Abstract

A vital element in integrated optofluidics is dynamic tuning and precise control of photonic devices, especially when employing electronic techniques which are challenging to utilize in an aqueous environment. We overcome this challenge by introducing a new platform in which the photonic device is controlled using electro-optical phase tuning. The phase tuning is generated by the thermo-optic effect using an on-chip electric microheater located outside the fluidic channel, and is transmitted to the optofluidic device through optical waveguides. The microheater is compact, high-speed (> 18 kHz), and consumes low power (~mW). We demonstrate dynamic optical trapping control of nanoparticles by an optofluidic resonator. This novel electro-optofluidic platform allows the realization of high throughput optofluidic devices with switching, tuning, and reconfiguration capability, and promises new directions in optofluidics.

© 2012 OSA

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2012 (2)

X. Serey, S. Mandal, Y. F. Chen, and D. Erickson, “DNA transport and delivery in thermal gradients near optofluidic resonators,” Phys. Rev. Lett. 108(4), 048102 (2012).
[CrossRef] [PubMed]

A. L. Forget and S. C. Kowalczykowski, “Single-molecule imaging of DNA pairing by RecA reveals a three-dimensional homology search,” Nature 482(7385), 423–427 (2012).
[CrossRef] [PubMed]

2011 (4)

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

X. D. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5(10), 591–597 (2011).
[CrossRef] [PubMed]

H. Schmidt and A. R. Hawkins, “Photonics integration of non-solid media using optofluidics,” Nat. Photonics 5(10), 598–604 (2011).
[CrossRef]

A. J. Chung and D. Erickson, “Optofluidic waveguides for reconfigurable photonic systems,” Opt. Express 19(9), 8602–8609 (2011).
[CrossRef] [PubMed]

2010 (4)

2009 (2)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

R. Shamai and U. Levy, “On chip tunable micro ring resonator actuated by electrowetting,” Opt. Express 17(2), 1116–1125 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (5)

2006 (5)

D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. 31(1), 59–61 (2006).
[CrossRef] [PubMed]

L. Diehl, B. G. Lee, P. Behroozi, M. Loncar, M. A. Belkin, F. Capasso, T. Aellen, D. Hofstetter, M. Beck, and J. Faist, “Microfluidic tuning of distributed feedback quantum cascade lasers,” Opt. Express 14(24), 11660–11667 (2006).
[CrossRef] [PubMed]

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[CrossRef] [PubMed]

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
[CrossRef]

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

2005 (1)

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

1980 (1)

A. L. Robinson, “New ways to make microcircuits smaller,” Science 208(4447), 1019–1022 (1980).
[CrossRef] [PubMed]

Adibi, A.

Aellen, T.

Almeida, V. R.

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Asghari, M.

Atabaki, A. H.

Beck, M.

Behroozi, P.

Belkin, M. A.

Bergman, K.

Biberman, A.

Brau, R. R.

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

Campbell, K.

Capasso, F.

Chen, L.

Chen, Y. F.

X. Serey, S. Mandal, Y. F. Chen, and D. Erickson, “DNA transport and delivery in thermal gradients near optofluidic resonators,” Phys. Rev. Lett. 108(4), 048102 (2012).
[CrossRef] [PubMed]

Chu, S.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466(7306), 647–651 (2010).
[CrossRef] [PubMed]

Chung, A. J.

Crozier, K.

S. Y. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Cunningham, J. E.

Diehl, L.

Domachuk, P.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1(2), 106–114 (2007).
[CrossRef]

Dong, P.

Eftekhar, A. A.

Eggleton, B. J.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1(2), 106–114 (2007).
[CrossRef]

Emery, T.

Erickson, D.

Fainman, Y.

Faist, J.

Fan, S. H.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Fan, X. D.

X. D. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5(10), 591–597 (2011).
[CrossRef] [PubMed]

Feng, D.

Ferrer, J. M.

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

Flagan, R. C.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Forget, A. L.

A. L. Forget and S. C. Kowalczykowski, “Single-molecule imaging of DNA pairing by RecA reveals a three-dimensional homology search,” Nature 482(7385), 423–427 (2012).
[CrossRef] [PubMed]

Fraser, S. E.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Groisman, A.

Haus, H. A.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Hawkins, A. R.

H. Schmidt and A. R. Hawkins, “Photonics integration of non-solid media using optofluidics,” Nat. Photonics 5(10), 598–604 (2011).
[CrossRef]

Hofstetter, D.

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Johnson, D. S.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Khan, M. J.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Klug, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Kowalczykowski, S. C.

A. L. Forget and S. C. Kowalczykowski, “Single-molecule imaging of DNA pairing by RecA reveals a three-dimensional homology search,” Nature 482(7385), 423–427 (2012).
[CrossRef] [PubMed]

Krishnamoorthy, A. V.

Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Lang, M. J.

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

Lee, B. G.

Lee, P.

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

Levy, U.

