F.

Guo, T.

Hao, K.

Haug, H.

H. Haug and S. W. Koch, Quantum theory of the optical and electronic properties of semiconductors (World Scientific, Singapore, 2004).
[Crossref]

He, J. H.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, Cambridge, 2012).
[Crossref]

Heintz, T.

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Heinz, T. F.

Hill, H. M.

Hollingsworth, J. A.

Hone, J.

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Htoon, H.

Jahnke, F.

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

Javey, A.

Kalantar-Zadeh, K.

Kavir Dass, C.

Kéna-Cohen, S.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Kinsey, N.

Kiriya, D.

Kis, A.

Knorr, A.

Koch, S. W.

H. Haug and S. W. Koch, Quantum theory of the optical and electronic properties of semiconductors (World Scientific, Singapore, 2004).
[Crossref]

Koppens, F.

Kozawa, D.

Krizhanovskii, D. N.

Kumar, A.

Kumar, R.

Lee, C.

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Lee, S. C.

Lee, Y.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Li, F.

Li, L.-J.

Li, X.

Y. N. Gartstein, X. Li, and C. Zhang, “Exciton polaritons in transition-metal dichalcogenides and their direct excitation via energy transfer,” Phys. Rev. B 92, 075445 (2015).
[Crossref]

Lien, D. H.

Lin, E.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Liu, G.

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]

Liu, X.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Loh, K. P.

B. Peng, P. K. Ang, and K. P. Loh, “Two-dimensional dichalcogenides for light-harvesting applications,” Nano Today 10, 128–137 (2015).
[Crossref]

Low, T.

Madhvapathy, S. R.

Mak, K.

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Mak, K. F.

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Phot. 10, 216–226 (2016).
[Crossref]

Malic, E.

Malko, A. V.

Malpuech, G.

Martin-Moreno, L.

Matsuda, K.

Menon, V. M.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Milonni, P. W.

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, Bristol, 2005).

Moody, G.

Nalitov, A.

Nguyen, H. M.

Noh, J.

Novoselov, K.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, Cambridge, 2012).
[Crossref]

Peng, B.

B. Peng, P. K. Ang, and K. P. Loh, “Two-dimensional dichalcogenides for light-harvesting applications,” Nano Today 10, 128–137 (2015).
[Crossref]

Peng, W.

Pozo-Zamudio, O. D.

Ribeiro, R. M.

Rigosi, A. F.

Robinson, J. A.

Rösner, M.

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

Rupich, S. M.

Ruppert, C.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, Hoboken, NJ, 2007).

Sampat, S.

Santosh, K. C.

Schwarz, S.

Seitz, O.

Shalaev, V. M.

Shan, J.

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Phot. 10, 216–226 (2016).
[Crossref]

K. Mak, C. Lee, J. Hone, J. Shan, and T. Heintz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105, 2–5 (2010).
[Crossref]

Sich, M.

Singh, A.

Skolnick, M. S.

Smith, J.

Solnyshkov, D. D.

Steinhoff, A.

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

Strano, M. S.

Sun, Z.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Tartakovskii, A. I.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, Hoboken, NJ, 2007).

Thygesen, K. S.

K. S. Thygesen, “Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures,” 2D Materials 4, 022004 (2017).
[Crossref]

Toh, M.

Tran, K.

Trichet, A. A. P.

Wallace, R. M.

Wang, Q. H.

Wang, S.

Wehling, T. O.

A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, “Influence of excited carriers on the optical and electronic properties of MoS2,” Nano Lett. 14, 3743–3748 (2015).
[Crossref]

Withers, F.

Xia, F.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E. Lin, Y. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light-matter coupling in two-dimensional atomic crystals,” Nat. Phot. 9, 30–34 (2015).
[Crossref]

Xiao, J.

Xu, X.

H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]

Yablonovitch, E.

Yao, W.

H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
[Crossref] [PubMed]

Yu, H.

