Abstract

We demonstrate the design, fabrication and characterization of nanobeam cavities with multiple higher order modes. Designs with two high Q modes with frequency separations of an octave are introduced, and we fabricate such cavities exhibiting resonances with wavelength separations of up to 740 nm.

© 2014 Optical Society of America

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2014 (3)

S. Buckley, M. Radulaski, J. Petykiewicz, K. G. Lagoudakis, J.-H. Kang, M. Brongersma, K. Biermann, and J. Vučković, “Second-Harmonic Generation in GaAs Photonic Crystal Cavities in (111)B and (001) Crystal Orientations,” ACS Photon. 1, 516–523 (2014).
[Crossref]

S. Yamada, B.-S. Song, S. Jeon, J. Upham, Y. Tanaka, T. Asano, and S. Noda, “Second-harmonic generation in a silicon-carbide-based photonic crystal nanocavity,” Opt. Lett. 39, 1768–1771 (2014).
[Crossref] [PubMed]

M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” SPIE Photonics Europe 9127, 8 (2014).

2013 (11)

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
[Crossref]

M. Radulaski, T. M. Babinec, S. Buckley, A. Rundquist, J. Provine, K. Alassaad, G. Ferro, and J. Vučković, “Photonic crystal cavities in cubic (3C) polytype silicon carbide films,” Opt. Express 21, 32623–32629 (2013).
[Crossref]

S. Azzini, D. Grassani, M. Galli, D. Gerace, M. Patrini, M. Liscidini, P. Velha, and D. Bajoni, “Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities,” Appl. Phys. Lett. 103, 031117 (2013).
[Crossref]

J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21, 13351–13367 (2013).
[Crossref] [PubMed]

S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103, 211117 (2013).
[Crossref]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21, 19778–19789 (2013).
[Crossref] [PubMed]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Self-frequency summing in quantum dot photonic crystal nanocavity lasers,” Appl. Phys. Lett. 103, 243115 (2013).
[Crossref]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref] [PubMed]

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102, 241110 (2013).
[Crossref]

A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87, 235319 (2013).
[Crossref]

2012 (3)

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6, 440–449 (2012).
[Crossref]

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100, 091105 (2012).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Lončar, 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] [PubMed]

2011 (7)

K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
[Crossref] [PubMed]

M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. Lončar, “High-q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
[Crossref]

T. M. Babinec, J. T. Choy, K. J. M. Smith, M. Khan, and M. Lončar, “Design and focused ion beam fabrication of single crystal diamond nanobeam cavities,” J. Vacuum Sci. Techn. B 29, 010601 (2011).
[Crossref]

M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. 36, 421–423 (2011).
[Crossref] [PubMed]

Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
[Crossref] [PubMed]

K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
[Crossref] [PubMed]

K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

2010 (8)

S. M. Thon, W. T. M. Irvine, D. Kleckner, and D. Bouwmeester, “Polychromatic photonic quasicrystal cavities,” Phys. Rev. Lett. 104, 243901 (2010).
[Crossref] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Silicon photonics: On-chip OPOs,” Nat. Photonics 4, 10–12 (2010).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, and J. Vučković, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97, 043103 (2010).
[Crossref]

Y. Gong and J. Vučković, “Photonic crystal cavities in silicon dioxide,” Appl. Phys. Lett. 96, 031107 (2010).
[Crossref]

M. Galli, D. Gerace, K. Welna, T. F. Krauss, L. O’Faolain, G. Guizzetti, and L. C. Andreani, “Low-power continuous-wave generation of visible harmonics in silicon photonic crystal nanocavities,” Opt. Express 18, 26613–26624 (2010).
[Crossref] [PubMed]

G. Shambat, Y. Gong, J. Lu, S. Yerci, R. Li, L. Dal Negro, and J. Vučković, “Coupled fiber taper extraction of 1.53 μm photoluminescence from erbium doped silicon nitride photonic crystal cavities,” Opt. Express 18, 5964–5973 (2010).
[Crossref] [PubMed]

2009 (7)

I. B. Burgess, Y. Zhang, M. W. McCutcheon, A. W. Rodriguez, J. Bravo-Abad, S. G. Johnson, and M. Lončar, “Design of an efficient terahertz sourceusing triply resonant nonlinearphotonic crystal cavities,” Opt. Express 17, 20099–20108 (2009).
[Crossref] [PubMed]

