Abstract

By directly simulating Maxwell’s equations via the finite-difference time-domain (FDTD) method, we numerically demonstrate the possibility of achieving high-efficiency second harmonic generation (SHG) in a structure consisting of a microscale doubly-resonant ring resonator side-coupled to two adjacent waveguides. We find that ≳ 94% conversion efficiency can be attained at telecom wavelengths, for incident powers in the milliwatts, and for reasonably large bandwidths (Q ∼ 1000s). We demonstrate that in this high efficiency regime, the system also exhibits limit-cycle or bistable behavior for light incident above a threshold power. Our numerical results agree to within a few percent with the predictions of a simple but rigorous coupled-mode theory framework.

© 2012 OSA

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2011 (9)

P. S. Kuo and G. S. Solomon, “On- and off-resonance second-harmonic generation in GaAs microdisks,” Opt. Express 19(18), 16,898–16,918 (2011).
[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99(1), 013,114 (2011).
[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19(22), 22,198–22,207 (2011).
[CrossRef]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett. 98(26), 263,113 (2011).
[CrossRef]

Y. Dumeige and P. Feron, “Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling,” Phys. Rev. A 84(4),  043,847 (2011).
[CrossRef]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11,415–11,421 (2011).
[CrossRef]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

M. Gandomkar and V. Ahmadi, “Design and analysis of enhanced second harmonic generation in AlGaAs/AlOx microring waveguide,” Opt. Express 19(10), 9408–9418 (2011).
[CrossRef] [PubMed]

L. Caspani, D. Duchesne, K. Dolgaleva, S. J. Wagner, M. Ferrera, L. Razzari, A. Pasquazi, M. Peccianti, D. J. Moss, J. S. Aitchison, and R. Morandotti, “Optical frequency conversion in integrated devices,” J. Opt. Soc. Am. B 28(12), A67–A82 (2011).
[CrossRef]

2010 (3)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97(4), 043,103 (2010).
[CrossRef]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett. 104(15),  153,901 (2010).
[CrossRef] [PubMed]

2009 (2)

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljacic, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant Kerr cavities,” Phys. Rev. A 79(1), 013,812 (2009).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22,609–22,615 (2009).
[CrossRef]

2008 (4)

K. K. Y. Lee, Y. Avniel, and S. G. Johnson, “Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides,” Opt. Express 16, 9261–9275 (2008).
[CrossRef] [PubMed]

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
[CrossRef]

H. Lohmeyer, J. Kalden, K. Sebald, C. Kruse, D. Hommel, and J. Gutowski, “Fine tuning of quantum-dot pillar microcavities by focused ion beam milling,” Appl. Phys. Lett. 92(1), 011,116 (2008).
[CrossRef]

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
[CrossRef]

2007 (3)

2006 (4)

M. Liscidini and L. A. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016,613 (2006).
[CrossRef]

I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
[CrossRef]

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74,  063,804 (2006).
[CrossRef]

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

2005 (4)

B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B 22,  1378 (2005).
[CrossRef]

G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
[CrossRef]

Q. Xu and M. Lipson, “Carrier-induced optical bistability in Silicon ring resonators,” Opt. Lett. 31(3), 341–343 (2005).
[CrossRef]

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
[CrossRef]

2004 (3)

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84, 1242–1245 (2004).
[CrossRef]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q ring resonators in thin silicon-on-insulator,” Appl. Phys. Lett. 85(16), 3346–3347 (2004).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear Optics and Crystalline Whispering Gallery Mode Cavities,” Phys. Rev. Lett. 92(4),  043,903 (2004).
[CrossRef] [PubMed]

2003 (2)

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

P. Scotto, P. Colet, and M. San Miguel, “All-optical image processing with cavity type II second-harmonic generation,” Opt. Lett. 28, 1695 (2003).
[CrossRef] [PubMed]

2002 (3)

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. E 65, 085,106 (2002).

A. H. Norton and C. M. de Sterke, “Optimal poling of nonlinear photonic crystals for frequency conversion,” Opt. Lett. 28,  188 (2002).

