Abstract

In this paper, the Cerenkov-type second-harmonic generation in bulk optical superlattices has been studied theoretically with the non-paraxial wave equations, where the paraxial approximation is avoided. The corresponding phase-matching condition is determined strictly by solving the non-paraxial wave equations under proper boundary conditions, and the result coincides well with the traditional Cerenkov phase-matching condition. In addition, a backward Cerenkov phase-matching condition is deduced from the wave equations as well, and the physical requirement of this condition is clarified.

© 2016 Optical Society of America

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References

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  1. A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
    [Crossref]
  2. P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
    [Crossref]
  3. U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).
  4. V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
    [Crossref]
  5. A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
    [Crossref]
  6. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
    [Crossref] [PubMed]
  7. C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
    [Crossref]
  8. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
    [Crossref] [PubMed]
  9. J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
    [Crossref]
  10. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
    [Crossref] [PubMed]
  11. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
    [Crossref] [PubMed]
  12. S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, “Cerenkov-type second-harmonic generation in two-dimensional nonlinear photonic structures,” IEEE J. Quantum Electron. 45(11), 1465–1472 (2009).
    [Crossref]
  13. Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
    [Crossref] [PubMed]
  14. Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
    [Crossref] [PubMed]
  15. W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35(22), 3790–3792 (2010).
    [Crossref] [PubMed]
  16. P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
    [Crossref]
  17. M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Domain-shape-based modulation of Čerenkov second-harmonic generation in multidomain strontium barium niobate,” Opt. Lett. 36(22), 4371–4373 (2011).
    [Crossref] [PubMed]
  18. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
    [Crossref]
  19. Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J. Opt. Soc. Am. B 29(3), 312–318 (2012).
    [Crossref]
  20. M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
    [Crossref]
  21. Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
    [Crossref] [PubMed]
  22. 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]

2012 (2)

2011 (2)

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Domain-shape-based modulation of Čerenkov second-harmonic generation in multidomain strontium barium niobate,” Opt. Lett. 36(22), 4371–4373 (2011).
[Crossref] [PubMed]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

2010 (5)

2009 (1)

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

2008 (4)

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

2004 (1)

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

2003 (1)

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

1996 (1)

V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
[Crossref]

1992 (1)

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

1974 (1)

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

1970 (1)

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
[Crossref]

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
[Crossref]

1962 (1)

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

Abdullin, U. A.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

Amstrong, J. A.

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

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.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35(22), 3790–3792 (2010).
[Crossref] [PubMed]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Ayoub, M.

Bausá, L. E.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Best, A.

Bloembergen, N.

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

Butt, H.-J.

Byer, R. L.

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Chen, C.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[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]

Chirkin, A. S.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

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]

Denz, C.

Ducuing, J.

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

Fejer, M. M.

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Fischer, R.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Fragemann, A.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

Gao, Z. D.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

García, B. J.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
[Crossref]

Hu, X.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Hu, X. P.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

Ibanescu, M.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

Imbrock, J.

Joannopoulos, J. D.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

Johnson, S. G.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

Jundt, D. H.

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Kalinowski, K.

Kivshar, Y.

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

Kivshar, Y. S.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Kong, Q.

Kong, Y.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35(22), 3790–3792 (2010).
[Crossref] [PubMed]

Koynov, K.

Krolikowski, W.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J. Opt. Soc. Am. B 29(3), 312–318 (2012).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010).
[Crossref] [PubMed]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35(22), 3790–3792 (2010).
[Crossref] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

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

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Laurell, F.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

Liu, Y.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Luo, C.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

Lv, X.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Lyakhov, G. A.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

Mager, G. A.

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

Mahalakshmi, V.

V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
[Crossref]

Martin, R. J.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
[Crossref]

Ming, N. B.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Molina, P.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Neshev, D.

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

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Pasiskevicius, V.

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

Pershan, P. S.

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

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
[Crossref]

Qi, Z.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Qi Wang, C. C.

Qin, Y. Q.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

Ramírez, M. O.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

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]

Roedig, P.

Roppo, V.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, “Theoretical study of Čerenkov-type second-harmonic generation in periodically poled ferroelectric crystals,” J. Opt. Soc. Am. B 29(3), 312–318 (2012).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Rudenko, O. V.

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

Saltiel, S.

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

Saltiel, S. M.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Sheng, Y.

Shenoy, M. R.

V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
[Crossref]

Shiloh, R.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

Su, J.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Thyagarajan, K.

V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
[Crossref]

Tien, P. K.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
[Crossref]

Ulrich, R.

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
[Crossref]

Voloch-Bloch, N.

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

Wang, W.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, “Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure,” Opt. Lett. 35(22), 3790–3792 (2010).
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C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
[Crossref]

Zhang, C.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

Zhang, Y.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Zhao, G.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

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.

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

Zhu, S. N.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Zhu, Y. Y.

