Abstract

We propose an efficient and low-power second harmonic generation (SHG) process in a silicon-compatible hybrid plasmonic microring resonator. By making the microring resonator doubly resonant at the fundamental wavelength of 3.1 μm and second harmonic wavelength of 1.55 μm, the SHG efficiency is enhanced by almost two orders of magnitude when compared to the previous result induced in a straight plasmonic waveguide. A SHG efficiency of 13.71% is predicted for a low pump power of 20 mW in a ring with radius of 2.325 μm. This device provides a potential route for realizing efficient frequency conversion between mid-infrared and near-infrared wavebands on a chip.

© 2014 Chinese Laser Press

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2014 (1)

2013 (4)

2012 (9)

H. S. Chu, Y. Akimov, P. Bai, and E. P. Li, “Submicrometer radius and highly confined plasmonic ring resonator filters based on hybrid metal-oxide-semiconductor waveguide,” Opt. Lett. 37, 4564–4566 (2012).
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S. Y. Zhu, G. Q. Lo, and D. L. Kwong, “Performance of ultracompact copper-capped silicon hybrid plasmonic waveguide-ring resonators at telecom wavelengths,” Opt. Express 20, 15232–15246 (2012).
[Crossref]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100, 223501 (2012).
[Crossref]

Z. A. F. Bi, A. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K. M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant chi((2)) microring resonators,” Opt. Express 20, 7526–7543 (2012).
[Crossref]

X. P. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6, 667–671 (2012).
[Crossref]

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

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

Z. Fang and C. Z. Zhao, “Recent progress in silicon photonics: a review,” ISRN Opt. 2012, 428690 (2012).

M. M. Milosevic, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. H. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101, 121105 (2012).
[Crossref]

2011 (7)

2010 (5)

2009 (3)

2008 (3)

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16, 4881–4887 (2008).
[Crossref]

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

R. Soref, “Toward silicon-based longwave integrated optoelectronics (LIO),” Proc. SPIE 689, 689809 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

Y. Liu, T. Chang, and A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44, 084601 (2005).
[Crossref]

1972 (1)

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

Ahmad, R.

Akimov, Y.

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4, 561–564 (2010).
[Crossref]

Alloatti, L.

Baehr-Jones, T. W.

A. Spott, Y. Liu, T. W. Baehr-Jones, R. Ilic, and M. Hochberg, “Mid-infrared photonics in silicon,” Proc. SPIE 7917, 79171B (2011).
[Crossref]

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

Baets, R.

X. P. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6, 667–671 (2012).
[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, 1304–1316 (2009).
[Crossref]

B. Kuyken, X. Liu, R. Osgood, Y. Vlasov, G. Roelkens, R. Baets, and W. M. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU4.

Bai, P.

Ben Masaud, T. M.

M. M. Milosevic, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. H. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101, 121105 (2012).
[Crossref]

Bi, Z. A. F.

Biaggio, I.

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, 1304–1316 (2009).
[Crossref]

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4, 561–564 (2010).
[Crossref]

Boyraz, O.

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, 1304–1316 (2009).
[Crossref]

Cassan, E.

Chang, T.

Y. Liu, T. Chang, and A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44, 084601 (2005).
[Crossref]

Cheben, P.

Chong, H. M. H.

M. M. Milosevic, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. H. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101, 121105 (2012).
[Crossref]

Christy, R. W.

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

Chu, H. S.

Chu, S.

Chu, S. T.

Craig, A. E.

Y. Liu, T. Chang, and A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44, 084601 (2005).
[Crossref]

Dai, D.

Dai, D. X.

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, 1304–1316 (2009).
[Crossref]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4, 561–564 (2010).
[Crossref]

Duchesne, D.

Duley, W. W.

Dumon, P.

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, 1304–1316 (2009).
[Crossref]

Emerson, N. G.

M. M. Milosevic, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. H. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101, 121105 (2012).
[Crossref]

Fan, S.

Fang, Z.

Z. Fang and C. Z. Zhao, “Recent progress in silicon photonics: a review,” ISRN Opt. 2012, 428690 (2012).

Fathpour, S.

Fejer, M. M.

Ferrera, M.

Fong, K. Y.

