Abstract

We report an integrated all-optical radio frequency spectrum analyzer based on a ~4cm long doped silica glass waveguide, with a bandwidth greater than 2.5 THz. We use this device to characterize the intensity power spectrum of ultrahigh repetition rate mode-locked lasers at repetition rates up to 400 GHz, and observe dynamic noise related behavior not observable with other techniques.

© 2014 Optical Society of America

Full Article  |  PDF Article
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    [Crossref] [PubMed]
  23. D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
    [Crossref] [PubMed]
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    [Crossref]
  26. S. Preussler, A. Zadok, A. Wiatrek, M. Tur, and T. Schneider, “Enhancement of spectral resolution and optical rejection ratio of Brillouin optical spectral analysis using polarization pulling,” Opt. Express 20(13), 14734–14745 (2012).
    [Crossref] [PubMed]
  27. T. Schneider, “Wavelength and line width measurement of optical sources with femtometre resolution,” Electron. Lett. 41(22), 1234–1235 (2005).
    [Crossref]
  28. J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
    [Crossref]
  29. K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
    [Crossref]

2014 (1)

2013 (2)

2012 (2)

S. Preussler, A. Zadok, A. Wiatrek, M. Tur, and T. Schneider, “Enhancement of spectral resolution and optical rejection ratio of Brillouin optical spectral analysis using polarization pulling,” Opt. Express 20(13), 14734–14745 (2012).
[Crossref] [PubMed]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

2011 (3)

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

2010 (2)

2009 (6)

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

M. D. Pelusi, T. D. Vo, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Terahertz bandwidth RF spectrum analysis of femtosecond pulses using a chalcogenide chip,” Opt. Express 17(11), 9314–9322 (2009).
[Crossref] [PubMed]

M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davies, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009).
[Crossref] [PubMed]

D. Duchesne, L. Razzari, L. Halloran, R. Morandotti, A. J. SpringThorpe, D. N. Christodoulides, and D. J. Moss, “Two-photon photodetector in a multiquantum well GaAs laser structure at 1.55μm,” Opt. Express 17(7), 5298–5310 (2009).

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

2008 (3)

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

2007 (1)

2006 (1)

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

2005 (1)

T. Schneider, “Wavelength and line width measurement of optical sources with femtometre resolution,” Electron. Lett. 41(22), 1234–1235 (2005).
[Crossref]

2004 (2)

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

C. Dorrer and D. N. Maywar, “RF spectrum analysis of optical signals using nonlinear optics,” J. Lightwave Technol. 22(1), 266–274 (2004).
[Crossref]

1995 (1)

P. M. W. French, “The generation of ultrashort laser pulses,” Rep. Prog. Phys. 58(2), 169–267 (1995).
[Crossref]

1990 (1)

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

1986 (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[Crossref]

Aggarwal, I. D.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Azaña, J.

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

Bashkansky, M.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Becker, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Bulla, D. A.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

Bulla, D. A. P.

Caspani, L.

Cheben, P.

Choi, D.-Y.

Christodoulides, D. N.

Chu, S.

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Chu, S. T.

Clausen, A. T.

Clerici, M.

Corcoran, B.

Densmore, A.

Dorrer, C.

Dreschmann, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Duchesne, D.

Dutton, Z.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Eggleton, B. J.

F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011).
[Crossref] [PubMed]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D.-X. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18(19), 20190–20200 (2010).
[Crossref] [PubMed]

M. D. Pelusi, T. D. Vo, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Terahertz bandwidth RF spectrum analysis of femtosecond pulses using a chalcogenide chip,” Opt. Express 17(11), 9314–9322 (2009).
[Crossref] [PubMed]

M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davies, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009).
[Crossref] [PubMed]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Ferrera, M.

Finch, A.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

Finsterbusch, K.

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

Florea, C. M.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Foster, M. A.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

French, P. M. W.

P. M. W. French, “The generation of ultrashort laser pulses,” Rep. Prog. Phys. 58(2), 169–267 (1995).
[Crossref]

Freude, W.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4(8), 535–544 (2010).
[Crossref]

Frey, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Gaeta, A.

