Abstract

In this paper we present a detailed theoretical investigation of second harmonic generation in strained germanium waveguides operating at the mid infrared pump wavelength of 4 μm. The effective second order susceptibility has been estimated through a multiphysics approach considering the residual stress of the SiNx cladding film. Furthermore, general physical features have been investigated by means of a comparative analysis of SHG performance as a function of input pump power, linear and nonlinear phase mismatching, effective recombination carrier lifetime, and temperature, taking into account both continuous and pulsed regimes. Finally, periodically poled germanium devices have been explored with the aim to improve the SHG efficiency. In the same operative conditions, efficiencies of 0.6% and 0.0018% have been obtained in poled and not-poled waveguides, respectively.

© 2016 Optical Society of America

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2016 (1)

2015 (11)

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

R. A. Soref, “Enabling 2 µm communications,” Nat. Photonics 9(6), 1–2 June (2015).

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

M. Nedeljkovic, R. A. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” IEEE Photonics J. 7(3), 2600214 (2015).
[Crossref]

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Investigation of germanium Raman lasers for the mid-infrared,” Opt. Express 23(13), 17237–17254 (2015).
[Crossref] [PubMed]

C. L. Manganelli, P. Pintus, and C. Bonati, “Modeling of strain-induced Pockels effect in Silicon,” Opt. Express 23(22), 28649–28666 (2015).
[Crossref] [PubMed]

J. B. Khurgin, T. H. Stievater, M. W. Pruessner, and W. S. Rabinovich, “On the origin of the second-order nonlinearity in strained Si–SiN structures,” J. Opt. Soc. Am. B 32(12), 2494–2499 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Germanium-on-Silicon Waveguide Engineering for Third Harmonic Generation in the Mid-Infrared,” J. Lightwave Technol. 33(24), 5103–5113 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Modelling of Supercontinuum Generation in the Germanium-on-Silicon Waveguided Platform,” J. Lightwave Technol. 33(21), 4437–4444 (2015).
[Crossref]

2014 (6)

M. W. Puckett, J. S. T. Smalley, M. Abashin, A. Grieco, and Y. Fainman, “Tensor of the second-order nonlinear susceptibility in asymmetrically strained silicon waveguides: analysis and experimental validation,” Opt. Lett. 39(6), 1693–1696 (2014).
[Crossref] [PubMed]

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

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22(22), 26517–26525 (2014).
[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]

C. Wolff, R. Soref, C. G. Poulton, and B. J. Eggleton, “Germanium as a material for stimulated Brillouin scattering in the mid-infrared,” Opt. Express 22(25), 30735–30747 (2014).
[Crossref] [PubMed]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

2013 (3)

F. De Leonardis, B. Troia, and V. M. N. Passaro, “Design rules for Raman lasers based on SOI racetrack resonators,” IEEE Photonics J. 6(5), 6648677 (2013).

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

B. Chmielak, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Waldow, and H. Kurz, “Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides,” Opt. Express 21(21), 25324–25332 (2013).
[Crossref] [PubMed]

2011 (4)

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

N. K. Hon, R. A. 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. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[Crossref] [PubMed]

I. Avrutsky and R. Soref, “Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility,” Opt. Express 19(22), 21707–21716 (2011).
[Crossref] [PubMed]

2010 (4)

J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, “Ge-on-Si laser operating at room temperature,” Opt. Lett. 35(5), 679–681 (2010).
[Crossref] [PubMed]

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

E. Luppi, H. Hübener, and V. Véniard, “Communications: ab initio second-order nonlinear optics in solids,” J. Chem. Phys. 132(24), 241104 (2010).
[Crossref] [PubMed]

E. Luppi, H. Hübener, and V. Véniard, “Ab-initio second-order nonlinear optics in solids: second-harmonic generation spectroscopy from time-dependent density-functional theory,” Phys. Rev. B 82(23), 235201 (2010).
[Crossref]

2009 (2)

2008 (1)

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

2007 (1)

2006 (2)

R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (1)

1998 (1)

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

1989 (1)

Abashin, M.

Ackert, J. J.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

Agrawal, G. P.

Aktsipetrov, O. A.

Alonso-Ramos, C.

