Abstract

Nonlinear photonic structures with a modulated second-order nonlinearity are used widely for quasi-phase-matched parametric processes. Creating three-dimensional (3D) nonlinear photonic structures is promising but still challenging, since standard poling methods are limited to two-dimensional structures. Light-induced quasi-phase matching (QPM) can overcome this issue by a depletion of the second-order nonlinearity with focused femtosecond laser pulses. We report, to the best of our knowledge, the first integration of a 3D QPM structure in the core of a lithium niobate waveguide applying light-induced fabrication. Depressed-cladding waveguides and embedded QPM structures are fabricated by femtosecond laser lithography. The 3D capability is exploited by splitting the QPM gratings in the waveguide core into two or four parts, respectively. These monolithic nonlinear waveguides feature parallel multi-wavelength frequency conversion. Finally, we demonstrate a concept for second-harmonic beam shaping taking advantage of a helically twisted nonlinear structure. Our results open new avenues for creating highly efficient advanced QPM devices.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2019 (2)

S. Liu, K. Switkowski, C. Xu, J. Tian, B. Wang, P. Lu, W. Krolikowski, and Y. Sheng, “Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals,” Nat. Commun. 10, 3208 (2019).
[Crossref]

D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
[Crossref]

2018 (3)

J. Imbrock, H. Hanafi, M. Ayoub, and C. Denz, “Local domain inversion in MgO-doped lithium niobate by pyroelectric field-assisted femtosecond laser lithography,” Appl. Phys. Lett. 113, 252901 (2018).
[Crossref]

D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
[Crossref]

T. Xu, K. Switkowski, X. Chen, S. Liu, K. Koynov, H. Yu, H. Zhang, J. Wang, Y. Sheng, and W. Krolikowski, “Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate,” Nat. Photonics 12, 591–595 (2018).
[Crossref]

2017 (2)

D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
[Crossref]

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

2016 (3)

2015 (2)

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, 141102 (2015).
[Crossref]

S. Kroesen, K. Tekce, J. Imbrock, and C. Denz, “Monolithic fabrication of quasi phase-matched waveguides by femtosecond laser structuring the χ(2) nonlinearity,” Appl. Phys. Lett. 107, 101109 (2015).
[Crossref]

2014 (3)

2013 (2)

K. Shemer, N. Voloch-Bloch, A. Shapira, A. Libster, I. Juwiler, and A. Arie, “Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals,” Opt. Lett. 38, 5470–5473 (2013).
[Crossref]

J. Thomas, V. Hilbert, R. Geiss, T. Pertsch, A. Tünnermann, and S. Nolte, “Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate,” Laser Photon. Rev. 7, L17–L20 (2013).
[Crossref]

2012 (2)

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
[Crossref]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref]

2011 (3)

2010 (4)

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser Photon. Rev. 4, 355–373 (2010).
[Crossref]

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[Crossref]

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

Z. Huang, C. Tu, S. Zhang, Y. Li, F. Lu, Y. Fan, and E. Li, “Femtosecond second-harmonic generation in periodically poled lithium niobate waveguides written by femtosecond laser pulses,” Opt. Lett. 35, 877–879 (2010).
[Crossref]

2009 (1)

2008 (1)

S. Zhang, J. Yao, Q. Shi, Y. Liu, W. Liu, Z. Huang, F. Lu, and E. Li, “Fabrication and characterization of periodically poled lithium niobate waveguide using femtosecond laser pulses,” Appl. Phys. Lett. 92, 2006–2009 (2008).
[Crossref]

2007 (3)

R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
[Crossref]

J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tünnermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[Crossref]

A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinearwave mixing,” Opt. Express 15, 17619–17624 (2007).
[Crossref]

2006 (1)

Y. L. Lee, N. E. Yu, C. Jung, B. A. Yu, I. B. Sohn, S. C. Choi, Y. C. Noh, D. K. Ko, W. S. Yang, H. M. Lee, W. K. Kim, and H. Y. Lee, “Second-harmonic generation in periodically poled lithium niobate waveguides fabricated by femtosecond laser pulses,” Appl. Phys. Lett. 89, 171103 (2006).
[Crossref]

