Abstract

We report nonlinear Cherenkov radiations (NCRs) in a Ti in-diffused LiNbO3 planar waveguide. The radiations were modulated exploiting different polarizations and orders of the guided modes, the fundamental wavelengths and the working temperatures. Some characteristics related to NCRs, such as radiation angles and relative intensities were investigated in detail. The experimental results matched well with theoretical calculations.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. P. A. Cherenkov, “Visible emission of clean liquids by action of radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).
  2. S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
    [Crossref]
  3. V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
    [Crossref] [PubMed]
  4. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
    [Crossref] [PubMed]
  5. C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
    [Crossref]
  6. C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
    [Crossref]
  7. H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
    [Crossref] [PubMed]
  8. R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
    [Crossref]
  9. M. Bazzana and C. Sada, “Optical waveguides in lithium niobate: Recent developments and applications,” Appl. Phys. Rev. 2(4), 040603 (2015).
    [Crossref]
  10. J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
    [Crossref] [PubMed]
  11. A. Yariv, Quantum Electronics (Wiley, 1975), Chap. 16.
  12. A. N. Kaul and K. Thyagarajan, “Inverse WKB method for refractive index profile estimation of monomode graded index planar optical waveguides,” Opt. Commun. 48(5), 313–316 (1984).
    [Crossref]
  13. P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
    [Crossref]
  14. P. Ganguly, J. C. Biswas, and S. K. Lahiri, “Analysis of titanium concentration and refractive index profiles of Ti: LiNbO3 channel waveguide,” J. Opt. 39(4), 175–180 (2010).
    [Crossref]
  15. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [Crossref]
  16. A. Gedeon, “Comparison between rigorous theory and WKB-analysis of modes in graded-index waveguides,” Opt. Commun. 12(3), 329–332 (1974).
    [Crossref]
  17. H. Tamada, “Coupled-mode analysis of second harmonic generation in the form of Cerenkov radiation from a planar optical waveguide,” IEEE J. Quantum Electron. 27(3), 502–508 (1991).
    [Crossref]

2016 (1)

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

2015 (2)

M. Bazzana and C. Sada, “Optical waveguides in lithium niobate: Recent developments and applications,” Appl. Phys. Rev. 2(4), 040603 (2015).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

2013 (1)

2012 (3)

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

2010 (1)

P. Ganguly, J. C. Biswas, and S. K. Lahiri, “Analysis of titanium concentration and refractive index profiles of Ti: LiNbO3 channel waveguide,” J. Opt. 39(4), 175–180 (2010).
[Crossref]

2009 (1)

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

2008 (1)

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

1996 (1)

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

1991 (1)

H. Tamada, “Coupled-mode analysis of second harmonic generation in the form of Cerenkov radiation from a planar optical waveguide,” IEEE J. Quantum Electron. 27(3), 502–508 (1991).
[Crossref]

1984 (2)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

A. N. Kaul and K. Thyagarajan, “Inverse WKB method for refractive index profile estimation of monomode graded index planar optical waveguides,” Opt. Commun. 48(5), 313–316 (1984).
[Crossref]

1974 (1)

A. Gedeon, “Comparison between rigorous theory and WKB-analysis of modes in graded-index waveguides,” Opt. Commun. 12(3), 329–332 (1974).
[Crossref]

1934 (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).

An, N.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Arie, A.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Bazzana, M.

M. Bazzana and C. Sada, “Optical waveguides in lithium niobate: Recent developments and applications,” Appl. Phys. Rev. 2(4), 040603 (2015).
[Crossref]

Biswas, J. C.

P. Ganguly, J. C. Biswas, and S. K. Lahiri, “Analysis of titanium concentration and refractive index profiles of Ti: LiNbO3 channel waveguide,” J. Opt. 39(4), 175–180 (2010).
[Crossref]

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

Chen, C. D.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

Chen, X.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Cheng, Y.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Cherenkov, P. A.

P. A. Cherenkov, “Visible emission of clean liquids by action of radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).

Cojocaru, C.

Datt, S.

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

Deng, X.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Du, L.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Fang, W.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Fang, Z.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Ganguly, P.

P. Ganguly, J. C. Biswas, and S. K. Lahiri, “Analysis of titanium concentration and refractive index profiles of Ti: LiNbO3 channel waveguide,” J. Opt. 39(4), 175–180 (2010).
[Crossref]

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

Gao, Z. D.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Gedeon, A.

A. Gedeon, “Comparison between rigorous theory and WKB-analysis of modes in graded-index waveguides,” Opt. Commun. 12(3), 329–332 (1974).
[Crossref]

Hu, X. P.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

Kalinowski, K.

Kaul, A. N.

A. N. Kaul and K. Thyagarajan, “Inverse WKB method for refractive index profile estimation of monomode graded index planar optical waveguides,” Opt. Commun. 48(5), 313–316 (1984).
[Crossref]

Kivshar, Y.

