Abstract

We study experimentally and theoretically the Čerenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced 270 times by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vector of the crystal can be used to compensate for the phase mismatch in the transverse direction enabling interaction in the nonlinear Bragg diffraction regime.

© 2012 Optical Society of America

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  1. S. Saltiel, Y. Sheng, N. Voloch-Bloch, D. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
    [CrossRef]
  2. S. M. Saltiel, D. N. Neshev, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
    [CrossRef]
  3. P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
    [CrossRef]
  4. M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, Opt. Lett. 36, 4371 (2011).
    [CrossRef]
  5. Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
    [CrossRef]
  6. Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
    [CrossRef]
  7. S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
    [CrossRef]
  8. Y. Sheng, V. Roppo, Q. Kong, K. Kalinowski, Q. Wang, C. Cojocaru, J. Trull, and W. Krolikowski, Opt. Lett. 36, 2593 (2011).
    [CrossRef]
  9. K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
    [CrossRef]
  10. Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, J. Opt. Soc. Am. B 29, 312 (2012).
    [CrossRef]
  11. T. Ellenbogen and A. Arie, Opt. Commun. 277, 423 (2007).
    [CrossRef]
  12. A. Shapira and A. Arie, Opt. Lett. 36, 1933 (2011).
    [CrossRef]
  13. X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
    [CrossRef]
  14. H. Ren, X. Deng, and X. Chen, arXiv:1010.1593v1 (2010).
  15. S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
    [CrossRef]
  16. Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
    [CrossRef]
  17. M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]

2012 (1)

2011 (5)

A. Shapira and A. Arie, Opt. Lett. 36, 1933 (2011).
[CrossRef]

Y. Sheng, V. Roppo, Q. Kong, K. Kalinowski, Q. Wang, C. Cojocaru, J. Trull, and W. Krolikowski, Opt. Lett. 36, 2593 (2011).
[CrossRef]

M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, Opt. Lett. 36, 4371 (2011).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

2010 (3)

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef]

2009 (2)

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

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

2008 (1)

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

2007 (1)

T. Ellenbogen and A. Arie, Opt. Commun. 277, 423 (2007).
[CrossRef]

2001 (2)

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

1992 (1)

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Arie, A.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

A. Shapira and A. Arie, Opt. Lett. 36, 1933 (2011).
[CrossRef]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef]

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

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

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

T. Ellenbogen and A. Arie, Opt. Commun. 277, 423 (2007).
[CrossRef]

Aubry, R.

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

Ayoub, M.

Bang, O.

Bausá, L. E.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Best, A.

Butt, H.-J.

Byer, R.

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Chen, X.

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

H. Ren, X. Deng, and X. Chen, arXiv:1010.1593v1 (2010).

Cojocaru, C.

Deng, X.

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

H. Ren, X. Deng, and X. Chen, arXiv:1010.1593v1 (2010).

Denz, C.

Ellenbogen, T.

T. Ellenbogen and A. Arie, Opt. Commun. 277, 423 (2007).
[CrossRef]

Fejer, M.

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Fischer, R.

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

García, B. J.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Grand, Y. L.

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

Imbrock, J.

Jundt, D.

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Kalinowski, K.

Kivshar, Y.

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

Kivshar, Y. S.

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

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

Kong, Q.

Kong, Y.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

Koynov, K.

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef]

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

Krolikowski, W.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, J. Opt. Soc. Am. B 29, 312 (2012).
[CrossRef]

Y. Sheng, V. Roppo, Q. Kong, K. Kalinowski, Q. Wang, C. Cojocaru, J. Trull, and W. Krolikowski, Opt. Lett. 36, 2593 (2011).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef]

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

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

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

Lao, H.

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

Magel, G.

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Mattauch, S.

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

Missey, M.

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

Molina, P.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Neshev, D.

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

Neshev, D. N.

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

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

Odin, C.

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

Powers, P.

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

Qi Wang, C. C.

Ramírez, M. O.

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Ren, H.

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

H. Ren, X. Deng, and X. Chen, arXiv:1010.1593v1 (2010).

Roedig, P.

Roppo, V.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, J. Opt. Soc. Am. B 29, 312 (2012).
[CrossRef]

Y. Sheng, V. Roppo, Q. Kong, K. Kalinowski, Q. Wang, C. Cojocaru, J. Trull, and W. Krolikowski, Opt. Lett. 36, 2593 (2011).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

Rouede, D.

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

Russell, S.

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

Saltiel, S.

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

Saltiel, S. M.

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

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

Schepler, K.

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

Shapira, A.

Sheng, Y.

Y. Sheng, Q. Kong, V. Roppo, K. Kalinowski, C. C. Qi Wang, and W. Krolikowski, J. Opt. Soc. Am. B 29, 312 (2012).
[CrossRef]

Y. Sheng, V. Roppo, Q. Kong, K. Kalinowski, Q. Wang, C. Cojocaru, J. Trull, and W. Krolikowski, Opt. Lett. 36, 2593 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef]

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

Shiloh, R.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

Trull, J.

Voloch-Bloch, N.

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

Wang, Q.

Wang, W.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

Appl. Phys. B (1)

X. Deng, H. Ren, H. Lao, and X. Chen, Appl. Phys. B 100, 755 (2010).
[CrossRef]

Appl. Phys. Lett. (3)

P. Molina, M. O. Ramírez, B. J. García, and L. E. Bausá, Appl. Phys. Lett. 96, 261111 (2010).
[CrossRef]

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, Y. Kong, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[CrossRef]

K. Kalinowski, Q. Kong, V. Roppo, A. Arie, Y. Sheng, and W. Krolikowski, Appl. Phys. Lett. 99, 181128 (2011).
[CrossRef]

IEEE J. Quantum Electron. (3)

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

S. Russell, P. Powers, M. Missey, and K. Schepler, IEEE J. Quantum Electron. 37, 877 (2001).
[CrossRef]

M. Fejer, G. Magel, D. Jundt, and R. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

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

Opt. Commun. (2)

Y. L. Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, Opt. Commun. 200, 249 (2001).
[CrossRef]

T. Ellenbogen and A. Arie, Opt. Commun. 277, 423 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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

Other (1)

H. Ren, X. Deng, and X. Chen, arXiv:1010.1593v1 (2010).

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Figures (4)

Fig. 1.
Fig. 1.

(a) The concept of Čerenkov SH in one-dimensional NLPCs. White and gray colors represent oppositely oriented ferroelectric domains. (b) and (c) Phase-matching diagram for general (b) and Čerenkov (c) SH process.

Fig. 2.
Fig. 2.

(a)–(c) Color map sequence showing the origin of Čerenkov SH radiation (color coding in logarithmic sale and adjusted arbitrary to emphasize key features). (d) Čerenkov SH enhancement profiles along ČSH+ and ČSH as indicated in (c).

Fig. 3.
Fig. 3.

(a) Experimentally measured SH enhancement η as a function of FF incidence angle α1 and external SH emission angle α2. (b) and (c) detailed scan around points where Čerenkov emission curve crosses Raman–Nath emission curves (m=1,3,4,5). (d) Numerically calculated SH enhancement map (see text for details). Color coding is the same on all maps.

Fig. 4.
Fig. 4.

Measured (solid line) and theoretical fit (dashed line) ČSH+ enhancement.

Equations (1)

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

I2=|E1|4ω2Lz2deff22c3ϵ0Lx2n22|M(qx)|2sinc2(Lzqz2),

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