Abstract

We report the observation of second-harmonic generation (SHG) in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapor deposition (LPCVD). Quasi-rectangular waveguides with a large cross section were used, with a height of 1 µm and various different widths, from 0.6 to 1.2 µm, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide depending on the waveguide cross section. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10−4 to 10−2 s−1, with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up (observed delay and growth), the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogalvanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 × 1 µm2 cross section and 36 mm length, corresponding to 53 µW at 532 nm with 13 mW of IR input coupled into the waveguide. The maximum equivalent χ(2)-susceptibility amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (2)

2016 (1)

Y. Fan, J. P. Epping, R. M. Oldenbeuving, C. G. H. Roeloffzen, M. Hoekman, R. Dekker, R. G. Heideman, P. J. M. van der Slot, and K.-J. Boller, “Optically integrated InP-Si3N4 hybrid laser,” IEEE Photonics J. 8, 1–11 (2016).
[Crossref]

2015 (7)

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823–4826 (2015).
[Crossref] [PubMed]

J. P. Epping, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, and K.-J. Boller, “High confinement, high yield Si3N4 waveguides for nonlinear optical applications,” Opt. Express 23, 642–648 (2015).
[Crossref] [PubMed]

K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4, 189–207 (2015).

J. P. Epping, T. Hellwig, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “On-chip visible-to-infrared supercontinuum generation with more than 495 THz spectral bandwidth,” Opt. Express 23, 19596–19604 (2015).
[Crossref] [PubMed]

T. Hellwig, J. P. Epping, M. Schnack, K.-J. Boller, and C. Fallnich, “Ultrafast, low-power, all-optical switching via birefringent phase-matched transverse mode conversion in integrated waveguides,” Opt. Express 23, 19189–19201 (2015).
[Crossref] [PubMed]

C. Xiong, X. Zhang, A. Mahendra, J. He, D.-Y. Choi, C. J. Chae, D. Marpaung, A. Leinse, R. G. Heideman, M. Hoekman, C. G. H. Roeloffzen, R. M. Oldenbeuving, P. W. L. van Dijk, C. Taddei, P. H. W. Leong, and B. J. Eggleton, “Compact and reconfigurable silicon nitride time-bin entanglement circuit,” Optica 2, 724 (2015).
[Crossref]

A. S. Mayer, A. Klenner, A. R. Johnson, K. Luke, M. R. E. Lamont, Y. Okawachi, M. Lipson, A. L. Gaeta, and U. Keller, “Frequency comb offset detection using supercontinuum generation in silicon nitride waveguides,” Opt. Express 23, 15440 (2015).
[Crossref] [PubMed]

2014 (7)

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
[Crossref]

V. Torres-Company and A. M. Weiner, “Optical frequency comb technology for ultra-broadband radio-frequency photonics,” Laser Photon. Rev. 8, 368–393 (2014).
[Crossref]

A. Kitao, K. Imakita, I. Kawamura, and M. Fujii, “An investigation into second harmonic generation by si-rich SiNx thin films deposited by RF sputtering over a wide range of si concentrations,” J. Phys. D: Appl. Phys. 47, 215101 (2014).
[Crossref]

Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE 9135, 91351B (2014).

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
[Crossref]

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
[Crossref]

D. T. Spencer, J. F. Bauters, M. J. R. Heck, and J. E. Bowers, “Integrated waveguide coupled Si3N4 resonators in the ultrahigh-q regime,” Optica 1, 153–157 (2014).
[Crossref]

2013 (4)

2012 (1)

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100, 161902 (2012).
[Crossref]

2011 (2)

2008 (1)

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photon. 2, 242–246 (2008).
[Crossref]

2007 (2)

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
[Crossref]

W. Yang, D. B. Conkey, B. Wu, D. Yin, A. R. Hawkins, and H. Schmidt, “Atomic spectroscopy on a chip,” Nat. Photon. 1, 331–335 (2007).
[Crossref]

2003 (3)

J. Čáp and P. Chmela, “Self-organized parametric down conversion and photoinduced reflectivity in optical fibers,” Opt. Quantum Electron. 35, 1079–1090 (2003).
[Crossref]

M. K. Balakirev, I. V. Kityk, V. A. Smirnov, L. I. Vostrikova, and J. Ebothe, “Anisotropy of the optical poling of glass,” Phys. Rev. A 67, 023806 (2003).
[Crossref]