D. J. Moss, R. Morandotti, A. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex glass for nonlinear optics,” Nat. Photon. 7(8), 597–607 (2013).
[Crossref]

Gaeta, A. L.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Galili, M.

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Halloran, L.

Hillerkuss, D.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Husko, C.

Janz, S.

Jeppesen, P.

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Kean, P. N.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Koos, C.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4(8), 535–544 (2010).
[Crossref]

Kues, M.

Lamont, M. R. E.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

Leuthold, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4(8), 535–544 (2010).
[Crossref]

Li, F.

Li, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Lipson, M.

D. J. Moss, R. Morandotti, A. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex glass for nonlinear optics,” Nat. Photon. 7(8), 597–607 (2013).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Liscidini, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Little, B. E.

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22(6), 6535–6546 (2014).
[Crossref] [PubMed]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21(11), 13333–13341 (2013).
[Crossref] [PubMed]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Luan, F.

Ludwig, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Luther-Davies, B.

Lutz, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Ma, R.

Madden, S.

Madden, S. J.

M. D. Pelusi, T. D. Vo, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Terahertz bandwidth RF spectrum analysis of femtosecond pulses using a chalcogenide chip,” Opt. Express 17(11), 9314–9322 (2009).
[Crossref] [PubMed]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

Marculescu, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Maywar, D. N.

Meyer, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Moeller, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Monat, C.

Morandotti, R.

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22(6), 6535–6546 (2014).
[Crossref] [PubMed]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21(11), 13333–13341 (2013).
[Crossref] [PubMed]

D. J. Moss, R. Morandotti, A. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex glass for nonlinear optics,” Nat. Photon. 7(8), 597–607 (2013).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

D. Duchesne, L. Razzari, L. Halloran, R. Morandotti, A. J. SpringThorpe, D. N. Christodoulides, and D. J. Moss, “Two-photon photodetector in a multiquantum well GaAs laser structure at 1.55μm,” Opt. Express 17(7), 5298–5310 (2009).

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Moss, D. J.

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22(6), 6535–6546 (2014).
[Crossref] [PubMed]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21(11), 13333–13341 (2013).
[Crossref] [PubMed]

D. J. Moss, R. Morandotti, A. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex glass for nonlinear optics,” Nat. Photon. 7(8), 597–607 (2013).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011).
[Crossref] [PubMed]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D.-X. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18(19), 20190–20200 (2010).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

D. Duchesne, L. Razzari, L. Halloran, R. Morandotti, A. J. SpringThorpe, D. N. Christodoulides, and D. J. Moss, “Two-photon photodetector in a multiquantum well GaAs laser structure at 1.55μm,” Opt. Express 17(7), 5298–5310 (2009).

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

Mulvad, H. C.

Narkiss, N.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Nebendahl, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Nguyen, H. C.

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

Nguyen, V. Q.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Oehler, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Oxenløwe, L. K.

Park, Y.

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Park, Y.-W.

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

Parmigiani, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Paschotta, R.

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

Pasquazi, A.

Peccianti, M.

Pelusi, M.

Pelusi, M. D.

Petropoulos, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Preussler, S.

Pureza, P.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Razzari, L.

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22(6), 6535–6546 (2014).
[Crossref] [PubMed]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21(11), 13333–13341 (2013).
[Crossref] [PubMed]

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

D. Duchesne, L. Razzari, L. Halloran, R. Morandotti, A. J. SpringThorpe, D. N. Christodoulides, and D. J. Moss, “Two-photon photodetector in a multiquantum well GaAs laser structure at 1.55μm,” Opt. Express 17(7), 5298–5310 (2009).

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Reimer, C.

Resan, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Rode, A.

Roeger, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Salem, R.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Sanghera, J. S.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Schellinger, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Schmogrow, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Schneider, T.

Shaw, L. B.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Sibbett, W.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

Sipe, J. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

SpringThorpe, A. J.

Tur, M.

Turner, A. C.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Vallaitis, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Valley, G. C.

Vo, T. D.

von der Linde, D.

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[Crossref]

Weingarten, K.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Wiatrek, A.

Winter, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

Xu, D.-X.

Xu, J.

