Abstract

We report on the fabrication of evanescently-coupled one-dimensional waveguide laser arrays in Nd:YAG crystals by employing femtosecond-laser direct writing (FsLDW). The far-field discrete diffraction patterns of fabricated waveguide arrays under a passive regime can be observed at the active regime. By adjusting the incoupling condition, diffraction patterns with different laser intensity distribution can be realized, which is also supported by our simulation. Results in this study suggest promising applications of such an active arrayed device for complex integrated photonic circuits.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]

2019 (3)

2018 (9)

G. Douglass, F. Dreisow, S. Gross, and M. J. Withford, “Femtosecond laser written arrayed waveguide gratings with integrated photonic lanterns,” Opt. Express 26(2), 1497–1505 (2018).
[Crossref]

P. Wu, S. He, and H. Liu, “Annular waveguide lasers at 1064 nm in Nd:YAG crystal produced by femtosecond laser inscription,” Appl. Opt. 57(19), 5420–5424 (2018).
[Crossref]

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

S. Mukherjee, M. D. Liberto, P. Öhberg, R. R. Thomson, and N. Goldman, “Experimental observation of Aharonov-Bohm cages in photonic lattices,” Phys. Rev. Lett. 121(7), 075502 (2018).
[Crossref]

M. Pan, H. Zhao, P. Miao, S. Longhi, and L. Feng, “Photonic zero mode in a non-Hermitian photonic lattice,” Nat. Commun. 9(1), 1308 (2018).
[Crossref]

Y. Yao, W. Wang, and B. Zhang, “Designing MMI structured beam-splitter in LiNbO3 crystal based on a combination of ion implantation and femtosecond laser ablation,” Opt. Express 26(15), 19648–19656 (2018).
[Crossref]

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

2017 (3)

2016 (4)

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
[Crossref]

R. Khomeriki and S. Flach, “Landau-Zener Bloch oscillations with perturbed flat bands,” Phys. Rev. Lett. 116(24), 245301 (2016).
[Crossref]

F. Xiao, W. Zhu, W. Shang, M. Wang, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, “Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices,” Opt. Express 24(16), 18332–18339 (2016).
[Crossref]

C. Grivas, “Optically pumped planar waveguide lasers: Part II: Gain media, laser systems, and applications,” Prog. Quantum Electron. 45-46, 3–160 (2016).
[Crossref]

2015 (5)

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

A. Mafi, “Transverse Anderson localization of light: a tutorial,” Adv. Opt. Photonics 7(3), 459–515 (2015).
[Crossref]

H. E. Kondakci, A. F. Abouraddy, and B. E. Saleh, “A photonic thermalization gap in disordered lattices,” Nat. Phys. 11(11), 930–935 (2015).
[Crossref]

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
[Crossref]

S. Gross and M. Withford, “Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications,” Nanophotonics 4(3), 332–352 (2015).
[Crossref]

2014 (1)

F. Chen and J. R. Vázquez de Aldana, “Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining,” Laser Photonics Rev. 8(2), 251–275 (2014).
[Crossref]

2011 (1)

2010 (3)

2009 (2)

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
[Crossref]

2008 (1)

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref]

1988 (1)

J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

Abouraddy, A. F.

Ancona, A.

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

Belic, M. R.

Bertrand, M.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

Caird, J. A.

J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

Calmano, T.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

Camacho-López, S.

Cantelar, E.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
[Crossref]

Cantillano, C.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
[Crossref]

Castillo, G. R.

Chandrasekhar, S.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

Chandrasekharan, H. K.

S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

Chase, L. L.

J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

Chen, F.

Chen, J.-Y.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Chen, X.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

Chen, Y.-F.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
[Crossref]

Cheng, C.

Christodoulides, D. N.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363(6427), 623–626 (2019).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref]

Di Giuseppe, G.

Dong, N.

Döring, S.

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

Douglass, G.

Dreisow, F.

El-Ganainy, R.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363(6427), 623–626 (2019).
[Crossref]

Fegadolli, W. S.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
[Crossref]

Feng, L.

M. Pan, H. Zhao, P. Miao, S. Longhi, and L. Feng, “Photonic zero mode in a non-Hermitian photonic lattice,” Nat. Commun. 9(1), 1308 (2018).
[Crossref]

Feng, Z.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Flach, S.