2004 (1)

2002 (1)

B. Chen, C. Xu, B. Zhou, and X. Tang, “Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 675–680 (2002).
[Crossref]

2000 (2)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[Crossref]

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping,” J. Opt. Soc. Am. B 17, 304–318 (2000).
[Crossref]

1998 (1)

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[Crossref]

1997 (3)

1995 (1)

M. Houe and P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[Crossref]

1993 (1)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
[Crossref]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Alibart, O.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
[Crossref]

Ancona, A.

J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tünnermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[Crossref]

Arbore, M. A.

Arie, A.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Ayoub, M.

J. Imbrock, H. Hanafi, M. Ayoub, and C. Denz, “Local domain inversion in MgO-doped lithium niobate by pyroelectric field-assisted femtosecond laser lithography,” Appl. Phys. Lett. 113, 252901 (2018).
[Crossref]

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

M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ2 media: from disorder to order,” Opt. Express 19, 11340–11354 (2011).
[Crossref]

Bahabad, A.

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).
[Crossref]

Best, A.

Bloch, N. V.

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

Boes, A.

Bookey, H. T.

R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
[Crossref]

Booth, M.

Booth, M. J.

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[Crossref]

Burghoff, J.

J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tünnermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[Crossref]

Butt, H.-J.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Cerullo, G.

R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
[Crossref]

Chen, B.

C.-Q. Xu and B. Chen, “Cascaded wavelength conversions based on sum-frequency generation and difference-frequency generation,” Opt. Lett. 29, 292–294 (2004).
[Crossref]

B. Chen, C. Xu, B. Zhou, and X. Tang, “Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 675–680 (2002).
[Crossref]

Chen, F.

F. Chen and J. R. V. de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photon. Rev. 8, 251–275 (2014).
[Crossref]

Chen, P.

D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
[Crossref]

Chen, X.

T. Xu, K. Switkowski, X. Chen, S. Liu, K. Koynov, H. Yu, H. Zhang, J. Wang, Y. Sheng, and W. Krolikowski, “Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate,” Nat. Photonics 12, 591–595 (2018).
[Crossref]

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, 2410–2413 (2016).
[Crossref]

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, 141102 (2015).
[Crossref]

L. Tian, F. Ye, and X. Chen, “Optical vortex converter with helical-periodically poled ferroelectric crystal,” Opt. Express 19, 11591–11596 (2011).
[Crossref]

Chiodo, N.

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S. Zhang, J. Yao, Q. Shi, Y. Liu, W. Liu, Z. Huang, F. Lu, and E. Li, “Fabrication and characterization of periodically poled lithium niobate waveguide using femtosecond laser pulses,” Appl. Phys. Lett. 92, 2006–2009 (2008).
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D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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S. Liu, K. Switkowski, C. Xu, J. Tian, B. Wang, P. Lu, W. Krolikowski, and Y. Sheng, “Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals,” Nat. Commun. 10, 3208 (2019).
[Crossref]

T. Xu, K. Switkowski, X. Chen, S. Liu, K. Koynov, H. Yu, H. Zhang, J. Wang, Y. Sheng, and W. Krolikowski, “Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate,” Nat. Photonics 12, 591–595 (2018).
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S. Zhang, J. Yao, Q. Shi, Y. Liu, W. Liu, Z. Huang, F. Lu, and E. Li, “Fabrication and characterization of periodically poled lithium niobate waveguide using femtosecond laser pulses,” Appl. Phys. Lett. 92, 2006–2009 (2008).
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S. Zhang, J. Yao, Q. Shi, Y. Liu, W. Liu, Z. Huang, F. Lu, and E. Li, “Fabrication and characterization of periodically poled lithium niobate waveguide using femtosecond laser pulses,” Appl. Phys. Lett. 92, 2006–2009 (2008).
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Z. Huang, C. Tu, S. Zhang, Y. Li, F. Lu, Y. Fan, and E. Li, “Femtosecond second-harmonic generation in periodically poled lithium niobate waveguides written by femtosecond laser pulses,” Opt. Lett. 35, 877–879 (2010).
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S. Zhang, J. Yao, Q. Shi, Y. Liu, W. Liu, Z. Huang, F. Lu, and E. Li, “Fabrication and characterization of periodically poled lithium niobate waveguide using femtosecond laser pulses,” Appl. Phys. Lett. 92, 2006–2009 (2008).
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S. Liu, K. Switkowski, C. Xu, J. Tian, B. Wang, P. Lu, W. Krolikowski, and Y. Sheng, “Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals,” Nat. Commun. 10, 3208 (2019).
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Lu, Y.

