Abstract

In this paper we propose a time-variant photonic crystal, which can be formed by a stream of wave-length-scale microdroplets flowing through a microfluidic channel. The functionality stems from the photonic bandgap generated from the 1D periodic perturbation of refractive index. The periodicity, volume fraction and composition of both the dispersed and the continuous phases can be conveniently tuned in real time by hydrodynamic or pneumatic methods. By simulation, it is found that the time-variant nature of the proposed structure can induce an abnormal energy evolution, which is distinct from any existing photonic crystal structures. As a basic component for optofluidic systems, the droplet-based photonic crystal may find potential applications in light modulation and light confinement, and could be an ideal model for pursuing physical insights into time-variant optofluidic systems.

©2012 Optical Society of America

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  1. 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]
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    [Crossref]
  3. H. Schmidt and A. R. Hawkins, “The photonic integration of non-solid media using optofluidics,” Nat. Photonics 5(10), 598–604 (2011).
    [Crossref]
  4. P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
    [Crossref] [PubMed]
  5. S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
    [Crossref] [PubMed]
  6. H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
    [Crossref] [PubMed]
  7. B. S. Schmidt, A. H. 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]
  8. 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]
  9. D. B. Wolfe, R. S. Conroy, P. Garstecki, B. T. Mayers, M. A. Fischbach, K. E. Paul, M. Prentiss, and G. M. Whitesides, “Dynamic control of liquid-core/liquid-cladding optical waveguides,” Proc. Natl. Acad. Sci. U.S.A. 101(34), 12434–12438 (2004).
    [Crossref] [PubMed]
  10. A. Groisman, S. Zamek, K. Campbell, L. Pang, U. Levy, and Y. Fainman, “Optofluidic 1x4 switch,” Opt. Express 16(18), 13499–13508 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  13. Z. Li, Z. Zhang, A. Scherer, and D. Psaltis, “Mechanically tunable optofluidic distributed feedback dye laser,” Opt. Express 14(22), 10494–10499 (2006).
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    [Crossref] [PubMed]
  25. E. Um and J.-K. Park, “A microfluidic abacus channel for controlling the addition of droplets,” Lab Chip 9(2), 207–212 (2009).
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  26. G. F. Christopher, J. Bergstein, N. B. End, M. Poon, C. Nguyen, and S. L. Anna, “Coalescence and splitting of confined droplets at microfluidic junctions,” Lab Chip 9(8), 1102–1109 (2009).
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  27. L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
    [Crossref] [PubMed]
  28. M. Hashimoto, B. Mayers, P. Garstecki, and G. M. Whitesides, “Flowing lattices of bubbles as tunable self-assembled diffraction gratings,” Small 2(11), 1292–1298 (2006).
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    [Crossref]
  30. L. K. Chin, A. Q. Liu, Y. C. Soh, C. S. Lim, and C. L. Lin, “A reconfigurable optofluidic Michelson interferometer using tunable droplet grating,” Lab Chip 10(8), 1072–1078 (2010).
    [Crossref] [PubMed]
  31. S. K. Y. Tang, Z. Li, A. R. Abate, J. J. Agresti, D. A. Weitz, D. Psaltis, and G. M. Whitesides, “A multi-color fast-switching microfluidic droplet dye laser,” Lab Chip 9(19), 2767–2771 (2009).
    [Crossref] [PubMed]
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  43. Carbon disulifide (CS2) sometimes can be used as infrared transparent solvent, whose transparent window mainly spans at wavelengths from 8 to16µm. We select it because of its high refractive index which is 1.628. The most popular infrared solvent is carbon tetrachloride (CCl4), which is transparent at all wavelength less than 12µm. Other infrared transparent solvents include tetrachloroethylene, chloroform, dimethylformamide, dioxane, cyclohexane and benzene.
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  50. J. G. Cuennet, A. E. Vasdekis, L. De Sio, and D. Psaltis, “Optofluidic modulator based on peristaltic nematogen microflows,” Nat. Photonics 5(4), 234–238 (2011).
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  53. According to ideal gas law, a heat source at a fixed location will enlarge the volume of microbubbles as they flow through.
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    [Crossref]
  55. W. Song and D. Psaltis, “Pneumatically tunable optofluidic 2×2 switch for reconfigurable optical circuit,” Lab Chip 11(14), 2397–2402 (2011).
    [Crossref] [PubMed]

2012 (4)

R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, “Droplet based microfluidics,” Rep. Prog. Phys. 75(1), 016601 (2012).
[Crossref] [PubMed]