R. Khomeriki and S. Flach, “Landau-Zener Bloch oscillations with perturbed flat bands,” Phys. Rev. Lett. 116(24), 245301 (2016).
[Crossref]

Gan, L.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
[Crossref]

Gao, J.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Goldman, N.

S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

S. Mukherjee, M. D. Liberto, P. Öhberg, R. R. Thomson, and N. Goldman, “Experimental observation of Aharonov-Bohm cages in photonic lattices,” Phys. Rev. Lett. 121(7), 075502 (2018).
[Crossref]

Greiner, M.

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

Grivas, C.

C. Grivas, “Optically pumped planar waveguide lasers: Part II: Gain media, laser systems, and applications,” Prog. Quantum Electron. 45-46, 3–160 (2016).
[Crossref]

Gross, S.

G. Douglass, F. Dreisow, S. Gross, and M. J. Withford, “Femtosecond laser written arrayed waveguide gratings with integrated photonic lanterns,” Opt. Express 26(2), 1497–1505 (2018).
[Crossref]

S. Gross and M. Withford, “Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications,” Nanophotonics 4(3), 332–352 (2015).
[Crossref]

He, R.

He, S.

Heinrich, M.

Hellmig, O.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

Hokmabadi, M. P.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363(6427), 623–626 (2019).
[Crossref]

Huber, G.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Islam, R.

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

Jaque, D.

Y. Tan, A. Rodenas, F. Chen, R. R. Thomson, A. K. Kar, D. Jaque, and Q. Lu, “70% slope efficiency from an ultrafast laser-written Nd:GdVO4 channel waveguide laser,” Opt. Express 18(24), 24994–24999 (2010).
[Crossref]

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A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
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M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363(6427), 623–626 (2019).
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H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
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Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
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Liu, S.

Liu, X.-P.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
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C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
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Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
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Lukin, A.

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
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S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
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Ma, R.

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
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A. Mafi, “Transverse Anderson localization of light: a tutorial,” Adv. Opt. Photonics 7(3), 459–515 (2015).
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M. Pan, H. Zhao, P. Miao, S. Longhi, and L. Feng, “Photonic zero mode in a non-Hermitian photonic lattice,” Nat. Commun. 9(1), 1308 (2018).
[Crossref]

Molina, M. I.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
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R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
[Crossref]

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S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

S. Mukherjee, M. D. Liberto, P. Öhberg, R. R. Thomson, and N. Goldman, “Experimental observation of Aharonov-Bohm cages in photonic lattices,” Phys. Rev. Lett. 121(7), 075502 (2018).
[Crossref]

Nolte, S.

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
[Crossref]

A. Szameit, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35(8), 1172–1174 (2010).
[Crossref]

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

Nye, N. S.

M. P. Hokmabadi, N. S. Nye, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Supersymmetric laser arrays,” Science 363(6427), 623–626 (2019).
[Crossref]

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S. Mukherjee, M. D. Liberto, P. Öhberg, R. R. Thomson, and N. Goldman, “Experimental observation of Aharonov-Bohm cages in photonic lattices,” Phys. Rev. Lett. 121(7), 075502 (2018).
[Crossref]

S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

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M. Pan, H. Zhao, P. Miao, S. Longhi, and L. Feng, “Photonic zero mode in a non-Hermitian photonic lattice,” Nat. Commun. 9(1), 1308 (2018).
[Crossref]

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J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

Perez-Leija, A.

Petermann, K.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

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S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

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P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

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Qiao, L.-F.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

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J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Ramponi, A. J.

J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

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R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
[Crossref]

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S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

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P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

Rodenas, A.

Ródenas, A.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
[Crossref]

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A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
[Crossref]

Saleh, B. E.

Scherer, A.

Y.-L. Xu, W. S. Fegadolli, L. Gan, M.-H. Lu, X.-P. Liu, Z.-Y. Li, A. Scherer, and Y.-F. Chen, “Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice,” Nat. Commun. 7(1), 11319 (2016).
[Crossref]

Segev, M.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

Shams-Ansari, A.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
[Crossref]

Shang, W.

Siebenmorgen, J.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref]

Staber, P. R.

