Abstract

We present an experimental study on the Čerenkov second harmonic emission in a novel sunflower spiral array of ferroelectric domains in LiNbO3 crystal. The spiral patterns offer a diffusive, circularly symmetric distribution of reciprocal lattice vectors, thereby enabling enhanced emission of the Čerenkov beam in a broad spectral range. Instead of the traditional electric field poling, the sunflower spiral patterns are fabricated here by using our pioneering method of ferroelectric domain engineering with ultrafast light. This all-optical method gives access to high quality domain structures with short periods, which is beneficial for efficient Čerenkov harmonic generation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. F. Higgins and S. Majumdar, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electronics 1, 64–66 (1969).
    [Crossref]
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    [Crossref]
  3. 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, 163904 (2008).
    [Crossref] [PubMed]
  4. Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of localised modulation of χ(2) in Čerenkov second harmonic generation in nonlinear bulk medium,” Opt. Lett. 37, 3864–3866 (2012).
    [Crossref] [PubMed]
  5. V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
    [Crossref] [PubMed]
  6. 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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
    [Crossref] [PubMed]
  7. Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualisation by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (2010).
    [Crossref] [PubMed]
  8. X. Deng and X. Chen, “Domain wall characterisation in ferroelectrics by using localised nonlinearities,” Opt. Express 18, 15597–15602 (2010).
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  9. B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24 (19), 22210–22218 (2016).
    [Crossref] [PubMed]
  10. X. Chen, K. Switkowski, X. Hu, W. Krolikowski, and Y. Sheng, “Enhanced fourth harmonic generation via nonlinear erenkov interaction in periodically poled lithium niobate crystal,” Opt. Express 24 (26), 29948–29954 (2016).
    [Crossref]
  11. M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
    [Crossref]
  12. K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
    [Crossref] [PubMed]
  13. N. Voloch, T. Ellenbogen, and A. Arie, “Radially symmetric nonlinear photonic crystals,” J. Opt. Soc. Am. B 26, 42–49 (2009).
    [Crossref]
  14. Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
    [Crossref]
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    [Crossref]
  16. P. Ferraro, S. Grilli, and P. De Natale, Ferroelectric Crystals for Photonic Applications (Springer Science & Business Media, 2008), Ch. 3.
  17. J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
    [Crossref]
  18. S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
    [Crossref]
  19. S. F. Liew, “Light transport and lasing in complex photonic structures,” Thesis (Ph.D.) Yale University (2014).
  20. H. Vogel, “A better way to construct the sunflower head,” Math. Biosci. 44, 179–189 (1979).
    [Crossref]
  21. X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
    [Crossref]
  22. X. Chen, P. Karpinski, V. Shvedov, A. Boes, A. Mitchell, W. Krolikowski, and Y. Sheng, “Quasi-phase matching via femtosecond laser-induced domain inversion in lithium niobate waveguides,”” Opt. Lett. 41 (11), 2410–2413 (2016).
    [Crossref] [PubMed]
  23. P. Karpinski, V. Shvedov, W. Krolikowski, and C. Hnatovsky, “Laser-writing inside uniaxially birefringent crystals: fine morphology of ultrashort pulse-induced changes in lithium niobate,” Opt. Express 24(7), 7456–7476 (2016).
    [Crossref] [PubMed]
  24. P. Karpinski, X. Chen, V. Shvedov, C. Hnatovsky, A. Grisard, E. Lallier, B. Luther-Davies, W. Krolikowski, and Y. Sheng, “Nonlinear diffraction in orientation-patterned semiconductors,” Opt. Express 23, 14903–14912 (2015).
    [Crossref] [PubMed]
  25. S. M. Saltiel, D. N. Neshev, R. Fisher, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second harmonic conical waves via Nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
    [Crossref]
  26. Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
    [Crossref]

2017 (1)

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[Crossref]

2016 (4)

2015 (2)

P. Karpinski, X. Chen, V. Shvedov, C. Hnatovsky, A. Grisard, E. Lallier, B. Luther-Davies, W. Krolikowski, and Y. Sheng, “Nonlinear diffraction in orientation-patterned semiconductors,” Opt. Express 23, 14903–14912 (2015).
[Crossref] [PubMed]

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

2013 (2)

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
[Crossref]

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (2)

J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
[Crossref]

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

2010 (3)

2009 (2)

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, 1465–1472 (2009).
[Crossref]

N. Voloch, T. Ellenbogen, and A. Arie, “Radially symmetric nonlinear photonic crystals,” J. Opt. Soc. Am. B 26, 42–49 (2009).
[Crossref]

2008 (2)

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, 163904 (2008).
[Crossref] [PubMed]

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

2007 (1)

C. Canalias and V. Pasiskevicius, “Mirroless optical parametric oscillator,” Nature Photon. 1(8), 459–462 (2007).
[Crossref]

1979 (1)

H. Vogel, “A better way to construct the sunflower head,” Math. Biosci. 44, 179–189 (1979).
[Crossref]

1969 (1)

J. F. Higgins and S. Majumdar, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electronics 1, 64–66 (1969).
[Crossref]

Arie, A.