Li, G.

Li, Q.

Liang, H.

Lin, S. Y.

S. Y. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Lipson, M.

Loncar, M.

Mandal, S.

X. Serey, S. Mandal, Y. F. Chen, and D. Erickson, “DNA transport and delivery in thermal gradients near optofluidic resonators,” Phys. Rev. Lett. 108(4), 048102 (2012).
[CrossRef] [PubMed]

Manolatou, C.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Mayers, B. T.

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
[CrossRef]

Monat, C.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1(2), 106–114 (2007).
[CrossRef]

Moore, S. D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Pandey, M.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Panepucci, R. R.

Pang, L.

Patel, G.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Patel, S. S.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Pertsinidis, A.

A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466(7306), 647–651 (2010).
[CrossRef] [PubMed]

Poon, A. W.

Pradhan, S.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Psaltis, D.

D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. 31(1), 59–61 (2006).
[CrossRef] [PubMed]

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[CrossRef] [PubMed]

Qian, W.

Quake, S. R.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442(7101), 381–386 (2006).
[CrossRef] [PubMed]

Robinson, A. L.

A. L. Robinson, “New ways to make microcircuits smaller,” Science 208(4447), 1019–1022 (1980).
[CrossRef] [PubMed]

Rockwood, T.

Scherer, A.

Schmidt, B.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Schmidt, B. S.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

B. S. Schmidt, A. H. J. Yang, D. Erickson, and M. Lipson, “Optofluidic trapping and transport on solid core waveguides within a microfluidic device,” Opt. Express 15(22), 14322–14334 (2007).
[CrossRef] [PubMed]

Schmidt, H.

H. Schmidt and A. R. Hawkins, “Photonics integration of non-solid media using optofluidics,” Nat. Photonics 5(10), 598–604 (2011).
[CrossRef]

Schonbrun, E.

S. Y. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
[CrossRef] [PubMed]

Serey, X.

X. Serey, S. Mandal, Y. F. Chen, and D. Erickson, “DNA transport and delivery in thermal gradients near optofluidic resonators,” Phys. Rev. Lett. 108(4), 048102 (2012).
[CrossRef] [PubMed]

Shafiiha, R.

Shah Hosseini, E.

Shamai, R.

Sherwood-Droz, N.

Smith, B. Y.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Soltani, M.

Sun, B.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

Tang, S. K. Y.

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
[CrossRef]

Tarsa, P. B.

R. R. Brau, P. B. Tarsa, J. M. Ferrer, P. Lee, and M. J. Lang, “Interlaced optical force-fluorescence measurements for single molecule biophysics,” Biophys. J. 91(3), 1069–1077 (2006).
[CrossRef] [PubMed]

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Vezenov, D. V.

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
[CrossRef]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[CrossRef]

Wang, H.

Wang, M. D.

B. Sun, D. S. Johnson, G. Patel, B. Y. Smith, M. Pandey, S. S. Patel, and M. D. Wang, “ATP-induced helicase slippage reveals highly coordinated subunits,” Nature 478(7367), 132–135 (2011).
[CrossRef] [PubMed]

White, I. M.

X. D. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5(10), 591–597 (2011).
[CrossRef] [PubMed]

Whitesides, G. M.

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
[CrossRef]

Xu, Q. F.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Yang, A. H. J.

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Appl. Phys. Lett. (1)

S. K. Y. Tang, B. T. Mayers, D. V. Vezenov, and G. M. Whitesides, “Optical waveguiding using thermal gradients across homogenous liquids in microfluidic channel,” Appl. Phys. Lett. 88(6), 061112 (2006).
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Microfluid Nanofluid (1)

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S. Y. Lin, E. Schonbrun, and K. Crozier, “Optical manipulation with planar silicon microring resonators,” Nano Lett. 10(7), 2408–2411 (2010).
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Nature (6)

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[CrossRef] [PubMed]

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
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A. Pertsinidis, Y. Zhang, and S. Chu, “Subnanometre single-molecule localization, registration and distance measurements,” Nature 466(7306), 647–651 (2010).
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M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Improvement of thermal properties of ultra-high Q silicon microdisk resonators,” Opt. Express 15(25), 17305–17312 (2007).
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Supplementary Material (1)

» Media 1: MOV (73 KB)     

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Figures (10)

