Abstract

We present for the first time an all-optical wavelength conversion (AOWC) scheme supporting modulation format independency without requiring phase matching. The new scheme is named “spoof” four wave mixing (SFWM) and in contrast to the well-known FWM theory, where the induced dynamic refractive index grating modulates photons to create a wave at a new frequency, the SFWM is different in that the dynamic refractive index grating is generated in a nonlinear Bragg Grating (BG) to excite additional reflective peaks at either side of the original BG bandgap in reflection spectrum. This fundamental difference enable the SFWM to avoid the intrinsic shortcoming of stringent phase matching required in the conventional FWM, and allows AOWC with modulation format transparency and ultrabroad conversion range, which may have great potential applications for next generation of all-optical networks.

© 2012 OSA

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2011 (8)

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

M. Matsuura and N. Kishi, “High-Speed Wavelength Conversion of RZ-DPSK Signal Using FWM in a Quantum-Dot SOA,” IEEE Photon. Technol. Lett. 23(10), 615–617 (2011).

A. Tzanakaki, K. Katrinis, T. Politi, A. Stavdas, M. Pickavet, P. Van Daele, D. Simeonidou, M. J. O’Mahony, S. Aleksi?, L. Wosinska, and P. Monti, “Dimensioning the future pan-European optical network with energy efficiency considerations,” J. Opt. Commun. Netw. 3(4), 272–280 (2011).
[CrossRef]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).

M. Matsuura, O. Raz, F. Gomez-Agis, N. Calabretta, and H. J. S. Dorren, “320 Gbit/s wavelength conversion using four-wave mixing in quantum-dot semiconductor optical amplifiers,” Opt. Lett. 36(15), 2910–2912 (2011).
[CrossRef]

N. Amaya, G. S. Zervas, B. R. Rofoee, M. Irfan, Y. Qin, and D. Simeonidou, “Field trial of a 1.5 Tb/s adaptive and gridless OXC supporting elastic 1000-fold all-optical bandwidth granularity,” Opt. Express 19(26), B235–B241 (2011).
[CrossRef] [PubMed]

M. Matsuura, O. Raz, F. Gomez-Agis, N. Calabretta, and H. J. S. Dorren, “Ultrahigh-speed and widely tunable wavelength conversion based on cross-gain modulation in a quantum-dot semiconductor optical amplifier,” Opt. Express 19(26), B551–B559 (2011).
[CrossRef]

2010 (4)

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
[CrossRef]

G. S. Zervas, V. Martini, Y. Qin, E. Escalona, R. Nejabati, D. Simeonidou, F. Baroncelli, B. Martini, K. Torkmen, and P. Castoldi, “Service-oriented multigranular optical network architecture for clouds,” J. Opt. Commun. Netw. 2(10), 883–891 (2010).
[CrossRef] [PubMed]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

2008 (1)

S. Singh, “Boost up of four wave mixing signal in semiconductor optical amplifier for 40 Gb/s optical frequency conversion,” Opt. Commun. 281(9), 2618–2626 (2008).
[CrossRef] [PubMed]

2007 (2)

G. W. Lu, K. K. Abedin, and T. Miyazaki, “All-optical RZ-DPSK WDM to RZ-DQPSK phase multiplexing using four-wave mixing in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 19(21), 1699–1701 (2007).
[CrossRef] [PubMed]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef] [PubMed]

2006 (4)

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Först, “Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mum femtosecond pulses,” Opt. Express 14(18), 8336–8346 (2006).
[CrossRef]

Y. H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14(24), 11721–11726 (2006).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

1998 (1)

1996 (2)

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

S. Subramaniam, M. Azizoglu, and A. K. Somani, “All-optical networks with sparse wavelength conversion,” IEEE/ACM Trans. Netw. 4(4), 544–557 (1996).
[CrossRef]

Abedin, K. K.

G. W. Lu, K. K. Abedin, and T. Miyazaki, “All-optical RZ-DPSK WDM to RZ-DQPSK phase multiplexing using four-wave mixing in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 19(21), 1699–1701 (2007).
[CrossRef] [PubMed]

Ahmad, H.

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Aleksic, S.

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Amaya, N.

Andersen, T.

Arbore, M. A.

Astar, W. B.

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Awang, N. A.

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Azizoglu, M.

S. Subramaniam, M. Azizoglu, and A. K. Somani, “All-optical networks with sparse wavelength conversion,” IEEE/ACM Trans. Netw. 4(4), 544–557 (1996).
[CrossRef]

Baroncelli, F.

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef] [PubMed]

Calabretta, N.

Carter, G. M.

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Castoldi, P.

Chou, M. H.

Cohen, O.

Dadap, J. I.

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Dekker, R.

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Dorren, H. J. S.

Driessen, A.

Driscoll, J. B.

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Escalona, E.

Fejer, M. M.

Först, M.

Foster, M. A.

Gaeta, A. L.

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Ghani, Z. A.

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Gomez-Agis, F.

Green, W. M. J.

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Grote, R. R.

Hansen, K.

Harun, S. W.

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Hasegawa, T.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

Hauden, J.

Hilligsøe, K.

Irfan, M.

Katrinis, K.

Keiding, S.

Kikuchi, K.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

Kishi, N.

M. Matsuura and N. Kishi, “High-Speed Wavelength Conversion of RZ-DPSK Signal Using FWM in a Quantum-Dot SOA,” IEEE Photon. Technol. Lett. 23(10), 615–617 (2011).

Kuo, Y. H.

Larsen, J.

Latif, A. A.

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Lau, R. K. W.

Lee, J. H.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

Lipson, M.

Liu, X. B.

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Liu, X. P.

Lu, G. W.

