Abstract

The application of on-chip optical trapping and Raman spectroscopy using a dual-waveguide trap has so far been limited to relatively big synthetic and biological particles (e.g., polystyrene beads and blood cells). Here, from simulations, we present the capabilities of dual-waveguide traps built from composite SiO2-Si3N4 waveguides for optical trapping of extracellular vesicles (EVs). EVs, tiny cell-derived particles of size in the range 30−1000 nm, strongly attract attention as potential biomarkers for cancer. EVs are hard to trap, because of their smallness and low index contract w.r.t. water. This poses a challenge for on-chip trapping. From finite-difference time-domain simulations we obtain the narrow beam emitted from the waveguide facet into water, for λ = 785 nm. For a pair of such beams, in a counter-propagating geometry and for facet separations of 5, 10 and 15 µm, we derive the inter-facet optical field, which has a characteristic interference pattern with hot spots for trapping, and calculate the optical force exerted on EVs of size in the range 50−1000 nm, as a function of EV position. We use two refractive index models for the EV optical properties. Integration of the force curves leads to the trapping potentials, which are well-shaped in the transverse and oscillatory in the longitudinal direction. By applying Ashkin’s criterion, the conditions for stable trapping are established, the central result of this work. Very small EVs can be stably trapped with the traps by applying a power also suitable for Raman spectroscopy, down to a smallest EV diameter of 115 nm. We thus argue that this dual-waveguide trap is a promising lab-on-a-chip device with clinical relevance for diagnosis of cancer.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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2018 (1)

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

2017 (2)

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
[Crossref] [PubMed]

2015 (4)

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4(2), 189–207 (2015).

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (4)

P. Løvhaugen, B. S. Ahluwalia, T. R. Huser, and O. G. Hellesø, “Serial Raman spectroscopy of particles trapped on a waveguide,” Opt. Express 21(3), 2964–2970 (2013).
[Crossref] [PubMed]

J. W. Chan, “Recent advances in laser tweezers Raman spectroscopy (LTRS) for label-free analysis of single cells,” J. Biophotonics 6(1), 36–48 (2013).
[Crossref] [PubMed]

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

F. Properzi, M. Logozzi, and S. Fais, “Exosomes: the future of biomarkers in medicine,” Biomarkers Med. 7(5), 769–778 (2013).
[Crossref] [PubMed]

2012 (3)

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
[Crossref] [PubMed]

2011 (2)

M. M. van Leest, F. Bernal Arango, and J. Caro, “Optical forces and trapping potentials of a dual-waveguide trap based on multimode solid-core waveguides,” J. Eur. Opt. Soc. 6, 11022 (2011).
[Crossref]

P. M. Bendix and L. B. Oddershede, “Expanding the optical trapping range of lipid vesicles to the nanoscale,” Nano Lett. 11(12), 5431–5437 (2011).
[Crossref] [PubMed]

2010 (3)

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

S. Vyawahare, A. D. Griffiths, and C. A. Merten, “Miniaturization and parallelization of biological and chemical assays in microfluidic devices,” Chem. Biol. 17(10), 1052–1065 (2010).
[Crossref] [PubMed]

2008 (2)

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (1)

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

2001 (1)

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

1998 (1)

P. Zemánek, A. Jonaš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151(4–6), 273–285 (1998).
[Crossref]

1986 (1)

Ahluwalia, B. S.

P. Løvhaugen, B. S. Ahluwalia, T. R. Huser, and O. G. Hellesø, “Serial Raman spectroscopy of particles trapped on a waveguide,” Opt. Express 21(3), 2964–2970 (2013).
[Crossref] [PubMed]

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

Ahmadi, A.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Albert, J.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Allard, W. J.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Alocilja, E.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Althani, A.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Ashkin, A.

Aziz, H.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Becker, M.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Beleites, C.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Bellini, N.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

Bendix, P. M.

P. M. Bendix and L. B. Oddershede, “Expanding the optical trapping range of lipid vesicles to the nanoscale,” Nano Lett. 11(12), 5431–5437 (2011).
[Crossref] [PubMed]

Bernal Arango, F.

M. M. van Leest, F. Bernal Arango, and J. Caro, “Optical forces and trapping potentials of a dual-waveguide trap based on multimode solid-core waveguides,” J. Eur. Opt. Soc. 6, 11022 (2011).
[Crossref]

Bjorkholm, J. E.

Boerkamp, M.

Böing, A. N.

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

Bragheri, F.

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Breakefield, X. O.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Brune, C.

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W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
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A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
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W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
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Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
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S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
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N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
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Flohr, P.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
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A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
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Girda, E.

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Heideman, R. G.

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Hellesø, O. G.

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Hoekman, M.

Hoorfar, M.

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Hwang, B.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
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Kalluri, R.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
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Kaye, J.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
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Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
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S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
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S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
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J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
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Kruglik, S. G.

I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
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Laaksonen, T.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
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Lam, K.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
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Lam, K. S.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
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I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
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Latka, I.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
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LeBleu, V. S.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
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Lee, C.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
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Leinse, A.

Leiserowitz, G. S.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
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Li, Y. Q.

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

Ling, D. X.

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

Ling, L.

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

Liška, M.

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

P. Zemánek, A. Jonaš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151(4–6), 273–285 (1998).
[Crossref]

Logozzi, M.

