Abstract

We perform time-domain measurements of optical transport dynamics in silicon nano-photonic devices. Using pulsed optical excitation the thermal and carrier induced optical nonlinearities of micro-ring resonators are investigated, allowing for identification of their individual contributions. Under pulsed excitation build-up of free carriers and heat in the waveguides leads to a beating oscillation of the cavity resonance frequency. When employing a burst of pulse trains shorter than the carrier life-time, the slower heating effect can be separated from the faster carrier effect. Our scheme provides a convenient way to thermally stabilize optical resonators for high-power time-domain applications and nonlinear optical conversion.

©2010 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
  28. W. H. P. Pernice, M. Li, and H. X. Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
    [Crossref]
  29. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13(23), 9623–9628 (2005).
    [Crossref] [PubMed]
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2009 (3)

2008 (1)

W. H. P. Pernice, M. Li, and H. X. Tang, “Gigahertz photothermal effect in silicon waveguides,” Appl. Phys. Lett. 93(21), 213106 (2008).
[Crossref]

2007 (4)

2006 (7)

2005 (5)

2004 (6)

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]

2002 (1)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

1992 (2)

M. Gorodetsky and V. Ilchenko, “Thermal Nonlinear Effects in Optical Whispering Gallery Microresonators,” Laser Phys. 2, 1004–1009 (1992).

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

1978 (1)

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free Carrier Absorption in Silicon,” IEEE Trans. Electron. Dev. 25(2), 254–261 (1978).
[Crossref]

Adibi, A.

Agrawal, G. P.

Almeida, V. R.

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Atabaki, A. H.

Baets, R.

Barclay, P.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Bogaerts, W.

Borselli, M.

Boyraz, O.

Boyraz, Ö.

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Carmon, T.

Chen, X.

Claps, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[Crossref] [PubMed]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Wavelength conversion in silicon using Raman induced four-wave mixing,” Appl. Phys. Lett. 85(1), 34 (2004).
[Crossref]

Cocorullo, G.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

Cohen, O.

Dadap, J. I.

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Dekker, R.

Dimitropoulos, D.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[Crossref] [PubMed]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Wavelength conversion in silicon using Raman induced four-wave mixing,” Appl. Phys. Lett. 85(1), 34 (2004).
[Crossref]

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]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Driessen, A.

Dumon, P.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Fauchet, P. M.

Först, M.

Foster, M. A.

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]

Gaeta, A. L.

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]

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]

Gorodetsky, M.

M. Gorodetsky and V. Ilchenko, “Thermal Nonlinear Effects in Optical Whispering Gallery Microresonators,” Laser Phys. 2, 1004–1009 (1992).

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

He, L.

Hsieh, I.-W.

Ilchenko, V.

M. Gorodetsky and V. Ilchenko, “Thermal Nonlinear Effects in Optical Whispering Gallery Microresonators,” Laser Phys. 2, 1004–1009 (1992).

Indukuri, T.

Jalali, B.

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Johnson, T. J.

Kira, G.

Koonath, P.

Kuo, Y. H.

Kuramochi, E.

Li, M.

W. H. P. Pernice, M. Li, and H. X. Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “Gigahertz photothermal effect in silicon waveguides,” Appl. Phys. Lett. 93(21), 213106 (2008).
[Crossref]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Lin, Q.

Lipson, M.

McNab, S. J.

Mitsugi, S.

Moormann, C.

Morthier, G.

Niehusmann, J.

Notomi, M.

Osgood, R. M.

Ozdemir, S. K.

Painter, O.

Painter, O. J.

Paniccia, M.

Panoiu, N. C.

Pernice, W. H. P.

W. H. P. Pernice, M. Li, and H. X. Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “Gigahertz photothermal effect in silicon waveguides,” Appl. Phys. Lett. 93(21), 213106 (2008).
[Crossref]

Preble, S. F.

Priem, G.

Quochi, F.

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

Raghunathan, V.

Rendina, I.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Rong, H.

Schmidt, B. S.

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]

S. F. Preble, Q. Xu, B. S. Schmidt, and M. Lipson, “Ultrafast all-optical modulation on a silicon chip,” Opt. Lett. 30(21), 2891–2893 (2005).
[Crossref] [PubMed]

Schroder, D. K.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free Carrier Absorption in Silicon,” IEEE Trans. Electron. Dev. 25(2), 254–261 (1978).
[Crossref]

Shah Hosseini, E.

Sharping, J. E.

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]

Shinya, A.

Sih, V.

Soltani, M.

Soref, R. A.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

R. A. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Srinivasan, K.

Swartz, J. C.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free Carrier Absorption in Silicon,” IEEE Trans. Electron. Dev. 25(2), 254–261 (1978).
[Crossref]

Tanabe, T.

