Abstract

We analyze the conical second-harmonic generation via Čerenkov-type phase matching in two-dimensional decagonal nonlinear photonic quasi-crystals for linear, circular, and elliptical polarized fundamental beams. Depending on the polarization state, we observe either centrosymmetric or noncentrosymmetric intensity modulation of the second-harmonic rings. We explain this effect by employing the concept of effective quadratic nonlinearity combined with the hexagonal symmetry of the individual ferroelectric domains.

© 2010 Optical Society of America

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  1. A. Zembrod, H. Puell, and J. Giordmaine, Opto-electronics (London) 1, 64 (1969).
    [CrossRef]
  2. J. V. Jelley, Čerenkov Radiation (Pergamon, 1958).
  3. A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
    [CrossRef]
  4. V. Vacaitis, Opt. Commun. 209, 485 (2002).
    [CrossRef]
  5. P. K. Tien, R. Ulrich, and V. Berger, Appl. Phys. Lett. 17, 447 (1970).
    [CrossRef]
  6. K. Hayata, K. Yanagawa, and M. Koshiba, Appl. Rev. Lett. 56, 206 (1990).
    [CrossRef]
  7. M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
    [CrossRef]
  8. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
    [CrossRef] [PubMed]
  9. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  10. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
    [CrossRef] [PubMed]
  11. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
    [CrossRef]
  12. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
    [CrossRef]
  13. A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
    [CrossRef]
  14. S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
    [CrossRef] [PubMed]
  15. S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
    [CrossRef] [PubMed]
  16. S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
    [CrossRef]
  17. R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
    [CrossRef]
  18. P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
    [CrossRef]
  19. R. Penrose, Bull. Inst. Math. Appl. 10, 266 (1974).
  20. Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
    [CrossRef]
  21. Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
    [CrossRef]
  22. D. H. Jundt, Opt. Lett. 22, 1553 (1997).
    [CrossRef]
  23. A. Ganany, A. Arie, and S. M. Saltiel, Appl. Phys. B 85, 97 (2006).
    [CrossRef]
  24. Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
    [CrossRef]

2009 (4)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

2008 (2)

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
[CrossRef] [PubMed]

2007 (3)

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

2006 (3)

A. Ganany, A. Arie, and S. M. Saltiel, Appl. Phys. B 85, 97 (2006).
[CrossRef]

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

2004 (1)

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

2002 (1)

V. Vacaitis, Opt. Commun. 209, 485 (2002).
[CrossRef]

2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

1998 (1)

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

1997 (1)

1996 (1)

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

1990 (2)

K. Hayata, K. Yanagawa, and M. Koshiba, Appl. Rev. Lett. 56, 206 (1990).
[CrossRef]

M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
[CrossRef]

1974 (1)

R. Penrose, Bull. Inst. Math. Appl. 10, 266 (1974).

1970 (1)

P. K. Tien, R. Ulrich, and V. Berger, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, Opto-electronics (London) 1, 64 (1969).
[CrossRef]

Alvarez-Garcia, S.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Arie, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

A. Ganany, A. Arie, and S. M. Saltiel, Appl. Phys. B 85, 97 (2006).
[CrossRef]

Bang, O.

Bausa, L. E.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Berger, V.

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

P. K. Tien, R. Ulrich, and V. Berger, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

Bloch, N.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Butashin, A. V.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Cheng, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

de Micheli, M.

M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
[CrossRef]

Dou, J.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

Fisher, R.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Fragemann, A.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Ganany, A.

A. Ganany, A. Arie, and S. M. Saltiel, Appl. Phys. B 85, 97 (2006).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

Gao, W.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Gao, Z. D.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
[CrossRef] [PubMed]

Garcia-Sole, J.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, Opto-electronics (London) 1, 64 (1969).
[CrossRef]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Hayata, K.

K. Hayata, K. Yanagawa, and M. Koshiba, Appl. Rev. Lett. 56, 206 (1990).
[CrossRef]

He, Q.

M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
[CrossRef]

Jelley, J. V.

J. V. Jelley, Čerenkov Radiation (Pergamon, 1958).

Jiang, M.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Jundt, D. H.

Kaminskii, A. A.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Koshiba, M.