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Koynov, K.

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Krolikowski, W.

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Lahiri, S. K.

P. Ganguly, J. C. Biswas, and S. K. Lahiri, “Analysis of titanium concentration and refractive index profiles of Ti: LiNbO3 channel waveguide,” J. Opt. 39(4), 175–180 (2010).
[Crossref]

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[Crossref]

Lin, J.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Ming, N. B.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Neshev, D.

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Ni, R.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

Qi, Z.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Qiao, L.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Ren, H.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Roppo, V.

Sada, C.

M. Bazzana and C. Sada, “Optical waveguides in lithium niobate: Recent developments and applications,” Appl. Phys. Rev. 2(4), 040603 (2015).
[Crossref]

Saltiel, S.

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Sen, D. C.

P. Ganguly, D. C. Sen, S. Datt, J. C. Biswas, and S. K. Lahiri, “Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides,” Fiber Integr. Opt. 15(2), 135–147 (1996).
[Crossref]

Sheng, Y.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Cerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Song, J.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Tamada, H.

H. Tamada, “Coupled-mode analysis of second harmonic generation in the form of Cerenkov radiation from a planar optical waveguide,” IEEE J. Quantum Electron. 27(3), 502–508 (1991).
[Crossref]

Thyagarajan, K.

A. N. Kaul and K. Thyagarajan, “Inverse WKB method for refractive index profile estimation of monomode graded index planar optical waveguides,” Opt. Commun. 48(5), 313–316 (1984).
[Crossref]

Trull, J.

Voloch-Bloch, N.

S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkovtype second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
[Crossref]

Wang, M.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Wang, N.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Wu, Y.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

Xu, P.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

Xu, Y.

J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5(1), 8072 (2015).
[Crossref] [PubMed]

Xu, Y. L.

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

Zhang, Y.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Zhao, G.

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

Zheng, Y.

H. Ren, X. Deng, Y. Zheng, N. An, and X. Chen, “Nonlinear Cherenkov radiation in an anomalous dispersive medium,” Phys. Rev. Lett. 108(22), 223901 (2012).
[Crossref] [PubMed]

Zhu, S. N.

R. Ni, L. Du, Y. Wu, X. P. Hu, J. Zou, Y. Sheng, A. Arie, Y. Zhang, and S. N. Zhu, “Nonlinear Cherenkov difference-frequency generation exploiting birefringence of KTP,” Appl. Phys. Lett. 108(3), 031104 (2016).
[Crossref]

C. D. Chen, X. P. Hu, Y. L. Xu, P. Xu, G. Zhao, and S. N. Zhu, “Čerenkov difference frequency generation in a two-dimensional nonlinear photonic crystal,” Appl. Phys. Lett. 101(7), 071113 (2012).
[Crossref]

C. D. Chen, Y. Zhang, G. Zhao, X. P. Hu, P. Xu, and S. N. Zhu, “Experimental realization of Cerenkov up-conversions in a 2D nonlinear photonic crystal,” J. Phys. D Appl. Phys. 45(40), 405101 (2012).
[Crossref]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov Radiation in Nonlinear Photonic Crystal Waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Zou, J.

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Figures (7)

Fig. 1
Fig. 1

(a) Temperature dependent dispersion relations of the FW at 1064nm and SH wave at 532 nm; (b) Zoom in view of the dispersion relations when the FW is in the TE0 and TE1 guided mode, while SH is e-polarized.

Fig. 2
Fig. 2

Temperature dependent dispersion relations of the FW at 1342nm and SH wave at 671 nm.

Fig. 3
Fig. 3

Schematic experimental setup. The inset on the upper left illustrates the origination of the two SH spots on the screen.

Fig. 4
Fig. 4

Cherenkov SHGs and SFGs at the fundamental wavelength of 1064nm. The left part illustrates the radiation patterns on the screen. The middle part is a zoom in view of the radiations in group ①, ② and ③. The right part gives the phase-matching types and the involved guide modes for the four groups of radiations.

Fig. 5
Fig. 5

oo-e type NCRs at different temperatures. The guide modes involved are indicated beside the radiation spots.

Fig. 6
Fig. 6

Experimental (the circle) and theoretical (the line) external radiation angles varying with temperatures for different types of NCRs.

Fig. 7
Fig. 7

Three groups of NCRs at the fundamental wavelength of 1342nm were shown in the left part. Right part is the zoom in view of the radiation spots in group ② and ③. The guide modes involved are indicated beside the radiation spots.

Tables (1)

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Table 1 Calculated relative output intensities of NCRs

Equations (3)

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P y =2 ε 0 ( d 22 E y 2 +2 d 31 E y E z ) P z =2 ε 0 ( d 31 E y 2 + d 33 E z 2 )
β i (ω)+ β j (ω)=k(2ω)cos(θ)
P SH P FW 2 [ ω 2 d (2) β SH S] 2 1 tanθ

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