M. K. Balakirev and V. A. Smirnov, “Kinetics of photoinduced optical anisotropy in oxide glass,” J. Exp. Theor. Phys. Lett. 77, 217–220 (2003).
[Crossref]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

1999 (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[Crossref]

1998 (1)

P. Chmela and J. Petráček, “First demonstration of χ(2) grating encoding function in optical fibers,” Opt. Commun. 156, 374–383 (1998).
[Crossref]

1996 (2)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[Crossref]

M. K. Balakirev, L. I. Vostrikova, V. A. Smirnov, and M. V. Entin, “Relaxation of the optical density of glass modulated with bichromatic radiation,” J. Exp. Theor. Phys. Lett. 63, 176–181 (1996).
[Crossref]

1995 (4)

E. M. Dianov and D. S. Starodubov, “Photoinduced generation of the second harmonic in centrosymmetric media,” Quantum Electron. 25, 395–407 (1995).
[Crossref]

V. O. Sokolov and V. B. Sulimov, “Theory of third-order nonlinear photoconductivity and third-order photogalvanic effect in glass,” Phys. Status Solidi B 187, 189–204 (1995).
[Crossref]

V. O. Sokolov and V. B. Sulimov, “On the phenomenological theory of the coherent photogalvanic effect in glass,” Phys. Status Solidi B 187, 177–187 (1995).
[Crossref]

J. Robertson, W. L. Warren, and J. Kanicki, “Nature of the Si and N dangling bonds in silicon nitride,” Journal of Non-Crystalline Solids 187, 297–300 (1995).
[Crossref]

1994 (1)

E. M. Dianov, P. G. Kazanskii, and D. S. Starodubov, “Transient gratings of a quadratic nonlinear susceptibility due to the coherent photogalvanic effect in semiconductor-microcrystallite-doped glasses,” Quantum Electron. 24, 632–635 (1994).
[Crossref]

1993 (1)

W. L. Warren, J. Robertson, and J. Kanicki, “Si and N dangling bond creation in silicon nitride thin films,” Appl. Phys. Lett. 63, 2685–2687 (1993).
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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. Quant. Electron. 28, 2631–2654 (1992).
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1991 (2)

1989 (1)

B. Batdorf, C. Krautschik, U. Österberg, G. Stegeman, J. W. Leitch, J. R. Rotgé, and T. F. Morse, “Study of the length dependence of frequency-doubled light in optical fibers,” Opt. Commun. 73, 393–397 (1989).
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1988 (3)

1987 (1)

1986 (1)

Achouche, M.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Ambrosius, H.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Anderson, D. Z.

Augustin, L.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Babin, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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Bakker, A.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Batdorf, B.

B. Batdorf, C. Krautschik, U. Österberg, G. Stegeman, J. W. Leitch, J. R. Rotgé, and T. F. Morse, “Study of the length dependence of frequency-doubled light in optical fibers,” Opt. Commun. 73, 393–397 (1989).
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Bauters, J. F.

Bente, E.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Bhat, S.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Billar, A.

A. Billar, D. Grassani, M. H. Pfeiffer, S. Kharitonov, T. J. Kippenberg, and C.-S. Brès, “Large second harmonic generation enhancement in Si3N4 waveguides by all-optically induced quasi-phase-matching,” Nat. Commun. 8, 1016 (2017).
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Bitincka, E.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Blumenthal, D. J.

Bolk, J.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Boller, K.-J.

M. A. G. Porcel, F. Schepers, J. P. Epping, T. Hellwig, M. Hoekman, R. G. Heideman, P. J. M. van der Slot, C. J. Lee, R. Schmidt, R. Bratschitsch, C. Fallnich, and K.-J. Boller, “Two-octave spanning supercontinuum generation in stoichiometric silicon nitride waveguides pumped at telecom wavelengths,” Opt. Express 25, 1542–1554 (2017).
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Y. Fan, J. P. Epping, R. M. Oldenbeuving, C. G. H. Roeloffzen, M. Hoekman, R. Dekker, R. G. Heideman, P. J. M. van der Slot, and K.-J. Boller, “Optically integrated InP-Si3N4 hybrid laser,” IEEE Photonics J. 8, 1–11 (2016).
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J. P. Epping, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, and K.-J. Boller, “High confinement, high yield Si3N4 waveguides for nonlinear optical applications,” Opt. Express 23, 642–648 (2015).
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T. Hellwig, J. P. Epping, M. Schnack, K.-J. Boller, and C. Fallnich, “Ultrafast, low-power, all-optical switching via birefringent phase-matched transverse mode conversion in integrated waveguides,” Opt. Express 23, 19189–19201 (2015).
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J. P. Epping, T. Hellwig, M. Hoekman, R. Mateman, A. Leinse, R. G. Heideman, A. van Rees, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “On-chip visible-to-infrared supercontinuum generation with more than 495 THz spectral bandwidth,” Opt. Express 23, 19596–19604 (2015).
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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE 9135, 91351B (2014).