2001 (4)

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

G. McConnell, A. I. Ferguson, and N. Langford, “Cavity-augmented frequency tripling of a continuous wave mode-locked laser,” J. Phys. D: Appl.Phys 34, 2408 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition,” Phys. Rev. E 63,  046,609 (2001).
[CrossRef]

2000 (1)

I. I. Zootoverkh, K. N. V, and E. G. Lariontsev, “Enhancement of the efficiency of second-harmonic generation in microlaser,” Quantum Electronics 30, 565 (2000).
[CrossRef]

1999 (1)

1998 (1)

V. A. Mandelshtam and H. S. Taylor, “Erratum: “Harmonic inversion of time signals and its applications”,” J. Chem. Phys. 109, 4128 (1998).
[CrossRef]

1997 (3)

V. Berger, “Second-harmonic generation in monolithic cavities,” J. Opt. Soc. Am. B 14, 1351 (1997).
[CrossRef]

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature 391, 463–466 (1997).

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997). See erratum.
[CrossRef]

1995 (1)

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Optics Communications 113, 463 (1995).
[CrossRef]

1994 (2)

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

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117 (1994).

1993 (2)

Z. Y. Ou and H. J. Kimble, “Enhanced conversion efficiency for harmonic generation with double resonance,” Opt. Lett. 18, 1053–1055 (1993).
[CrossRef] [PubMed]

M. Ohashi, T. Kondo, and R. Ito, “Determination of quadratic nonlinear optical coefficient of AlxGa1−xAs system by the method of reflected second harmonics,” J. Appl. Phys. 74(1), 596–601 (1993).
[CrossRef]

1992 (2)

K. Grygiel and P. Szlatchetka, “Chaos in second-harmonic generation of light. The case of a strain of pulses.”Opt. Comm. 91, 241–246 (1992).
[CrossRef]

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant. Elec. 28(11), 2631–2654 (1992).
[CrossRef]

1981 (1)

M. Brieger, H. Busener, A. Hese, F. V. Moers, and A. Renn, “Enhancement of single frequency SHG in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

1980 (1)

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I: Semiclassical theory,” Optica Acta. 27(3), 321–335 (1980).
[CrossRef]

1977 (1)

A. I. Gerguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

1970 (1)

R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6, 215–223 (1970).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

1962 (1)

J. A. Armstrong, N. loembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Aers, G. C.

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
[CrossRef]

Aguanno, G. D.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Ahmadi, V.

Aitchison, J. S.

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett. 104(15),  153,901 (2010).
[CrossRef] [PubMed]

Andreani, L. A.

M. Liscidini and L. A. Andreani, “Second-harmonic generation in doubly resonant microcavities with periodic dielectric mirrors,” Phys. Rev. E 73, 016,613 (2006).
[CrossRef]

M. Liscidini and L. A. Andreani, “Highly efficient second-harmonic generation in doubly resonant planar microcavities,” Appl. Phys. Lett. 85, 1883 (2004).

Andreani, L. C.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. loembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Asobe, M.

I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
[CrossRef]

Avniel, Y.

Avrahami, Y.

G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
[CrossRef]

Baehr-Jones, T.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q ring resonators in thin silicon-on-insulator,” Appl. Phys. Lett. 85(16), 3346–3347 (2004).
[CrossRef]

Baets, R.

B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B 22,  1378 (2005).
[CrossRef]

Balakin, A. V.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition,” Phys. Rev. E 63,  046,609 (2001).
[CrossRef]

Barbastathis, G.

G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
[CrossRef]

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84, 1242–1245 (2004).
[CrossRef]

Bedford, R.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature 391, 463–466 (1997).

V. Berger, “Second-harmonic generation in monolithic cavities,” J. Opt. Soc. Am. B 14, 1351 (1997).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express 15(24), 16,161–16,176 (2007).
[CrossRef]

Bertolotti, M.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Bienstman, P.

B. Maes, P. Bienstman, and R. Baets, “Modeling second-harmonic generation by use of mode expansion,” J. Opt. Soc. Am. B 22,  1378 (2005).
[CrossRef]

Bloemer, M. J.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Bowden, C. M.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Boyd, G. D.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, California, 1992).

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature 391, 463–466 (1997).

Bravo-Abad, J.

J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express 15(24), 16,161–16,176 (2007).
[CrossRef]

Brieger, M.

M. Brieger, H. Busener, A. Hese, F. V. Moers, and A. Renn, “Enhancement of single frequency SHG in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Bristow, A. D.

Büchter, D.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
[CrossRef]

Buckley, S.

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett. 98(26), 263,113 (2011).
[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99(1), 013,114 (2011).
[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19(22), 22,198–22,207 (2011).
[CrossRef]

Busener, H.

