Abstract

This work explores the use of Ge-rich graded-index Si1-xGex rib waveguides as building blocks to develop integrated nonlinear optical devices for broadband operation in the mid-IR. The vertical Ge gradient concentration in the waveguide core renders unique properties to the guided optical mode, providing tight mode confinement over a broadband mid-IR wavelength range from λ = 3 µm to 8 µm. Additionally, the gradual vertical confinement pulls the optical mode upwards in the waveguide core, overlapping with the Ge-rich area where the nonlinear refractive index is larger. Moreover, the Ge-rich graded-index Si1-xGex waveguides allow efficient tailoring of the chromatic dispersion curves, achieving flat anomalous dispersion for the quasi-TM optical mode with D ≤ 14 ps/nm/km over a ~1.4 octave span while retaining an optimum third-order nonlinear parameter, γeff. These results confirm the potential of Ge-rich graded-index Si1-xGex waveguides as an attractive platform to develop mid-IR nonlinear approaches requiring broadband dispersion engineering.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (2)

2015 (3)

2014 (5)

2013 (4)

H. Lin, L. Li, Y. Zou, S. Danto, J. D. Musgraves, K. Richardson, S. Kozacik, M. Murakowski, D. Prather, P. T. Lin, V. Singh, A. Agarwal, L. C. Kimerling, and J. Hu, “Demonstration of high-Q mid-infrared chalcogenide glass-on-silicon resonators,” Opt. Lett. 38(9), 1470–1472 (2013).
[Crossref] [PubMed]

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

P. Barritault, M. Brun, P. Labeye, O. Lartigue, J. M. Hartmann, and S. Nicoletti, “Mlines characterization of the refractive index profile of SiGe gradient waveguides at 2.15 µm,” Opt. Express 21(9), 11506–11515 (2013).
[Crossref] [PubMed]

2012 (3)

P. Moontragoon, R. A. Soref, and Z. Ikonic, “The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications,” J. Appl. Phys. 112(7), 073106 (2012).
[Crossref]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20(2), 1685–1690 (2012).
[Crossref] [PubMed]

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

2011 (2)

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref] [PubMed]

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[Crossref]

2010 (2)

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

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

2004 (1)

1994 (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

1984 (1)

Agarwal, A.

Agarwal, A. M.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Allioux, D.

Alonso-Ramos, C.

Atanackovic, P.

Baehr-Jones, T.

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

Baets, R.

Ballabio, A.

Barritault, P.

Beausoleil, R. G.

Boodhoo, L. A.

Boulila, F.

Brasch, V.

Brun, M.

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Carletti, L.

Carras, M.

Casas-Bedoya, A.

Chaisakul, P.

Chang, Y. C.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Cheben, P.

Chiles, J.

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Danto, S.

De Leonardis, F.

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys,” Sci. Rep. 6(1), 32622 (2016).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, and V. M. Passaro, “Mid-IR optical and nonlinear properties of germanium on silicon optical waveguides,” J. Lightwave Technol. 32(22), 3747–3757 (2014).
[Crossref]

de Rooij, N. F.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Di Francesco, J.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Duvall, S. G.

Dwivedi, S.

Eggleton, B. J.

Faist, J.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Fathpour, S.

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

Foster, M.

Frigerio, J.

Gaeta, A.

Gilles, C.

Grand, G.

Green, W. M.

Grillet, C.

Guo, H.

Hartmann, J. M.

Herzig, H. P.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Hochberg, M.

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

Homsy, A.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Hon, N. K.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[Crossref]

Hu, J.

Hudson, D. D.

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Hvozdara, L.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Ikonic, Z.

P. Moontragoon, R. A. Soref, and Z. Ikonic, “The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications,” J. Appl. Phys. 112(7), 073106 (2012).
[Crossref]

Ilic, R. R.

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

Isella, G.

Jackson, S. D.

Jalali, B.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[Crossref]

Khan, S.

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

Khokhar, A. Z.

Kimerling, L. C.

Kippenberg, T. J.

Kordts, A.

Kozacik, S.

Kuyken, B.

Labeye, P.

Lartigue, O.

Lepage, G.

Li, L.