C. G. H. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. I. Marpaung, M. Burla, and K.-J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21, 22937 (2013).
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J. P. Epping, M. Kues, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “Integrated CARS source based on seeded four-wave mixing in silicon nitride,” Opt. Express 21, 32123–32129 (2013).
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Bowers, J. E.

Boyd, R. W.

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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
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Bratschitsch, R.

Brès, C.-S.

A. Billar, D. Grassani, M. H. Pfeiffer, S. Kharitonov, T. J. Kippenberg, and C.-S. Brès, “Large second harmonic generation enhancement in Si3N4 waveguides by all-optically induced quasi-phase-matching,” Nat. Commun. 8, 1016 (2017).
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Broeke, R.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Burla, M.

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. Quant. Electron. 28, 2631–2654 (1992).
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Cabrini, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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Calafiore, G.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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Chae, C. J.

Chen, G. F. R.

Chmela, P.

J. Čáp and P. Chmela, “Self-organized parametric down conversion and photoinduced reflectivity in optical fibers,” Opt. Quantum Electron. 35, 1079–1090 (2003).
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P. Chmela and J. Petráček, “First demonstration of χ(2) grating encoding function in optical fibers,” Opt. Commun. 156, 374–383 (1998).
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Corradi, A.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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D’Agostino, D.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Dabbs, A.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Dai, D.

de Vries, T.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Debregeas, H.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Dekker, R.

Y. Fan, J. P. Epping, R. M. Oldenbeuving, C. G. H. Roeloffzen, M. Hoekman, R. Dekker, R. G. Heideman, P. J. M. van der Slot, and K.-J. Boller, “Optically integrated InP-Si3N4 hybrid laser,” IEEE Photonics J. 8, 1–11 (2016).
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Dhuey, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
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M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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J. P. Epping, M. Kues, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “Integrated CARS source based on seeded four-wave mixing in silicon nitride,” Opt. Express 21, 32123–32129 (2013).
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M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4, 189–207 (2015).

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Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photon. 2, 242–246 (2008).
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W. Yang, D. B. Conkey, B. Wu, D. Yin, A. R. Hawkins, and H. Schmidt, “Atomic spectroscopy on a chip,” Nat. Photon. 1, 331–335 (2007).
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G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator kerr frequency combs,” Nat. Photon. 8, 375–380 (2014).
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Zhao, J.

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
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Adv. Opt. Technol. (1)

K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4, 189–207 (2015).

Appl. Phys. B (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
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G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3, e203 (2014).
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A. Billar, D. Grassani, M. H. Pfeiffer, S. Kharitonov, T. J. Kippenberg, and C.-S. Brès, “Large second harmonic generation enhancement in Si3N4 waveguides by all-optically induced quasi-phase-matching,” Nat. Commun. 8, 1016 (2017).
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Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photon. 2, 242–246 (2008).
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C. G. H. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. I. Marpaung, M. Burla, and K.-J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21, 22937 (2013).
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J. P. Epping, M. Kues, P. J. M. van der Slot, C. J. Lee, C. Fallnich, and K.-J. Boller, “Integrated CARS source based on seeded four-wave mixing in silicon nitride,” Opt. Express 21, 32123–32129 (2013).
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Optica (2)

Phys. Rev. A (1)

M. K. Balakirev, I. V. Kityk, V. A. Smirnov, L. I. Vostrikova, and J. Ebothe, “Anisotropy of the optical poling of glass,” Phys. Rev. A 67, 023806 (2003).
[Crossref]

Phys. Status Solidi B (2)

V. O. Sokolov and V. B. Sulimov, “Theory of third-order nonlinear photoconductivity and third-order photogalvanic effect in glass,” Phys. Status Solidi B 187, 189–204 (1995).
[Crossref]

V. O. Sokolov and V. B. Sulimov, “On the phenomenological theory of the coherent photogalvanic effect in glass,” Phys. Status Solidi B 187, 177–187 (1995).
[Crossref]

Proc. SPIE (2)

Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE 9135, 91351B (2014).