M. Brieger, H. Busener, A. Hese, F. V. Moers, and A. Renn, “Enhancement of single frequency SHG in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Bushuev, V. A.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition,” Phys. Rev. E 63,  046,609 (2001).
[CrossRef]

Businaro, L.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

Byer, R.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant. Elec. 28(11), 2631–2654 (1992).
[CrossRef]

Caspani, L.

Centini, M.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Chak, P.

Chen, C. L.

C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006).
[CrossRef]

Cheung, E. C.

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Optics Communications 113, 463 (1995).
[CrossRef]

Colet, P.

Cowan, A. R.

A. R. Cowan and J. F. Young, “Mode matching for second-harmonic generation in photonic crystal waveguides,” Phys. Rev. E 65, 085,106 (2002).

Dalacu, D.

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
[CrossRef]

de Sterke, C. M.

A. H. Norton and C. M. de Sterke, “Optimal poling of nonlinear photonic crystals for frequency conversion,” Opt. Lett. 28,  188 (2002).

Dolgaleva, K.

Drummond, P. D.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I: Semiclassical theory,” Optica Acta. 27(3), 321–335 (1980).
[CrossRef]

Duchesne, D.

Ducuing, J.

J. A. Armstrong, N. loembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dumeige, Y.

Y. Dumeige and P. Feron, “Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling,” Phys. Rev. A 84(4),  043,847 (2011).
[CrossRef]

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74,  063,804 (2006).
[CrossRef]

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Dunn, M. H.

A. I. Gerguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Elser, D.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett. 104(15),  153,901 (2010).
[CrossRef] [PubMed]

Fabrizio, E. D.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

Fallahi, M.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Fan, L.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Fan, S.

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
[CrossRef]

Fejer, M.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant. Elec. 28(11), 2631–2654 (1992).
[CrossRef]

Fejer, M. M.

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
[CrossRef]

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

Ferguson, A. I.

G. McConnell, A. I. Ferguson, and N. Langford, “Cavity-augmented frequency tripling of a continuous wave mode-locked laser,” J. Phys. D: Appl.Phys 34, 2408 (2001).
[CrossRef]

Feron, P.

Y. Dumeige and P. Feron, “Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling,” Phys. Rev. A 84(4),  043,847 (2011).
[CrossRef]

Y. Dumeige and P. Feron, “Wispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74,  063,804 (2006).
[CrossRef]

Ferrera, M.

Fiedler, K.

R. Paschotta, K. Fiedler, P. Kurz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. Lett. 58, 117 (1994).

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature 391, 463–466 (1997).

Fong, K. Y.

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

Foster, M. A.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11,415–11,421 (2011).
[CrossRef]

Frederick, S.

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
[CrossRef]

Fürst, J. U.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett. 104(15),  153,901 (2010).
[CrossRef] [PubMed]

Gaeta, A. L.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11,415–11,421 (2011).
[CrossRef]

Gandomkar, M.

Gerguson, A. I.

A. I. Gerguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

Grundkötter, W.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
[CrossRef]

Grygiel, K.

K. Grygiel and P. Szlatchetka, “Chaos in second-harmonic generation of light. The case of a strain of pulses.”Opt. Comm. 91, 241–246 (1992).
[CrossRef]

Guizzeti, G.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

Gutowski, J.

H. Lohmeyer, J. Kalden, K. Sebald, C. Kruse, D. Hommel, and J. Gutowski, “Fine tuning of quantum-dot pillar microcavities by focused ion beam milling,” Appl. Phys. Lett. 92(1), 011,116 (2008).
[CrossRef]

Hader, J.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Harris, J. S.

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
[CrossRef]

Hashemi, H.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljacic, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant Kerr cavities,” Phys. Rev. A 79(1), 013,812 (2009).
[CrossRef]

Hatami, F.

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett. 98(26), 263,113 (2011).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97(4), 043,103 (2010).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22,609–22,615 (2009).
[CrossRef]

Haus, H.

G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
[CrossRef]

Haus, J. W.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Herrmann, H.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
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K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22,609–22,615 (2009).
[CrossRef]

Rodriguez, A.

Rodriguez, A. W.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljacic, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant Kerr cavities,” Phys. Rev. A 79(1), 013,812 (2009).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express 15(24), 16,161–16,176 (2007).
[CrossRef]

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A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
[CrossRef]

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A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Letters to Nature 391, 463–466 (1997).

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

Ryu, K. K.

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

San Miguel, M.

Sandhu, S.

