Abstract

We theoretically investigate the possible increase of the second harmonic generation (SHG) efficiency in silicon compatible waveguides by considering an asymmetrical plasmonic slot waveguide geometry and a χ(2) nonlinear polymer infiltrating the slot. The needed phase matching condition is satisfied between the fundamental waveguide mode at the fundamental frequency (FF) and second-order waveguide mode at the second harmonic frequency (SHF) by an appropriate design of the waveguide opto-geometrical parameters. The SHG signal generated in our starting waveguide is three orders of magnitude higher than those previously reported for a FF corresponding to λ = 1550 nm. Then, the SHG performance was further improved by increasing the asymmetry of the structure where nonlinear coupling coefficients as large as 292 psm−1W-1/2 are predicted. The device length is shorter than 20 µm and the normalized SHG conversion efficiency comes up to more than 1 × 105 W−1cm−2.

© 2013 OSA

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2012 (6)

2011 (7)

2010 (3)

2009 (4)

Z. Ruan, G. Veronis, K. L. Vodopyanov, M. M. Fejer, and S. Fan, “Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides,” Opt. Express 17(16), 13502–13515 (2009).
[CrossRef] [PubMed]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Quadratic phase matching in nonlinear plasmonic nanoscale waveguides,” Opt. Express 17(22), 20063–20068 (2009).
[CrossRef] [PubMed]

2008 (2)

T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: a platform for practical nonlinear optics†,” J. Phys. Chem. C 112(21), 8085–8090 (2008).
[CrossRef]

M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1298–1311 (2008).
[CrossRef]

2007 (3)

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
[CrossRef]

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46(33), 8118–8133 (2007).
[CrossRef] [PubMed]

2004 (2)

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004).
[CrossRef]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

2002 (1)

1992 (1)

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Alloatti, L.

Anceau, C.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Baehr-Jones, T. W.

T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: a platform for practical nonlinear optics†,” J. Phys. Chem. C 112(21), 8085–8090 (2008).
[CrossRef]

Baets, R.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Bergman, D. J.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[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]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Bonod, N.

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]

Brasselet, S.

P. Schön, N. Bonod, E. Devaux, J. Wenger, H. Rigneault, T. W. Ebbesen, and S. Brasselet, “Enhanced second-harmonic generation from individual metallic nanoapertures,” Opt. Lett. 35(23), 4063–4065 (2010).
[CrossRef] [PubMed]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Brongersma, M. L.

W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[CrossRef] [PubMed]

Brosi, J. M.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Cai, W. S.

W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[CrossRef] [PubMed]

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]

Cheng, Q. Q.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Davoyan, A. R.

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]

Derose, C. T.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Devaux, E.

Diederich, F.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Ebbesen, T. W.

Ebrahimzadeh, M.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004).
[CrossRef]

Elezzabi, A. Y.

Enami, Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Fan, S.

Fejer, M. M.

Foster, M. A.

Frank, B.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Freude, W.

L. Alloatti, D. Korn, C. Weimann, C. Koos, W. Freude, and J. Leuthold, “Second-order nonlinear silicon-organic hybrid waveguides,” Opt. Express 20(18), 20506–20515 (2012).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Fujimura, M.

Gaeta, A. L.

Genty, G.

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]

Grange, R.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Greenlee, C.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Gunter, P.

M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1298–1311 (2008).
[CrossRef]

Han, Z.

Hasan, S. B.

Hochberg, M. J.

T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: a platform for practical nonlinear optics†,” J. Phys. Chem. C 112(21), 8085–8090 (2008).
[CrossRef]

Hu, W.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Hu, X.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Hu, X. P.

Hyvärinen, O.

Ikonic, Z.

Jazbinsek, M.

M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1298–1311 (2008).
[CrossRef]

Jen, A. K.-Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Jonasz, M.

Jundt, D. H.

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Kaplas, T.

Kauranen, M.

Kelsall, R. W.

Kim, T. D.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Kitamura, R.

Kivshar, Y. S.

Koos, C.