I. B. Burgess, A. W. Rodriguez, M. W. McCutcheon, J. Bravo-Abad, Y. Zhang, S. G. Johnson, and M. Lončar, “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Opt. Express 17, 9241–9251 (2009).
[Crossref] [PubMed]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[Crossref]

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

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558–16570 (2009).
[Crossref] [PubMed]

Y. Zhang, M. W. McCutcheon, I. B. Burgess, and M. Lončar, “Ultra-high-Q TE/TM dual-polarized photonic crystal nanocavities,” Opt. Lett. 34, 2694–2696 (2009).
[Crossref] [PubMed]

M. W. McCutcheon, D. E. Chang, Y. Zhang, M. D. Lukin, and M. Lončar, “Broadband frequency conversion and shaping of single photons emitted from a nonlinear cavity,” Opt. Express 17, 22689–22703 (2009).
[Crossref]

2008 (1)

2007 (3)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frdrick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
[Crossref]

A. Rodriguez, M. Soljačić, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[Crossref] [PubMed]

2006 (1)

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong coupling between single photons in semiconductor microcavities,” Phys. Rev. Lett. 96, 057405 (2006).
[Crossref] [PubMed]

2005 (2)

2004 (1)

2001 (1)

2000 (1)

1997 (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Alassaad, K.

Alcorn, T.

Z. Lin, T. Alcorn, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “High-efficiency degenerate four wave-mixing in triply resonant nanobeam cavities,” arXiv:1311.4100 [physics] (2013).

Andreani, L. C.

Arakawa, Y.

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21, 19778–19789 (2013).
[Crossref] [PubMed]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Self-frequency summing in quantum dot photonic crystal nanocavity lasers,” Appl. Phys. Lett. 103, 243115 (2013).
[Crossref]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Asano, T.

S. Yamada, B.-S. Song, S. Jeon, J. Upham, Y. Tanaka, T. Asano, and S. Noda, “Second-harmonic generation in a silicon-carbide-based photonic crystal nanocavity,” Opt. Lett. 39, 1768–1771 (2014).
[Crossref] [PubMed]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref] [PubMed]

Azzini, S.

S. Azzini, D. Grassani, M. Galli, D. Gerace, M. Patrini, M. Liscidini, P. Velha, and D. Bajoni, “Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities,” Appl. Phys. Lett. 103, 031117 (2013).
[Crossref]

Babinec, T.

Babinec, T. M.

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S. M. Thon, W. T. M. Irvine, D. Kleckner, and D. Bouwmeester, “Polychromatic photonic quasicrystal cavities,” Phys. Rev. Lett. 104, 243901 (2010).
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T. M. Babinec, J. T. Choy, K. J. M. Smith, M. Khan, and M. Lončar, “Design and focused ion beam fabrication of single crystal diamond nanobeam cavities,” J. Vacuum Sci. Techn. B 29, 010601 (2011).
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M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. 36, 421–423 (2011).
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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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S. M. Thon, W. T. M. Irvine, D. Kleckner, and D. Bouwmeester, “Polychromatic photonic quasicrystal cavities,” Phys. Rev. Lett. 104, 243901 (2010).
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S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013).
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K. Rivoire, Z. Lin, F. Hatami, and J. Vučković, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97, 043103 (2010).
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K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
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J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
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S. Azzini, D. Grassani, M. Galli, D. Gerace, M. Patrini, M. Liscidini, P. Velha, and D. Bajoni, “Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities,” Appl. Phys. Lett. 103, 031117 (2013).
[Crossref]

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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Lončar, 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).
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M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. 36, 421–423 (2011).
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P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
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I. B. Burgess, Y. Zhang, M. W. McCutcheon, A. W. Rodriguez, J. Bravo-Abad, S. G. Johnson, and M. Lončar, “Design of an efficient terahertz sourceusing triply resonant nonlinearphotonic crystal cavities,” Opt. Express 17, 20099–20108 (2009).
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I. B. Burgess, A. W. Rodriguez, M. W. McCutcheon, J. Bravo-Abad, Y. Zhang, S. G. Johnson, and M. Lončar, “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Opt. Express 17, 9241–9251 (2009).
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Lukin, M. D.

