Abstract

Enhanced four-wave-mixing (FWM) effects have been observed with the help of large group-indices near the band edges in one-dimensional (1-D) silicon photonic crystal waveguides (Si PhCWs). A significant increase of the FWM conversion efficiency of about 17 dB was measured near the transmission band edge of the 1-D PhCW through an approximate 3.2 times increase of the group index from 8 to 24 with respect to the central transmission band region despite a large group-velocity dispersion. Numerical analyses based on the coupled-mode equations for the degenerated FWM process describe the experimentally measured results well. Our results indicate that the 1-D PhCWs are good candidates for large group-index enhanced nonlinearity devices even without having any special dispersion engineering.

© 2013 Optical Society of America

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  1. C. Monat, M. de Strerke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12(10), 104003 (2010).
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  3. B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express18(8), 7770–7781 (2010).
    [CrossRef] [PubMed]
  4. J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express20(16), 17474–17479 (2012).
    [CrossRef] [PubMed]
  5. A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
    [CrossRef]
  6. D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express15(6), 3156–3168 (2007).
    [CrossRef] [PubMed]
  7. D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Mendlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express16(8), 5585–5595 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express17(25), 22442–22451 (2009).
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    [CrossRef] [PubMed]
  25. M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express12(13), 2880–2887 (2004).
    [CrossRef] [PubMed]
  26. S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express17(4), 2298–2318 (2009).
    [CrossRef] [PubMed]
  27. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15(25), 16604–16644 (2007).
    [CrossRef] [PubMed]
  28. M. Santagiustina, C. G. Someda, G. Vadalà, S. Combrié, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express18(20), 21024–21029 (2010).
    [CrossRef] [PubMed]

2012 (2)

2010 (7)

2009 (2)

2008 (3)

2007 (3)

2006 (2)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

2005 (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
[CrossRef]

2001 (1)

1999 (1)

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

1998 (1)

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

1989 (1)

D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

Aceves, A. B.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Afshar V, S.

Agrawal, G. P.

Becker, C.

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

Beggs, D. M.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12(10), 104004 (2010), doi:.
[CrossRef]

Blair, S.

J. Goeckeritz and S. Blair, “One-dimensional photonic crystal rib waveguides,” J. Lightwave Technol. Vol.25(9), 2435–2439 (2007).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

Combrié, S.

Corcoran, B.

David, Y.

De Rossi, A.

de Sterke, C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

de Strerke, M.

C. Monat, M. de Strerke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12(10), 104003 (2010).

del Barco, O.

O. del Barco and M. Ortuno, “Slow-light transmission in one-dimensional periodic structures,” Phys. Rev. A81(2), 023833 (2010).
[CrossRef]

Dotan, I. E.

Ebnali-Heidari, M.

Eggleton, B. J.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express18(22), 22915–22927 (2010).
[CrossRef] [PubMed]

C. Monat, M. de Strerke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12(10), 104003 (2010).

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express18(8), 7770–7781 (2010).
[CrossRef] [PubMed]

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Foster, M. A.

Fuji, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Gaeta, A. L.

García, J.

Goeckeritz, J.

J. Goeckeritz and S. Blair, “One-dimensional photonic crystal rib waveguides,” J. Lightwave Technol. Vol.25(9), 2435–2439 (2007).
[CrossRef]

Goldring, D.

Grillet, C.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Hattori, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Husko, C.

Inoue, K.

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

Kim, G.

Kim, K.-J.

Krauss, T. F.

Kwong, D.-L.

Lee, J.-M.

Levy, U.

Li, J.

Lin, Q.

Littler, I. C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

Martí, J.

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
[CrossRef]

Martínez, A.

McMillan, J. F.

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Melloni, A.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12(10), 104004 (2010), doi:.
[CrossRef]

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
[CrossRef]

Mendlovic, D.

Mok, J. T.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

Moll, K. D.

Monat, C.

Monro, T. M.

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
[CrossRef]

Moss, D. J.

Mukai, T.

Muroi, N.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Nakatsuka, H.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

O’Faolain, L.

Oksman, M.

Ortuno, M.

O. del Barco and M. Ortuno, “Slow-light transmission in one-dimensional periodic structures,” Phys. Rev. A81(2), 023833 (2010).
[CrossRef]

Painter, O. J.

Pelusi, M.

Premaratne, M.

Raineri, F.

Rubin, I.

Rukhlenko, I. D.

Sanchis, P.

Santagiustina, M.

Schulz, S. A.

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12(10), 104004 (2010), doi:.
[CrossRef]

Sipe, J. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Someda, C. G.

Strasser, T. A.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Tran, Q. V.

Tsukernik, A.

Tsurumachi, N.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Vadalà, G.

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

von Freymann, G.

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

Wegener, M.

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

White, T. P.

Wong, C. W.

Wong, S.

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

Yamashita, S.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Yu, M.

