B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).

[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

S. L. Portalupi, M. Galli, C. Reardon, T. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–16073 (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]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

M. Liscidini and L. C. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016613 (2006).

[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]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).

[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

E. Estephan, C. Larroque, F. J. Cuisinier, Z. Bálint, and C. Gergely, “Tailoring GaN semiconductor surfaces with biomolecules,” J. Phys. Chem. B 112, 8799–8805 (2008).

[Crossref]

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. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

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]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

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. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).

[Crossref]

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

[Crossref]

P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21, 1356 (2003).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).

[Crossref]

E. Estephan, C. Larroque, F. J. Cuisinier, Z. Bálint, and C. Gergely, “Tailoring GaN semiconductor surfaces with biomolecules,” J. Phys. Chem. B 112, 8799–8805 (2008).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

E. Estephan, C. Larroque, F. J. Cuisinier, Z. Bálint, and C. Gergely, “Tailoring GaN semiconductor surfaces with biomolecules,” J. Phys. Chem. B 112, 8799–8805 (2008).

[Crossref]

X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018).

[Crossref]

L. Scaccabarozzi, M. M. Fejer, Y. Huo, S. Fan, X. Yu, and J. S. Harris, “Enhanced second-harmonic generation in AlGaAs/AlxOy tightly confining waveguides and resonant cavities,” Opt. Lett. 31, 3626–3628 (2006).

[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[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]

S. L. Portalupi, M. Galli, C. Reardon, T. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–16073 (2010).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

D. Gerace and V. Savona, “Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity,” Phys. Rev. A 89, 031803 (2014).

[Crossref]

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

[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]

S. L. Portalupi, M. Galli, C. Reardon, T. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–16073 (2010).

[Crossref]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

E. Estephan, C. Larroque, F. J. Cuisinier, Z. Bálint, and C. Gergely, “Tailoring GaN semiconductor surfaces with biomolecules,” J. Phys. Chem. B 112, 8799–8805 (2008).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).

[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).

[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]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).

[Crossref]

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).

[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]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).

[Crossref]

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]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).

[Crossref]

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]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

E. Estephan, C. Larroque, F. J. Cuisinier, Z. Bálint, and C. Gergely, “Tailoring GaN semiconductor surfaces with biomolecules,” J. Phys. Chem. B 112, 8799–8805 (2008).

[Crossref]

X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018).

[Crossref]

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” Opt. Lett. 42, 2818–2821 (2017).

[Crossref]

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).

[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]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

M. Liscidini and L. C. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016613 (2006).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

P. J. Campagnola and L. M. Loew, “Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms,” Nat. Biotechnol. 21, 1356 (2003).

[Crossref]

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” Opt. Lett. 42, 2818–2821 (2017).

[Crossref]

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).

[Crossref]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786 (2010).

[Crossref]

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

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” Proc. SPIE 9127, 91270C (2014).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[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]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).

[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).

[Crossref]

S. L. Portalupi, M. Galli, C. Reardon, T. Krauss, L. O’Faolain, L. C. Andreani, and D. Gerace, “Planar photonic crystal cavities with far-field optimization for high coupling efficiency and quality factor,” Opt. Express 18, 16064–16073 (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]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[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]

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. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).

[Crossref]

S. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).

[Crossref]

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]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786 (2010).

[Crossref]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).

[Crossref]

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

[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]

Z. Lin, M. Lončar, and A. W. Rodriguez, “Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion,” Opt. Lett. 42, 2818–2821 (2017).

[Crossref]

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

E. Estephan, D. Bajoni, M.-B. Saab, T. Cloitre, R. Aulombard, C. Larroque, L. C. Andreani, M. Liscidini, A. M. Malvezzi, and C. Gergely, “Sensing by means of nonlinear optics with functionalized GaAs/AlGaAs photonic crystals,” Langmuir 26, 10373–10379 (2010).

[Crossref]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

D. Gerace and V. Savona, “Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity,” Phys. Rev. A 89, 031803 (2014).

[Crossref]

M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” Proc. SPIE 9127, 91270C (2014).

[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]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

T. F. Heinz, C. K. Chen, D. Ricard, and Y. R. Shen, “Spectroscopy of molecular monolayers by resonant second-harmonic generation,” Phys. Rev. Lett. 48, 478–481 (1982).

[Crossref]

M. S. Mohamed, A. Simbula, J.-F. Carlin, M. Minkov, D. Gerace, V. Savona, N. Grandjean, M. Galli, and R. Houdré, “Efficient continuous-wave nonlinear frequency conversion in high-Q gallium nitride photonic crystal cavities on silicon,” APL Photon. 2, 031301 (2017).

[Crossref]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786 (2010).

[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).

[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]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).

[Crossref]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).

[Crossref]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786 (2010).

[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[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]

M. T. Rakher, L. Ma, O. Slattery, X. Tang, and K. Srinivasan, “Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion,” Nat. Photonics 4, 786 (2010).

[Crossref]

N.-V.-Q. Tran, S. Combrié, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79, 041101 (2009).

[Crossref]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, “Measurement of second order susceptibilities of GaN and AlGaN,” J. Appl. Phys. 97, 053512 (2005).

[Crossref]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).

[Crossref]

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. Buckley, M. Radulaski, J. L. Zhang, J. Petykiewicz, K. Biermann, and J. Vučković, “Multimode nanobeam cavities for nonlinear optics: high quality resonances separated by an octave,” Opt. Express 22, 26498–26509 (2014).

[Crossref]

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

[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]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light Sci. Appl. 6, e17100 (2017).

[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]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

Y. Zeng, I. Roland, X. Checoury, Z. Han, M. El Kurdi, S. Sauvage, B. Gayral, C. Brimont, T. Guillet, M. Mexis, F. Semond, and P. Boucaud, “Resonant second harmonic generation in a gallium nitride two-dimensional photonic crystal on silicon,” Appl. Phys. Lett. 106, 081105 (2015).

[Crossref]

A. W. Bruch, X. Liu, X. Guo, J. B. Surya, Z. Gong, L. Zhang, J. Wang, J. Yan, and H. X. Tang, “17000%/W second-harmonic conversion efficiency in single-crystalline aluminum nitride microresonators,” Appl. Phys. Lett. 113, 131102 (2018).

[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).

[Crossref]

X. Ge, M. Minkov, S. Fan, X. Li, and W. Zhou, “Low index contrast heterostructure photonic crystal cavities with high quality factors and vertical radiation coupling,” Appl. Phys. Lett. 112, 141105 (2018).

[Crossref]