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M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. Lončar, “High-q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
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M. Khan, T. Babinec, M. W. McCutcheon, P. Deotare, and M. Lončar, “Fabrication and characterization of high-quality-factor silicon nitride nanobeam cavities,” Opt. Lett. 36, 421–423 (2011).
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I. B. Burgess, Y. Zhang, M. W. McCutcheon, A. W. Rodriguez, J. Bravo-Abad, S. G. Johnson, and M. Lončar, “Design of an efficient terahertz sourceusing triply resonant nonlinearphotonic crystal cavities,” Opt. Express 17, 20099–20108 (2009).
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M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frdrick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” SPIE Photonics Europe 9127, 8 (2014).

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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Moss, D. J.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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O’Faolain, L.

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Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Self-frequency summing in quantum dot photonic crystal nanocavity lasers,” Appl. Phys. Lett. 103, 243115 (2013).
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Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21, 19778–19789 (2013).
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S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
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Quan, Q.

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S. Buckley, M. Radulaski, J. Petykiewicz, K. G. Lagoudakis, J.-H. Kang, M. Brongersma, K. Biermann, and J. Vučković, “Second-Harmonic Generation in GaAs Photonic Crystal Cavities in (111)B and (001) Crystal Orientations,” ACS Photon. 1, 516–523 (2014).
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S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103, 211117 (2013).
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M. Radulaski, T. M. Babinec, S. Buckley, A. Rundquist, J. Provine, K. Alassaad, G. Ferro, and J. Vučković, “Photonic crystal cavities in cubic (3C) polytype silicon carbide films,” Opt. Express 21, 32623–32629 (2013).
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S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Nonlinear frequency conversion using high quality modes in GaAs nanobeam cavities,” arXiv 1407.1446, 4 (2014).

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frdrick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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Rodriguez, A.

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S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
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Savona, V.

M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” SPIE Photonics Europe 9127, 8 (2014).

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A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6, 440–449 (2012).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013).
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W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100, 091105 (2012).
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Shambat, G.

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Smith, K. J. M.

T. M. Babinec, J. T. Choy, K. J. M. Smith, M. Khan, and M. Lončar, “Design and focused ion beam fabrication of single crystal diamond nanobeam cavities,” J. Vacuum Sci. Techn. B 29, 010601 (2011).
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Song, B.-S.

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
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Tanaka, Y.

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W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100, 091105 (2012).
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Terawaki, R.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Velha, P.

S. Azzini, D. Grassani, M. Galli, D. Gerace, M. Patrini, M. Liscidini, P. Velha, and D. Bajoni, “Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities,” Appl. Phys. Lett. 103, 031117 (2013).
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S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103, 211117 (2013).
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M. Radulaski, T. M. Babinec, S. Buckley, A. Rundquist, J. Provine, K. Alassaad, G. Ferro, and J. Vučković, “Photonic crystal cavities in cubic (3C) polytype silicon carbide films,” Opt. Express 21, 32623–32629 (2013).
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K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
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K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
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K. Rivoire, Z. Lin, F. Hatami, and J. Vučković, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97, 043103 (2010).
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G. Shambat, Y. Gong, J. Lu, S. Yerci, R. Li, L. Dal Negro, and J. Vučković, “Coupled fiber taper extraction of 1.53 μm photoluminescence from erbium doped silicon nitride photonic crystal cavities,” Opt. Express 18, 5964–5973 (2010).
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Y. Gong and J. Vučković, “Photonic crystal cavities in silicon dioxide,” Appl. Phys. Lett. 96, 031107 (2010).
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K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
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S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Nonlinear frequency conversion using high quality modes in GaAs nanobeam cavities,” arXiv 1407.1446, 4 (2014).

Wang, K.-M.

Watanabe, K.

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21, 19778–19789 (2013).
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Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Self-frequency summing in quantum dot photonic crystal nanocavity lasers,” Appl. Phys. Lett. 103, 243115 (2013).
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Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frdrick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2011).

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J. Witzens, T. Baehr-Jones, and M. Hochberg, “Silicon photonics: On-chip OPOs,” Nat. Photonics 4, 10–12 (2010).
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Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102, 241110 (2013).
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W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100, 091105 (2012).
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Yamada, S.

Yamamoto, Y.

Yariv, A.

Yerci, S.