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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

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

N. Voloch, T. Ellenbogen, and A. Arie, “Radially symmetric nonlinear photonic crystals,” J. Opt. Soc. Am. B 26, 42–49 (2009).
[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, 1465–1472 (2009).
[Crossref]

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

Ayoub, M.

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[Crossref]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
[Crossref] [PubMed]

Best, A.

Boes, A.

Butt, H.

Canalias, C.

C. Canalias and V. Pasiskevicius, “Mirroless optical parametric oscillator,” Nature Photon. 1(8), 459–462 (2007).
[Crossref]

Cao, H.

J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
[Crossref]

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

Chen, X.

Cojocaru, C.

De Natale, P.

P. Ferraro, S. Grilli, and P. De Natale, Ferroelectric Crystals for Photonic Applications (Springer Science & Business Media, 2008), Ch. 3.

Deng, X.

Denz, C.

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[Crossref]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
[Crossref] [PubMed]

Ellenbogen, T.

Ferraro, P.

P. Ferraro, S. Grilli, and P. De Natale, Ferroelectric Crystals for Photonic Applications (Springer Science & Business Media, 2008), Ch. 3.

Fisher, R.

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

Futterlieb, H.

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[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, 163904 (2008).
[Crossref] [PubMed]

Grilli, S.

P. Ferraro, S. Grilli, and P. De Natale, Ferroelectric Crystals for Photonic Applications (Springer Science & Business Media, 2008), Ch. 3.

Grisard, A.

Higgins, J. F.

J. F. Higgins and S. Majumdar, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electronics 1, 64–66 (1969).
[Crossref]

Hnatovsky, C.

Hu, X.

Imbrock, J.

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[Crossref]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
[Crossref] [PubMed]

Kalinowski, K.

Karpinski, P.

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, 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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

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

Kong, Q.

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
[Crossref]

Koynov, K.

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualisation by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (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 polrarizations,” 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, 1465–1472 (2009).
[Crossref]

Krolikowski, W.

P. Karpinski, V. Shvedov, W. Krolikowski, and C. Hnatovsky, “Laser-writing inside uniaxially birefringent crystals: fine morphology of ultrashort pulse-induced changes in lithium niobate,” Opt. Express 24(7), 7456–7476 (2016).
[Crossref] [PubMed]

X. Chen, P. Karpinski, V. Shvedov, A. Boes, A. Mitchell, W. Krolikowski, and Y. Sheng, “Quasi-phase matching via femtosecond laser-induced domain inversion in lithium niobate waveguides,”” Opt. Lett. 41 (11), 2410–2413 (2016).
[Crossref] [PubMed]

X. Chen, K. Switkowski, X. Hu, W. Krolikowski, and Y. Sheng, “Enhanced fourth harmonic generation via nonlinear erenkov interaction in periodically poled lithium niobate crystal,” Opt. Express 24 (26), 29948–29954 (2016).
[Crossref]

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24 (19), 22210–22218 (2016).
[Crossref] [PubMed]

P. Karpinski, X. Chen, V. Shvedov, C. Hnatovsky, A. Grisard, E. Lallier, B. Luther-Davies, W. Krolikowski, and Y. Sheng, “Nonlinear diffraction in orientation-patterned semiconductors,” Opt. Express 23, 14903–14912 (2015).
[Crossref] [PubMed]

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
[Crossref]

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of localised modulation of χ(2) in Čerenkov second harmonic generation in nonlinear bulk medium,” Opt. Lett. 37, 3864–3866 (2012).
[Crossref] [PubMed]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
[Crossref] [PubMed]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
[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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualisation by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (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, 1465–1472 (2009).
[Crossref]

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

Lallier, E.

Liew, S. F.

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

S. F. Liew, “Light transport and lasing in complex photonic structures,” Thesis (Ph.D.) Yale University (2014).

Luther-Davies, B.

Ma, D.

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
[Crossref]

Majumdar, S.

J. F. Higgins and S. Majumdar, “Surface Radiation from Non-linear Optical Polarisation,” Opto-electronics 1, 64–66 (1969).
[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, 163904 (2008).
[Crossref] [PubMed]

Mitchell, A.

Negro, L. D.

J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
[Crossref]

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[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, 1465–1472 (2009).
[Crossref]

Neshev, D. N.