Y. Yang, A. Q. Liu, L. K. Chin, X. M. Zhang, D. P. Tsai, C. L. Lin, C. Lu, G. P. Wang, and N. I. Zheludev, “Optofluidic waveguide as a transformation optics device for lightwave bending and manipulation,” Nat Commun 3, 651 (2012).
[Crossref] [PubMed]

M. T. Guo, A. Rotem, J. A. Heyman, and D. A. Weitz, “Droplet microfluidics for high-throughput biological assays,” Lab Chip 12(12), 2146–2155 (2012).
[Crossref] [PubMed]

M. Mancuso, J. M. Goddard, and D. Erickson, “Nanoporous polymer ring resonators for biosensing,” Opt. Express 20(1), 245–255 (2012).
[Crossref] [PubMed]

2011 (9)

S. Xiong, A. Q. Liu, L. K. Chin, and Y. Yang, “An optofluidic prism tuned by two laminar flows,” Lab Chip 11(11), 1864–1869 (2011).
[Crossref] [PubMed]

S. Jakiela, S. Makulska, P. M. Korczyk, and P. Garstecki, “Speed of flow of individual droplets in microfluidic channels as a function of the capillary number, volume of droplets and contrast of viscosities,” Lab Chip 11(21), 3603–3608 (2011).
[Crossref] [PubMed]

J. G. Cuennet, A. E. Vasdekis, L. De Sio, and D. Psaltis, “Optofluidic modulator based on peristaltic nematogen microflows,” Nat. Photonics 5(4), 234–238 (2011).
[Crossref]

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

E. Castro-Hernández, W. van Hoeve, D. Lohse, and J. M. Gordillo, “Microbubble generation in a co-flow device operated in a new regime,” Lab Chip 11(12), 2023–2029 (2011).
[Crossref] [PubMed]

L. Shui, A. van den Berg, and J. C. T. Eijkel, “Scalable attoliter monodisperse droplet formation using multiphase nano-microfluidics,” Microfluid. Nanofluid. 11(1), 87–92 (2011).
[Crossref]

K. Zhang, A. Jian, X. Zhang, Y. Wang, Z. Li, and H. Y. Tam, “Laser-induced thermal bubbles for microfluidic applications,” Lab Chip 11(7), 1389–1395 (2011).
[Crossref] [PubMed]

J.-M. Lim, J. P. Urbanski, T. Thorsen, and S.-M. Yang, “Pneumatic control of a liquid-core/liquid-cladding waveguide as the basis for an optofluidic switch,” Appl. Phys. Lett. 98(4), 044101 (2011).
[Crossref]

W. Song and D. Psaltis, “Pneumatically tunable optofluidic 2×2 switch for reconfigurable optical circuit,” Lab Chip 11(14), 2397–2402 (2011).
[Crossref] [PubMed]

2010 (3)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

A. B. Theberge, F. Courtois, Y. Schaerli, M. Fischlechner, C. Abell, F. Hollfelder, and W. T. S. Huck, “Microdroplets in microfluidics: an evolving platform for discoveries in chemistry and biology,” Angew. Chem. Int. Ed. Engl. 49(34), 5846–5868 (2010).
[PubMed]

L. K. Chin, A. Q. Liu, Y. C. Soh, C. S. Lim, and C. L. Lin, “A reconfigurable optofluidic Michelson interferometer using tunable droplet grating,” Lab Chip 10(8), 1072–1078 (2010).
[Crossref] [PubMed]

2009 (7)

S. K. Y. Tang, Z. Li, A. R. Abate, J. J. Agresti, D. A. Weitz, D. Psaltis, and G. M. Whitesides, “A multi-color fast-switching microfluidic droplet dye laser,” Lab Chip 9(19), 2767–2771 (2009).
[Crossref] [PubMed]

E. Um and J.-K. Park, “A microfluidic abacus channel for controlling the addition of droplets,” Lab Chip 9(2), 207–212 (2009).
[Crossref] [PubMed]

G. F. Christopher, J. Bergstein, N. B. End, M. Poon, C. Nguyen, and S. L. Anna, “Coalescence and splitting of confined droplets at microfluidic junctions,” Lab Chip 9(8), 1102–1109 (2009).
[Crossref] [PubMed]

X. Mao, S.-C. S. Lin, M. I. Lapsley, J. Shi, B. K. Juluri, and T. J. Huang, “Tunable liquid gradient refractive index (L-GRIN) lens with two degrees of freedom,” Lab Chip 9(14), 2050–2058 (2009).
[Crossref] [PubMed]

