Abstract

Photonic nanostructures simultaneously maximizing spectral and spatial overlap between fundamental and second-harmonic confined modes are highly desirable for enhancing second-order nonlinear effects in nonlinear media. These conditions have thus far remained challenging to satisfy in photonic crystal cavities because of the difficulty in designing a band gap at the second-harmonic frequency. Here, we solve this issue by using instead a bound state in the continuum at that frequency, and we design a doubly resonant photonic crystal slab cavity with strongly improved figures of merit for nonlinear frequency conversion when compared to previous photonic crystal designs. Furthermore, we show that the far-field emission at both frequencies is highly collimated around normal incidence, which allows for simultaneously efficient pump excitation and collection of the generated nonlinear signal. Our results could lead to unprecedented conversion efficiencies in both parametric down-conversion and second-harmonic generation in an extremely compact architecture.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. I. Freund and M. Deutsch, “Second-harmonic microscopy of biological tissue,” Opt. Lett. 11, 94–96 (1986).
    [Crossref]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. V. Berger, “Second-harmonic generation in monolithic cavities,” J. Opt. Soc. Am. B 14, 1351–1360 (1997).
    [Crossref]
  7. M. Liscidini and L. C. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016613 (2006).
    [Crossref]
  8. 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]
  9. A. Hayat and M. Orenstein, “Standing-wave nonlinear optics in an integrated semiconductor microcavity,” Opt. Lett. 32, 2864–2866 (2007).
    [Crossref]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
    [Crossref]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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]
  23. 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]
  24. K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
    [Crossref]
  25. 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]
  26. 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]
  27. M. Minkov and V. Savona, “Optimizing doubly resonant photonic crystal cavity modes for second harmonic generation,” Proc. SPIE 9127, 91270C (2014).
    [Crossref]
  28. 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]
  29. 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]
  30. A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87, 235319 (2013).
    [Crossref]
  31. D. Gerace and V. Savona, “Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity,” Phys. Rev. A 89, 031803 (2014).
    [Crossref]
  32. 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]
  33. 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]
  34. 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]
  35. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
    [Crossref]
  36. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
    [Crossref]
  37. 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]
  38. 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]

2018 (2)

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]

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]

2017 (3)

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. 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]

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]

2016 (2)

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]

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]

2015 (1)

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]

2014 (5)

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

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

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]

2013 (1)

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

2012 (1)

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]

2011 (1)

2010 (4)

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]

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]

2009 (2)

2008 (1)

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]

2007 (2)

2006 (3)

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]

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

2005 (2)

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

2003 (2)

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]

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]

2002 (1)

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

2001 (1)

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

1999 (1)

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]

1997 (1)

1986 (1)

1982 (1)

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]

Akahane, Y.

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]

Andreani, L. C.

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]

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]

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]

Aulombard, R.

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]

Bajoni, D.

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]

Bálint, Z.

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]

Berger, V.

Biermann, K.

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]

Boucaud, P.

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]

Brimont, C.

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]

Brongersma, M.

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]

Bruch, A. W.

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]

Buckley, S.

Campagnola, P. J.

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]

Carlin, J.-F.

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]

Caspani, L.

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]

Checoury, X.

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]

Chen, C. K.

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]

Cloitre, T.

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]

Combrié, S.

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]

Cuisinier, F. J.

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]

Davydov, A. V.

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]

De Rossi, A.

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]

DenBaars, S. P.

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]

Deutsch, M.

Dmitriev, A. V.

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]

Eggleton, B. J.

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]

El Kurdi, M.

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]

Estephan, E.

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]

Fan, S.

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]

Fejer, M. M.

Freund, I.

Galli, M.

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]

Gayral, B.

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]

Ge, X.

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]

Gerace, D.

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]

Gergely, C.

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]

Gong, Z.

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]

Grandjean, N.

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]

Guillet, T.

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]

Guizzetti, G.

Guo, X.

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]

Han, J. Y.

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]

Han, Z.

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]

Harris, J. S.

Hatami, F.

Hayat, A.

Heinz, T. F.

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]

Houdré, R.

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]

Hsu, C. W.

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]

Huo, Y.

Jeon, S.

Joannopoulos, J. D.

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]

Johnson, S. G.

Kang, J.-H.

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]

Keller, S.

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]

Kolodziejski, L. A.

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]

Krauss, T.

Krauss, T. F.

Lagoudakis, K. G.

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]

Larroque, C.

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]

Li, X.

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]

Liang, X.

Lin, Z.

Liscidini, M.

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]

Liu, X.

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]

Loew, L. M.

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]

Loncar, M.

Ma, L.

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]

Majumdar, A.

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

Malvezzi, A. M.

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]

Masselink, W. T.

Mexis, M.

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]

Minkov, M.

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]

Mishra, U. K.

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]

Mohamed, M. S.

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]

Molnar, R. J.

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]

Morandotti, R.

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]

Moss, D. J.

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]

Noda, S.

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]

O’Faolain, L.

Ochiai, T.

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

Orenstein, M.

Park, S. S.

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]

Pernice, W. H. P.

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]

Petykiewicz, J.

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]

Portalupi, S. L.

Radulaski, M.

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]

Rakher, M. T.

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]

Reardon, C.