D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
[Crossref]

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M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
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R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
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Martin, A.

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[Crossref]

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J. Thomas, V. Hilbert, R. Geiss, T. Pertsch, A. Tünnermann, and S. Nolte, “Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate,” Laser Photon. Rev. 7, L17–L20 (2013).
[Crossref]

J. Thomas, M. Heinrich, J. Burghoff, S. Nolte, A. Ancona, and A. Tünnermann, “Femtosecond laser-written quasi-phase-matched waveguides in lithium niobate,” Appl. Phys. Lett. 91, 151108 (2007).
[Crossref]

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N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
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[Crossref]

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S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143 (2012).
[Crossref]

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J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[Crossref]

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J. Thomas, V. Hilbert, R. Geiss, T. Pertsch, A. Tünnermann, and S. Nolte, “Quasi phase matching in femtosecond pulse volume structured x-cut lithium niobate,” Laser Photon. Rev. 7, L17–L20 (2013).
[Crossref]

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R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
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R. Osellame, M. Lobino, N. Chiodo, M. Marangoni, G. Cerullo, R. Ramponi, H. T. Bookey, R. R. Thomson, N. D. Psaila, and A. K. Kar, “Femtosecond laser writing of waveguides in periodically poled lithium niobate preserving the nonlinear coefficient,” Appl. Phys. Lett. 90, 241107 (2007).
[Crossref]

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N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
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Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).
[Crossref]

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M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435–436 (1993).
[Crossref]

Saleh, B. E. A.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[Crossref]

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M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photon. J. 2, 736–752 (2010).
[Crossref]

Shapira, A.

K. Shemer, N. Voloch-Bloch, A. Shapira, A. Libster, I. Juwiler, and A. Arie, “Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals,” Opt. Lett. 38, 5470–5473 (2013).
[Crossref]

N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
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N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting light by nonlinear photonic crystals,” Phys. Rev. Lett. 108, 233902 (2012).
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S. Liu, K. Switkowski, C. Xu, J. Tian, B. Wang, P. Lu, W. Krolikowski, and Y. Sheng, “Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals,” Nat. Commun. 10, 3208 (2019).
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B. Chen, C. Xu, B. Zhou, and X. Tang, “Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 675–680 (2002).
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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, 141102 (2015).
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S. Liu, K. Switkowski, C. Xu, J. Tian, B. Wang, P. Lu, W. Krolikowski, and Y. Sheng, “Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals,” Nat. Commun. 10, 3208 (2019).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
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D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
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Zhang, C.

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T. Xu, K. Switkowski, X. Chen, S. Liu, K. Koynov, H. Yu, H. Zhang, J. Wang, Y. Sheng, and W. Krolikowski, “Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate,” Nat. Photonics 12, 591–595 (2018).
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D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
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D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
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B. Chen, C. Xu, B. Zhou, and X. Tang, “Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 675–680 (2002).
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D. Wei, C. Wang, H. Wang, X. Hu, D. Wei, X. Fang, Y. Zhang, D. Wu, Y. Hu, J. Li, S. Zhu, and M. Xiao, “Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal,” Nat. Photonics 12, 596–600 (2018).
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Zhu, Y.