L. Alloatti, D. Korn, C. Weimann, C. Koos, W. Freude, and J. Leuthold, “Second-order nonlinear silicon-organic hybrid waveguides,” Opt. Express 20(18), 20506–20515 (2012).
[CrossRef] [PubMed]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Korn, D.

Kumar, R.

Kurz, J. R.

Lederer, F.

Leuthold, J.

L. Alloatti, D. Korn, C. Weimann, C. Koos, W. Freude, and J. Leuthold, “Second-order nonlinear silicon-organic hybrid waveguides,” Opt. Express 20(18), 20506–20515 (2012).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Levy, J. S.

Li, L.

Li, T.

Lipson, M.

Loychik, C.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Lu, F. F.

Lu, Y.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Luo, J.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

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]

Magel, G.

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Mathine, D.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[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]

Moutzouris, K.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004).
[CrossRef]

Mutter, L.

M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1298–1311 (2008).
[CrossRef]

Ning, T. Y.

Norwood, R. A.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[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]

Parameswaran, K. R.

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]

Pertsch, T.

S. B. Hasan, C. Rockstuhl, T. Pertsch, and F. Lederer, “Second-order nonlinear frequency conversion processes in plasmonic slot waveguides,” J. Opt. Soc. Am. B 29(7), 1606–1611 (2012).
[CrossRef]

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Peyghambarian, N.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

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]

Pietarinen, H.

Pilon, L.

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]

Rao, S. V.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004).
[CrossRef]

Richter, J.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Rigneault, H.

Rockstuhl, C.

Roussev, R. V.

Route, R. K.

Ruan, Z.

Schön, P.

Scimeca, M. L.

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Shadrivov, I. V.

Steinberg, B. Z.

Steinbrück, A.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[CrossRef] [PubMed]

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Thomas, R.

Tian, Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Tünnermann, A.

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Van, V.

Vasudev, A. P.

W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[CrossRef] [PubMed]

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]

Veronis, G.

Vodopyanov, K. L.

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

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]

Weimann, C.

Wenger, J.

Wu, Z.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xie, Z. D.

Xu, F.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xu, J.

Yu, Z.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[CrossRef]

Zhu, S. N.

Zhu, Y. Y.

Zyss, J.

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. 14(5), 1298–1311 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: a platform for practical nonlinear optics†,” J. Phys. Chem. C 112(21), 8085–8090 (2008).
[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)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K.-Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol–gel waveguide modulators with exceptionally large electro–optic coefficients,” Nat. Photonics 1(3), 180–185 (2007).
[CrossRef]

Opt. Express (8)

Opt. Lett. (5)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

M. I. Stockman, D. J. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. 92(5), 057402 (2004).
[CrossRef] [PubMed]

Plasmonics (1)

J. Richter, A. Steinbrück, T. Pertsch, A. Tünnermann, and R. Grange, “Plasmonic core–shell nanowires for enhanced second-harmonic generation,” Plasmonics 8, 115–120 (2012).

Proc. IEEE (1)

J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology—A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Science (1)

W. S. Cai, A. P. Vasudev, and M. L. Brongersma, “Electrically controlled nonlinear generation of light with plasmonics,” Science 333(6050), 1720–1723 (2011).
[CrossRef] [PubMed]

Other (7)

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).

R. E. P. de Oliveira, M. Lipson, and C. J. S. de Matos, “Electrically controlled silicon nitride ring resonator for quasi-phase matched second-harmonic generation,” in CLEO: Science and Innovations (Optical Society of America, 2012).

R. W. Boyd, Nonlinear Optics (Academic, 2008).

G. T. Reed and A. P. Knights, Silicon Photonics (Wiley Online Library, 2008).

Z. Zalevsky and I. Abdulhalim, Integrated Nanophotonic Devices (Elsevier, 2010).

H. Kogenlnik, “2. Theory of dielectric waveguides,” in Integrated Optics (Springer Berlin / Heidelberg, 1975), pp. 13–81.