E. M. Dianov, P. G. Kazansky, and D. Y. Stepanov, “Photoinduced effects in optical waveguides,” Proc. SPIE 1516, 81 – 98 (1991).
[Crossref]

Quantum Electron. (2)

E. M. Dianov and D. S. Starodubov, “Photoinduced generation of the second harmonic in centrosymmetric media,” Quantum Electron. 25, 395–407 (1995).
[Crossref]

E. M. Dianov, P. G. Kazanskii, and D. S. Starodubov, “Transient gratings of a quadratic nonlinear susceptibility due to the coherent photogalvanic effect in semiconductor-microcrystallite-doped glasses,” Quantum Electron. 24, 632–635 (1994).
[Crossref]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smalbrugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin, P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili, A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko, J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuindersma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth, F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner, A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti, D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “An introduction to InP-based generic integration technology,” Semicond. Sci. Technol. 29, 083001 (2014).
[Crossref]

Other (7)

L. Pavesi, Silicon Photonics (Springer, 2004).

T. Tekin, N. Pleros, R. Pitwon, and A. Hakansson, Optical Interconnects for Data Centers (Woodhead Publishing, 2016).

R. Hunsperger, Integrated Optics: Theory and Technology (Springer, 2013).

T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices (Springer, 2003).
[Crossref]

www.comsol.com , “COMSOL Multiphysics V5.0,” (2014).