Appl. Phys. Lett. (1)

C. Becker, M. Wegener, S. Wong, and G. von Freymann, “Phase-matched nondegenerate four-wave mixing in one-dimensional photonic crystals,” Appl. Phys. Lett.89(13), 131122 (2006).
[CrossRef]

J. Lightwave Technol. Vol. (1)

J. Goeckeritz and S. Blair, “One-dimensional photonic crystal rib waveguides,” J. Lightwave Technol. Vol.25(9), 2435–2439 (2007).
[CrossRef]

J. Opt. (2)

C. Monat, M. de Strerke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12(10), 104003 (2010).

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt.12(10), 104004 (2010), doi:.
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures,” Jpn. J. Appl. Phys.38(11), 6302–6308 (1999).
[CrossRef]

Nat. Phys. (1)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys.2(11), 775–780 (2006).
[CrossRef]

Nature (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton generation in apodized fiber gratings,” Opt. Commun.149(4-6), 267–271 (1998).
[CrossRef]

Opt. Express (13)

J. García, P. Sanchis, A. Martínez, and J. Martí, “1D periodic structures for slow-wave induced non-linearity enhancement,” Opt. Express16(5), 3146–3160 (2008).
[CrossRef] [PubMed]

D. Goldring, U. Levy, I. E. Dotan, A. Tsukernik, M. Oksman, I. Rubin, Y. David, and D. Mendlovic, “Experimental measurement of quality factor enhancement using slow light modes in one dimensional photonic crystal,” Opt. Express16(8), 5585–5595 (2008).
[CrossRef] [PubMed]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express18(22), 22915–22927 (2010).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express18(8), 7770–7781 (2010).
[CrossRef] [PubMed]

J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express20(16), 17474–17479 (2012).
[CrossRef] [PubMed]

D. Goldring, U. Levy, and D. Mendlovic, “Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis,” Opt. Express15(6), 3156–3168 (2007).
[CrossRef] [PubMed]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express18(15), 15484–15497 (2010).
[CrossRef] [PubMed]

C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express17(25), 22442–22451 (2009).
[CrossRef] [PubMed]

J.-M. Lee, K.-J. Kim, and G. Kim, “Enhancing alignment tolerance of silicon waveguide by using a wide grating coupler,” Opt. Express16(17), 13024–13031 (2008).
[CrossRef] [PubMed]

M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express12(13), 2880–2887 (2004).
[CrossRef] [PubMed]

S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express17(4), 2298–2318 (2009).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15(25), 16604–16644 (2007).
[CrossRef] [PubMed]

M. Santagiustina, C. G. Someda, G. Vadalà, S. Combrié, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express18(20), 21024–21029 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron.35(4/5), 365–379 (2003).
[CrossRef]

Phys. Rev. A (1)

O. del Barco and M. Ortuno, “Slow-light transmission in one-dimensional periodic structures,” Phys. Rev. A81(2), 023833 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

D. N. Christodoulides and R. I. Joseph, “Slow Bragg Solitons in Nonlinear Periodic Structures,” Phys. Rev. Lett.62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, Inc., 1989) Chapter 2.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd edition, (John Wiley & Sons, Inc., 2007) Chapter 7.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram and (b) scanning electron microscope (SEM) image of the 1D PhC waveguide used in this research.

Fig. 2
Fig. 2

(a) Transmitted output powers of the plain strip waveguides of four different lengths for an optical input power of 0dBm at 1,550nm wavelength showing the optical loss of the plain Si strip waveguide section, and (b) the fiber coupling loss, including combined losses of the Bragg grating section and the tapered waveguide region, except the central plain strip waveguide section as a function of wavelength.

Fig. 3
Fig. 3

(a) Measured (black solid line) and simulated (red solid line) transmission spectra of the 1-D PhCW and measured transmission spectrum of a plain strip waveguide of the same total waveguide length (blue dotted line). (b) Spectral profiles of the group indices of the 1-D PhCW calculated from the measured (black squares) and the simulated (red circles) transmittance curves.

Fig. 4
Fig. 4

Experimental setup used for measuring the FWM effect in the 1-D PhCW.

Fig. 5
Fig. 5

(a) Measured FWM beam spectra at points B (black line) and D (red line), and (b) measured (black squares) and calculated (open diamonds, squares and circles, closed diamonds) FWM efficiency profiles and. the calculated β2 profile (solid blue line) vs. pump wavelength. The open diamonds, squares and circles represent for the cases when α = α, α = α⋅ng/neff, and α = α⋅(ng/neff)1.5. The closed diamonds indicate the case when α = α⋅(ng/neff)1.5 and no dispersion exists. The inset represents the generated idler power at the end of the waveguide versus the coupled input signal power at the point B.

Fig. 6
Fig. 6

Calculated pump beam power and FWM-signal-conversion efficiency along the 1-D PhCW for the group-index profile of point A. Tin and Tout indicate the transmission losses due to the Fresnel reflections at the input and output boundaries of the 1-D PhC section.

Fig. 7
Fig. 7

Measured and calculated idler beam output powers as functions of the coupled pump power. Black open square and red open circle are measured idler output powers at points B and D, respectively. Dotted, dashed and solid lines indicate calculated idler powers using the coupled-mode Eqs. (1)-(4) for three different group-index-dependent absorption parameters of α = α, α = α ng/neff, and α = α (ng/neff)1.5, respectively.

Tables (1)

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Table 1 Parameters Used for FWM Measurements and Measured FWM Efficiencies

Equations (6)

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d P p dz =α P p 4γ P p 2 P s P i sinθ,
d P s dz =α P s +2γ P p 2 P s P i sinθ,
d P i dz =α P i +2γ P p 2 P s P i sinθ,
dθ dz =Δk+γ( 2 P p P s P i ) +γ[ P p 2 P i / P s + P p 2 P s / P i 4 P s P i ]cosθ,
n ˜ eff = n eff ( Λd )+ n air d Λ
n g λ 0 2 2LΔλ

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