L. Shui, E. S. Kooij, D. Wijnperle, A. van der Berg, and J. C. T. Eijkel, “Liquid crystallography: 3D microdroplet arrangements using microfluidics,” Soft Matter 5(14), 2708–2712 (2009).
[Crossref]

E. Brouzes, M. Medkova, N. Savenelli, D. Marran, M. Twardowski, J. B. Hutchison, J. M. Rothberg, D. R. Link, N. Perrimon, and M. L. Samuels, “Droplet microfluidic technology for single-cell high-throughput screening,” Proc. Natl. Acad. Sci. U.S.A. 106(34), 14195–14200 (2009).
[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]

2008 (3)

A. Groisman, S. Zamek, K. Campbell, L. Pang, U. Levy, and Y. Fainman, “Optofluidic 1x4 switch,” Opt. Express 16(18), 13499–13508 (2008).
[Crossref] [PubMed]

S. Y. Teh, R. Lin, L. H. Hung, and A. P. Lee, “Droplet microfluidics,” Lab Chip 8(2), 198–220 (2008).
[Crossref] [PubMed]

L. K. Chin, A. Q. Liu, J. B. Zhang, C. S. Lim, and Y. C. Soh, “An on-chip liquid tunable grating using multiphase droplet microfluidics,” Appl. Phys. Lett. 93(16), 164107 (2008).
[Crossref]

2007 (6)

M. Prakash and N. Gershenfeld, “Microfluidic bubble logic,” Science 315(5813), 832–835 (2007).
[Crossref] [PubMed]

V. Lien and F. Vollmer, “Microfluidic flow rate detection based on integrated optical fiber cantilever,” Lab Chip 7(10), 1352–1356 (2007).
[Crossref] [PubMed]

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, “Optofluidic ring resonator based dye laser,” Appl. Phys. Lett. 90(22), 221101 (2007).
[Crossref]

H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express 15(15), 9139–9146 (2007).
[Crossref] [PubMed]

B. S. Schmidt, A. H. 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]

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

2006 (5)

Z. Li, Z. Zhang, A. Scherer, and D. Psaltis, “Mechanically tunable optofluidic distributed feedback dye laser,” Opt. Express 14(22), 10494–10499 (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]

P. S. Dittrich and A. Manz, “Lab-on-a-chip: microfluidics in drug discovery,” Nat. Rev. Drug Discov. 5(3), 210–218 (2006).
[Crossref] [PubMed]

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442(7102), 551–554 (2006).
[Crossref] [PubMed]

M. Hashimoto, B. Mayers, P. Garstecki, and G. M. Whitesides, “Flowing lattices of bubbles as tunable self-assembled diffraction gratings,” Small 2(11), 1292–1298 (2006).
[Crossref] [PubMed]

2005 (3)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nat. Mater. 4(7), 530–533 (2005).
[Crossref] [PubMed]

2004 (3)

D. B. Wolfe, R. S. Conroy, P. Garstecki, B. T. Mayers, M. A. Fischbach, K. E. Paul, M. Prentiss, and G. M. Whitesides, “Dynamic control of liquid-core/liquid-cladding optical waveguides,” Proc. Natl. Acad. Sci. U.S.A. 101(34), 12434–12438 (2004).
[Crossref] [PubMed]

Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
[Crossref] [PubMed]

Y.-C. Tan, J. S. Fisher, A. I. Lee, V. Cristini, and A. P. Lee, “Design of microfluidic channel geometries for the control of droplet volume, chemical concentration, and sorting,” Lab Chip 4(4), 292–298 (2004).
[Crossref] [PubMed]

2003 (3)

S. L. Anna, N. Bontoux, and H. A. Stone, “Formation of dispersions using flow focusing in microchannels,” Appl. Phys. Lett. 82(3), 364–366 (2003).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

J. Lee, H. Park, J. Jung, and H. Kwak, “Bubble nucleation micro line heaters,” J. Heat Transfer 125(4), 687–692 (2003).
[Crossref]

2001 (1)

T. Thorsen, R. W. Roberts, F. H. Arnold, and S. R. Quake, “Dynamic pattern formation in a vesicle-generating microfluidic device,” Phys. Rev. Lett. 86(18), 4163–4166 (2001).
[Crossref] [PubMed]

1999 (2)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54(1-2), 3–15 (1999).
[Crossref]

J. S. Forsi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1999).

1975 (1)

H. Kogelnik, “An introduction to integrated optics,” IEEE Trans. Microw. Theory Tech. 23(1), 2–16 (1975).
[Crossref]

Abate, A. R.