R. W. Boyd, Nonlinear Optics (Academic Press, 2013).

V. O. Sokolov and V. B. Sulimov, “Formation of electrostatic field gratings in glass by optical and acoustical waves,” in “Optics Quebec,” (International Society for Optics and Photonics, 1993), pp. 213–222.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 (a) Calculated effective refractive index vs. waveguide width, w, for the IR fundamental mode (E11) with quasi-horizontal polarization (red curve), and for various transverse modes at 532 with quasi-horizontal polarization. The waveguide height is fixed at 1 µm. (b) Analogous calculation of dispersion for quasi-vertically polarized modes. The black circles indicate where modal phase matching is expected, namely with w = 0.65 µm or 0.68 µm.
Fig. 2
Fig. 2 Schematic of the experimental setup used for second-harmonic (SH) generation in Si3N4 waveguides. The infrared pump laser with a wavelength near 1 μm is sent through two half-wave plates (HWP), through a telescope arrangement (TA), and a polarizing beam splitter (PBS) and focused into a waveguide sample with an aspheric lens (AL). Output from the waveguide is collected with a microscope objective (MO). A polarizing beam splitter (VIS PBS) for the SH light and transparent for the IR pump light is used as analyzer and to separate the SH output from the IR pump light. The SH output is directed to a photodiode (PD VIS) via a dichroic mirror (DM1) for further suppression of any residual IR pump light. The transmitted IR pump light, together with about 1% residual transmitted SH light, is directed towards a infrared power meter (PM IR). Part of the transmitted IR pump power is sampled (16%) by a dichroic mirror (DM2) and send into an infrared spectrometer (IR) using a collection lend (CL) and a large mode area fiber. A second dichroic mirror (DM1) separates the residual transmitted SH light from the IR path and sends it to the spectrometer for visible light (VIS).
Fig. 3
Fig. 3 (a) to (d). Initial growth of the second-harmonic output power vs. time (green traces) in four waveguides of different widths, w, and lengths, L. The red traces show the average infrared pump power in the waveguide. The dashed curves are least-square fits of the exponential function f (t) (see main text) to the experimental data. (e). Shown is the rate of growth, R, where the SH output has reached a 1/e-fraction of its steady-state value, as retrieved from the fits to the data in (a–d), vs. the waveguide-internal pump power. The triangular and square symbols represent growth rates as obtained with waveguide widths of w = 0.9 µm and 1.2 µm, respectively. The dashed curve is a linear least-square fit to the data.
Fig. 4
Fig. 4 Measured second-harmonic (SH) output as function of input infrared pump power. The used waveguide has a width of 0.9 µm, a height of 1.0 µm and a length of 22 mm. The dashed line is a quadratic fit curve (slope m = 2).
Fig. 5
Fig. 5 Power spectra of the generated visible radiation (green trace) compared with the autocorrelated infrared pump power spectrum (red trace) in a logarithmic plot, with peak values normalized to 0 dB. The SH was generated in a waveguide with a 0.6 × 1 µm2 cross-section and a length of 36 mm, with a waveguide-internal pump power of 4.8 mW.
Fig. 6
Fig. 6 Far-field intensity pattern formed by the second-harmonic output beam, normalized to the maximum intensity, recorded with a CCD behind an immersion objective (a) and calculated normalized intensity pattern for the waveguide modes E13 (b), E21 (c) and E31 (d). The waveguide has a width of 0.7 µm and a height of 1 µm. The SH output and waveguide modes are horizontally polarized.
Fig. 7
Fig. 7 (a) Measured second-harmonic (SH) output power for different waveguide widths with a fixed input power of 10 mW, horizontally polarized (squares) and vertically polarized light (triangles) for a waveguide length of 36 mm. (b) Measured second-harmonic power for different waveguide lengths with a fixed input power of 10 mW, for a waveguide with 0.9 × 1 µm2 cross-section.
Fig. 8
Fig. 8 Normalized charge distribution in the waveguide core induced by the coherent photogalvanic effect. The generating optical fields are assumed to be the fundamental mode E 11 ( ω ; r ) for the IR field and the E 13 ( 2 ω ; r ) mode for the SH field, both polarized along the x-direction. For clarity only charge values with |ρ| above 80% of the maximum value are plotted, where red and blue represents positive and negative charge, respectively. The sign of the effective χ(2) is then given from blue to red. The horizontal arrow indicates the coherence length for SHG, c = π Δ k, in absence of quasi-phase matching.
Fig. 9
Fig. 9 QPM period required for SHG in the various different modes shown in Fig. 1 with the infrared pump power in the E11 mode. All modes are horizontally polarized. As can be seen, E13 has the largest period for the range of waveguide widths discussed in Fig. 1.
Fig. 10
Fig. 10 Nonlinear coupling (orange markers) and equivalent χ eq ( 2 ) (blue markers) as a function of the length of the waveguide. The core of the waveguide has a cross-section of 0.9 × 1 µm2. The shown error bar (0.2 pm/V half-width) seen at the highest data points represents the statistical uncertainty of the fit in Fig. 4 and the experimental uncertainty in measuring the output coupling efficiency at the waveguide exit facet.

Equations (10)

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E ( ω ; r ) = A 1 ( z ) E ( ω ; x , y ) cos ( k ( ω ) z + φ 1 ) ,
E ( 2 ω ; r ) = A 2 ( z ) E ( 2 ω ; x , y ) cos ( k ( 2 ω ) z + φ 2 ) .
P D C ( 3 ) ( 0 ; r ) = 3 8 ϵ 0 χ ( 3 ) ( 0 = ω + ω 2 ω ) E ( ω ; r ) E ( ω ; r ) E * ( 2 ω ; r ) .
j p h ( r ) = C ( x , y ) | A 1 ( z ) | 2 A 2 ( z ) | E ( ω ; x , y ) | 2 E * ( 2 ω ; x , y ) cos ( Δ k z + Δ φ )
ϵ 0 χ ( 1 ) D C = ϵ 0 χ ( 1 ) E D C = P D C ( 3 ) ( 0 ; r ) .
D C ( r ) = j p h ( r ) / σ eff ,
P ( 3 ) ( 2 ω ; z ) = 3 8 ϵ 0 χ ( 3 ) ( z ) D C ( r ) E ( ω ; r ) E ( ω ; r ) .
χ eff ( 2 ) ( r ) = 3 χ ( 3 ) D C ( r ) .
χ eq ( 2 ) = 2 ( κ ϵ 0 ) 2 2 ( n ( ω ) eff ) 2 n ( 2 ω ) eff ( 2 ω ) 2 ( μ 0 ϵ 0 ) 3 / 2 S eff .
η = P ( 2 ω ) / P 0 ( ω ) = κ 2 P 0 ( ω ) L 2 ,

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