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M. W. McCutcheon, J. F. Young, G. W. Rieger, D. Dalacu, S. Frdrick, P. J. Poole, and R. L. Williams, “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102, 241110 (2013).
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S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Nonlinear frequency conversion using high quality modes in GaAs nanobeam cavities,” arXiv 1407.1446, 4 (2014).

Zhang, Y.

Zhou, Q.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102, 241110 (2013).
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Zilk, M.

S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013).
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ACS Photon. (1)

S. Buckley, M. Radulaski, J. Petykiewicz, K. G. Lagoudakis, J.-H. Kang, M. Brongersma, K. Biermann, and J. Vučković, “Second-Harmonic Generation in GaAs Photonic Crystal Cavities in (111)B and (001) Crystal Orientations,” ACS Photon. 1, 516–523 (2014).
[Crossref]

Appl. Phys. Lett. (12)

S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013).
[Crossref]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Self-frequency summing in quantum dot photonic crystal nanocavity lasers,” Appl. Phys. Lett. 103, 243115 (2013).
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P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
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Y. Gong and J. Vučković, “Photonic crystal cavities in silicon dioxide,” Appl. Phys. Lett. 96, 031107 (2010).
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W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100, 091105 (2012).
[Crossref]

S. Azzini, D. Grassani, M. Galli, D. Gerace, M. Patrini, M. Liscidini, P. Velha, and D. Bajoni, “Stimulated and spontaneous four-wave mixing in silicon-on-insulator coupled photonic wire nano-cavities,” Appl. Phys. Lett. 103, 031117 (2013).
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M. W. McCutcheon, P. B. Deotare, Y. Zhang, and M. Lončar, “High-q transverse-electric/transverse-magnetic photonic crystal nanobeam cavities,” Appl. Phys. Lett. 98, 111117 (2011).
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K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99, 013114 (2011).
[Crossref]

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102, 241110 (2013).
[Crossref]

K. Rivoire, Z. Lin, F. Hatami, and J. Vučković, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97, 043103 (2010).
[Crossref]

S. Buckley, M. Radulaski, K. Biermann, and J. Vučković, “Second harmonic generation in photonic crystal cavities in (111)-oriented GaAs,” Appl. Phys. Lett. 103, 211117 (2013).
[Crossref]

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103, 181104 (2013).
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J. Opt. Soc. Am. B (1)

J. Vacuum Sci. Techn. B (1)

T. M. Babinec, J. T. Choy, K. J. M. Smith, M. Khan, and M. Lončar, “Design and focused ion beam fabrication of single crystal diamond nanobeam cavities,” J. Vacuum Sci. Techn. B 29, 010601 (2011).
[Crossref]

Nat. Photonics (4)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Silicon photonics: On-chip OPOs,” Nat. Photonics 4, 10–12 (2010).
[Crossref]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6, 440–449 (2012).
[Crossref]

Nature (3)

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Opt. Express (19)

P. Lalanne, S. Mias, and J. Hugonin, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Opt. Express 12, 458–467 (2004).
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C. Sauvan, G. Lecamp, P. Lalanne, and J. Hugonin, “Modal-reflectivity enhancement by geometry tuning in photonic crystal microcavities,” Opt. Express 13, 245–255 (2005).
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M. Galli, D. Gerace, K. Welna, T. F. Krauss, L. O’Faolain, G. Guizzetti, and L. C. Andreani, “Low-power continuous-wave generation of visible harmonics in silicon photonic crystal nanocavities,” Opt. Express 18, 26613–26624 (2010).
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M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap,” Opt. Express 16, 11095–11102 (2008).
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K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vučković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17, 22609–22615 (2009).
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Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
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M. Radulaski, T. M. Babinec, S. Buckley, A. Rundquist, J. Provine, K. Alassaad, G. Ferro, and J. Vučković, “Photonic crystal cavities in cubic (3C) polytype silicon carbide films,” Opt. Express 21, 32623–32629 (2013).
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S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558–16570 (2009).
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K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
[Crossref] [PubMed]

Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21, 19778–19789 (2013).
[Crossref] [PubMed]

M. W. McCutcheon, D. E. Chang, Y. Zhang, M. D. Lukin, and M. Lončar, “Broadband frequency conversion and shaping of single photons emitted from a nonlinear cavity,” Opt. Express 17, 22689–22703 (2009).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of a nanobeam photonic crystal with parameters and coordinate directions indicated. (b)–(d) Band diagram for nanobeam with hx = 0.7w, hy = 0.5a, n = 3.34 for membrane thickness t/a = 0.5, t/a = 0.75 and t/a = 1, respectively. The blue solid lines show TE modes, the green dashed lines show TM modes.