Yang, Z.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

Zadok, A.

Zhu, X.

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

Appl. Phys. B (2)

R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[Crossref]

Electron. Lett. (2)

T. Schneider, “Wavelength and line width measurement of optical sources with femtometre resolution,” Electron. Lett. 41(22), 1234–1235 (2005).
[Crossref]

K. Finsterbusch, H. C. Nguyen, D. J. Moss, and B. J. Eggleton, “Dispersion in nonlinear figure of merit of As2Se3 chalcogenide fibre,” Electron. Lett. 42(10), 571–572 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Finch, X. Zhu, P. N. Kean, and W. Sibbett, “Noise characterization of mode-locked color-center laser sources,” IEEE J. Quantum Electron. 26(6), 1115–1123 (1990).
[Crossref]

J. Lightwave Technol. (1)

J. Non-Cryst. Solids (1)

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354(2-9), 462–467 (2008).
[Crossref]

Nat. Commun. (1)

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref] [PubMed]

Nat. Photon. (7)

D. J. Moss, R. Morandotti, A. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex glass for nonlinear optics,” Nat. Photon. 7(8), 597–607 (2013).
[Crossref]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s super-channel transmission with all-optical fast Fourier transform processing,” Nat. Photon. 5(6), 364–371 (2011).
[Crossref]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photon. 3(3), 139–143 (2009).
[Crossref]

A. Pasquazi, M. Peccianti, Y.-W. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photon. 5(9), 618–623 (2011).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photon. 2(12), 737–740 (2008).
[Crossref]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4(8), 535–544 (2010).
[Crossref]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on a silicon chip,” Nat. Photon. 2(1), 35–38 (2008).
[Crossref]

Opt. Express (11)

D. Duchesne, L. Razzari, L. Halloran, R. Morandotti, A. J. SpringThorpe, D. N. Christodoulides, and D. J. Moss, “Two-photon photodetector in a multiquantum well GaAs laser structure at 1.55μm,” Opt. Express 17(7), 5298–5310 (2009).

M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davies, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009).
[Crossref] [PubMed]

F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011).
[Crossref] [PubMed]

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007).
[Crossref] [PubMed]

M. D. Pelusi, T. D. Vo, F. Luan, S. J. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Terahertz bandwidth RF spectrum analysis of femtosecond pulses using a chalcogenide chip,” Opt. Express 17(11), 9314–9322 (2009).
[Crossref] [PubMed]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D.-X. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18(19), 20190–20200 (2010).
[Crossref] [PubMed]

S. Preussler, A. Zadok, A. Wiatrek, M. Tur, and T. Schneider, “Enhancement of spectral resolution and optical rejection ratio of Brillouin optical spectral analysis using polarization pulling,” Opt. Express 20(13), 14734–14745 (2012).
[Crossref] [PubMed]

C. Reimer, L. Caspani, M. Clerici, M. Ferrera, M. Kues, M. Peccianti, A. Pasquazi, L. Razzari, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Integrated frequency comb source of heralded single photons,” Opt. Express 22(6), 6535–6546 (2014).
[Crossref] [PubMed]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21(11), 13333–13341 (2013).
[Crossref] [PubMed]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 1.2 million,” Opt. Express 17(16), 14098–14103 (2009).
[Crossref] [PubMed]

D. Duchesne, M. Ferrera, L. Razzari, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient self-phase modulation in low loss, high index doped silica glass integrated waveguides,” Opt. Express 17(3), 1865–1870 (2009).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

P. M. W. French, “The generation of ultrashort laser pulses,” Rep. Prog. Phys. 58(2), 169–267 (1995).
[Crossref]

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D. B. Butledge, “The wireless world,” in The Electronics of Radio (Cambridge University, 1999).

I. A. Glover, S. R. Pennock, and P. R. Shepherd, “Mixers: theory and design,” in Microwave Devices, Circuits and Subsystems for Communications Engineering (John Wiley, 2005).

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Figures (6)

Fig. 1
Fig. 1

General schematic of the nonlinear RF spectrum analyzer. The pulsed signal under test is combined with a CW laser and they interact in a nonlinear medium, in this case a 4cm-long doped silica-glass spiral waveguide. The signal after the nonlinear interaction is detected using a standard optical spectrum analyzer (OSA).