Fig. 1
Fig. 1

Design architecture for the integration of an electric microheater into an optofluidic resonator. (a) A schematic of a device. In this device, a traveling-wave resonator (such as a microring, microdisk, or racetrack) resides within a fluidic channel and is side-coupled to two waveguides that are themselves connected to form a feedback loop for the resonator. The feedback loop is extended outside the fluidic channel and is buried in an oxide layer for interfacing with a metal heater. The heater is located above the feedback arm and isolated from the fluid (electrically) and the waveguide (optically) via oxide layers. The two ends of the heater are connected to metal electrodes. The oxide cladding transfers heat from the metal heater to the waveguide. The cladding over the heater is also oxide. The yellow spheres in the fluidic channel indicate nanoparticles. (b) A simplified two-dimensional schematic of the device presented in (a) with general design parameters indicated. (c) Calculated temperature distribution of the microheater (nickel) with a Si waveguide underneath. The calculations are for a cross-section of the device as indicated in (a). A bending in the heater has been considered for the heater geometry because of the morphology of the underlying oxide layer deposited on top of the waveguide. These parameters were chosen to closely match those in fabricated devices. The waveguide is implemented on silicon-on-insulator (SOI) with a silicon device thickness of 250 nm and a buried oxide (BOX) thickness of 3 µm. In all the simulations, the cross-section of the waveguides is 440 nm (width) and 250 nm (height), and the cross-section of the heater is 2.5 µm (width) and 200 nm (height). (d) Calculated distribution of the squared magnitude of the electric field (|E|2) for the fundamental TM mode of a silicon resonator for the cross section as indicated in (a). A nanoparticle would be trapped on top of the resonator where the field strength is maximal.

Fig. 2
Fig. 2

An optical microscope image of a fabricated optofluidic resonator integrated with a microheater. Note that the resonator is within the fluidic channel, whereas the microheater is located outside. The resonator is a ‘racetrack’ with a bend radius of 10 µm and a straight length of 5 µm.

Fig. 3
Fig. 3

Experimental demonstration of electrical tuning of the optofluidic resonator shown in Fig. 2. (a) Resonator tuning by the microheater. The resonator spectrum was measured via the transmission of the waveguide as different voltages were applied to the microheater. The input power to the waveguide was in the sub-mW range. (b) Resonance wavelength dependence on the applied voltage to the microheater. Solid dots are measurements and the solid line is a prediction based on theoretical calculations.

Fig. 4
Fig. 4

Determination of the response time of the resonator to the microheater. The response of the resonator was measured via the transmission of the waveguide as a square-wave voltage, at a frequency of 3 kHz, was applied to the microheater.

Fig. 5
Fig. 5

Demonstration of nanoparticle trapping control using the electrically tunable resonator. (a) The trajectory of a single nanoparticle, optically trapped by the resonator, is presented in overlaid progressive images, taken at 0.24 s time intervals. The particle circulated on the resonator in the direction of light propagation. For t = 0 to 1.2 s, no voltage was applied to the microheater and the resonator was on resonance. For t = 1.2 to 3.3 s, a 10 kHz square-wave voltage was applied to the microheater so that the resonator was periodically tuned on- and off-resonance. The subfigure (to the right) shows the resonance shift when voltage was applied. A video of the trapping experiment is available online (Media 1). (b) The corresponding distance versus time for the particle measured by image tracking shown in (a).

Fig. 6
Fig. 6

(a) A ring resonator side-coupled to two waveguides, which are themselves connected at one end. A tunable phase shifter has been added to the connection arm. (b) Transmission spectrum of the device in (a) for three values of θ′ = + π/2 (red), 0 (green), -π/2 (blue), respectively. In (b) we have assumed τ0 = τc.

Fig. 7
Fig. 7

Experimental results on the variation of the optofluidic resonator spectrum when different voltages are applied to the microheater (from 0 V to 2 V with steps of 0.4 V).

Fig. 8
Fig. 8

Calculated distribution of the squared magnitude of the electric field (|E|2) on a cross section of a silicon waveguide. (a) The TM mode (electric field is predominantly normal to the plane of the chip). (b) The TE mode (electric field is predominantly parallel to the plane of the chip). The waveguide dimensions are the same as defined in the main text.

Fig. 9
Fig. 9

Calculated drag force on a 790 nm polystyrene nanoparticle moving with a speed of ~17 µm/s at different distances above a surface. The inset shows the nanoparticle and its distance from the resonator top surface.

Fig. 10
Fig. 10

(a) The applied square-wave voltage to the microheater at 10 kHz and the response of the resonator by measuring its transmission through the waveguide for data shown in Fig. 4. (b) Measured spectrum of the resonator at low (~sub-milli Watt) and high (~6-8 mW) input optical power.

Equations (7)

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da dt =(i ω 0 1 τ 0 1 τ c 1 τ c )a+k S in +k S 2 , S 1 = S in k * a, S 2 = S 1 e i θ ,( θ =θ+ θ 0 ), S out = S 2 k * a,
P out P in = | i(ω ω 0 )+1/ τ 0 1/ τ c i(ω ω 0 )+1/ τ 0 +1/ τ c e i θ | 2 ,
1 τ = 1 τ 0 + 1 τ c .
τ 0 = τ c = τ c /[2(1+cos θ )].
Δλ= A T V 2 KR .
Δλ= 2 θ τ c λ 0 ω 0 = θ λ 0 Q c
Δλ= 2π α T ΔT Q c = 2π α T L Q c V 2 KR

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