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Avrutsky, I.

Baets, R.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Bolten, J.

Bonati, C.

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Camacho-Aguilera, R.

Cao, K.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Capellini, G.

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

Cardenas, J.

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Cerutti, L.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Chaben, P.

Chen, Q.-D.

Chen, X.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Chen, Z.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Chen, Z.-G.

Chmielak, B.

Dave, U.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

De Leonardis, F.

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Dolgova, T. V.

Dominguez Bucio, T.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Dwivedi, S.

Eggleton, B. J.

Emel’yanov, V. I.

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Fainman, Y.

Foster, M. A.

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Gaeta, A. L.

Gardes, F. Y.

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Gassenq, A.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Gencarelli, F.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Govorkov, S. V.

Green, W. M. J.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Grieco, A.

Grosso, G.

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Hattasan, N.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Healy, N.

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Hens, Z.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Hon, N. K.

N. K. Hon, R. A. 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]

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

Hu, C.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Hu, Y.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Hübener, H.

E. Luppi, H. Hübener, and V. Véniard, “Communications: ab initio second-order nonlinear optics in solids,” J. Chem. Phys. 132(24), 241104 (2010).
[Crossref] [PubMed]

E. Luppi, H. Hübener, and V. Véniard, “Ab-initio second-order nonlinear optics in solids: second-harmonic generation spectroscopy from time-dependent density-functional theory,” Phys. Rev. B 82(23), 235201 (2010).
[Crossref]

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Jalali, B.

N. K. Hon, R. A. 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]

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

Janz, S.

Jessop, P. E.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

Jia, G.

J.-H. Zhao, Q.-D. Chen, Z.-G. Chen, G. Jia, W. Su, Y. Jiang, Z.-X. Yan, T. V. Dolgova, O. A. Aktsipetrov, and H.-B. Sun, “Enhancement of second-harmonic generation from silicon stripes under external cylindrical stain,” Opt. Lett. 34(21), 3340–3342 (2009).
[Crossref]

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Jiang, Y.

Khokhar, A. Z.

B. Troia, J. S. Penades, A. Z. Khokhar, M. Nedeljkovic, C. Alonso-Ramos, V. M. N. Passaro, and G. Z. Mashanovich, “Germanium-on-silicon Vernier-effect photonic microcavities for the mid-infrared,” Opt. Lett. 41(3), 610–613 (2016).
[Crossref] [PubMed]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Khokhlov, R. V.

Khurgin, J. B.

J. B. Khurgin, T. H. Stievater, M. W. Pruessner, and W. S. Rabinovich, “On the origin of the second-order nonlinearity in strained Si–SiN structures,” J. Opt. Soc. Am. B 32(12), 2494–2499 (2015).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

Kimerling, L. C.

Knights, A. P.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

Koroteev, N. I.

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Kurz, H.

Kuyken, B.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Lamontagne, B.

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Leo, F.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Lepage, G.

Levy, J. S.

Li, G. L.

Li, K.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Lin, Q.

Lipson, M.

Littlejohns, C. G.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Liu, J.

Liu, X.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Loo, R.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Luke, K.

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

E. Luppi, H. Hübener, and V. Véniard, “Communications: ab initio second-order nonlinear optics in solids,” J. Chem. Phys. 132(24), 241104 (2010).
[Crossref] [PubMed]

E. Luppi, H. Hübener, and V. Véniard, “Ab-initio second-order nonlinear optics in solids: second-harmonic generation spectroscopy from time-dependent density-functional theory,” Phys. Rev. B 82(23), 235201 (2010).
[Crossref]

Malik, A.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Manganelli, C. L.

C. L. Manganelli, P. Pintus, and C. Bonati, “Modeling of strain-induced Pockels effect in Silicon,” Opt. Express 23(22), 28649–28666 (2015).
[Crossref] [PubMed]

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

Mashanovich, G.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Mashanovich, G. Z.

B. Troia, J. S. Penades, A. Z. Khokhar, M. Nedeljkovic, C. Alonso-Ramos, V. M. N. Passaro, and G. Z. Mashanovich, “Germanium-on-silicon Vernier-effect photonic microcavities for the mid-infrared,” Opt. Lett. 41(3), 610–613 (2016).
[Crossref] [PubMed]

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

M. Nedeljkovic, R. A. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” IEEE Photonics J. 7(3), 2600214 (2015).
[Crossref]

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Matheisen, C.