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
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J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
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G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
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Scherer, A.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q ring resonators in thin silicon-on-insulator,” Appl. Phys. Lett. 85(16), 3346–3347 (2004).
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C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

Scotto, P.

Sebald, K.

H. Lohmeyer, J. Kalden, K. Sebald, C. Kruse, D. Hommel, and J. Gutowski, “Fine tuning of quantum-dot pillar microcavities by focused ion beam milling,” Appl. Phys. Lett. 92(1), 011,116 (2008).
[CrossRef]

Seneviratne, D.

G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
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Shimony, Y.

Shkurinov, A. P.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band edge under the quasiphase matching condition,” Phys. Rev. E 63,  046,609 (2001).
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Sibilia, C.

G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Generalized coupled-mode theory for χ(2) interactions in finite multi-layered structures,” J. Opt. Soc. Am. B 19, 2111–2122 (2002).
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Sipe, J. E.

Smirl, A. L.

Smith, H. I.

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84, 1242–1245 (2004).
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R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6, 215–223 (1970).
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W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
[CrossRef]

Soljacic, M.

H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljacic, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly resonant Kerr cavities,” Phys. Rev. A 79(1), 013,812 (2009).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express 15(24), 16,161–16,176 (2007).
[CrossRef]

A. Rodriguez, M. Soljačić, J. D. Joannopulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
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Solomon, G. S.

P. S. Kuo and G. S. Solomon, “On- and off-resonance second-harmonic generation in GaAs microdisks,” Opt. Express 19(18), 16,898–16,918 (2011).
[CrossRef]

Steven, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
[CrossRef]

Stolz, W.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
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J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally Phase-Matched Second-Harmonic Generation in a Whispering-Gallery-Mode Resonator,” Phys. Rev. Lett. 104(15),  153,901 (2010).
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I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
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K. Grygiel and P. Szlatchetka, “Chaos in second-harmonic generation of light. The case of a strain of pulses.”Opt. Comm. 91, 241–246 (1992).
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L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Tang, H. X.

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
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J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
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I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
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G. Nielson, D. Seneviratne, F. Lopez-Royo, P. Rakich, Y. Avrahami, M. Watts, H. Haus, H. Tuller, and G. Barbastathis, “Integrated wavelength-selective optical MEMS switching using ring resonator filters,” Photonics Technology Letters, IEEE 17(6), 1190 –1192 (2005).
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I. I. Zootoverkh, K. N. V, and E. G. Lariontsev, “Enhancement of the efficiency of second-harmonic generation in microlaser,” Quantum Electronics 30, 565 (2000).
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Vannahme, C.

W. Sohler, H. Hu, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. O. H. Suche, R. Nouroozi, and Y. Min, “Integrated Optical Devices in Lithium Niobate,” Opt. Photon. News 19(1), 24–31 (2008).
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A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
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G. D. Aguanno, M. Centini, M. Scalora, C. Sibilia, Y. Dumeige, P. Vidavovic, J. A. Levenson, M. J. Bloemer, C. M. Bowden, J. W. Haus, and M. Bertolotti, “Photonic band edge effects in finite structures and applications to χ(2) interactions,” Phys. Rev. E 64, 016,609 (2001).

Vittorio, M. D.

A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzeti, L. C. Andreani, F. Romanato, L. Businaro, E. D. Fabrizio, A. Passaseo, and M. D. Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B 68, 161,306 (2003).
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K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19(22), 22,198–22,207 (2011).
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K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99(1), 013,114 (2011).
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K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett. 98(26), 263,113 (2011).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97(4), 043,103 (2010).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22,609–22,615 (2009).
[CrossRef]

Wagner, S. J.

Walker, C.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q ring resonators in thin silicon-on-insulator,” Appl. Phys. Lett. 85(16), 3346–3347 (2004).
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[CrossRef]

Williams, R. L.

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
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Wong, C. W.

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84, 1242–1245 (2004).
[CrossRef]

Xiong, C.

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

Xu, Q.

XZakharian, A. R.

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
[CrossRef]

Yamanaka, K.

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
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Yang, Z.

Yoshikuni, Y.

I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
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I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
[CrossRef]

Zootoverkh, I. I.

