Abstract

We propose optical frequency comb generation in a monolithic micro-ring resonator. Being different from the previously reported nonlinear optical frequency combs, our scheme is based on more efficient quadratic frequency conversion rather than the third-order nonlinearity. To overcome the phase mismatch, a partly poled nonlinear ring is employed. Cascading second harmonic generation and parametric down conversion processes thus are realized through quasi-phase matching (QPM). Coupling equations are used to describe the related nonlinear interactions among different whispering-gallery modes, showing some interesting characteristics that are different from conventional QPM technology.

© 2012 OSA

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  1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
    [CrossRef] [PubMed]
  2. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
    [CrossRef]
  3. I. H. Agha, Y. Okawachi, and A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express 17(18), 16209–16215 (2009).
    [CrossRef] [PubMed]
  4. S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
    [CrossRef]
  5. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
    [CrossRef] [PubMed]
  6. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [CrossRef]
  7. P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35(1), 23–39 (1963).
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    [CrossRef] [PubMed]
  10. Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
    [CrossRef]
  11. A. Rose and D. R. Smith, “Overcoming phase mismatch in nonlinear metamaterials,” Opt. Mater. Express 1(7), 1232–1243 (2011).
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    [CrossRef]
  13. 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), 153901 (2010).
    [CrossRef] [PubMed]
  14. V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. B 20(6), 1304–1308 (2003).
    [CrossRef]
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2011 (3)

2010 (3)

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (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), 153901 (2010).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

2009 (1)

2007 (2)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

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), 043903 (2004).
[CrossRef] [PubMed]

2003 (1)

1997 (2)

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n(e), in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997).
[CrossRef] [PubMed]

S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

1996 (1)

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

1963 (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35(1), 23–39 (1963).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Agha, I. H.

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), 153901 (2010).
[CrossRef] [PubMed]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Chen, X. F.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[CrossRef] [PubMed]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[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), 153901 (2010).
[CrossRef] [PubMed]

Eom, T. J.

Feng, B. H.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Foster, M. A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Franken, P. A.

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35(1), 23–39 (1963).
[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), 153901 (2010).
[CrossRef] [PubMed]

Gaeta, A. L.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

I. H. Agha, Y. Okawachi, and A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express 17(18), 16209–16215 (2009).
[CrossRef] [PubMed]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Hu, W.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Hu, X. K.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Ilchenko, V. S.

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), 043903 (2004).
[CrossRef] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. B 20(6), 1304–1308 (2003).
[CrossRef]

Jundt, D. H.

Jung, C.

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Ko, D. K.

Lassen, M.

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), 153901 (2010).
[CrossRef] [PubMed]

Lee, J.

Lee, Y. L.

Leuchs, G.

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), 153901 (2010).
[CrossRef] [PubMed]

Levy, J. S.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Lipson, M.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Lu, Y. L.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Lu, Y. Q.

X. S. Song, Z. Y. Yu, Q. Wang, F. Xu, and Y. Q. Lu, “Polarization independent quasi-phase-matched sum frequency generation for single photon detection,” Opt. Express 19(1), 380–386 (2011).
[CrossRef] [PubMed]

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Luo, G. P.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Maleki, L.

Marquardt, C.

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), 153901 (2010).
[CrossRef] [PubMed]

Matsko, A. B.

Ming, N. B.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Ming, N.-B.

S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Mohageg, M.

Noh, Y. C.

Oh, K.

Okawachi, Y.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Rose, A.

Savchenkov, A. A.

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Shin, W.

Smith, D. R.

Song, X. S.

Strekalov, D. V.

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), 153901 (2010).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[CrossRef] [PubMed]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Wang, Q.

Ward, J. F.

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35(1), 23–39 (1963).
[CrossRef]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Wu, Z. J.

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xu, F.

X. S. Song, Z. Y. Yu, Q. Wang, F. Xu, and Y. Q. Lu, “Polarization independent quasi-phase-matched sum frequency generation for single photon detection,” Opt. Express 19(1), 380–386 (2011).
[CrossRef] [PubMed]

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Xue, C. C.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Yu, B. A.

Yu, Z. Y.

X. S. Song, Z. Y. Yu, Q. Wang, F. Xu, and Y. Q. Lu, “Polarization independent quasi-phase-matched sum frequency generation for single photon detection,” Opt. Express 19(1), 380–386 (2011).
[CrossRef] [PubMed]

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Zhang, X. L.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Zheng, J. J.

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

Zhu, S. N.

S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Q. Lu, Y. L. Lu, C. C. Xue, J. J. Zheng, X. F. Chen, G. P. Luo, N. B. Ming, B. H. Feng, and X. L. Zhang, “Femtosecond violet light generation by quasi-phase-matched frequency doubling in optical superlattice LiNbO3,” Appl. Phys. Lett. 69(21), 3155–3157 (1996).
[CrossRef]

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

Nat. Photonics (1)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Phys. Rev. B (1)

Z. J. Wu, X. K. Hu, Z. Y. Yu, W. Hu, F. Xu, and Y. Q. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

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), 153901 (2010).
[CrossRef] [PubMed]

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), 043903 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35(1), 23–39 (1963).
[CrossRef]

Science (2)

S. N. Zhu, Y. Y. Zhu, and N.-B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[CrossRef] [PubMed]

Other (2)

Kiyotaka Sasagawa, and Masahiro Tsuchiya, “High efficiency third harmonic generation in PPMgLN disk resonator,” in CLEO 2007 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), Paper CThC6.

J. Heebner, R. Grover, and T. A. Ibrahim, Optical Microresonators (Springer, 2008), Chap. 3.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of a partially poled LN ring coupled with a waveguide; (b) Schematic of the similarity between a partially poled LN ring and a PPLN.

Fig. 2
Fig. 2

The (a) internal and (b) external SHG efficiencies with different pump power, where the solid, dashed and dash-dot curves correspond to τ = 0.1, 0.2, 0.3, respectively; (c) The external SHG efficiencies with different τ, where the solid, dashed and dash-dot curves correspond to pump power = 0.1, 1, 3 MW/m.

Fig. 3
Fig. 3

The output spectra of (a) the second harmonic mode and (b) the pump mode and the comb-like modes generated from the second harmonic mode.

Equations (8)

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E z = n a n f n ( r ) ,
f n (r,ϕ)= g n (r) e inϕ ,
d a p (t) dt =- γ p a p + n,m ω p κ pnm a n a m ,
d a n (t) dt =- γ n a n + n,m ω n F nm κ pnm * a p a m * ,
1 2 d | a n (t) | 2 dt =- γ n | a n | 2 + n,m ω n 2 F nm κ pnm * a p a m * a n + τ 2 P ε 0 ,
κ pnm =-i d r 3 χ (2) f p ( r ) f n ( r ) f m ( r ) =-i g p (r) g n (r) g m (r) χ (2) (ϕ) e i(m+n-p)ϕ dϕ .
Δ=m+np=0.
h(ϕ)={ 1 0<ϕθ 1 θ<ϕ2π .

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