Michel, J.

Miller, S.

Mitchell, C. J.

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Muneeb, M.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Nedeljkovic, M.

B. Troia, J. S. Penades, A. Z. Khokhar, M. Nedeljkovic, C. Alonso-Ramos, V. M. N. Passaro, and G. Z. Mashanovich, “Germanium-on-silicon Vernier-effect photonic microcavities for the mid-infrared,” Opt. Lett. 41(3), 610–613 (2016).
[Crossref] [PubMed]

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

M. Nedeljkovic, R. A. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” IEEE Photonics J. 7(3), 2600214 (2015).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Okawachi, Y.

Osgood, R.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Painter, O. J.

Passaro, V. M. N.

B. Troia, J. S. Penades, A. Z. Khokhar, M. Nedeljkovic, C. Alonso-Ramos, V. M. N. Passaro, and G. Z. Mashanovich, “Germanium-on-silicon Vernier-effect photonic microcavities for the mid-infrared,” Opt. Lett. 41(3), 610–613 (2016).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Modelling of Supercontinuum Generation in the Germanium-on-Silicon Waveguided Platform,” J. Lightwave Technol. 33(21), 4437–4444 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Germanium-on-Silicon Waveguide Engineering for Third Harmonic Generation in the Mid-Infrared,” J. Lightwave Technol. 33(24), 5103–5113 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Investigation of germanium Raman lasers for the mid-infrared,” Opt. Express 23(13), 17237–17254 (2015).
[Crossref] [PubMed]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

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

F. De Leonardis, B. Troia, and V. M. N. Passaro, “Design rules for Raman lasers based on SOI racetrack resonators,” IEEE Photonics J. 6(5), 6648677 (2013).

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Peacock, A. C.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Penades, J. S.

Petrov, G. I.

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Picard, M.-J.

Pierobon, R.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Pintus, P.

Pizzi, G.

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

Poulton, C. G.

Pruessner, M. W.

Pucker, G.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Puckett, M. W.

Rabinovich, W. S.

Reed, G. T.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

Ren, C.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Reynolds, S. A.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Ripperda, C.

Rodriguez, J.-B.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Roelkens, G.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Rossi, C.

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

Ryckeboer, E.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Saint-Etienne, E.

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

Sanchez, D.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Scheid, E.

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

Shen, L.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

L. Shen, N. Healy, C. J. Mitchell, J. S. Penades, M. Nedeljkovic, G. Z. Mashanovich, and A. C. Peacock, “Mid-infrared all-optical modulation in low-loss germanium-on-silicon waveguides,” Opt. Lett. 40(2), 268–271 (2015).
[Crossref] [PubMed]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Shi, B.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Shimura, Y.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Shumay, I. L.

Smalley, J. S. T.

Soler Penades, J.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Soler Penadés, J.

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Solli, D. R.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

Soref, R.

Soref, R. A.

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Investigation of germanium Raman lasers for the mid-infrared,” Opt. Express 23(13), 17237–17254 (2015).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Germanium-on-Silicon Waveguide Engineering for Third Harmonic Generation in the Mid-Infrared,” J. Lightwave Technol. 33(24), 5103–5113 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Modelling of Supercontinuum Generation in the Germanium-on-Silicon Waveguided Platform,” J. Lightwave Technol. 33(21), 4437–4444 (2015).
[Crossref]

M. Nedeljkovic, R. A. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” IEEE Photonics J. 7(3), 2600214 (2015).
[Crossref]

R. A. Soref, “Enabling 2 µm communications,” Nat. Photonics 9(6), 1–2 June (2015).

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

R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Stankovic, S.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

Stievater, T. H.

Su, W.

Sun, H.-B.

Sun, J.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Sun, X.

Tarr, N. G.

Temple-Boyer, P.

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

Thomson, D. J.

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Topley, R.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Tournie, E.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Troia, B.