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, 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, 20506–20515 (2012).
[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, 1304–1316 (2009).
[Crossref]

Gaeta, A. L.

Gao, D.

Gao, S. M.

Z. Q. Li, S. M. Gao, Q. A. Liu, and S. L. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[Crossref]

E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18, 21981–21989 (2010).
[Crossref]

Green, W. M.

B. Kuyken, X. Liu, R. Osgood, Y. Vlasov, G. Roelkens, R. Baets, and W. M. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU4.

Green, W. M. J.

X. P. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6, 667–671 (2012).
[Crossref]

Hashemi, H.

He, S. L.

Z. Q. Li, S. M. Gao, Q. A. Liu, and S. L. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[Crossref]

D. X. Dai, Y. C. Shi, S. L. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express 19, 23671–23682 (2011).
[Crossref]

Hochberg, M.

A. Spott, Y. Liu, T. W. Baehr-Jones, R. Ilic, and M. Hochberg, “Mid-infrared photonics in silicon,” Proc. SPIE 7917, 79171B (2011).
[Crossref]

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, 8085–8090 (2008).
[Crossref]

Hu, A.

Hu, Y. F.

Huang, Y. W.

Ilic, R.

A. Spott, Y. Liu, T. W. Baehr-Jones, R. Ilic, and M. Hochberg, “Mid-infrared photonics in silicon,” Proc. SPIE 7917, 79171B (2011).
[Crossref]

Jaberansary, E.

M. M. Milosevic, M. Nedeljkovic, T. M. Ben Masaud, E. Jaberansary, H. M. H. Chong, N. G. Emerson, G. T. Reed, and G. Z. Mashanovich, “Silicon waveguides and devices for the mid-infrared,” Appl. Phys. Lett. 101, 121105 (2012).
[Crossref]

Jalali, B.

Janz, S.

Johnson, P. B.

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

Johnson, S. G.

Jonasz, M.

Kalyoncu, S. K.

Kauranen, M.

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

Kitamura, R.

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, 20506–20515 (2012).
[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, 1304–1316 (2009).
[Crossref]

Korn, D.

Kuyken, B.

X. P. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6, 667–671 (2012).
[Crossref]

B. Kuyken, X. Liu, R. Osgood, Y. Vlasov, G. Roelkens, R. Baets, and W. M. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU4.

Kwong, D. L.

Lamont, M.

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, 20506–20515 (2012).
[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, 1304–1316 (2009).
[Crossref]

Levy, J. S.

Li, E. P.

Li, Z. Q.

Z. Q. Li, S. M. Gao, Q. A. Liu, and S. L. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[Crossref]

Lipson, M.

Little, B. E.

Liu, Q. A.

Z. Q. Li, S. M. Gao, Q. A. Liu, and S. L. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[Crossref]

Liu, X.

B. Kuyken, X. Liu, R. Osgood, Y. Vlasov, G. Roelkens, R. Baets, and W. M. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU4.

Liu, X. P.

X. P. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation,” Nat. Photonics 6, 667–671 (2012).
[Crossref]

Liu, Y.

A. Spott, Y. Liu, T. W. Baehr-Jones, R. Ilic, and M. Hochberg, “Mid-infrared photonics in silicon,” Proc. SPIE 7917, 79171B (2011).
[Crossref]

Y. Liu, T. Chang, and A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44, 084601 (2005).
[Crossref]

Lo, G. Q.

Loncar, M.

Lou, F.

Mashanovich, G. Z.

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C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19, 10462–10470 (2011).
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B. Kuyken, X. Liu, R. Osgood, Y. Vlasov, G. Roelkens, R. Baets, and W. M. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU4.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the SOHPMR. Cross-sectional views along the (a) XY and (b) XZ planes.

Fig. 2.
Fig. 2.

Δn=nSHnFF as functions of the radius and width of the bended waveguides. The black line represents the zero value, i.e., the phase-matching line.

Fig. 3.
Fig. 3.

(a) neffkFFR and (b) loss of a 90° bend at the phase-matching line as functions of the radius. The inset in (a) is an enlarged view near neffkFFR=9.

Fig. 4.
Fig. 4.