Lin, H.

Lin, P. T.

Lin, Q.

Liu, X.

Liu, Y.

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

Loo, R.

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

Luther-Davies, B.

Ma, J.

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

Ma, P.

Madden, S.

Maisons, G.

Malik, A.

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

Marris-Morini, D.

Mashanovich, G. Z.

Michel, J.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Molina-Fernández, I.

Moll, K.

Monat, C.

Moontragoon, P.

P. Moontragoon, R. A. Soref, and Z. Ikonic, “The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications,” J. Appl. Phys. 112(7), 073106 (2012).
[Crossref]

Moss, D. J.

Muneeb, M.

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

Murakowski, M.

Musgraves, J. D.

Nedeljkovic, M.

Nicoletti, S.

Orobtchouk, R.

Ortega-Moñux, A.

Ortiz, S.

Osgood, R. M.

Paeder, V.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Palomba, S.

Passaro, V. M.

Passaro, V. M. N.

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys,” Sci. Rep. 6(1), 32622 (2016).
[Crossref] [PubMed]

Pathak, S.

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

Penadés, J. S.

Pfeiffer, M. H. P.

Prather, D.

Ramirez, J. M.

Read, A.

Richardson, K.

Roelkens, G.

Roux, X. L.

Shimura, Y.

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

Singh, N.

Singh, V.

Sinobad, M.

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Soref, R.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[Crossref]

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

Soref, R. A.

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys,” Sci. Rep. 6(1), 32622 (2016).
[Crossref] [PubMed]

P. Moontragoon, R. A. Soref, and Z. Ikonic, “The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications,” J. Appl. Phys. 112(7), 073106 (2012).
[Crossref]

Spott, A.

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

Tatian, B.

Troia, B.

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys,” Sci. Rep. 6(1), 32622 (2016).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, and V. M. Passaro, “Mid-IR optical and nonlinear properties of germanium on silicon optical waveguides,” J. Lightwave Technol. 32(22), 3747–3757 (2014).
[Crossref]

Vakarin, V.

Van Campenhout, J.

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

van der Wal, P.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Van Landschoot, L.

Van Opstal, T.

Vanherle, W.

Vivien, L.

Wägli, P.

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Willner, A. E.

Yan, Y.

Yu, Y.

Yue, Y.

Zhang, L.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20(2), 1685–1690 (2012).
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Zou, Y.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Spott, Y. Liu, T. Baehr-Jones, R. R. Ilic, and M. Hochberg, “Silicon Waveguides and Ring Resonators at 5.5 µm,” Appl. Phys. Lett. 97, 213501 (2010).
[Crossref]

S. Khan, J. Chiles, J. Ma, and S. Fathpour, “Silicon-on-nitride waveguides for mid-and near-infrared integrated photonics,” Appl. Phys. Lett. 102(12), 121104 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013).
[Crossref]

J. Appl. Phys. (2)

P. Moontragoon, R. A. Soref, and Z. Ikonic, “The direct and indirect bandgaps of unstrained SixGe1-x-ySny and their photonic device applications,” J. Appl. Phys. 112(7), 073106 (2012).
[Crossref]

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[Crossref]

J. Lightwave Technol. (1)

Lab Chip (1)

Y. C. Chang, P. Wägli, V. Paeder, A. Homsy, L. Hvozdara, P. van der Wal, J. Di Francesco, N. F. de Rooij, and H. P. Herzig, “Cocaine detection by a mid-infrared waveguide integrated with a microfluidic chip,” Lab Chip 12(17), 3020–3023 (2012).
[Crossref] [PubMed]

Nanophotonics (1)

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Nat. Photonics (1)

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

Opt. Express (8)

P. Barritault, M. Brun, P. Labeye, O. Lartigue, J. M. Hartmann, and S. Nicoletti, “Mlines characterization of the refractive index profile of SiGe gradient waveguides at 2.15 µm,” Opt. Express 21(9), 11506–11515 (2013).
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M. Brun, P. Labeye, G. Grand, J. M. Hartmann, F. Boulila, M. Carras, and S. Nicoletti, “Low loss SiGe graded index waveguides for mid-IR applications,” Opt. Express 22(1), 508–518 (2014).
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M. Foster, K. Moll, and A. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004).
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B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[Crossref] [PubMed]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20(2), 1685–1690 (2012).
[Crossref] [PubMed]