B. Troia, J. S. Penades, A. Z. Khokhar, M. Nedeljkovic, C. Alonso-Ramos, V. M. N. Passaro, and G. Z. Mashanovich, “Germanium-on-silicon Vernier-effect photonic microcavities for the mid-infrared,” Opt. Lett. 41(3), 610–613 (2016).
[Crossref] [PubMed]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Modelling of Supercontinuum Generation in the Germanium-on-Silicon Waveguided Platform,” J. Lightwave Technol. 33(21), 4437–4444 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Germanium-on-Silicon Waveguide Engineering for Third Harmonic Generation in the Mid-Infrared,” J. Lightwave Technol. 33(24), 5103–5113 (2015).
[Crossref]

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Investigation of germanium Raman lasers for the mid-infrared,” Opt. Express 23(13), 17237–17254 (2015).
[Crossref] [PubMed]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

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

F. De Leonardis, B. Troia, and V. M. N. Passaro, “Design rules for Raman lasers based on SOI racetrack resonators,” IEEE Photonics J. 6(5), 6648677 (2013).

Tsia, K. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

Uvin, S.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Van Campenhout, J.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

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]

Van Landschoot, L.

Van Opstal, T.

Vanherle, W.

Véniard, V.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

E. Luppi, H. Hübener, and V. Véniard, “Ab-initio second-order nonlinear optics in solids: second-harmonic generation spectroscopy from time-dependent density-functional theory,” Phys. Rev. B 82(23), 235201 (2010).
[Crossref]

E. Luppi, H. Hübener, and V. Véniard, “Communications: ab initio second-order nonlinear optics in solids,” J. Chem. Phys. 132(24), 241104 (2010).
[Crossref] [PubMed]

Vincent, B.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
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Virgilio, M.

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
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Wabnitz, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Wahlbrink, T.

Waldow, M.

Wang, R.

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

Wang, S.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Wang, Y.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Wilson, P. R.

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

Wolff, C.

Wu, W.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Xu, D.-X.

Yakovlev, V. V.

Yan, Z.-X.

Ye, W. N.

Yu, P. K. L.

Zhang, Y.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Zhao, J.

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

Zhao, J.-H.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

Z. Chen, J. Zhao, Y. Zhang, G. Jia, X. Liu, C. Ren, W. Wu, J. Sun, K. Cao, S. Wang, and B. Shi, “Pockel’s effect and optical rectification in (111)-cut near-intrinsic silicon crystals,” Appl. Phys. Lett. 92(25), 251111 (2008).
[Crossref]

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

R. A. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

G. Roelkens, U. Dave, A. Gassenq, N. Hattasan, C. Hu, B. Kuyken, F. Leo, A. Malik, M. Muneeb, E. Ryckeboer, D. Sanchez, S. Uvin, R. Wang, Z. Hens, R. Baets, Y. Shimura, F. Gencarelli, B. Vincent, R. Loo, J. Van Campenhout, L. Cerutti, J.-B. Rodriguez, E. Tournie, X. Chen, M. Nedeljkovic, G. Mashanovich, L. Shen, N. Healy, A. C. Peacock, X. Liu, R. Osgood, and W. M. J. Green, “Silicon-based photonic integration beyond the telecommunication wavelength range,” IEEE J. Sel. Top. Quantum Electron. 20(4), 394–404 (2014).
[Crossref]

G. Z. Mashanovich, F. Y. Gardes, D. J. Thomson, Y. Hu, K. Li, M. Nedeljkovic, J. Soler Penades, A. Z. Khokhar, C. J. Mitchell, S. Stankovic, R. Topley, S. A. Reynolds, Y. Wang, B. Troia, V. M. N. Passaro, C. G. Littlejohns, T. Dominguez Bucio, P. R. Wilson, and G. T. Reed, “Silicon photonic waveguides and devices for near- and mid-IR applications,” IEEE J. Sel. Top. Quantum Electron. 21(4), 8200112 (2015).
[Crossref]

IEEE Photonics J. (2)

F. De Leonardis, B. Troia, and V. M. N. Passaro, “Design rules for Raman lasers based on SOI racetrack resonators,” IEEE Photonics J. 6(5), 6648677 (2013).