Tang, H. X.

W. H. P. Pernice, M. Li, and H. X. Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

W. H. P. Pernice, M. Li, and H. X. Tang, “Gigahertz photothermal effect in silicon waveguides,” Appl. Phys. Lett. 93(21), 213106 (2008).
[Crossref]

Thomas, R. N.

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free Carrier Absorption in Silicon,” IEEE Trans. Electron. Dev. 25(2), 254–261 (1978).
[Crossref]

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Turner, A. C.

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]

Vahala, K. J.

Van Thourhout, D.

Vlasov, Y. A.

Wahlbrink, T.

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Woo, J.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

Xiao, Y.-F.

Xu, Q.

Xu, S.

Yang, L.

Yegnanarayanan, S.

Yin, L.

Zhang, J.

Zhu, J.

Appl. Phys. Lett. (5)

D. Dimitropoulos, R. Jhaveri, R. Claps, J. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

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

W. H. P. Pernice, M. Li, and H. X. Tang, “Gigahertz photothermal effect in silicon waveguides,” Appl. Phys. Lett. 93(21), 213106 (2008).
[Crossref]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption, and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Wavelength conversion in silicon using Raman induced four-wave mixing,” Appl. Phys. Lett. 85(1), 34 (2004).
[Crossref]

Electron. Lett. (1)

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5μm in silicon etalon,” Electron. Lett. 28(1), 83–85 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

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

R. A. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

IEEE Trans. Electron. Dev. (1)

D. K. Schroder, R. N. Thomas, and J. C. Swartz, “Free Carrier Absorption in Silicon,” IEEE Trans. Electron. Dev. 25(2), 254–261 (1978).
[Crossref]

J. Appl. Phys. (1)

W. H. P. Pernice, M. Li, and H. X. Tang, “Photothermal actuation in nanomechanical waveguide devices,” J. Appl. Phys. 105(1), 014508 (2009).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[Crossref]

Laser Phys. (1)

M. Gorodetsky and V. Ilchenko, “Thermal Nonlinear Effects in Optical Whispering Gallery Microresonators,” Laser Phys. 2, 1004–1009 (1992).

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. Express (16)

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005).
[Crossref] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[Crossref] [PubMed]

O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12(5), 829–834 (2004).
[Crossref] [PubMed]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[Crossref] [PubMed]

Ö. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13(23), 9623–9628 (2005).
[Crossref] [PubMed]

T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14(2), 817–831 (2006).
[Crossref] [PubMed]

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14(11), 4786–4799 (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] [PubMed]

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]

I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15(3), 1135–1146 (2007).
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M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15(8), 4694–4704 (2007).
[Crossref] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[Crossref] [PubMed]

L. He, Y.-F. Xiao, J. Zhu, S. K. Ozdemir, and L. Yang, “Oscillatory thermal dynamics in high-Q PDMS-coated silica toroidal microresonators,” Opt. Express 17(12), 9571–9581 (2009).
[Crossref] [PubMed]

E. Shah Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range,” Opt. Express 17(17), 14543–14551 (2009).
[Crossref]

Opt. Lett. (3)

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Figures (11)

Fig. 1
Fig. 1 Device layout: (a) A long silicon nanowire is arranged in a spiral pattern to preserve chip area. The waveguide has total length of 1cm using and bend radius of 30μm. (b) An optical micrograph of a fabricated photonic circuit including optical grating couplers, waveguides and a ring resonator.

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Fig. 2
Fig. 2 The measurement setup used for the time-domain analysis. Wavelength tunable optical pulse of variable width and repetition rate are generated using a tunable laser source combined with an electro-optical modulator and an electrical pulse generator. The sample under test is mounted in a vacuum chamber on a temperature stabilized stage. The optical signal is readout using an optical oscilloscope.

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Fig. 3
Fig. 3 (a) The time-domain response of the spiral waveguide shown in Fig. 1(a). The total length of the waveguide is 1cm in order to allow optical nonlinear effects to manifest. The waveguide is excited with pulses of 10ns length with a pulse power of up to 650μW. The repetition rate is set to 100kHz. For high pulse powers free-carrier absorption during the initial period of the pulse limits the peak pulse power in the stabilized regime. (b) Zoom-in from (a) in the high-power regime. From the fit the free-carrier life-time in the waveguide is estimated to be ~1.9ns.