I. I. Zootoverkh, K. N. V, and E. G. Lariontsev, “Enhancement of the efficiency of second-harmonic generation in microlaser,” Quantum Electronics 30, 565 (2000).
[CrossRef]

Appl. Phys. Lett (1)

L. Fan, H. Ta-Chen, M. Fallahi, J. T. Murray, R. Bedford, Y. Kaneda, J. Hader, A. R. XZakharian, J. Moloney, S. W. Koch, and W. Stolz, “Tunable watt-level blue-green vertical-external-cavity surface-emitting lasers by intracavity frequency doubling,” Appl. Phys. Lett 88, 117–251,119 (2006).
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[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant high quality photonic crystal nanocavities,” Appl. Phys. Lett. 99(1), 013,114 (2011).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, and J. Vuckovic, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97(4), 043,103 (2010).
[CrossRef]

K. Rivoire, S. Buckley, F. Hatami, and J. Vuckovic, “Second harmonic generation in GaP photonic crystal waveguides,” Appl. Phys. Lett. 98(26), 263,113 (2011).
[CrossRef]

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84, 1242–1245 (2004).
[CrossRef]

D. Dalacu, S. Frederick, P. J. Poole, G. C. Aers, and R. L. Williams, “Postfabrication fine-tuning of photonic crystal microcavities in InAs/InP quantum dot membranes,” Appl. Phys. Lett. 87(15), 151,107 (2005).
[CrossRef]

H. Lohmeyer, J. Kalden, K. Sebald, C. Kruse, D. Hommel, and J. Gutowski, “Fine tuning of quantum-dot pillar microcavities by focused ion beam milling,” Appl. Phys. Lett. 92(1), 011,116 (2008).
[CrossRef]

J. Pan, Y. Hio, K. Yamanaka, S. Sandhu, L. Scaccabarozzi, R. Timp, M. L. Povinelli, S. Fan, M. M. Fejer, and J. S. Harris, “Aligning microcavity resonances in silicon photonic-crystal slabs using laser-pumped thermal tuning,” Appl. Phys. Lett. 92(10), 103,114 (2008).
[CrossRef]

Comp. Phys. Comm. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Steven, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Comm. 181, 687–702 (2010).
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V. A. Mandelshtam and H. S. Taylor, “Erratum: “Harmonic inversion of time signals and its applications”,” J. Chem. Phys. 109, 4128 (1998).
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J. of Appl. Phys. (1)

I. Tomita, M. Asobe, H. Suzuki, J. Yumoto, and Y. Yoshikuni, “Broadband quasi-phase-matched second-harmonic generation in a nonlinear photonic crystal,” J. of Appl. Phys. 100(2), 023,120 (2006).
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J. Opt. Soc. Am. B (5)

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Opt. Comm. (1)

K. Grygiel and P. Szlatchetka, “Chaos in second-harmonic generation of light. The case of a strain of pulses.”Opt. Comm. 91, 241–246 (1992).
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P. S. Kuo and G. S. Solomon, “On- and off-resonance second-harmonic generation in GaAs microdisks,” Opt. Express 19(18), 16,898–16,918 (2011).
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C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10,462–10,470 (2011).
[CrossRef]

J. Bravo-Abad, A. W. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal nanocavities,” Opt. Express 15(24), 16,161–16,176 (2007).
[CrossRef]

K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vuckovic, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22,609–22,615 (2009).
[CrossRef]

K. Rivoire, S. Buckley, and J. Vuckovic, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19(22), 22,198–22,207 (2011).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).

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Figures (10)

Fig. 1:
Fig. 1:

Schematic ring-resonator waveguide-cavity system: input light from a waveguide supporting a propagating mode of frequency ω1 (input power P1, in2) is coupled to a ring-resonator cavity mode of frequency ω1, converted to a cavity mode of twice the frequency ω2 = 2ω1 by a nonlinear χ(2) process, and coupled out by another waveguide supporting a propagating mode of frequency ω2 (the waveguide does not support a propagating ω1 mode).

Fig. 2:
Fig. 2:

Plot of the frequency difference Δω = ω2 – 2ω1 (units of 2πc/a) of two LiNbO3 ring-resonator modes of frequencies ω1 and ω2, and azimuthal momentum m1 = 15 and m2 = 30, respectively, corresponding to two different ring-resonator geometries (insets), as a function of inner radius R. The blue and red lines correspond to the single-ring (right inset) and double-ring resonators.

Fig. 3:
Fig. 3:

(a) Semilog plot of the radiative (Q rad ), waveguide-coupling (Q w ), and total (Q tot ) lifetimes of the ω1 mode of Fig. 5, as a function of the ring-waveguide separation d1. (b) Corresponding transmission spectrum at various separations.