M. Nedeljkovic, R. A. Soref, and G. Z. Mashanovich, “Predictions of free-carrier electroabsorption and electrorefraction in Germanium,” IEEE Photonics J. 7(3), 2600214 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

M. Nedeljkovic, J. Soler Penadés, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. Dominguez 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 Photonics Technol. Lett. 27(10), 1040–1043 (2015).
[Crossref]

J. Appl. Phys. (1)

N. K. Hon, R. A. 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. Chem. Phys. (1)

E. Luppi, H. Hübener, and V. Véniard, “Communications: ab initio second-order nonlinear optics in solids,” J. Chem. Phys. 132(24), 241104 (2010).
[Crossref] [PubMed]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. B (2)

J. Vac. Sci. Technol. A (1)

P. Temple-Boyer, C. Rossi, E. Saint-Etienne, and E. Scheid, “Residual stress in low pressure chemical vapor deposition SiNx films deposited from silane and ammonia,” J. Vac. Sci. Technol. A 16(4), 2003–2007 (1998).
[Crossref]

Nat. Mater. (1)

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[Crossref] [PubMed]

Nat. Photonics (3)

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

R. A. Soref, “Enabling 2 µm communications,” Nat. Photonics 9(6), 1–2 June (2015).

J. J. Ackert, D. J. Thomson, L. Shen, A. C. Peacock, P. E. Jessop, G. T. Reed, G. Z. Mashanovich, and A. P. Knights, “High speed detection at two micrometers with monolithic silicon photodiodes,” Nat. Photonics 9(6), 393–396 (2015).
[Crossref]

Nature (1)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Opt. Express (9)

F. De Leonardis, B. Troia, R. A. Soref, and V. M. N. Passaro, “Investigation of germanium Raman lasers for the mid-infrared,” Opt. Express 23(13), 17237–17254 (2015).
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C. L. Manganelli, P. Pintus, and C. Bonati, “Modeling of strain-induced Pockels effect in Silicon,” Opt. Express 23(22), 28649–28666 (2015).
[Crossref] [PubMed]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22(22), 26517–26525 (2014).
[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]

C. Wolff, R. Soref, C. G. Poulton, and B. J. Eggleton, “Germanium as a material for stimulated Brillouin scattering in the mid-infrared,” Opt. Express 22(25), 30735–30747 (2014).
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Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
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J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[Crossref] [PubMed]

I. Avrutsky and R. Soref, “Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility,” Opt. Express 19(22), 21707–21716 (2011).
[Crossref] [PubMed]

B. Chmielak, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Waldow, and H. Kurz, “Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides,” Opt. Express 21(21), 25324–25332 (2013).
[Crossref] [PubMed]

Opt. Lett. (5)

Phys. Rev. B (2)

M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini, “Radiative recombination and optical gain spectra in biaxially strained n-type germanium,” Phys. Rev. B 87(23), 235313 (2013).
[Crossref]

E. Luppi, H. Hübener, and V. Véniard, “Ab-initio second-order nonlinear optics in solids: second-harmonic generation spectroscopy from time-dependent density-functional theory,” Phys. Rev. B 82(23), 235201 (2010).
[Crossref]

Other (3)

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, “Stress induced χ(2) in silicon - comparison between theoretical and experimental values,” in Proceedings of the IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, USA9–11 September (2009).

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Figures (9)

Fig. 1
Fig. 1 Waveguide cross-section based on GOS technology platform with SiNx deposited film.
Fig. 2
Fig. 2 In plane strain distribution: (a) ε xx ; (b) ε yy ; (c) ε xy .
Fig. 3
Fig. 3 ε xx strain component: (a) ε xx versus y-direction (at x=0 μm, according to the plot of Fig. 2(a)); ε xx versus x-direction (at y=43 μm, according to the plot of Fig. 2(a)).
Fig. 4
Fig. 4 Effective second-order susceptibility as a function of the deposited film thickness for different values of σ film .
Fig. 5
Fig. 5 Output SH power as a function of the propagation length and phase mismatching parameter Δk ; (a) without third-order nonlinearity, P in =500 mW; (b) with third-order nonlinearity, P in =100 mW; (c) with third-order nonlinearity, P in =500 mW; (d) with third-order nonlinearity, P in =1 W.
Fig. 6
Fig. 6 (a) Efficiency conversion as a function of effective recombination lifetime for several value of input pump power; (b) Total phase mismatching parameter as a function of effective recombination lifetime for various values of input pump power.
Fig. 7
Fig. 7 (a) Efficiency conversion as a function of temperature; (b) Effective strain-induced second-order susceptibility as a function of temperature; (c) ε xx in-plane distribution for T=313 K, σ film =0 GPa; (d) ε xx in- plane distribution for T=383 K, σ film =0 GPa.
Fig. 8
Fig. 8 (a) Efficiency conversion as a function of pulse FWHM. (b) Space-time pulse evolution, t FWHM =5 ps.
Fig. 9
Fig. 9 Efficiency conversion versus the propagation length for both p TM S H TM , and p TE S H TM .

