Abstract

We investigate theoretically the Čerenkov-type second-harmonic generation in two-dimensional bulk nonlinear photonic crystal with longitudinal modulation of the χ(2) nonlinearity. We show that in this scheme the Čerenkov radiation can be achieved simultaneously at multiple directions with comparable intensities. The angles of emission are controllable by the spatial modulation of the nonlinearity. We propose a design of the periodically poled domain pattern, which maximizes the efficiency of the second-harmonic emission.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  2. 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]
  3. J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  4. S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
    [CrossRef]
  5. A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
    [CrossRef]
  6. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
    [CrossRef]
  7. A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
    [CrossRef]
  8. A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
    [CrossRef]
  9. 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]
  10. P. K. Tien, R. Ulrich, and R. J. Martin, Appl. Phys. Lett. 17, 447 (1970).
    [CrossRef]
  11. Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, Phys. Rev. Lett. 100, 163904 (2008).
    [CrossRef] [PubMed]
  12. Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
    [CrossRef]
  13. W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, Opt. Lett. 35, 3790 (2010).
    [CrossRef] [PubMed]
  14. Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
    [CrossRef] [PubMed]
  15. J. Chen and X. Chen, Opt. Express 18, 15597 (2010).
    [CrossRef] [PubMed]
  16. J. Chen and X. Chen, J. Opt. Soc. Am. B 28, 241 (2011).
    [CrossRef]
  17. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
    [CrossRef]

2011

2010

2009

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

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]

2008

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

2007

A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
[CrossRef]

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

2004

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

2000

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

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

1997

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[CrossRef]

1970

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

1962

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Amstrong, J. A.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Arie, A.

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, Opt. Lett. 35, 3790 (2010).
[CrossRef] [PubMed]

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

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

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]

A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
[CrossRef]

Bahabad, A.

A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
[CrossRef]

Berger, V.

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

Best, A.

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]

Bloembergen, N.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[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]

Butt, H.

Chen, J.

Chen, X.

Cheng, B.

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

Dolev, I.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Dou, J.

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

Ducuing, J.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fragemann, A.

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

Gadret, G.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Ganany-Padowicz, A.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (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]

Gayer, O.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Habshoosh, N.

A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
[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]

Kivshar, Y. S.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

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]

Kong, Y.

Koynov, K.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

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

Krolikowski, W.

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, Opt. Lett. 35, 3790 (2010).
[CrossRef] [PubMed]

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

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

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]

Laurell, F.

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

Ma, B.

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

Mangin, J.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Martin, R. J.

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

Ming, N.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[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]

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]

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]

Pasiskevicus, V.

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

Pershan, P. S.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[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]

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.

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

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]

Sheng, Y.

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, Opt. Lett. 35, 3790 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

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

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

Tien, P. K.

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

Ulrich, R.

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

Voloch, N.

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

Wang, W.

Zhang, D.

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

Zhang, Y.

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

Zhu, S.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[CrossRef]

Zhu, S. N.

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

Zhu, Y.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[CrossRef]

Appl. Phys. B

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Appl. Phys. Lett.

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

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

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

IEEE J. Quantum Electron.

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]

J. Opt. Soc. Am. B

Laser Photon. Rev.

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

W. Wang, Y. Sheng, Y. Kong, A. Arie, and W. Krolikowski, Opt. Lett. 35, 3790 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35,1317 (2010).
[CrossRef]

Opt. Quantum Electron.

A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
[CrossRef]

Phys. Rev.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. Lett.

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

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]

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

Science

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Čerenkov SHG with fundamental beam propagating along domain walls. (b) Definition of domain walls. (c) Čerenkov SHG with fundamental beam propagating in the plane of χ ( 2 ) modulation.

Fig. 2
Fig. 2

(a) Čerenkov SHG with m = 0 , ± 1 . (b) Different shapes of the reversed domains: circular, square, and chessboard-like structures.

Fig. 3
Fig. 3

Left column: Čerenkov SHG in 2D NPC formed by circular, square, and chessboard-like reversed domains. Right column: the effect of duty cycle.

Fig. 4
Fig. 4

(a) Čerenkov SHG at multiple directions. (b) The generated SH signal as a function of propagation distance.

Equations (3)

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

( x + i 2 k 2 2 ) A 2 ( x , y ) = i g ( x , y ) β 2 A 1 2 ( y ) e i Δ k x ,
S 2 ( x , κ y ) = π w 2 x 2 Γ 2 / 2 ( m , n = ± 1 , ± 2 , g m n sinc [ x ( Δ k + m G x κ y 2 / 2 k 2 ) / 2 ] × e w 2 ( n G y + κ y ) 2 / 8 ) 2 ,
Δ k + m G x κ y 2 / 2 k 2 = 0 ,

Metrics