Fig. 2
Fig. 2

Field profiles for the first seven modes of the nanobeam with thickness t/a = 0.75 shown in Fig 1 (c). The coordinate axes indicated in part (a) are repeated for part (b).

Fig. 3
Fig. 3

(a) The Ey field component of the first to fifth order TE modes localized by the presence of the cavity from the TE000 band in order of increasing frequency for t/a = 0.75. (b) The Ex and Ey field components of the first localized TE002 mode.

Fig. 4
Fig. 4

The Ex, Ey and Ez field profiles of the localized (a) TM030, (b) TE110 mode and (c) TM020 mode. (d) The mode frequency versus membrane thickness t/a for the nanobeam with hx = 0.5w, hy = 0.5a. The solid black lines indicate the first five localized modes of the TE000 mode. The red dashed line indicates the position of the light line at the X point. (e) Q factor versus membrane thickness.

Fig. 5
Fig. 5

(a) The spatial profile of the nonlinear overlap between the Ey field components of the modes shown in Fig. 3 (a) part (i) and Fig. 3 (b). (b) (i) The nonlinear overlap for each of the five modes shown in Fig. 3 (a) with the mode in Fig. 3 (b) for three different GaAs orientations. Part (ii) shows that if a cavity shift is introduced the nonlinear overlap can be significantly increased, but the Q factors of the modes will also be significantly decreased.

Fig. 6
Fig. 6

(a) Measured mode wavelength versus lattice constant for 8 different fabricated structures. 5–6 modes were measured for each structure, corresponding to the modes in Fig. 3. (b) Representative spectra for two of the modes measured by fiber taper, with loaded Q factors of 10,000 and 8,000. (c) SEM images of a typical nanobeam with lattice constant 480 nm. Scalebars are (i) 5 μm and (ii) 500 nm

Fig. 7
Fig. 7

Demonstration of modes with large frequency separations. (a) The fundamental TE000 mode and a higher order mode at 920 nm, for a nanobeam with lattice constant 450 nm. (b) The fifth confined TE000 mode and first confined TE110 mode of a nanobeam with lattice constant 610 nm.

Equations (10)

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| β | 2 = | 1 4 NL d V ε 0 i j k χ i j k ( 2 ) E 1 i * ( E 2 j * E 3 k + E 2 k * E 3 j ) d V ε | E 1 | 2 d V ε | E 2 | d V ε | E 3 | 2 | 2
γ = | ε NL ( E 1 x E 2 z + E 2 z E 1 y ) d V ε | E 1 | 2 d V ε | E 2 | 2 d V |
γ = | ε NL ( E 1 x E 2 y + E 2 x E 1 y ) d V ε | E 1 | 2 d V ε | E 2 | 2 d V |
d i j k = 1 2 χ i j k ( 2 )
P i ( ω n + ω m ) = ε 0 j k n m 2 d i j k E j ( ω n ) E k ( ω m )
d eff = ( 0 0 0 d 41 0 0 0 0 0 0 d 41 0 0 0 0 0 0 d 41 )
( P x ( 2 ω ) P y ( 2 ω ) P z ( 2 ω ) ) = 2 ε 0 d eff ( E x ( ω ) 2 E y ( ω ) 2 E z ( ω ) 2 2 E y ( ω ) E z ( ω ) 2 E x ( ω ) E z ( ω ) 2 E y ( ω ) E x ( ω ) )
( P x ( 2 ω ) P y ( 2 ω ) P z ( 2 ω ) ) = 2 ε 0 d eff , 111 ( E x ( ω ) 2 E y ( ω ) 2 E z ( ω ) 2 2 E y ( ω ) E z ( ω ) 2 E x ( ω ) E z ( ω ) 2 E y ( ω ) E x ( ω ) )
d eff = ( 1 6 1 6 0 0 1 3 0 0 0 0 1 3 0 1 6 1 2 3 1 2 3 1 3 0 0 0 ) d 41
d eff = ( 0 1 / 2 1 / 2 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 ) d 41

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