Tables (2)

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Table 1 Physical Parameters used in the Simulations.

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Table 2 Residual stress in SiNx film deposited by LPCVD (40.5 Pa typically) [34].

Equations (13)

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a p z = m=1 j ( m+1 ) m! β m,p m a p t m 1 2 ( α p + α p FCA ) a p 1 2 β p,p TPA A p,p TPA | a p | 2 a p β p,SH TPA A p,SH TPA | a SH | 2 a p +j 2π λ p Δ n p a p +j( γ p A p,p Kerr | a p | 2 +2 γ p A p,SH Kerr | a SH | 2 ) a p +j f p,p,SH ω p ε 0 c 0 3/2 μ 0 3/2 2 n SH n p 2 χ eff (2) a SH a p * e +jΔkz
a SH z = m=1 j ( m+1 ) m! β m,SH m a SH t m 1 2 ( α SH + α SH FCA ) a SH 1 2 β SH,SH TPA A SH,SH TPA | a SH | 2 a SH β SH,p TPA A SH,p TPA | a p | 2 a SH +j 2π λ SH Δ n SH a SH +j( γ SH A SH,SH Kerr | a SH | 2 +2 γ SH A SH,p Kerr | a p | 2 ) a SH +j f p,p,SH ω SH ε 0 c 0 3/2 μ 0 3/2 2 2 n SH n p 2 χ eff (2) a p a p e jΔkz
d N c dt = N c τ eff + 1 2 [ β p,p TPA | a p | 4 ( A p,p TPA ) 2 ω p + β SH,SH TPA | a SH | 4 ( A SH,SH TPA ) 2 ω SH + 2 β p,SH TPA | a SH | 2 | a p | 2 ( A p,SH TPA A p,p TPA ) ω p + 2 β SH,p TPA | a SH | 2 | a p | 2 ( A SH,p TPA A SH,SH TPA ) ω SH ]
σ=S( ε α thermal ( T T ref ) )+ σ 0
{ n x,i n 0,i = n 0,i 3 2 E Y,i ( p 11,i 2 ν i p 12,i ) σ xx n 0,i 3 2 E Y,i ( ν i p 11,i +( 1 ν i ) p 12,i )( σ yy + σ zz ) n y,i n 0,i = n 0,i 3 2 E Y,i ( p 11,i 2 ν i p 12,i ) σ yy n 0,i 3 2 E Y,i ( ν i p 11,i +( 1 ν i ) p 12,i )( σ xx + σ zz )
σ film = 1 6R E Y,sub D 2 ( 1 ν sub )t
χ eff (2) = 4 q 3 m 0 ε 0 ω p 4 a 4 S
S= ε ^ ( x,y ) | E( x,y ) | 2 dxdy | E( x,y ) | 2 dxdy
α p FCA =1.66x 10 21 N c 1.012 +1.25x 10 20 N c 0.989
α SH FCA =6.3x 10 22 N c 1.007 +1.03x 10 19 N c 0.935
Δ n p =3.43x 10 27 N c 1.024 4.64x 10 27 N c 1.007
Δ n SH =8.91x 10 28 N c 1.023 2.04x 10 21 N c 0.948
κ=Δk+Δ k NL =Δk+[ 2 P in ( γ SH A SH,SH Kerr γ p A p,p Kerr )+( 2π λ SH Δ n SH 4π λ p Δ n p ) ]

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