Fig. 2
Fig. 2

Experimental setup for measuring the frequency response bandwidth of the all-optical RF spectrum analyzer. Four polarization controllers ensure the same polarization (TM) for all the three CW signals coupled into the doped silica glass waveguide. The use of a band-pass filter was necessary to filter out the noise generated by one of the two amplifiers. The overall power at the waveguide input was constantly monitored by a power meter while the optical spectra were recorded by an OSA.

Fig. 3
Fig. 3

Bandwidth measurement of our RF spectrum analyzer. a) Power spectral density for λ1↔λ2 = 20nm. In the inset we zoom on the idler peak. b) Normalized idler peak power as a function of the frequency detuning between signal 1 and 2. The green circle indicates that for a detuning exceeding 2.5 THz spurious nonlinear components start being visible.

Fig. 4
Fig. 4

Typical RF spectrum PS(ω) of a non-ideal mode-locked laser source affected by amplitude noise and time jitter. All the standard parameters evaluated from the RF spectrum, e.g. transform-limited duration of the optical pulse (tp), repetition rate of the source (1/T), reciprocal of the cavity round trip time (1/T'), noise band of random fluctuations in the pulse train (1/tBN), and the reciprocal of the duration of such a fluctuations (1/tN), are also indicated.

Fig. 5
Fig. 5

Experimental setup for measuring the RF spectrum of the modelocked lasers. The source under investigation is a mode-locked filter-driven four-wave mixing laser (grey inset with dashed contours). A CW laser source was first amplified and filtered then properly polarized (TM) before being sent into a 50:50 fiber coupler (top arm). On the second arm (bottom) a mode-locked laser generated a train of optical pulses that served as the signal under test. The signal was TM-polarized before being coupled into the second arm of the fiber coupler. The two outputs of the fiber coupler were directed to the 4cm-long doped silica glass waveguide and a power meter, respectively. Finally, the optical spectrum at the output of the waveguide was recorded by an OSA.

Fig. 6
Fig. 6

Experimental RF spectra as seen from the optical spectra of both lasers - 200 GHz (bottom) and 400 GHz (top) near the probe frequency. The inset is a zoom of the first RF component for the signal at 200 GHz. The magenta arrow (color online) in the inset points at the typical feature related to the cavity length mismatch noise. The same feature is seen in the second components of the RF spectrum at 200 GHz and the first component of the signal at 400 GHz.

Equations (11)

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

E CW out ( t )= E CW ( t )exp(iα I s ( t )) E 0 exp(i ω 0 t)(1+iα I s ( t ))
E CW out (t) E CW out (t)= lim T 1 T T/2 T/2 E CW out (t+τ) [ E CW out (τ) ] dτexp(i ω 0 t)( 1+α I s (t)α I s (t) )
S CW out (ω)δ(ω ω 0 )+ α 2 P S (ω ω 0 )
ω 0 + = ω 0 + ω S + ω S = ω 0 +Δ ω S
ω 0 = ω 0 + ω S ω S + = ω 0 Δ ω S
Δ β + β( ω 0 + )β( ω 0 )β( ω S + )+β( ω S )( β (1) ( ω 0 ) β (1) ( ω S ) )Δ ω S + 1 2 β (2) ( ω 0 )Δ ω S 2
Δ β β( ω 0 )β( ω 0 )β( ω S )+β( ω S + )( β (1) ( ω 0 ) β (1) ( ω S ) )Δ ω S + 1 2 β (2) ( ω 0 )Δ ω S 2
P S (ω)=F(ω)[ k=0 δ( ω 2kπ T ) + P k A ( ω 2kπ T )+ (2kπ) 2 P k j ( ω 2kπ T ) ]
ΔφL( β (1) ( ω 0 ) β (1) ( ω S ) )Δ ω S
( β (1) ( ω 0 ) β (1) ( ω S ) )| DΔλ+ 1 2 D λ | λ S Δ λ 2 |
Δ f Max = 1 L WG | 2DΔλ+ D λ | λ S Δ λ 2 |

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