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

Noh, J.

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

Pasiskevicius, V.

C. Canalias and V. Pasiskevicius, “Mirroless optical parametric oscillator,” Nature Photon. 1(8), 459–462 (2007).
[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, 163904 (2008).
[Crossref] [PubMed]

Roedig, P.

Roppo, V.

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, 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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

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

Sheng, Y.

X. Chen, P. Karpinski, V. Shvedov, A. Boes, A. Mitchell, W. Krolikowski, and Y. Sheng, “Quasi-phase matching via femtosecond laser-induced domain inversion in lithium niobate waveguides,”” Opt. Lett. 41 (11), 2410–2413 (2016).
[Crossref] [PubMed]

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24 (19), 22210–22218 (2016).
[Crossref] [PubMed]

X. Chen, K. Switkowski, X. Hu, W. Krolikowski, and Y. Sheng, “Enhanced fourth harmonic generation via nonlinear erenkov interaction in periodically poled lithium niobate crystal,” Opt. Express 24 (26), 29948–29954 (2016).
[Crossref]

P. Karpinski, X. Chen, V. Shvedov, C. Hnatovsky, A. Grisard, E. Lallier, B. Luther-Davies, W. Krolikowski, and Y. Sheng, “Nonlinear diffraction in orientation-patterned semiconductors,” Opt. Express 23, 14903–14912 (2015).
[Crossref] [PubMed]

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
[Crossref]

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

Y. Sheng, V. Roppo, K. Kalinowski, and W. Krolikowski, “Role of localised modulation of χ(2) in Čerenkov second harmonic generation in nonlinear bulk medium,” Opt. Lett. 37, 3864–3866 (2012).
[Crossref] [PubMed]

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett. 37(11), 1832–1835 (2012).
[Crossref] [PubMed]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
[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 polrarizations,” Opt. Lett. 35(9), 1317–1319 (2010).
[Crossref] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualisation by Čerenkov-type second harmonic generation,” Opt. Express 18, 16539–16545 (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, 1465–1472 (2009).
[Crossref]

Shvedov, V.

Switkowski, K.

Trevino, J.

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
[Crossref]

Trull, J.

Vogel, H.

H. Vogel, “A better way to construct the sunflower head,” Math. Biosci. 44, 179–189 (1979).
[Crossref]

Voloch, N.

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, 1465–1472 (2009).
[Crossref]

Wang, B.

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24 (19), 22210–22218 (2016).
[Crossref] [PubMed]

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

Wang, W.

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
[Crossref]

Zhang, Y.

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, 163904 (2008).
[Crossref] [PubMed]

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, 163904 (2008).
[Crossref] [PubMed]

Adv. Mater. (1)

M. Ayoub, H. Futterlieb, J. Imbrock, and C. Denz, “3D imaging of ferroelectric kinetics during electrically driven switching,” Adv. Mater. 2017 (29), 1603325 (2017).
[Crossref]

Appl. Phys. Lett. (1)

X. Chen, P. Karpinski, V. Shvedov, K. Koynov, B. Wang, J. Trull, C. Cojocaru, W. Krolikowski, and Y. Sheng, “Ferroelectric domain engineering by focused infrared femtosecond pulses,” Appl. Phys. Lett. 107 (14), 141102 (2015).
[Crossref]

IEEE J. Quantum Electron. (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, 1465–1472 (2009).
[Crossref]

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

J. Phys. B: At. Mol. Opt. Phys. (2)

Y. Sheng, D. Ma, and W. Krolikowski, “Randomized nonlinear photonic crystals for broadband optical frequency conversion,” J. Phys. B: At. Mol. Opt. Phys. 46 (21), 215401 (2013).
[Crossref]

Y. Sheng, Q. Kong, W. Wang, K. Kalinowski, and W. Krolikowski, “Theoretical investigations of nonlinear Raman-Nath diffraction in the frequency doubling process,” J. Phys. B: At. Mol. Opt. Phys. 45, 055401 (2012).
[Crossref]

Math. Biosci. (1)

H. Vogel, “A better way to construct the sunflower head,” Math. Biosci. 44, 179–189 (1979).
[Crossref]

Nano. Lett. (1)

J. Trevino, H. Cao, and L. D. Negro, “Circularly symmetric light scattering for nanoplasmonic spirals,” Nano. Lett. 2001(11), 2008–2016 (2011).
[Crossref]

Nature Photon. (1)

C. Canalias and V. Pasiskevicius, “Mirroless optical parametric oscillator,” Nature Photon. 1(8), 459–462 (2007).
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Opt. Express (8)

