Abstract

We demonstrate the potential of birefringence-based, all-optical, ultrafast conversion between the transverse modes in integrated optical waveguides by modelling the conversion process by numerically solving the multi-mode coupled nonlinear Schroedinger equations. The observed conversion is induced by a control beam and due to the Kerr effect, resulting in a transient index grating which coherently scatters probe light from one transverse waveguide mode into another. We introduce birefringent phase matching to enable efficient all-optically induced mode conversion at different wavelengths of the control and probe beam. It is shown that tailoring the waveguide geometry can be exploited to explicitly minimize intermodal group delay as well as to maximize the nonlinear coefficient, under the constraint of a phase matching condition. The waveguide geometries investigated here, allow for mode conversion with over two orders of magnitude reduced control pulse energy compared to previous schemes and thereby promise nonlinear mode switching exceeding efficiencies of 90% at switching energies below 1 nJ.

© 2015 Optical Society of America

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2015 (1)

2014 (2)

2013 (6)

T. Hellwig, T. Walbaum, and C. Fallnich, “Optically induced mode conversion in graded-index fibers using ultra-short laser pulses,” Appl. Phys. B 112, 499–505 (2013).
[Crossref]

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).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Y. Ding, J. Xu, F. D. Ros, and B. Huang, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21, 10376–10382 (2013).
[Crossref] [PubMed]

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

T. Walbaum and C. Fallnich, “Theoretical analysis of transverse mode conversion using transient long-period gratings induced by ultrashort pulses in optical fibers,” Appl. Phys. B 115, 225–235 (2013).
[Crossref]

2011 (3)

2010 (2)

N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers,” Opt. Express 18, 4411–4416 (2010).
[Crossref] [PubMed]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

2009 (2)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[Crossref]

2008 (4)

2007 (1)

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

2005 (1)

2004 (3)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
[Crossref]

H. Nakamura, Y. Sugimoto, K. Kanamoto, N. Ikeda, Y. Tanaka, Y. Nakamura, S. Ohkouchi, Y. Watanabe, K. Inoue, H. Ishikawa, and K. Asakawa, “Ultra-fast photonic crystal/quantum dot all-optical switch for future photonic networks,” Opt. Express 12, 6606–6614 (2004).
[Crossref]

Alic, N.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Anand, S.

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
[Crossref]

Andermahr, N.

Asakawa, K.

Baets, R.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Barton, J.

Bauters, J.

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Blumenthal, D.

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Boller, K.

Boller, K.-J.

Bowers, J.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

Bruinink, C.

Bures, J.

J. Bures, Guided Optics (Wiley/VCH, 2009).

Claes, T.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Deshpande, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Dhakal, A.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Ding, C.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
[Crossref]

Ding, Y.

Dobner, S.

Dubois, B.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Epping, J. P.

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Fainman, Y.

Fallahkhair, A. B.

Fallnich, C.

Ferrini, R.

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
[Crossref]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Foster, M. A.

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Fukuda, H.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Gaeta, A. L.

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[Crossref]

Gong, Q.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
[Crossref]

Heck, M.

Heideman, R.

Heidemann, R. G.

Helin, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Hellwig, T.

T. Hellwig, M. Schnack, T. Walbaum, S. Dobner, and C. Fallnich, “Experimental realization of femtosecond transverse mode conversion using optically induced transient long-period gratings,” Opt. Express 22, 24951–24958 (2014).
[Crossref] [PubMed]

T. Hellwig, T. Walbaum, and C. Fallnich, “Optically induced mode conversion in graded-index fibers using ultra-short laser pulses,” Appl. Phys. B 112, 499–505 (2013).
[Crossref]

Hoekman, M.

Horak, P.

Houdre, R.

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
[Crossref]

Hu, X.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
[Crossref]

Huang, B.

Ikeda, K.

Ikeda, N.

Inokawa, H.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Inoue, K.

Ishikawa, H.

Itabashi, S.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Jansen, R.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Jiang, P.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
[Crossref]

John, D.

Kanamoto, K.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Kues, M.

Kuramochi, E.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Kuzucu, O.

Lee, C. J.

Leinse, A.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Levy, J. S.

Leyssens, K.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

Li, K. S.

Lipson, M.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19, 11415–11421 (2011).
[Crossref] [PubMed]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (SpringerUS, 1983).

Mateman, R.

Matsuo, S.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Mulot, M.

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
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Murphy, T. E.

Nakamura, H.

Nakamura, Y.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Neutens, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
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Nishiguchi, K.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Notomi, M.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
[Crossref]

Nozaki, K.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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Ohkouchi, S.

Ou, H.

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[Crossref] [PubMed]

Peucheret, C.

Peyskens, F.

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Poletti, F.

Ramachandran, S.

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
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Rottenberg, X.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
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Saperstein, R. E.

Sato, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
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T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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Shinya, A.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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Smith, C. J. M.

B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
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Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (SpringerUS, 1983).

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A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
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Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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Tanaka, Y.

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
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Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
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Van Dorpe, P.

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
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T. Hellwig, T. Walbaum, and C. Fallnich, “Optically induced mode conversion in graded-index fibers using ultra-short laser pulses,” Appl. Phys. B 112, 499–505 (2013).
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T. Walbaum and C. Fallnich, “Theoretical analysis of transverse mode conversion using transient long-period gratings induced by ultrashort pulses in optical fibers,” Appl. Phys. B 115, 225–235 (2013).
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T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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Watanabe, Y.

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B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
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Yamada, K.