A. Malik, S. Dwivedi, L. Van Landschoot, M. Muneeb, Y. Shimura, G. Lepage, J. Van Campenhout, W. Vanherle, T. Van Opstal, R. Loo, and G. Roelkens, “Ge-on-Si and Ge-on-SOI thermo-optic phase shifters for the mid-infrared,” Opt. Express 22(23), 28479–28488 (2014).
[Crossref] [PubMed]

N. Singh, D. D. Hudson, and B. J. Eggleton, “Silicon-on-sapphire pillar waveguides for Mid-IR supercontinuum generation,” Opt. Express 23(13), 17345–17354 (2015).
[Crossref] [PubMed]

L. Carletti, M. Sinobad, P. Ma, Y. Yu, D. Allioux, R. Orobtchouk, M. Brun, S. Ortiz, P. Labeye, J. M. Hartmann, S. Nicoletti, S. Madden, B. Luther-Davies, D. J. Moss, C. Monat, and C. Grillet, “Mid-Infrared nonlinear optical response of Si-Ge waveguides with ultra-short optical pulses,” Opt. Express 23(25), 32202–32214 (2015).
[Crossref] [PubMed]

Opt. Lett. (4)

Optica (1)

Sci. Rep. (1)

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys,” Sci. Rep. 6(1), 32622 (2016).
[Crossref] [PubMed]

Science (1)

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Other (1)

Editorial “Extending opportunities,” Nat. Photonics6(7), 407 (2012).

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Figures (3)

Fig. 1
Fig. 1 a) Representative scheme of the graded-index Si1-xGex waveguide cross-section. b) Calculated vertical refractive index profile of a graded-index Si1- x Ge x waveguide (hcore = 6 µm and λ = 3 µm). y (µm) corresponds to the vertical position in the waveguide, being its origin located at the interface between the Si substrate and the graded-index Si1-xGex waveguide, as marked with a horizontal dashed line in figure (a)).

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Fig. 2
Fig. 2 Top panels in (a), (b) and (c) show the dispersion parameter (D) of the quasi-TE polarization mode (in multicolor scale) of a waveguide with hcore = 6 µm as a function of the etching depth and the waveguide width for λ = 3 µm / 5.5 µm / 8 µm. Multicolored areas correspond to positive (anomalous) dispersion. The grey dot indicates the selected waveguide parameters, with width = 4 µm and etching depth = 4 µm. Bottom panels in (a), (b) and (c) display the simulated optical propagation mode (quasi-TE) of the selected waveguide geometry for increasing λ, according to top panels. (d) Spectral evolution of the dispersion parameter of the quasi-TE (black squares) and quasi-TM (red dots) polarizations for the optimized waveguide design (hcore = 6 µm, width = 4 µm, etch depth = 4 µm).

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Fig. 3
Fig. 3 (a) Color map of the calculated Kerr coefficient, n2, extracted from [21], as a function of the Ge concentration and wavelength, λ. A constant value of n2 ≈ 1 × 10−17 m2/W was obtained for the Ge concentrations not displayed (i. e. for Ge conc. < 65%). (b) Spatial distribution of n2 in the waveguide, with the simulated modal intensity superimposed for λ = 3 µm (inner lines denote higher intensity). (c) Calculated quasi-TE mode profile (|E|||, black curves, left y-axis) and n2 (red curves, right y-axis) along the waveguide vertical direction for λ = 3 µm (solid lines) and λ = 8 µm (dashed dotted lines). (d) Calculated nonlinear parameter (γeff, filled data, left y-axis) and nonlinear modal effective area (Aeff NL, empty data, right y-axis) of the quasi-TE (squares) and quasi-TM (circles) optical modes as a function of λ.

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Equations (1)

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γ e f f ( λ ) = 2 π ∬ W g n 2 ( x , y ) ⋅ S z 2 d x d y / λ ( ∫ ∫ − ∞ ∞ S z d x d y ) 2

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