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Fig. 4
Fig. 4 (a) The spectral response of the ring resonator from Fig. 1(b) in the DWDM regime. The radius of the resonator is chosen such that the free-spectral range coincides with the DWDM channels. The sample is heated to 304K in order to position the resonator in close vicinity of the filter channels. Shown are the measured transmission spectra in the through port (red) and the drop port (black). The ring resonator is close to critically coupled with an extinction ratio of almost 20dB. (b) Zoom into one resonance close to DWDM channel 30 at 1553.329nm (linear scale). The fitted optical Q is 26,500. Low insertion loss into the drop port is achieved, illustrating that the ring is almost critically coupled to the bus waveguide.

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Fig. 5
Fig. 5 (a) The time-domain response of the ring resonator shown in Fig. 1(b). The waveguide is excited with pulses of 40ns length with a pulse power of 300μW. Shown is the response in dependence of wavelength and time. The blue regions correspond to low optical transmission when the pulse wavelength overlaps with the ring resonance. (b) A cut through the measured profile of for a time delay of 27ns showing the optical resonance dip of the ring resonator. (c) The time-wavelength response of the ring resonator at an optical input power of 650μW, close to the ring resonance. The measured response is shown in dependence of wavelength, showing the thermal resonance tuning of the ring resonator. The generation of free-carriers leads to a rapid change of the resonance frequency which is then compensated by thermal heating.

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Fig. 6
Fig. 6 Shown is the time-domain response of the ring resonator under excitation with long single pulses. The repetition period is kept at 10μs while the amplifier current is varied from 900mA to 1400mA. At lowest pulse power the thermal shift of the resonance during the pulse is apparent. When the pulse power is increased, competition between free-carrier absorption and thermal heating leads to oscillations during the pulse train. The oscillation amplitude increases with increasing pulse power. Simultaneously the onset of the oscillations shifts towards the beginning of the pulse, which is a signature of increased free-carrier effects. Inset: The origin of the oscillations is shown schematically. Thermal drift shifts the resonance wavelength to the right to a blue detuned wavelength. FCD leads to a backward shift and resulting oscillating thermal drift due to power modulation when the resonance passes through the pulse wavelength.

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Fig. 7
Fig. 7 (a) Shown is the ring resonator response under burst excitation in the through port. The pulse wavelength is tuned to the optical resonance, therefore the pulse amplitude increases as the resonator heats up during the pulse train and the resonance wavelength is shifted. (b) The complementary response of the ring in the drop port. Here the amplitude decreases as the resonance wavelength is shifted away from the pulse wavelength. (c) A zoom into the pulse train showing the pulse profile of the individual pulses in the through port. (d) The equivalent measurement of the pulse profile in the drop port.

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Fig. 8
Fig. 8 The response of the drop port of the ring resonator under burst excitation with trains of 40μs length. The width of the individual pulses is set to 1ns. The wavelength of the pulse is tuned into the resonance. The pulse period is tuned from 5ns to 200ns from top to bottom. When the duty cycle is high, thermal drift of the resonance leads to reduced pulse amplitudes towards the end of the pulse train. When the duty cycle is reduced, the temperature of the ring resonator is stabilized and the pulse amplitude remains constant.

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Fig. 9
Fig. 9 (a) The simulated amplitude response of a ring resonator over 350ns in the through port. The pulsed driving input field is shown by the light blue profile. The input wavelength is tuned into the cavity resonance. Due to thermal heating the resonance shifts away from the pulse wavelength and thus the pulse amplitude increases. (b) The simulated temperature response of the device. The overall temperature increases during the pulse duration and drops only slightly during the dead time. (c) The simulated free-carrier density inside the ring resonator, showing free-carrier stabilization after 3 cycles. Inset: the first through cycles of the burst showing the free-carriers settling into steady-state amplitude. After three cycles the carriers have achieved equilibrium dynamics.

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Fig. 10
Fig. 10 (a) Shown is the simulated ring response in the through port to excitation with pulses of 40ns length and a period of 80ns. The resonator is simulated in a regime, where the temperature drift has stabilized. The driving wavelength is slightly red detuned from the cavity resonance. (b) The measured response of the ring resonator, agreeing well with the modeled behavior.

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Fig. 11
Fig. 11 (a) The measured profile for the excitation of a ring resonator with a 450ns long pulse. The oscillations are measured in the through port. (b) The corresponding simulated result. Good qualitative agreement is observed between the measurement and the simulation.

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Equations (4)

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d a d t = ( − γ 2 + i Δ ω ) a + i κ s
d T ( t ) d t = − T ( t ) τ t h + α t h P ( t )
d N ( t ) d t = − N ( t ) τ F C A + α F C A U ( t )
Δ ω ( t ) = Δ ω i − ω 0 n ( g t o T ( t ) + g F C N ( t ) )

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