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
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Appl. Phys. B (2)

T. Hellwig, T. Walbaum, and C. Fallnich, “Optically induced mode conversion in graded-index fibers using ultra-short laser pulses,” Appl. Phys. B 112, 499–505 (2013).
[Crossref]

T. Walbaum and C. Fallnich, “Theoretical analysis of transverse mode conversion using transient long-period gratings induced by ultrashort pulses in optical fibers,” Appl. Phys. B 115, 225–235 (2013).
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Appl. Phys. Lett. (2)

T. Tanabe, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90, 031115 (2007).
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B. Wild, R. Ferrini, R. Houdre, M. Mulot, S. Anand, and C. J. M. Smith, “Temperature tuning of the optical properties of planar photonic crystal microcavities,” Appl. Phys. Lett. 84, 846–848 (2004).
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IEEE Photon. J. (1)

A. Z. Subramanian, P. Neutens, A. Dhakal, R. Jansen, T. Claes, X. Rottenberg, F. Peyskens, S. Selvaraja, P. Helin, B. Dubois, K. Leyssens, S. Severi, P. Deshpande, R. Baets, and P. Van Dorpe, “Low-Loss singlemode PECVD silicon nitride photonic wire waveguides for 532–900 nm wavelength window fabricated within a CMOS pilot line,” IEEE Photon. J. 5, 2202809 (2013).
[Crossref]

J. Lightwave Technol. (2)

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

Nat. Photonics (5)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2, 185–189 (2008).
[Crossref]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
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Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
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R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

J. Bures, Guided Optics (Wiley/VCH, 2009).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (SpringerUS, 1983).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the proposed all-optical mode conversion scheme (dimensions not to scale). Potentially, tapered directional couplers could be used to excite a superposition of the TM0- and TM1-mode at the control wavelength as well as the TE0-mode at the probe wavelength in the multimode waveguide channel marked by 2. In this work, only the nonlinear interaction of control and probe beam in the straight section of the multi-mode waveguide and the corresponding mode conversion to the higher-order mode is studied by numerically solving the multi-mode coupled nonlinear Schroedinger equations. An illustration of the probe mode’s intensity profile along the propagation path is shown color-coded in the waveguide to depict the conversion process. For details see text.
Fig. 2
Fig. 2 Difference in propagation constants Δβ (λ) for TE- (blue curve) and TM-modes (red dashed curve) in a Si3N4 ridge waveguide in SiO2 with an air on top cladding (ridge height: 380 nm, ridge width: 949 nm). The black dash-dotted line indicates phase matching (Δ = 0) with a combination of 1030 nm and 780 nm for control and probe beam wavelengths.
Fig. 3
Fig. 3 (a) Schematic of the different cladding configurations of the rectangular waveguides discussed here. The symbols within the depicted cladding (black cross, red diamond and blue square) are the ones used in (c) and (d) to distinguish between the different cladding configurations. (b) Phase mismatch as a function of the waveguide dimensions for mode conversion at a center wavelength of 780 nm via an optically induced long-period grating induced by a control beam at a center wavelength of 1030 nm or vice versa. The cladding configuration assumed here is shown as (i) in (a). Waveguide dimensions that fulfill the phase matching condition are marked with black crosses. (c) Standard deviation of the group delays per unit length (σGD) of the involved modes for cladding configurations (i–iii) as a function of the ridge height and the corresponding ridge widths, for which phase matching is fulfilled (see black crosses in (b)). (d) Effective modal area (Aeff = (3 · Q0000)−1, see appendix A) of the fundamental TE0-mode at 780 nm for the same cladding configurations (i–iii) and related waveguide dimensions as in (c).
Fig. 4
Fig. 4 All-optical mode conversion efficiency (red pluses and blue crosses) as well as conversion full width half maximum bandwidth (red diamonds and blue squares) as a function of the control beam peak power for two different waveguide dimensions and cladding configurations. The dotted lines are added to guide the eye. The dimensions as well as cladding configurations of the two waveguides are the ones - as discussed in section 4 - exhibiting lowest group delay (marked by blue crosses and squares) and highest nonlinear coefficient (marked by red pluses and diamonds), respectively. In (a) the probe pulses are assumed to be in the x-polarized TE-modes and at a center wavelength of 780 nm while the control beam is assumed to by y-polarized and at a center wavelength of 1030 nm. In (b) the roles are reversed and the probe beam is assumed to be in the y-polarized TM-modes and at a center wavelength of 1030 nm and the control beam in the x-polarized TE-modes and at a center wavelength of 780 nm.
Fig. 5
Fig. 5 Time trace of the individual modes at the waveguide position zmax, where maximum conversion has occurred in a type (i) waveguide. Displayed are the probe beam pulses at a center wavelength of 1030 nm (solid red curve: fundamental mode, dash-dotted blue curve: TM1-mode) as well as the corresponding control beam pulses at a center wavelength of 780 nm (solid black curve: fundamental mode, dashed black curve: TE1 - mode). The power of the probe pulses is magnified by a factor of 40 for visibility. (a) The control beam was launched into the waveguide with a peak power of PL = 100W and the inset shows the mode intensity profile of the TE0-mode, while in (b) the launched peak power of the control beam was 225 W and the intensity profile of the TE1-mode is displayed.

Tables (2)

Tables Icon

Table 1 Non-zero and unique nonlinear coupling coefficients of the waveguide modes studied in this paper. All parameters are given in SI-units: Qklmn in 1 m 2, τklmn in s.

Tables Icon

Table 2 Dispersion constants of the waveguide modes studied here. All values are given in SI-units: βn in s n m.

Equations (3)

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

Δ = Δ β c Δ β p , with Δ β c = β 0 , 1 ( λ c ) β 0 , 2 ( λ c ) , Δ β p = β 0 , 3 ( λ p ) β 0 , 4 ( λ p ) ,
σ GD = ( 1 n 1 i = 1 n = 4 | β 1 , i β ¯ 1 | 2 ) 1 2 ,
FoM = ( σ GVD A eff ) 1 .

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