Fig. 4:
Fig. 4:

Band diagram or frequency ω (units of 2πc/a) as a function of wave-vector k (units of 2π/a), corresponding to the fundamental (red line) and second-order (blue line) modes of two different LiNbO3 waveguides of thickness w1 = 0.5a and w2 = 0.35a, respectively. Here, a denotes the thickness of the double-ring resonator of Fig. 2. The bottom and upper insets show the E z field profile (blue/white/red denote positive/zero/negative amplitude) of two different modes, with frequencies ω1 = 0.277(2πc/a) and ω2 = 2ω1, and corresponding wave-vectors k1 = 0.39(2π/a) and k2 = 2k1, respectively.

Fig. 5:
Fig. 5:

E z field snapshot of two double-ring (Fig. 2 inset) resonator modes propagating counter-clockwise, with frequencies ω1 = 0.277(2πc/a) (left) and ω2 = 2ω1 (right) and azimuthal momentum m1 = 15 and m2 = 30 (effective k1 = 0.39(2π/a) and k2 = 2k1). The ring resonator is side-coupled to two adjacent waveguides, separated by a distance d1 = d2 = 0.5a, supporting phase-matched propagating modes at ω1 (top waveguide) and ω2 (bottom waveguide).

Fig. 6:
Fig. 6:

(a) Plot of SHG efficiency η = P SH /P in versus P in , for the double-ring resonator system of Fig. 5 with waveguide-separations d1 = 1.05a and d2 = 0.7a, obtained both via FDTD simulations (red circles) and CMT (blue line). The gray region denotes the presence of instabilities that lead to limit-cycle behavior. (b) An example of a limit cycle at point A. (c) E z temporal snapshot of the nonlinear conversion process at point B (the efficiency peak).

Fig. 7:
Fig. 7:

Maximum efficiency vs. separation distance between input waveguide and ring resonator. (inset: Conversion efficiency from CMT and FDTD in the case d1 = 0.9a)

Fig. 8:
Fig. 8:

Schematic diagram of 3d ring-resonator waveguide-cavity system.

Fig. 9:
Fig. 9:

Field distribution (left) and corresponding lateral cross-section (right) for the (a) ω1 (E r component) and (b) ω2 (E z component) modes.

Fig. 10:
Fig. 10:

Band diagram of the 3d waveguides. The bottom and upper insets show the E r and E z field profile (blue/white/red denote positive/zero/negative amplitude) of two different modes, with frequencies ω1 = 0.24(2πc/a) and ω2 = 2ω1, respectively.

Equations (6)

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T ( ω ) = P out P in = ω 0 2 ( 1 / Q w 1 / Q rad ) 2 + 4 ( ω ω 0 ) 2 ω 0 2 ( 1 / Q w + 1 / Q rad ) 2 + 4 ( ω ω 0 ) 2 ,
β 1 = 1 4 d 3 x i j k ε 0 χ i j k ( 2 ) [ E 1 i * ( E 2 j E 1 k * + E 1 j * E 2 k ) ] ( d 3 x ε | E 1 | 2 ) ( d 3 x ε | E 2 | 2 ) 1 / 2 ,
| P crit | 2 = ω 1 Q 1 2 | β 1 | 2 Q w , 2 Q w , 1 3 ,
E 1 x E 1 y = ( E 1 r 2 E 1 θ 2 ) sin ( 2 θ ) / 2 + E 1 r E 1 θ cos ( 2 θ )
E 1 x E 2 y + E 2 x E 1 y = 2 ( E 1 r E 2 r E 1 θ E 2 θ ) sin ( θ ) cos ( θ ) + ( E 1 r E 2 θ + E 2 r E 1 θ ) [ cos 2 ( θ ) sin 2 ( θ ) ] .
β 1 = 1 2 r d r d z ε 0 χ x y z ( 2 ) [ E 1 r E 1 θ E 2 z + ( E 1 r E 2 θ + E 2 r E 1 θ ) E 1 z ] ( d 3 x ε | E 1 | 2 ) ( d 3 x ε | E 2 | 2 ) 1 / 2 ± i 4 r d r d z ε 0 χ x y z ( 2 ) [ 2 ( E 1 r E 2 r E 1 θ E 2 θ ) E 1 z + ( E 1 r 2 E 1 θ 2 ) E 2 z ] ( d 3 x ε | E 1 | 2 ) ( d 3 x ε | E 2 | 2 ) 1 / 2 ,

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