Abstract

We theoretically and numerically investigate the quadratic cascading effect of third-harmonic (TH) generation in a locally quasi-periodic nonlinear photonic structure. We study the effect of structure parameters on the acceptance bandwidth and conversion efficiency of the cascading process. We demonstrate that the conversion efficiency of the cascading process can be enhanced by using a longer locally quasi-periodic nonlinear photonic crystal, without adversely affecting the acceptance bandwidth of the emitted radiation.

© 2014 Optical Society of America

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  1. J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
    [CrossRef]
  2. S. Zhu, Y. Zhu, B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
    [CrossRef]
  3. K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
    [CrossRef] [PubMed]
  4. C. Zhang, H. Wei, Y. Y. Zhu, H. T. Wang, S. N. Zhu, N. B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).
    [CrossRef]
  5. N. Fujioka, S. Ashihara, H. Ono, T. Shimura, K. Kuroda, “Group-velocity-mismatch compensation in cascaded third-harmonic generation with two dimensional quasi-phase-matching gratings,” Opt. Lett. 31, 2780–2782 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. M. Asobe, I. Yokohama, H. Itoh, T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
    [CrossRef]
  14. K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
    [CrossRef]
  15. A. Tehranchi, R. Kashyap, “Design of novel unapodized and apodized step-chirped quasi-phase matched gratings for broadband frequency converters based on second harmonic generation,” IEEE J. Lightwave Technology, IEEE J. Lightwave Technol. 26, 343–349, (2008).
    [CrossRef]
  16. A. Tehranchi, R. Morandotti, R. Kashyap, “Efficient flattop ultra-wideband wavelength converters based on double-pass cascaded sum and difference frequency generation using engineered chirped gratings,” Opt. Express 19, 22528–22534 (2011).
    [CrossRef] [PubMed]
  17. J. Yang, X. P. Hu, P. Xu, X. J. Lv, C. Zhang, G. Zhao, H. J. Zhou, S. N. Zhu, “Chirped-quasi-periodic structure for quasi-phase-matching,” Opt. Express 18, 14717–14723 (2010).
    [CrossRef] [PubMed]
  18. Y. Sheng, W. Krolikowski, “Broadband frequency tripling in locally ordered nonlinear photonic crystal,” Opt. Express 21, 4475–4480 (2013).
    [CrossRef] [PubMed]
  19. W. Wang, V. Roppo, K. Kalinowski, Y. Kong, D. N. Neshev, C. Cojocaru, J. Trull, R. Vilaseca, K. Staliunas, W. Krolikowski, S. M. Saltiel, Yu. Kivshar, “Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media,” Opt. Express 17, 20117–20123 (2009).
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    [CrossRef] [PubMed]
  21. K. Fradkin-Kashi, A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum. Elect. 35, 1649–1656 (1999).
    [CrossRef]
  22. G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quant. Electron. 16, 373–375 (1984).
    [CrossRef]
  23. M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Elect. 28, 2631–2654 (1992).
    [CrossRef]

2013

2011

2010

2009

2008

A. Tehranchi, R. Kashyap, “Design of novel unapodized and apodized step-chirped quasi-phase matched gratings for broadband frequency converters based on second harmonic generation,” IEEE J. Lightwave Technology, IEEE J. Lightwave Technol. 26, 343–349, (2008).
[CrossRef]

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

2007

2006

2004

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

2002

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

2001

1999

K. Fradkin-Kashi, A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum. Elect. 35, 1649–1656 (1999).
[CrossRef]

1998

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

1997

1994

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

1992

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

1984

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quant. Electron. 16, 373–375 (1984).
[CrossRef]

Arie, A.

I. Varon, G. Porat, A. Arie, “Controlling the disorder properties of quadratic nonlinear photonic crystals,” Opt. Lett. 36, 3978–3980 (2011).
[CrossRef] [PubMed]

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

K. Fradkin-Kashi, A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum. Elect. 35, 1649–1656 (1999).
[CrossRef]

Ashihara, S.

Asobe, M.

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Byer, R.L.

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

Cha, M.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Chen, Y. B.

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

Cojocaru, C.

DeLong, K. W.

Ding, Y. J.

J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
[CrossRef]

Dou, J.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Du, Y.

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

Edwards, G. J.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quant. Electron. 16, 373–375 (1984).
[CrossRef]

Fejer, M.

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

Fittinghoff, D. N.

Fradkin-Kashi, K.

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

K. Fradkin-Kashi, A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum. Elect. 35, 1649–1656 (1999).
[CrossRef]

Fujioka, N.

Hu, X. P.

Itoh, H.

Jundt, D.H.

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

Kaino, T.

Kalinowski, K.

Kashyap, R.