G. Lifante and J. Wiley, Integrated Photonics: Fundamentals (Wiley Online Library, 2003).

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Figures (8)

Fig. 1
Fig. 1

Schematic cross-section of the proposed plasmonic slot waveguide with second-order nonlinear polymer infiltrating into the slot and substrate compatible with silicon-on-insulator platform.

Fig. 2
Fig. 2

Design of the waveguide geometry for satisfying the PMC. (a) Effective indices of the obtained guided optical modes versus the slot height h for the plasmonic waveguide geometry depicted in (b), (c), (d) in which the slot width is w = 50 nm. Notation “(0)” and “(1)” stand for the fundamental and second-order waveguide modes, respectively, and the signs “ω” and “2ω” correspond to the FF and SHF, respectively. The 1-st mode of the SHF has a crossing with the red line at h = 489 nm indicating a point of phase-matching. Ex distribution of 0-th plasmonic mode at FF (b); 0-th plasmonic mode at SHF (c); and 1-st plasmonic mode at SHF (d) when w = 50 nm, h = 489 nm.

Fig. 3
Fig. 3

Optical powers of the FF and SHF waves versus the propagation distance for a pump power of 1 W in the structure depicted in Fig. 2.

Fig. 4
Fig. 4

(a) Slot height h to satisfy the PMC needed for the SHG process and associated coupling coefficient κ between the two coupled modes, (b) peak efficiency ηp and peak position Lp of the SHF field, (c) normalized conversion efficiency of the SHG process as functions of the plasmonic slot width under a pump power of 1 W.

Fig. 5
Fig. 5

Design of the waveguide with Si3N4 sunstrate for satisfying the PMC. (a) Effective indices of the obtained guided optical modes versus the slot height h for the plasmonic waveguide geometry depicted in (b), (c), (d) in which the slot width is w = 50 nm. Ex distribution of 0-th plasmonic mode at FF (b); 0-th plasmonic mode at SHF (c); and 1-st plasmonic mode at SHF (d) at the phase-matching point (w = 50 nm, h = 490nm).

Fig. 6
Fig. 6

Optical powers of the FF and SHF waves versus the propagation distance for a pump power of 1 W in the structure depicted in Fig. 5.

Fig. 7
Fig. 7

Normalized Ex distribution at x = 0 for the case of SiO2 substrate (a); Si3N4 substrate (b).The red solid line and blue dotted line correspond to 0-th mode at the FF and 1-st mode at the SHF, respectively. The domain between the two vertical lines is the nonlinear area to integrate.

Fig. 8
Fig. 8

Peak position Lp, peak efficiency ηp, normalized conversion efficiency η and maximum output power P2(Lp) of SHF versus the input pumping power of FF.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

× E =μ H t =iωμ H × H =ε E t + P NL t =iωε E iω P NL
E = v A ˜ v (z) E v = v A ˜ v (z) E v (x,y) exp(i k v z) H = v A ˜ v (z) H v = v A ˜ v (z) H v (x,y) exp(i k v z)
1 2 e z { E i (x,y) × H j (x,y)}dxdy= δ ij
× E u =μ H u t =iωμ H u × H u =ε E u t =iωε E u
E u =[ E u,t (x,y) E u,z (x,y) ]exp(i k u z) H u =[ H u,t (x,y)+ H u,z (x,y) ]exp(i k u z)
( E × H u E u × H )=iω P NL E u
A ˜ u z = iω 4 { P NL E u }dxdy
A u z = α u 2 A u + iω 4 exp(i β u z) { P NL E u (x,y) }dxdy
A 1 z = α 1 2 A 1 +i ω 1 4 κ 1 A 1 * A 2 exp(iΔβz) A 2 z = α 2 2 A 2 +i ω 1 4 κ 2 A 1 A 1 exp(iΔβz)
κ 1 = ε 0 { χ (2) : E 2 (x,y) E 1 * (x,y) E 1 (x,y) }dxdy κ 2 = ε 0 { χ (2) : E 1 (x,y) E 1 (x,y) E 2 (x,y) }dxdy
η= P 2 ( L p ) [ P 1 (0) ] 2 [ L p (cm) ] 2

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