Ricard, D.

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]

Rivoire, K.

Rodriguez, A.

Rodriguez, A. W.

Roland, I.

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]

Saab, M.-B.

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]

Sakoda, K.

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

Sanford, N. A.

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]

Sauvage, S.

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]

Savona, V.

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]

Scaccabarozzi, L.

Schuck, C.

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]

Semond, F.

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]

Shen, Y. R.

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]

Simbula, A.

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]

Slattery, O.

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]

Soljacic, M.

Song, B.

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]

Song, B.-S.

Srinivasan, K.

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]

Stone, A. D.

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]

Surya, J. B.

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]

Tanaka, Y.

Tang, H. X.

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]

Tang, X.

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]

Tran, N.-V.-Q.

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]

Tsvetkov, D. V.

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]

Upham, J.

Villeneuve, P. R.

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]

Vuckovic, J.

Wang, J.

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]

Welna, K.

Xiong, C.

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]

Yamada, S.

Yan, J.

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]

Yu, X.

Zeng, Y.

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]

Zhang, J. L.

Zhang, L.

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]

Zhen, B.

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]

Zhou, W.

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]

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]

APL Photon. (1)

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]

Appl. Phys. Lett. (4)

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]

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]

J. Appl. Phys. (1)

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]

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

J. Phys. Chem. B (1)

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]

Langmuir (1)

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]

Light Sci. Appl. (1)

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]

Nat. Biotechnol. (1)

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]

Nat. Mater. (1)

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

Nat. Photonics (1)

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]

Nat. Rev. Mater. (1)

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]

Nature (1)

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]

Opt. Express (6)

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (1)

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

Phys. Rev. B (6)

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

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

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

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]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

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]

Proc. SPIE (1)

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

Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. (a) Schematic of a photonic crystal slab of thickness d with a hexagonal lattice with lattice period a of air holes with radius r. (b) Schematic of a heterostructure cavity—dashed hexagons show the core, transition, and outer regions, which have Nc, Nt, and No layers of holes, respectively, such that the hexagon side lengths are l1=Nca, l2=(Nc+Nt)a, and l3=(Nc+Nt+No)a. In the image, Nc=Nt=No=4, and the corresponding hole radii are rc=0.2a, rt=0.26a, and ro=0.32a. (c) Photonic bands for the quasi-TE modes for a regular PhC slab with d=0.28a, r=0.22a, and refractive index n=2.32. The light cone is shaded gray. (d) Photonic bands for the quasi-TM modes for the same d and r as in (c) and slab refractive index n=2.38. The green and red bands in panels (c), (d) highlight the bands from which the heterostructure modes are later derived. The dotted green/red lines show the corresponding bands computed for r=0.25a. (e) Electric field Ex2+Ey2 in the center of the slab for the mode at the M point, marked by a cross in (c) with a k vector in the y direction. (f) Electric field Ez in the center of the slab for the mode at the Γ point, marked by a cross in (d). (g) Radiative quality factors for the two highlighted bands in (c) and (d).
Fig. 2.
Fig. 2. (a) Electric field R(Ez) in the center of the slab for a heterostructure cavity mode at reduced frequency ω¯2=ω2a/(2πc)=0.889 in a PhC with d=0.28a. The heterostructure parameters are (Nc,Nt,No)=(6,4,14) and (rc,rt,ro)=(0.22a,0.23a,0.25a), and the dashed hexagons mark the core and transition regions. (b), (c) Electric field |Ex2+Ey2| in the slab center for the same cavity, for two degenerate resonant modes at frequency ω¯1=0.444. The slab refractive index was set to 2.38 in (a) and 2.32 in (b) and (c). For a more detailed image of the structure and the calculated modes, see Supplement 1.
Fig. 3.
Fig. 3. (a) Radiative quality factors of the two FH modes and of the SH mode versus core region size Nc. The rest of the heterostructure parameters are the same as in Fig. 2. (b) The two figures of merit relevant to SH generation for the different core sizes Nc shown in (a). (c)–(e) Polar far-field emission profiles in the upper half space for the two FH modes and the SH mode, respectively (cf. Fig. 2). Dashed white lines show emission angles in steps of 10°. (f) Schematic of a proposed experimental setup for SH generation with pump excitation and signal collection from the vertical direction. (g) SH conversion efficiency in the limit of undepleted pump versus Nc for three different ratios rc of the overlap between the input/output channels and the heterostructure far field at the FH and SH frequencies, assuming no extrinsic losses (Qe). (h) Maximum attainable efficiency versus core size for three different values of the extrinsic Qe.

Equations (4)

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β1=14drϵ0ijkχijk(2)(r)(E1i*E2jE1k*+E1i*E1j*E2k)(drϵ0ϵ1(r)|E1|2)(drϵ0ϵ2(r)|E2|2)1/2,
En,p(r)=BZdkfn,p(k)eik·ρEkn(r),
β¯=λ13/2drϵ¯(r)(E1x2E2z*+E1y2E2z*)(drϵ1(r)|E1|2)(drϵ2(r)|E2|2)1/2,
PoPi2=8ω1(χeff(2)ϵ0λ1)2|β¯|2Q1t4Q1r2Q2t2Q2rr1c2r2c,