Abstract

We report on the observation of multiple third-harmonic conical waves generated in an annular periodically poled nonlinear photonic crystal. We show that the conical beams are formed as a result of the cascading effect involving two parametric processes that satisfy either the transverse and/or longitudinal phase-patching conditions. This is the first experimental observation of third-harmonic generation based on nonlinear Raman–Nath diffraction.

© 2011 Optical Society of America

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  3. 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]
  4. A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. A. Arie, N. Habshoosh, and A. Bahabad, Opt. Quantum Electron. 39, 361 (2007).
    [CrossRef]
  8. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, Appl. Phys. Lett. 91, 011101 (2007).
    [CrossRef]
  9. M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
    [CrossRef]
  10. S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), Chap. 12.
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    [CrossRef]
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    [CrossRef]
  20. Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
    [CrossRef] [PubMed]

2011

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

J. Chen and X. Chen, J. Opt. Soc. Am. B 28, 241 (2011).
[CrossRef]

2010

2009

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]

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

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

Y. Sheng, S. M. Saltiel, and K. Koynov, Opt. Lett. 34, 656(2009).
[CrossRef] [PubMed]

2008

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

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]

1999

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), Chap. 12.

1998

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

1997

1995

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

1992

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

1984

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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.

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

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

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

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

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

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]

Bang, O.

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]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), Chap. 12.

Bosenberg, W. R.

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.

Byer, R. L.

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

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]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. 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] [PubMed]

Fister, O.

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]

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]

Hollberg, L.

Houe, M.

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[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] [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, R. Fischer, W. Krolikowski, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902(2008).
[CrossRef] [PubMed]

Koynov, K.

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, S. M. Saltiel, and K. Koynov, Opt. Lett. 34, 656(2009).
[CrossRef] [PubMed]

Krolikowski, W.

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

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

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

Levenson, M. D.

Ma, B.

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

Magel, G. A.

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

Mangin, J.

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

Ming, N.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[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, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef] [PubMed]

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

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]

Pershan, P. S.

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

Roppo, V.

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

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, and K. Koynov, Opt. Lett. 34, 656(2009).
[CrossRef] [PubMed]

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

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Sheng, Y.

Y. Sheng, W. Wang, R. Shiloh, V. Roppo, A. Arie, and W. Krolikowski, Appl. Phys. Lett. 98, 241114 (2011).
[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, S. M. Saltiel, and K. Koynov, Opt. Lett. 34, 656(2009).
[CrossRef] [PubMed]

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

Shiloh, R.

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

Townsend, P. D.

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Van Baak, D. A.

Voloch, N.

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

Wang, W.

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

Wells, J. S.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), Chap. 12.

Zhang, D.

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

Zhu, S.

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

Zhu, Y.

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

Zink, L.

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.

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

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

IEEE J. Quantum Electron.

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

J. Opt. Soc. Am. B

J. Phys. D

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Laser Photon. Rev.

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

Opt. Express

Opt. Lett.

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]

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

Science

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

Other

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), Chap. 12.

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Figures (3)

Fig. 1
Fig. 1

(a) Front facet of the SLT sample with annular domain structure. (b) Far-field image of the SH and TH signal generated via the nonlinear diffraction. (c) and (d) Enlarged section of the SH and TH emission pattern located near the direction of propagation of the fundamental beam.

Fig. 2
Fig. 2

Phase-matching diagrams of (a) Raman–Nath (transverse matching) and Čerenkov (longitudinal matching) SHG; (b) Raman–Nath THG and (c) Čerenkov THG. The angles for the different cases are given in Table 1.

Fig. 3
Fig. 3

(a) Calculated harmonic emission in the far-field; (b) the TH power growth with the propagation length.

Tables (1)

Tables Icon

Table 1 The Harmonics and Corresponding Transverse (TPM)/Longitudinal (LPM) Phase-Matching Conditions

Equations (2)

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

k 3 ( m , n ) sin β m , n = ( m + n ) G + Δ k 3 t ,
k 3 ( m , n ) cos β m , n = k 1 + k 2 ( m ) cos α m + Δ k 3 l ,

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