Abstract

A micrometer-scaled optical wavelength converter based on a multilayer structure is presented. The proposed structure is comprised of a grating of GaP nano-ribs heterogeneously integrated on the upper layer of a silicon-on-insulator waveguide. The GaP grating is used to couple the incident wave into the propagating modes of the waveguide and also to double the frequency of the incident light due to the second-harmonic generation process in GaP. The performance of this structure is numerically investigated using the generalized multipole technique for the linear analysis and the finite-difference time-domain method for the nonlinear analysis.

© 2010 Optical Society of America

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2010 (1)

2009 (3)

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
[CrossRef]

2008 (4)

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

N. Talebi and M. Shahabadi, “Plasmonic ring resonator,” J. Opt. Soc. Am. B 25, 2116–2122 (2008).
[CrossRef]

N. Talebi and M. Shahabadi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole technique,” J. Comput. Theor. Nanosci. 5, 711–716 (2008).
[CrossRef]

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

2007 (3)

2006 (5)

2005 (3)

2003 (1)

Y. Dumeige, F. Raineri, A. Levenson, and X. Letarte, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E 68, 066617 (2003).
[CrossRef]

1998 (2)

1997 (1)

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997).
[CrossRef]

1994 (1)

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47(5), 25–32 (1994).
[CrossRef]

1965 (1)

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Adibi, A.

Almeida, V. R.

Arbore, M. A.

Assanto, G.

Baets, R.

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
[CrossRef] [PubMed]

Benson, T.

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Bienstman, P.

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

Bloembergen, N.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Boyd, R. W.

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

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Brenner, M. R.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Broderick, N. G. R.

Busacca, A. C.

Campenhout, J. V.

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
[CrossRef] [PubMed]

Chang, R. K.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Chen, K.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef] [PubMed]

Chou, M. H.

Codemard, C.

Cohen, O.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14, 1182–1188 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Dehoff, R.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Di Cioccio, L.

Ducuing, J.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Dispersion of the optical nonlinearity in semiconductors,” Phys. Rev. Lett. 15, 415–418 (1965).
[CrossRef]

Dumeige, Y.

Y. Dumeige, F. Raineri, A. Levenson, and X. Letarte, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E 68, 066617 (2003).
[CrossRef]

Durak, C.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef] [PubMed]

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Fedeli, J. M.

Fédéli, J.

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

Fejer, M. M.

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Fraser, H.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Gallo, K.

Gawith, C. B.

Grassman, T. J.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Halioua, Y.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Hatami, F.

Hauden, J.

Heflin, J. R.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef] [PubMed]

Hu, B.

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

Jafarpour, A.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Joseph, R. M.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations models for nonlinear electrodynamics and optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997).
[CrossRef]

Kaller, R. S.

S. Singh and R. S. Kaller, “Wide-band optical wavelength converter based on four-wave mixing using optimized semiconductor optical amplifier,” Fiber Integr. Opt. 25, 213–230 (2006).
[CrossRef]

Karle, T. J.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Khorasani, S.

Kuo, Y.

Lagahe, C.

Lee, R. K.

Letarte, X.

Y. Dumeige, F. Raineri, A. Levenson, and X. Letarte, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E 68, 066617 (2003).
[CrossRef]

Levenson, A.

Y. Dumeige, F. Raineri, A. Levenson, and X. Letarte, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E 68, 066617 (2003).
[CrossRef]

Lin, Z.

Lipson, M.

Liu, A.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14, 1182–1188 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Liu, L.

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

Luo, C.

Maes, B.

B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
[CrossRef]

Martienssen, M.

M. Martienssen and H. Warlimont, Springer Handbook of Condensed Matter and Materials Data (Springer, 2005).
[CrossRef]

Masselink, W. T.

Mills, M.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Momeni, B.

Monnier, P.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Morandotti, R.

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Nilsson, J.

Oliveri, R. L.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Paniccia, M.

Pannicia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Pannicia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Pasquazi, A.

Qiang, Z.

Raineri, F.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Y. Dumeige, F. Raineri, A. Levenson, and X. Letarte, “Second-harmonic generation in one-dimensional photonic edge waveguides,” Phys. Rev. E 68, 066617 (2003).
[CrossRef]

Raj, R.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

Rajagopalan, S.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Regreny, P.

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
[CrossRef] [PubMed]

Reinke, C. M.

Richardson, D. J.

Ringel, S. A.

T. J. Grassman, M. R. Brenner, S. Rajagopalan, R. Unocic, R. Dehoff, M. Mills, H. Fraser, and S. A. Ringel, “Control and elimination of nucleation-related defects in GaP/Si (001) heteroepitaxy,” Appl. Phys. Lett. 94, 232106 (2009).
[CrossRef]

Rivoire, K.

Robinson, H. D.