G. W. Lu, K. K. Abedin, and T. Miyazaki, “All-optical RZ-DPSK WDM to RZ-DQPSK phase multiplexing using four-wave mixing in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 19(21), 1699–1701 (2007).
[CrossRef] [PubMed]

Martini, B.

Martini, V.

Matsuura, M.

Ménard, M.

Miyazaki, T.

G. W. Lu, K. K. Abedin, and T. Miyazaki, “All-optical RZ-DPSK WDM to RZ-DQPSK phase multiplexing using four-wave mixing in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 19(21), 1699–1701 (2007).
[CrossRef] [PubMed]

Monti, P.

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Moormann, C.

Moro, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Nagashima, T.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

Nejabati, R.

Niehusmann, J.

Nielsen, C.

O’Mahony, M. J.

Ohara, S.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Wide-band tunable wavelength conversion of 10-Gb/s nonreturn-to-zero signal using cross-phase-Modulation-induced polarization rotation in 1-m bismuth oxide-based nonlinear optical fiber,” IEEE Photon. Technol. Lett. 18(1), 298–300 (2006).
[CrossRef] [PubMed]

Okawachi, Y.

Osgood, J. R. M.

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

Osgood, R. M.

Paniccia, M.

Panoiu, N. C.

Park, J. S.

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[CrossRef]

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M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

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[CrossRef] [PubMed]

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M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
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[CrossRef]

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M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
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H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
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Appl. Phys. Lett. (2)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

J. B. Driscoll, W. B. Astar, X. B. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and J. R. M. Osgood, “All-optical wavelength conversion of 10 Gb/s RZ-OOK data in a silicon nanowire via cross-phase modulation: experiment and theoretical investigation,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1448–1459 (2010).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (3)

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S. Subramaniam, M. Azizoglu, and A. K. Somani, “All-optical networks with sparse wavelength conversion,” IEEE/ACM Trans. Netw. 4(4), 544–557 (1996).
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J. Lightwave Technol. (1)

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

J. Opt. Commun. Netw. (2)

Laser Phys. Lett. (1)

H. Ahmad, N. A. Awang, A. A. Latif, M. Z. Zulkifli, Z. A. Ghani, and S. W. Harun, “Wavelength conversion based on four-wave mixing in a highly nonlinear fiber in ring configuration,” Laser Phys. Lett. 8(10), 742–746 (2011).
[CrossRef] [PubMed]

Nat. Photonics (1)

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Nature (1)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Singh, “Boost up of four wave mixing signal in semiconductor optical amplifier for 40 Gb/s optical frequency conversion,” Opt. Commun. 281(9), 2618–2626 (2008).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (4)

Other (3)

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A. Tzanakaki, M. P. Anastasopoulos, K. Georgakilas, and D. Simeonidou, “Energy aware planning of multiple virtual infrastructuresover converged optical network and IT physical resources,” in Proceedings of ECOC’2011, Switzerland, (2011).

E. Hecht, Optics, 4th ed. (Adison Wesley 2001) Chap. 6.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Dispersion diagram both for the perturbed (dashed line) and unperturbed BG (solid line). The red circles mark the position of the induced bandgaps. The parameters are na = 1.5, nb = 1.6, da = db = 220 nm, nc = nd = 2.5 × 10−3, Λ = 11d, and ϕ = 0. (b) Reflectivity spectra for the perturbed (red solid line) and unperturbed BG (black circle line), respectively. The insets show the dual ARPs’ reflectivity and phase spectra in detail. (c) and (d) illustrate dependence of the induced ARPs’ wavelengths on Λ and λB, respectively. (e) Phase variations versus ϕ at the ARPs’ wavelengths λl and λr, respectively.

Fig. 2
Fig. 2

Reflectivity of the perturbed BG when nc,d is 2.5 × 10−3 (blue dashed line) and 2.5 × 10−2 (red solid line), respectively. The other parameters are same with that in Fig. 1(b).

Fig. 3
Fig. 3

(a) Schematic diagram of the proposed SFWM for AOWC. The pump and signal light should locate outside of BG bandgap for a high transmission. (b) The induced refractive index Δn(z) along the nonlinear BG. The inset shows the zoomed Δn(z) in the region of 3.45 mm<z<3.47 mm. Here, signal and pump wavelengths are λ1 = 1.55 μm and λ2 = 0.98 μm, their intensities are I1 = I2 = 5 × 10−3/(4n2), and their phase difference is φ = 0. The BG parameters are the same to that used in Fig. 1(b). (c) Reflectivity spectra for the perturbed BG when λ1 = 1.55 μm while λ2 = 0.85 μm, 0.95 μm, and 1.0 μm, respectively. (d) Dependence of the ARPs’ wavelengths on λ2 when λ1 = 1.55 μm.

Fig. 4
Fig. 4

(a) Peak value of the right ARP (i.e, at wavelength λr = 1584.2nm) versus the signal intensity I1 when the pump intensity I2 = 5 × 10−3/(4n2), λ1 = 1.55 μm, λ2 = 0.98 μm, and φ = 0. (b) Reflectivity and phase spectra for the right ARP when I1 = I2 = 5 × 10−3/(4n2), λ1 = 1.55 μm and λ2 = 0.98 μm. Here, Red and blue graphs relate to the ARP when φ is -π/2 and π/2, respectively.

Equations (5)

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M= j=1 Q ( cos δ j isin( δ j ) γ j i γ j sin( δ j ) cos( δ j ) ) ,
cosKΛ= M 11 + M 22 2 .
β=mΩ,
n eff = 0 Λ n(z)dz /Λ= 1 Λ ( ( n a d a + n b d b )Λ d + 0 Λ Δn(z)dz ) ).
λ band = 2 n eff Λ m Λ λ B md .

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