H. Yu, X. Cui, X. Xu, and W. Yao, “Valley excitons in two-dimensional semiconductors,” Natl. Sci. Rev. 2, 57 (2015).
[Crossref]

H. Yu, G. Liu, P. Gong, X. Xu, and W. Yao, “Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides,” Nat. Commun. 5, 3876 (2014).
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Fig. 1 (a) and (b) Schematically, two types of structures under consideration. The bare waveguide of thickness d is a dielectric of dielectric constant ε₂ embedded in the medium with constant ε₁. The 2D semiconductor layers are described by the in-plane dielectric susceptibility χ. In structure (a), two such layers are used at the interfaces. In structure (b), the layer is positioned in the middle of the waveguide. (c) The exemplary dispersion ω(k) of the bare waveguide modes in between the two bulk-media light lines: red lines for s-polarized and green lines for p-polarized waves. Their crossing with a dispersionless resonance at frequency ω₀ is depicted.

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Fig. 2 Dispersion of the intrinsic eigen modes as a function of the dimensionless in-plane wave number ck/ω for different thicknesses of the glass (index n₂ = 1.5) waveguide in air (n₁ = 1): d = 250 nm (first column), d = 500 nm (second column), and d = 700 nm (third column). Rows (a) and (b) show the behavior for the model configuration of Fig. 1(a), rows (c) and (d) for the configuration of Fig. 1(b). Rows (a) and (c) marked with S are for the s-polarized; rows (b) and (d) marked with P are for the p-polarized modes. Solid red and blue lines display, respectively, the behavior for “+” and “−” modes, Eqs. (1) and (5), in the waveguide with 2D semiconductors, which is compared to the behavior of the modes in the bare waveguide, shown by dashed colored lines. Columns 1, 2, and 3 thereby illustrate the cases of bare wave guides sustaining correspondingly one, two or three eigen modes of each polarization in the vicinity of the resonance frequency

(ℏ ω_{0} = 2 e V)

. The black dashed lines show the position of the ideal excitonic resonance at ω = ω₀, and of the light line in glass, ck/ω = 1.5. See text for more detail.

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Fig. 3 The effect of dissipation γ on the dispersion of the s-polarized “+” mode in the waveguide of Fig. 1(a) with thickness d = 200 nm. The red lines show the dispersion in the absence of dissipation: the dashed line for the bare waveguide, the solid lines with the 2D layers. Panel (a) refers to the resulting real part k′ of the in-plane wave number k, panel (b) to its imaginary part k″. The blue lines are for ħ γ = 2 meV, green for ħγ = 4 meV. The black dashed lines show the position of the resonance and of the light line in glass.

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Fig. 4 Dispersion (panels a,c) and linear absorption coefficient (b,d) for eigen modes in the waveguide of Fig. 1(a) with thickness d = 250 nm that employs monolayer MoS₂ for the 2D semiconductor layers. Red lines are for “+” and blue for “−” modes of both s- (panels a,b) and p- (c,d) polarizations, they are compared to the dispersion of the bare waveguide modes (dashed lines). The inset: the real and imaginary parts of

\tilde{χ} (ω)

used for response of a MoS₂ monolayer.

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Equations (7)

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r_{21} \exp (i k_{2 z} d) = \pm 1,

r_{21}^{(s)} = (k_{2_{z}} - k_{1_{z}} + i k_{0} \tilde{χ}) / (k_{2_{z}} + k_{1_{z}} - i k_{0} \tilde{χ})

r_{21}^{(p)} = (\frac{ε_{1}}{k_{1_{z}}} - \frac{ε_{2}}{k_{2_{z}}} - i \frac{\tilde{χ}}{k_{0}}) {(\frac{ε_{1}}{k_{1_{z}}} + \frac{ε_{2}}{k_{2_{z}}} - i \frac{\tilde{χ}}{k_{0}})}^{- 1},

\tilde{χ} (ω, k) = k_{0} (ω) χ (ω, k) = ω χ / c .

r_{21} \exp (i k_{2_{z}} d) (r_{22} \pm t_{22}) = 1,

t_{22}^{(s)} = 2 k_{2_{z}} / (2 k_{2_{z}} - i k_{0} \tilde{χ}); t_{22}^{(p)} = 2 ε_{2} / (2 ε_{2} - i k_{2_{z}} \tilde{χ} / k_{0}) .

χ (ω) = χ_{0} + A / (ω_{0}^{2} - ω^{2} - 2 i γ ω),