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

Appl. Phys. Lett. (5)

P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17(10), 447–450 (1970).
[Crossref]

A. Fragemann, V. Pasiskevicius, and F. Laurell, “Second-order nonlinearities in the domain walls of periodically poled KTiOPO4,” Appl. Phys. Lett. 85(3), 375–377 (2004).
[Crossref]

C. Chen, J. Su, Y. Zhang, P. Xu, X. Hu, G. Zhao, Y. Liu, X. Lv, and S. Zhu, “Mode-coupling Cerenkov sum-frequency-generation in a multimode planar waveguide,” Appl. Phys. Lett. 97(16), 161112 (2010).
[Crossref]

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, “Directional dependence of the second harmonic response in two-dimensional nonlinear photonic crystals,” Appl. Phys. Lett. 96(26), 261111 (2010).
[Crossref]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, “Čerenkov third-harmonic generation in χ(2) nonlinear photonic crystal,” Appl. Phys. Lett. 98(24), 241114 (2011).
[Crossref]

IEEE J. Quantum Electron. (3)

M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[Crossref]

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

V. Mahalakshmi, M. R. Shenoy, and K. Thyagarajan, “Evolution of the intensity profile of Cerenkov second-harmonic radiation with propagation distance in planar waveguides,” IEEE J. Quantum Electron. 32(1), 137–144 (1996).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (3)

Optoelectronics (1)

A. Zembrod, H. Puell, and J. Giordmaine, “Surface radiation from non-linear optical polarisation,” Optoelectronics 1(1), 64–66 (1969).
[Crossref]

Phys. Rev. (1)

J. A. Amstrong, 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. Lett. (5)

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear Bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Y. Q. Qin, C. Zhang, Y. Y. Zhu, X. P. Hu, and G. Zhao, “Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures,” Phys. Rev. Lett. 100(6), 063902 (2008).
[Crossref] [PubMed]

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]

S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second-harmonic conical waves via nonlinear bragg diffraction,” Phys. Rev. Lett. 100(10), 103902 (2008).
[Crossref] [PubMed]

Science (1)

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, “Difference-frequency excitation in nonlinear optics and the conditions for Cerenkov-radiation emission,” Sov. Phys. JETP 39(4), 633–637 (1974).

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Figures (4)

Fig. 1
Fig. 1

A schematic of the CSHG process in optical superlattices.

Fig. 2
Fig. 2

The intensity distribution for the SH wave when k 2z =2 k 1 . The arrow indicates the propagation direction of the SH wave which is normal to the direction of the main flow.

Fig. 3
Fig. 3

The radiation intensity of the whole plane. We assumed that k 1 =1 and k 2 =2.01 . The angle measured in the figure is between 5.70° and 5.75° while the theoretical result is 5.72°.

Fig. 4
Fig. 4

The mathematical intensity distribution for the SH wave when k 2z =2 k 1 . The arrow indicates the propagation direction of the SH wave which is opposite to its main flow.

Equations (10)

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

k 2z = k 2 cosθ=2 k 1
Δk k 2x 2 2 k 2 =0
{ 2 A 2 x 2 + 2 A 2 z 2 + k 2 2 A 2 = 1 2 K 1 f( x ) A 1 2 (x)exp(2i k 1 z), 0<z<L 2 A 2 x 2 + 2 A 2 z 2 + k 2 2 A 2 =0, z<0,z>L
d 2 A 2 ( k 2x ,z) d z 2 + k 2z 2 A 2 ( k 2x ,z)=g( k 2x )exp(2i k 1 z)
A 2 ( k 2x ,z)={ C 1 exp(i k 2z z)+ C 2 exp(i k 2z z)+ 1 ( k 2z +2 k 1 )( k 2z 2 k 1 ) g( k 2x )exp(2i k 1 z), k 2z ±2 k 1 C 1 exp(i k 2z z)+ C 2 exp(i k 2z z) iz 4 k 1 g( k 2x )exp(2i k 1 z), k 2z =±2 k 1
{ A ' ( k 2x ,z=0)=i k 2z A( k 2x ,z=0) A ' ( k 2x ,z=L)=i k 2z A( k 2x ,z=L)
{ C 1 = g( k 2x ) 2 k 2z ( k 2z 2 k 1 ) C 2 = g( k 2x ) 2 k 2z ( k 2z +2 k 1 ) exp[ i( k 2z +2 k 1 )L ] C 3 = g( k 2x ) 2 k 2z ( k 2z +2 k 1 ) { exp[ i( k 2z +2 k 1 )L ]1 } C 4 = g( k 2x ) 2 k 2z ( k 2z 2 k 1 ) { exp[ i( k 2z 2 k 1 )L ]1 }
A 2 ( k 2x ,z)= g( k 2x ) 16 k 1 2 { exp(2i k 1 z)+exp[ 2i k 1 (z2L) ]+4i k 1 zexp(2i k 1 z) }
2 k 1 = k 2z = k 2 2 k 2x 2 = k 2 k 2x 2 2 k 2 k 2x 4 8 k 2 2
A 2 ( k 2x ,z)= g( k 2x ) 16 k 1 2 [ exp(2i k 1 z)exp(2i k 1 z)+4i k 1 (zL)exp(2i k 1 z) ]

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