A. Tehranchi, R. Morandotti, R. Kashyap, “Efficient flattop ultra-wideband wavelength converters based on double-pass cascaded sum and difference frequency generation using engineered chirped gratings,” Opt. Express 19, 22528–22534 (2011).
[CrossRef] [PubMed]

A. Tehranchi, R. Kashyap, “Design of novel unapodized and apodized step-chirped quasi-phase matched gratings for broadband frequency converters based on second harmonic generation,” IEEE J. Lightwave Technology, IEEE J. Lightwave Technol. 26, 343–349, (2008).
[CrossRef]

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

Khurgin, J.B.

J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
[CrossRef]

Kitamura, K.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Kivshar, Yu.

Kong, Y.

Koynov, K.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Krolikowski, W.

Krumbugel, M. A.

Kurimura, S.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Kuroda, K.

Lawrence, M.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quant. Electron. 16, 373–375 (1984).
[CrossRef]

Lee, S. J.

J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
[CrossRef]

Li, J.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Liu, Z. W.

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

Lv, X. J.

Ma, B.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Magel, G.A.

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

Ming, B.

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

Ming, N. B.

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

C. Zhang, H. Wei, Y. Y. Zhu, H. T. Wang, S. N. Zhu, N. B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).
[CrossRef]

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

Morandotti, R.

Neshev, D. N.

Obeidat, A.

J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
[CrossRef]

Ono, H.

Petrov, G. I.

Porat, G.

Roppo, V.

Rosenman, G.

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

Saltiel, S. M.

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

Sheng, Y.

Y. Sheng, W. Krolikowski, “Broadband frequency tripling in locally ordered nonlinear photonic crystal,” Opt. Express 21, 4475–4480 (2013).
[CrossRef] [PubMed]

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Shimura, T.

Staliunas, K.

Sweetser, J. N.

Taira, T.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Tehranchi, A.

A. Tehranchi, R. Morandotti, R. Kashyap, “Efficient flattop ultra-wideband wavelength converters based on double-pass cascaded sum and difference frequency generation using engineered chirped gratings,” Opt. Express 19, 22528–22534 (2011).
[CrossRef] [PubMed]

A. Tehranchi, R. Kashyap, “Design of novel unapodized and apodized step-chirped quasi-phase matched gratings for broadband frequency converters based on second harmonic generation,” IEEE J. Lightwave Technology, IEEE J. Lightwave Technol. 26, 343–349, (2008).
[CrossRef]

Trebino, R.

Trull, J.

Urenski, P.

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

Varon, I.

Vilaseca, R.

Wang, H. T.

Wang, W.

Wei, H.

Xu, P.

J. Yang, X. P. Hu, P. Xu, X. J. Lv, C. Zhang, G. Zhao, H. J. Zhou, S. N. Zhu, “Chirped-quasi-periodic structure for quasi-phase-matching,” Opt. Express 18, 14717–14723 (2010).
[CrossRef] [PubMed]

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

Yakovlev, V. V.

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

Yang, J.

Yokohama, I.

Yu, N. E.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Zhang, C.

Zhang, D.

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

Zhao, G.

Zhi, M.

Zhou, H. J.

Zhu, S.

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

Zhu, S. N.

Zhu, Y.

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

Zhu, Y. Y.

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

C. Zhang, H. Wei, Y. Y. Zhu, H. T. Wang, S. N. Zhu, N. B. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. 26, 899–901 (2001).
[CrossRef]

Appl. Phys. Lett.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).
[CrossRef]

Y. Du, S. N. Zhu, Y. Y. Zhu, P. Xu, C. Zhang, Y. B. Chen, Z. W. Liu, N. B. Ming, “Parametric and cascaded parametric interactions in a quasiperiodic optical superlattice,” Appl. Phys. Lett. 81, 1573–1575 (2002).
[CrossRef]

Y. Sheng, K. Koynov, J. Dou, B. Ma, J. Li, D. Zhang, “Collinear second harmonic generations in a nonlinear photonic quasicrystal,” Appl. Phys. Lett. 92, 201113 (2008).
[CrossRef]

IEEE J. Lightwave Technology, IEEE J. Lightwave Technol.

A. Tehranchi, R. Kashyap, “Design of novel unapodized and apodized step-chirped quasi-phase matched gratings for broadband frequency converters based on second harmonic generation,” IEEE J. Lightwave Technology, IEEE J. Lightwave Technol. 26, 343–349, (2008).
[CrossRef]

IEEE J. Quantum Electron.

K. Mizuuchi, K. Yamamoto, M. Kato, H. Sato, “Broadening of the phase-matching bandwidth in quasi-phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 30, 1596–604 (1994).
[CrossRef]

IEEE J. Quantum. Elect.

K. Fradkin-Kashi, A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum. Elect. 35, 1649–1656 (1999).
[CrossRef]

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

J. Opt. Soc. Am.

J.B. Khurgin, A. Obeidat, S. J. Lee, Y. J. Ding, “Cascaded optical nonlinearities: microscopic understanding as a collective effect,” J. Opt. Soc. Am. 14, 1977–1983 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Opt. Quant. Electron.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quant. Electron. 16, 373–375 (1984).
[CrossRef]

Phys. Rev. Lett.