J. A. Caird, S. A. Payne, P. R. Staber, A. J. Ramponi, L. L. Chase, and W. F. Krupke, “Quantum electronic properties of the Na3Ga2Li3F12:Cr3+ laser,” IEEE J. Quantum Electron. 24(6), 1077–1099 (1988).
[Crossref]

Stützer, S.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

Sun, K.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Szameit, A.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19(14), 13636–13646 (2011).
[Crossref]

A. Szameit, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35(8), 1172–1174 (2010).
[Crossref]

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

Tai, M. E.

P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347(6227), 1229–1233 (2015).
[Crossref]

Tan, Y.

Tang, H.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Thomas, J.

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
[Crossref]

Thomson, R. R.

S. Mukherjee, H. K. Chandrasekharan, P. Öhberg, N. Goldman, and R. R. Thomson, “State-recycling and time-resolved imaging in topological photonic lattices,” Nat. Commun. 9(1), 4209 (2018).
[Crossref]

S. Mukherjee, M. D. Liberto, P. Öhberg, R. R. Thomson, and N. Goldman, “Experimental observation of Aharonov-Bohm cages in photonic lattices,” Phys. Rev. Lett. 121(7), 075502 (2018).
[Crossref]

Y. Tan, A. Rodenas, F. Chen, R. R. Thomson, A. K. Kar, D. Jaque, and Q. Lu, “70% slope efficiency from an ultrafast laser-written Nd:GdVO4 channel waveguide laser,” Opt. Express 18(24), 24994–24999 (2010).
[Crossref]

Titum, P.

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

Torchia, G. A.

A. Ródenas, G. A. Torchia, G. Lifante, E. Cantelar, J. Lamela, F. Jaque, L. Roso, and D. Jaque, “Refractive index change mechanisms in femtosecond laser written ceramic Nd:YAG waveguides: micro-spectroscopy experiments and beam propagation calculations,” Appl. Phys. B: Lasers Opt. 95(1), 85–96 (2009).
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Tsutomu, K.

K. Kawano and K. Tsutomu, Introduction to optical waveguide analysis (Wiley, 2004).

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A. Szameit, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35(8), 1172–1174 (2010).
[Crossref]

J. Siebenmorgen, K. Petermann, G. Huber, K. Rademaker, S. Nolte, and A. Tünnermann, “Femtosecond laser written stress-induced Nd:Y3Al5O12 (Nd:YAG) channel waveguide laser,” Appl. Phys. B: Lasers Opt. 97(2), 251–255 (2009).
[Crossref]

M. Heinrich, A. Szameit, F. Dreisow, S. Döring, J. Thomas, S. Nolte, A. Tünnermann, and A. Ancona, “Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate,” Appl. Phys. Lett. 93(10), 101111 (2008).
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Vicencio, R. A.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
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C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
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Wang, C.-Y.

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
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Wang, M.

Wang, W.

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H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
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Weimann, S.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Mejía-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114(24), 245503 (2015).
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Winzer, P.

C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018).
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Figures (5)

Fig. 1.
Fig. 1. Schematic diagram of the end-face coupling arrangement for waveguide array characterization. The inset is the cross-sectional microscopic image of the fabricated waveguide array. Scale bar denotes 30 µm.
Fig. 2.
Fig. 2. (a) Reconstructed refractive index profile of the fabricated 1D waveguide array. (b, d) Simulated and (c, e) experimental results of the intensity distribution at 1.06 µm of the waveguide array (using focal lens with f = 25 mm). White dotted lines and circles denote the laser-induced tracks position and the focal spot location of the incident light, respectively. Scale bar denotes 30 µm.
Fig. 3.
Fig. 3. Discrete diffraction of 1.06-µm light propagation in the waveguide array when placing the incident beam at (a) WG0, (b) WG+7, and (c) again at WG0 but with 3° tilting (laterally). The white frame area in (c) is already outside the waveguide array region.
Fig. 4.
Fig. 4. (a) Simulation and (b) experimental results of discrete diffraction of 1.06-µm light propagation in the waveguide array when using incoupling lens with f = 50 mm (placing the incident focal spot at WG0). White dotted lines and circles denote the laser-induced tracks position and the focal spot location of the incident light, respectively. Scale bar denotes 30 µm.
Fig. 5.
Fig. 5. Output power as a function of incident power obtained from fabricated waveguide array with pump beam located at WG0 (red), WG+7 (olive) and WG−7 (blue). Solid and dashed lines represent linear fit of the experimental data.