D. Wei, C. Wang, X. Xu, H. Wang, Y. Hu, P. Chen, J. Li, Y. Zhu, C. Xin, X. Hu, Y. Zhang, D. Wu, J. Chu, S. Zhu, and M. Xiao, “Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals,” Nat. Commun. 10, 4193 (2019).
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D. Wei, Y. Zhu, W. Zhong, G. Cui, H. Wang, Y. He, Y. Zhang, Y. Lu, and M. Xiao, “Directly generating orbital angular momentum in second-harmonic waves with a spirally poled nonlinear photonic crystal,” Appl. Phys. Lett. 110, 261104 (2017).
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Supplementary Material (1)

NameDescription
» Visualization 1       3D view of SHG microscope images of the helical LiQPM grating fabricated in magnesium doped x-cut lithium niobate.

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Figures (11)

Fig. 1.
Fig. 1. Schematic design of a LiQPM waveguide that consists of a multiscan $ {\chi ^{(2)}} $ grating and a circular type-II waveguide fabricated in a single inscription sequence.
Fig. 2.
Fig. 2. Calculated SH build-up inside the nonlinear material assuming phase matching (PM) and QPM by PPLN and LiQPM structures where the second-order nonlinearity is periodically damped to a certain degree instead of domain inversion. The dashed lines are the analytical solutions of the second-harmonic power in the undepleted pump regime of the form $ {P_{2\omega }} \propto d_{{\rm eff}}^2{z^2} $, with the respective nonlinear coefficient $ {d_{{\rm eff}}} $.
Fig. 3.
Fig. 3. Three schemes to modulate the $ {\chi ^{(2)}} $ nonlinearity inside the waveguide core for QPM. One period (A), two periods (A, B), and four periods (A, B, C, D). For SHG of 1064 nm, the core diameter is typically 12 µm, and the period of the QPM grating is approximately 6.6 µm (cfg. Fig. 1).
Fig. 4.
Fig. 4. Laser-scanning SHG microscope image of waveguide and LiQPM grating with a period of $ \Lambda = 6.6\,\, \unicode{x00B5}{\rm m} $. The first part of the grating is not surrounded by a waveguide in this example to illustrate that the grating is located in the middle of the waveguide.
Fig. 5.
Fig. 5. Power of the SH and insertion losses at both wavelengths measured in dependence on the writing pulse energy.
Fig. 6.
Fig. 6. Experimental temperature tuning of a chirped LiQPM device for broadband SHG at 291 W fundamental power in comparison to a single-period device fabricated with equal parameters. Right: images of the fundamental and chirped second-harmonic mode at the end of the waveguide.
Fig. 7.
Fig. 7. Sequential multi-wavelength SHG. The sequential scheme is composed of two successive LiQPM gratings inscribed into a single waveguide.
Fig. 8.
Fig. 8. Parallel multi-wavelength SHG. Parallel waveguide SHG is realized in a novel split-core approach as illustrated in the schematic.
Fig. 9.
Fig. 9. Split-core LiQPM device for multi-wavelength SHG. A three-dimensional LiQPM grating composed of four segments is inscribed into the waveguide core to enable simultaneous frequency conversion of four individual design wavelengths.
Fig. 10.
Fig. 10. SHG with helical twisted structure. (a) Illustration of a helical LiQPM grating that transfers a fundamental Gaussian beam into a vortex second-harmonic beam. (b) 3D view of SHG microscope images of the helical LiQPM grating fabricated in magnesium doped $x$-cut lithium niobate (see Visualization 1).
Fig. 11.
Fig. 11. Microscope images and SH power. (a) Microscope image of the front face of a large-scale helical QPM structure. (b) Microscope image from the top where the bended periods of the helical structure are visible. (c) Temperature tuning of SH power.

Equations (5)

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d d y A ω = i κ d ( r ) A ω A 2 ω exp ( i Δ k y ) α ω A ω ,
d d y A 2 ω = i κ d ( r ) A ω 2 exp ( i Δ k y ) α 2 ω A 2 ω ,
κ 2 = 2 ω 2 ϵ 0 c 3 1 n ω 2 n 2 ω S e f f ,
Δ k = k 2 ω 2 k ω ,
d e f f = d m a x π ( 1 v ) ,

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