K. Chen, C. Durak, J. R. Heflin, and H. D. Robinson, “Plasmon-enhanced second-harmonic generation from ionic self-assembled multilayer films,” Nano Lett. 7, 254–258 (2007).
[CrossRef] [PubMed]

Roelkens, G.

Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

Rojo-Romeo, P.

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
[CrossRef] [PubMed]

Rong, H.

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Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
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L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
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B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
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[CrossRef]

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N. Talebi and M. Shahabadi, “Analysis of the propagation of light along an array of nanorods using the generalized multipole technique,” J. Comput. Theor. Nanosci. 5, 711–716 (2008).
[CrossRef]

N. Talebi and M. Shahabadi, “Plasmonic ring resonator,” J. Opt. Soc. Am. B 25, 2116–2122 (2008).
[CrossRef]

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Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
[CrossRef]

L. Liu, J. V. Campenhout, G. Roelkens, D. V. Thourhout, P. Rojo-Romeo, P. Regreny, C. Seassal, J. Fédéli, and R. Baets, “Ultralow-power all-optical wavelength conversion in a silicon-on-insulator waveguide based on a heterogeneously integrated III-V microdisk laser,” Appl. Phys. Lett. 93, 061107 (2008).
[CrossRef]

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007).
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Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, G. Roelkens, D. V. Thourhout, and R. Raj, “Hybrid InP-based photonic crystal lasers on silicon on insulator wires,” Appl. Phys. Lett. 95, 201119 (2009).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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B. Maes, P. Bienstman, R. Baets, B. Hu, P. Sewell, and T. Benson, “Modeling comparison of second-harmonic generation in high-index-contrast devices,” Opt. Quantum Electron. 40, 13–22 (2008).
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Figures (9)

Fig. 1
Fig. 1

Schematic of the proposed multilayer optical wavelength converter. The structure is comprised of a grating of GaP nano-ribs on a SOI waveguide.

Fig. 2
Fig. 2

Band diagram of the multilayer structure computed using GMT for the (a) TM z modes. The insets visualize the computed E z field component at the normalized frequencies of ω L / 2 π c = 0.1 and 0.348. (b) TE z modes. The insets show the computed H z field component at the normalized frequencies of ω L / 2 π c = 0.167 and 0.252.

Fig. 3
Fig. 3

Zero-order reflection r 0 and transmission t 0 at λ = 900   nm . The inset shows the z-component of the electric field at θ = 58 ° .

Fig. 4
Fig. 4

Incident power ( P i ) and guided power ( P g ) in the proposed structure with perpendicular excitation. The left inset shows the z-component of the magnetic field at t = 1.6   fs . The right inset shows the z-component of the electric field at the same time.

Fig. 5
Fig. 5

Conversion efficiency versus the incident angle. The inset shows the spatial distribution of H z at t = 3.5   fs . The unit of the color bar is ampere per meter.

Fig. 6
Fig. 6

Average guided power for the incident angles of θ = 30 ° and θ = 80 ° . The incident beam is similar to the one depicted in the inset of Fig. 4. The right inset shows the field pattern at θ = 30 ° and t = 0.35   ps . The left inset shows the field pattern at θ = 80 ° and t = 0.35   ps .

Fig. 7
Fig. 7

Conversion efficiency versus the total number of GaP nano-ribs.

Fig. 8
Fig. 8

Conversion efficiency versus the incident power at the fundamental frequency for the incident angle of θ = 30 ° and N = 25 . The inset shows the guided power at P in = 6.5   dB .

Fig. 9
Fig. 9

Conversion efficiency versus the incident angle for the structure depicted in Fig. 1 and the parameters L = 300   nm , H co = 300   nm , d = 200   nm , and h = 200   nm . The inset shows the guided power at θ = 30 ° .

Equations (7)

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P ( r , t ) = ε 0 β χ α β ( 1 ) E β ( r , t ) + ε 0 β γ χ α β γ ( 2 ) E β ( r , t ) E γ ( r , t ) ,
P ( NL ) = ε 0 [ χ x y z ( 2 ) 0 0 0 χ y x z ( 2 ) 0 0 0 χ z x y ( 2 ) ] [ E y E z E x E z E x E y ] ,
D = ε 0 E + P = ε 0 [ ε r 0 χ ( 2 ) E y χ ( 2 ) E z ε r 0 0 χ ( 2 ) E x ε r ] [ E x E y E z ] .
P i , g ( ω ) = 1 2 Re { S i , S g E ( ω ) × H ( ω ) d S i , g } ,
E ( x , y ) = + E ̃ ( k x , y ) exp ( j k x x j k y y ) d k x ,
k y = { k 0 2 k x 2 , | k x | k 0 j k x 2 k 0 2 , | k x | > k 0 . }
β ( 2 ω ) = 2 ω c sin   θ + 2 m π L ,

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