K. Hayata, K. Yanagawa, and M. Koshiba, Appl. Rev. Lett. 56, 206 (1990).
[CrossRef]

Koynov, K.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Krolikowski, W.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Laurell, F.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Li, J.

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Li, M. J.

M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
[CrossRef]

Ma, B.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

Ming, N. B.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
[CrossRef] [PubMed]

Molina, P.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Nishioka, H.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Odajima, W.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Ostrowsky, D. B.

M. J. Li, M. de Micheli, Q. He, and D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990).
[CrossRef]

Pasiskevicus, V.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Penrose, R.

R. Penrose, Bull. Inst. Math. Appl. 10, 266 (1974).

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, Opto-electronics (London) 1, 64 (1969).
[CrossRef]

Qi, Z.

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
[CrossRef] [PubMed]

Qu, E.

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

Ramirez, M. O.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345 (2000).
[CrossRef] [PubMed]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, O. Bang, A. Arie, and Y. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

R. Fisher, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

A. Ganany, A. Arie, and S. M. Saltiel, Appl. Phys. B 85, 97 (2006).
[CrossRef]

Sasaki, K.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Sheng, Y.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

Tateno, M.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ulrich, and V. Berger, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

Ueda, K.

A. A. Kaminskii, H. Nishioka, K. Ueda, W. Odajima, M. Tateno, K. Sasaki, and A. V. Butashin, Quantum Electron. 26, 381 (1996).
[CrossRef]

Ulrich, R.

P. K. Tien, R. Ulrich, and V. Berger, Appl. Phys. Lett. 17, 447 (1970).
[CrossRef]

Vacaitis, V.

V. Vacaitis, Opt. Commun. 209, 485 (2002).
[CrossRef]

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

Wang, J.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Wang, T.

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

Yanagawa, K.

K. Hayata, K. Yanagawa, and M. Koshiba, Appl. Rev. Lett. 56, 206 (1990).
[CrossRef]

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, Opto-electronics (London) 1, 64 (1969).
[CrossRef]

Zhang, D.

Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Cheng, and D. Zhang, Appl. Phys. B 87, 603 (2007).
[CrossRef]

Y. Sheng, J. Dou, J. Li, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 101109 (2007).
[CrossRef]

Y. Sheng, T. Wang, B. Ma, E. Qu, B. Cheng, and D. Zhang, Appl. Phys. Lett. 88, 041121 (2006).
[CrossRef]

Zhang, H.

P. Molina, S. Alvarez-Garcia, M. O. Ramirez, J. Garcia-Sole, L. E. Bausa, H. Zhang, W. Gao, J. Wang, and M. Jiang, Appl. Phys. Lett. 94, 071111 (2009).
[CrossRef]

Zhang, Y.

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Figures (4)

Fig. 1
Fig. 1

(a) Phase-matching condition for Čerenkov-type SHG. (b) Schematic of the experiment. (c), (d) Micrographs of the quasiperiodic domain structures at the ± Z surfaces, respectively.

Fig. 2
Fig. 2

(a) Experimentally recorded and (b), (c) theoretically predicted Čerenkov SH rings with fundamental beams of different polarizations. The angles marked in the figure correspond to δ in Eqs. (1, 2).

Fig. 3
Fig. 3

Polarization properties of the Čerenkov SH rings. From left to right images are taken without analyzer, analyzer oriented horizontally, analyzer at 60°, and analyzer oriented vertically. The input beam is circularly polarized.

Fig. 4
Fig. 4

Definitions of the angles and vectors for the derivation of the effective nonlinearities.

Equations (3)

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d eff ( o ) = d 22 [ cos ( φ + 2 γ ) i   sin   2 δ   sin ( φ + 2 γ ) ] ,
d eff ( e ) = d 32   sin   θ e   cos   2 δ + d 22   cos   θ e [ sin ( φ + 2 γ ) + i   sin   2 δ   cos ( φ + 2 γ ) ] ,
I 2 ( o , e ) ( φ ) = A | d eff ( o , e ) | 2 | g ( φ ) | 2 L 2 ( sin [ ( | G | Δ k ) L / 2 ] ( | G | Δ k ) L / 2 ) 2 ,

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