Ez distributions for the phase-matched modes at (a) FF and (b) SHF when R=2.325μm and w=351nm. (c) is the normalized Ez distribution on the center line of the slot along the r direction.

Fig. 5.
Fig. 5.

SHG efficiency η2 as a function of the transmission coefficients for FF tFF and SHF tSH.

Fig. 6.
Fig. 6.

(a) Transmission coefficients for two wavelengths, (b) final SHG conversion efficiency, and (c) enhancement factor in the ring as a function of the gap.

Fig. 7.
Fig. 7.

Transmission spectra of the 3D MRR structure around (a) SHF of 1.55 μm and (c) FF of 3.1 μm when R=2.325μm, wa=358.3nm, w=351nm, and g=175nm. The two resonant wavelengths are 1548.4 and 3099 nm. (b) and (d) are the Ez distributions at the SHF and the FF, respectively.

Fig. 8.
Fig. 8.

SHG efficiency η2 as a function of the attenuation coefficients for FF (αFF) and SHF (αSH).

Fig. 9.
Fig. 9.

Schematic of SHG in a single-pass MRR.

Fig. 10.
Fig. 10.

Analytic solution and numerical solution of the SHG efficiency as functions of the propagation length in (a) straight waveguide and (b) bended waveguide.

Equations (16)

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

η1=PSH(out)PFF(in)=ωFF216cSH2Leff2(L)exp(αSHL)PFF(0),
Leff(L)=1exp[(αFFαSH/2+iΔβ)L]αFFαSH/2+iΔβ.
η2=PSH(out)PFF(in)=ωFF216cSH2Leff2(L)FFF4FSH2exp(αSHL)PFF(in).
FFF,SH=κFF,SH1tFF,SHexp[(iβFF,SHαFF,SH/2)L].
Leff(L)=1exp[(αFFαSH/2)L]αFFαSH/2,FFF,SH=κFF,SH1tFF,SHexp(αFF,SH2L).
AFFz=αFF2AFF+iωFF4cFFAFF*ASHexp(iΔβz),ASHz=αSH2ASH+iωFF4cSHAFFAFFexp(iΔβz),
cFF=ε0{χ(2):E⃗SH(x,y)E⃗FF*(x,y)·E⃗FF(x,y)}dxdy,cSH=ε0{χ(2):E⃗FF(x,y)E⃗FF(x,y)·E⃗SH(x,y)}dxdy,
AFF=AFF(0)exp(αFF2z),ASH=iωFF4cSHLeff(z)AFF2(0)exp(αSH2z),+ASH(0)exp(αSH2z),
Leff(z)=1exp[(αFFαSH/2+iΔβ)z]αFFαSH/2+iΔβ.
η1=|ASH(L)|2|AFF(0)|2=ωFF216cSH2Leff2(L)exp(αSHL)PFF(0).
AFF,SH(2)=tFF,SHAFF,SH(1)+iκFF,SHAFF,SH(4),AFF,SH(3)=iκFF,SHAFF,SH(1)+tFF,SHAFF,SH(4).
AFF(4)=AFF(3)exp[(iβFFαFF2)L],ASH(4)=iωFF4cSHLeff(L)[AFF(3)]2exp[(iβSHαSH2)L]+ASH(3)exp[(iβSHαSH2)L],
AFF(1)=AFF(in),ASH(1)=0.
AFF(2)={tFFκFFFFFexp[(iβFFαFF2)L]}AFF(in),AFF(3)=iFFFAFF(in),AFF(4)=iFFFexp[(iβFFαFF2)L]AFF(in),ASH(2)=ωFF4cSHLeff(L)FFF2FSHexp[(iβSHαSH2)L][AFF(in)]2,ASH(3)=iωFF4tSHκSHcSHLeff(L)FFF2FSHexp[(iβSHαSH2)L][AFF(in)]2,ASH(4)=iωFF4κSHcSHLeff(L)FFF2FSHexp[(iβSHαSH2)L][AFF(in)]2,
FFF,SH=κFF,SH1tFF,SHexp[(iβFF,SHαFF,SH/2)L].
η2=|ASH(2)|2|AFF(in)|2=ωFF216cSH2Leff2(L)FFF4FSH2exp(αSHL)PFF(in).

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