K. Fradkin-Kashi, A. Arie, P. Urenski, G. Rosenman, “Multiple nonlinear optical interactions with arbitrary wave vector differences,” Phys. Rev. Lett. 88, 023903 (2002).
[CrossRef] [PubMed]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[CrossRef]

Science

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

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Figures (4)

Fig. 1
Fig. 1

The concept of the locally quasi-periodic quadratic structure for broadband second harmonic and cascading third harmonic generation. The locally quasi-periodic structure is constructed by repeating a set of quasi-periodic segments (consisting blocks A and B that are arranged into a quasi-periodic sequence) and separating them with an extended domain of random length. The insets below depict schematically the SHG and THG in the structure.

Fig. 2
Fig. 2

Dependence of normalized harmonic intensity on the incident fundamental wavelengths for SHG process (a) and SFG process (b), respectively, in the locally quasi-periodic nonlinear photonic structure with the same number M = 40 of building blocks in each quasi-periodic segment. The spectrum plots of harmonic waves (solid lines) in the figures are sampled at different lengths of the crystal where L = nxh, with nx = 217, 218, 219, which agreeing well with the spectrum lines (dotted lines) calculated from Eqs. (9) and (12), respectively. The intensities have been calculated by averaging over 512 realizations of nonlinear photonic structures.

Fig. 3
Fig. 3

Normalized SH intensity (a) and TH intensity (b) as a function of the incident fundamental wavelengths in the locally quasi-periodic domain structures with different values of number M = 30, 40, 50 in each segment, but with the same crystal length L. The corresponding acceptance bandwidth (FWHM) is 56nm, 42nm and 33nm for the second harmonic and 14nm, 10nm and 8nm for the third harmonic, respectively. The intensities have been obtained by averaging over 512 realizations of nonlinear photonic structures.

Fig. 4
Fig. 4

Dependence of SH intensity (a) and TH intensity (b) on the interaction distance in the locally quasi-periodic nonlinear photonic structures with number M = 40 in each segment for different incident fundamental wavelengths λ = 1.496μm, 1.50μm, and 1.504μm. The analytical results derived from Eqs. (13) and (14) are plotted as dotted lines in (a) and (b), respectively, which show a good agreement with the corresponding numerical simulation. The results have been calculated by averaging over 512 realizations of nonlinear photonic structures.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

d E 2 ( x ) d x = i β 1 E 1 2 d ( x ) e i Δ k 1 x ,
d E 3 ( x ) d x = i β 2 E 1 E 2 ( x ) d ( x ) e i Δ k 2 x ,
E 2 n = Γ 1 Δ x sinc ( Δ k 1 2 Δ x ) e i Δ k 1 ( x n 1 + x n ) / 2 ,
E 3 n = 1 2 Γ 1 Γ 2 Δ x 2 sinc ( Δ k 1 2 Δ x ) sinc ( Δ k 2 2 Δ x ) e i Δ k 3 ( x n 1 + x n ) / 2 + Γ 2 E 2 ( x n 1 ) Δ x sinc ( Δ k 2 2 Δ x ) e i Δ k 2 ( x n 1 + x n ) / 2 ,
E 2 = n = 1 N E 2 n e i ϕ n ,
E 3 = n = 1 N E 3 n e i Φ n .
I 2 = N I 2 n + n = 1 N m = 1 , m n N E 2 n * E 2 m e i ( ϕ n ϕ m ) ,
I 3 = n = 1 N I 3 n + n = 1 N m = 1 , m n N E 3 n * E 3 m e i ( Φ n Φ m ) ,
I 2 n = Γ 1 2 Δ x 2 sinc 2 ( Δ k 1 2 Δ x ) .
E 2 ( n ) = n Γ 1 Δ x sinc ( Δ k 1 2 Δ x ) e i Δ k 1 ( x n 1 + x n ) / 2 .
E 3 n = ( n 1 + 1 2 ) Γ 1 Γ 2 Δ x 2 sinc ( Δ k 1 2 Δ x ) sinc ( Δ k 2 2 Δ x ) e i Δ k 3 ( x n 1 + x n ) / 2 ,
I 3 n = ( n 1 + 1 2 ) 2 Γ 1 2 Γ 2 2 Δ x 4 sinc 2 ( Δ k 1 2 Δ x ) sinc 2 ( Δ k 2 2 Δ x ) .
I 2 = N Γ 1 2 Δ x 2 sinc 2 ( Δ k 1 2 Δ x ) ,
I 3 = N 2 2 Γ 1 2 Γ 2 2 Δ x 4 sinc 2 ( Δ k 1 2 Δ x ) sinc 2 ( Δ k 2 2 Δ x ) .

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