S. K. Y. Tang, Z. Li, A. R. Abate, J. J. Agresti, D. A. Weitz, D. Psaltis, and G. M. Whitesides, “A multi-color fast-switching microfluidic droplet dye laser,” Lab Chip 9(19), 2767–2771 (2009).
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Carbon disulifide (CS2) sometimes can be used as infrared transparent solvent, whose transparent window mainly spans at wavelengths from 8 to16µm. We select it because of its high refractive index which is 1.628. The most popular infrared solvent is carbon tetrachloride (CCl4), which is transparent at all wavelength less than 12µm. Other infrared transparent solvents include tetrachloroethylene, chloroform, dimethylformamide, dioxane, cyclohexane and benzene.

According to ideal gas law, a heat source at a fixed location will enlarge the volume of microbubbles as they flow through.

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Figures (9)

Fig. 1
Fig. 1 Schematic illustration of droplet-based U-shape PC waveguide.

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Fig. 2
Fig. 2 (a) Normal index-guiding waveguide. (b) Waveguide with periodic modulation of RI. (c) Linear dispersion curve in (a). (d) Splitting of the waveguide modes in (b).

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Fig. 3
Fig. 3 The two-dimensional FDTD model and results of the TvPC structure. (a) The model of as-proposed droplet-based TvPC waveguide for calculation. (b) The empty waveguide model for reference. (c) The transmittance vs. frequency observed at the output point when the waveguide is excited at the light source point.

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Fig. 4
Fig. 4 Energy evolution in droplet-based 1D TvPC. (a) The energy distributions in a finite TvPC at the 1st and the 2nd order waveguide modes, respectively. The waveguide is excited by a continuous source outside the left end of the channel. (b)-(e) The 1st and 2nd order energy distributions in an infinite 1D droplet-based TvPC at (b) t = 0, (c) t = T/4, (d) t = T/2 and (e) t = 3T/4, where T is the time period for the TvPC to restore. The dashed arrows indicate the evolution of electromagnetic energy, along with the flow of microbubbles.

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Fig. 5
Fig. 5 Relationships between transmittance and lengths of microbubbles. (a) Schematic illustration of different microbubble sizes L. (b) The transmittance spectra of the 1D TvPC waveguide for different microbubble lengths, of 1.0a, 1.2a, 1.4a, 1.6a, respectively.

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Fig. 6
Fig. 6 Relationships between transmittance and RI of continuous phase adopted in droplet-based 1D TvPCs (a) The transmittance of TvPC with different RIs, where center frequencies of the bandgaps are marked by orange triangles. (b) The center frequency of the bandgap as a function of RIs.

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Fig. 7
Fig. 7 Light modulation at the bandedge frequency of the droplet-based 1D TvPC. (a) The energy evolution at the frequency f = 0.31c/a, in a time period T. (b) The transmission spectra of the waveguide at t = 0, t = T/4, t = T/2, t = 3T/4, respectively. (c) The transmittance modulation at f1 = c/a, f2 = 0.33c/a, respectively, as a function of time from 0 to 5T.

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Fig. 8
Fig. 8 Relationships between defect lengths and defect mode frequencies. (a) Schematic models showing different defective TvPCs produced by inserting a longer liquid section at the center. The defect length d is defined to be the distance between two bubbles closest to the center. (b) The transmittance spectra of the defective TvPC, where the dashed arrows indicate the shifts of the defect mode by variation of d. (c) The plot of defect mode frequency as a function of defect length.

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Fig. 9
Fig. 9 Behaviors of dynamic defects in droplet-based 1D TvPC. (a) Electromagnetic energy distribution in a defective TvPC waveguide at t = 2.5T, t = 3.5T, t = 4.5T, t = 5.5T and t = 6.5T, the defect length is 3.2a. The points with highest energy density are marked by orange triangles. (b) Transmittance spectra of the defective TvPC, where the defect mode peaks are clearly shown. (c) The transmittance at the defect mode frequency as a function of time, from 0 to 9T, the period for a dynamic defect to flow through the TvPC structure; blue circles are data points, and the red line is only guide for eyes.

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Equations (2)

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∇× [n(x)] −2 ∇× e ik⋅r E k (x)= (ω(k)/c) 2 e ik⋅r E k (x),
T= ∫ |E | 2 dl/ ∫ | E 0 | 2 dl,

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