V. Roppo, K. Kalinowski, Y. Sheng, W. Krolikowski, C. Cojocaru, and J. Trull, “Unified approach to Čerenkov second harmonic generation,” Opt. Express 21(22), 25715–25726 (2013).
[Crossref] [PubMed]

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

X. Deng and X. Chen, “Domain wall characterisation in ferroelectrics by using localised nonlinearities,” Opt. Express 18, 15597–15602 (2010).
[Crossref] [PubMed]

B. Wang, C. Cojocaru, W. Krolikowski, Y. Sheng, and J. Trull, “Transverse single-shot cross-correlation scheme for laser pulse temporal measurement via planar second harmonic generation,” Opt. Express 24 (19), 22210–22218 (2016).
[Crossref] [PubMed]

X. Chen, K. Switkowski, X. Hu, W. Krolikowski, and Y. Sheng, “Enhanced fourth harmonic generation via nonlinear erenkov interaction in periodically poled lithium niobate crystal,” Opt. Express 24 (26), 29948–29954 (2016).
[Crossref]

S. F. Liew, J. Noh, J. Trevino, L. D. Negro, and H. Cao, “Localized photonic band edge modes and orbital angular momenta of light in a golden-angle spiral,” Opt. Express 19(24), 154833 (2011).
[Crossref]

P. Karpinski, V. Shvedov, W. Krolikowski, and C. Hnatovsky, “Laser-writing inside uniaxially birefringent crystals: fine morphology of ultrashort pulse-induced changes in lithium niobate,” Opt. Express 24(7), 7456–7476 (2016).
[Crossref] [PubMed]

P. Karpinski, X. Chen, V. Shvedov, C. Hnatovsky, A. Grisard, E. Lallier, B. Luther-Davies, W. Krolikowski, and Y. Sheng, “Nonlinear diffraction in orientation-patterned semiconductors,” Opt. Express 23, 14903–14912 (2015).
[Crossref] [PubMed]

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Phys. Rev. Lett. (2)

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, 163904 (2008).
[Crossref] [PubMed]

S. M. Saltiel, D. N. Neshev, R. Fisher, W. Krolikowski, A. Arie, and Y. S. Kivshar, “Generation of second harmonic conical waves via Nonlinear Bragg diffraction,” Phys. Rev. Lett. 100, 103902 (2008).
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Other (2)

S. F. Liew, “Light transport and lasing in complex photonic structures,” Thesis (Ph.D.) Yale University (2014).

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Figures (5)

Fig. 1
Fig. 1 (a) Phase matching diagram of the Čerenkov-type second harmonic generation. (b) The Čerenkov harmonic is usually a conical wave when illuminating a two-dimensional nonlinear photonic crystal with a Gaussian-profile beam. (c) The Čerenkov harmonic emission will be enhanced if the transverse phase matching condition is also fulfilled. For example, the square lattice can be used to enhance the Čerenkov signal along two orthogonal directions.
Fig. 2
Fig. 2 (a) The sunflower spiral lattice created with b=1.45 μm and q=0, 1, . . ., 2000 in Eq. (1). (b) The Fourier space of the sunflower pattern, in which there are diffuse and rotational symmetric reciprocal lattice vectors for efficient nonlinear Čerenkov radiation. (c) The structure and (d) Fourier space of a periodic annular structure for comparison.
Fig. 3
Fig. 3 (a–c) Three examples of the fabricated sunflower spiral nonlinear photonic structure in a congruent LiNbO3 crystal, visualised by the Čerenkov second harmonic microscopy [7]. The structure parameters are as follows: structure (a): scaling factor b=5 μm, q=0, 1, . . ., 200; (b): scaling factor b=2 μm, q=0, 1, . . ., 625; (c): scaling factor b=1.45 μm, q=0, 1, . . ., 3086. (d) 3D visualisation of the 30μm×30μm section of the structure from graph (b). Radius of the inverted domains r ≈1 μm in all three structures.
Fig. 4
Fig. 4 (a) Experimentally recorded far-field images of the Čerenkov second harmonic at different wavelengths. (b) Measured (dots) and calculated (solid) wavelength tuning response of the Čerenkov second harmonic generation in the sunflower structure.
Fig. 5
Fig. 5 (a) The emission angles of the Čerenkov and Raman-Nath second harmonic as a functional of fundamental wavelength. The dots and asterisks are experimental values and the lines represent theoretical predictions. (b) Radial profile of the Fourier spectrum of the sunflower spiral nonlinear photonic crystal (scaling factor b=1.45 μm, q=0, 1, . . ., 1189). The shaded area indicates the range of reciprocal vectors contributing to the broadband enhancement of Čerenkov second harmonic generation in our structure.

Equations (1)

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r = b q , θ = q α ,

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