F. Properzi, M. Logozzi, and S. Fais, “Exosomes: the future of biomarkers in medicine,” Biomarkers Med. 7(5), 769–778 (2013).
[Crossref] [PubMed]

Løvhaugen, P.

P. Løvhaugen, B. S. Ahluwalia, T. R. Huser, and O. G. Hellesø, “Serial Raman spectroscopy of particles trapped on a waveguide,” Opt. Express 21(3), 2964–2970 (2013).
[Crossref] [PubMed]

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Luecke, L. B.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Luka, G.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Malki, A.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Matera, J.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Mayer, G.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Mazilu, M.

Meijer, D. H.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Melo, S. A.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Merten, C. A.

S. Vyawahare, A. D. Griffiths, and C. A. Merten, “Miniaturization and parallelization of biological and chemical assays in microfluidic devices,” Chem. Biol. 17(10), 1052–1065 (2010).
[Crossref] [PubMed]

Miller, M. C.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Minzioni, P.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

Mittendorf, E. A.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Mulligan, M. S.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
[Crossref] [PubMed]

Najjaran, H.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Nanou, A.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Nieuwland, R.

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

Oddershede, L. B.

P. M. Bendix and L. B. Oddershede, “Expanding the optical trapping range of lipid vesicles to the nanoscale,” Nano Lett. 11(12), 5431–5437 (2011).
[Crossref] [PubMed]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Onstenk, W.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Osellame, R.

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Otto, C.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Paterson, L.

Pilarsky, C.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Piwnica-Worms, D.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Pokorny, P.

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

Popp, J.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Properzi, F.

F. Properzi, M. Logozzi, and S. Fais, “Exosomes: the future of biomarkers in medicine,” Biomarkers Med. 7(5), 769–778 (2013).
[Crossref] [PubMed]

Rahbari, N.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Ramponi, R.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

Rao, C.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Reissfelder, C.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Repollet, M.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Rescigno, P.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Riches, A.

Rojalin, T.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Roos, D.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Rothhardt, M.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Saari, H.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Schuster, K.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Sena-Esteves, M.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Šery, M.

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

Sibbett, W.

Skog, J.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Sleijfer, S.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Smith, D.

Smith, Z. J.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
[Crossref] [PubMed]

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Spittel, R.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Šrámek, L.

P. Zemánek, A. Jonaš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151(4–6), 273–285 (1998).
[Crossref]

Stanca, S.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Sturk, A.

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

Subramaniam, V.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Subramanian, A. Z.

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

Tatischeff, I.

I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
[Crossref] [PubMed]

Terstappen, L. W.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Terstappen, L. W. M. M.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Tibbe, A. G.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Tran, D.

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
[Crossref] [PubMed]

Turpin, P. Y.

I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
[Crossref] [PubMed]

Uhr, J. W.

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

Unger, S.

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

van Dalum, G.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

van den Berg, T. K.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

van der Pol, E.

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

van Leest, M. M.

M. M. van Leest, F. Bernal Arango, and J. Caro, “Optical forces and trapping potentials of a dual-waveguide trap based on multimode solid-core waveguides,” J. Eur. Opt. Soc. 6, 11022 (2011).
[Crossref]

van Leest, T.

van Manen, H. J.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

van Rijn, S.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Verkuijlen, P.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Viitala, T.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Vishnubhatla, K. C.

N. Bellini, K. C. Vishnubhatla, F. Bragheri, L. Ferrara, P. Minzioni, R. Ramponi, I. Cristiani, and R. Osellame, “Femtosecond laser fabricated monolithic chip for optical trapping and stretching of single cells,” Opt. Express 18(5), 4679–4688 (2010).
[Crossref] [PubMed]

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Vyawahare, S.

S. Vyawahare, A. D. Griffiths, and C. A. Merten, “Miniaturization and parallelization of biological and chemical assays in microfluidic devices,” Chem. Biol. 17(10), 1052–1065 (2010).
[Crossref] [PubMed]

Wachsmann-Hogiu, S.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Weitz, J.

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Wilkinson, J. S.

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

Wittendorp, P.

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Wolthers, K.

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Wörhoff, K.

K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4(2), 189–207 (2015).

Wu, M. Y.

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

Würdinger, T.

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Yliperttula, M.

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

Zemánek, P.

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

P. Zemánek, A. Jonaš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151(4–6), 273–285 (1998).
[Crossref]

Zeune, L. L.

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Adv. Opt. Technol. (1)

K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform,” Adv. Opt. Technol. 4(2), 189–207 (2015).

Anal. Chem. (1)

R. P. Carney, S. Hazari, M. Colquhoun, D. Tran, B. Hwang, M. S. Mulligan, J. D. Bryers, E. Girda, G. S. Leiserowitz, Z. J. Smith, and K. S. Lam, “Multispectral optical tweezers for biochemical fingerprinting of CD9-positive exosome subpopulations,” Anal. Chem. 89(10), 5357–5363 (2017).
[Crossref] [PubMed]

Biomarkers Med. (1)

F. Properzi, M. Logozzi, and S. Fais, “Exosomes: the future of biomarkers in medicine,” Biomarkers Med. 7(5), 769–778 (2013).
[Crossref] [PubMed]

Biophys. J. (1)

H. J. van Manen, P. Verkuijlen, P. Wittendorp, V. Subramaniam, T. K. van den Berg, D. Roos, and C. Otto, “Refractive index sensing of green fluorescent proteins in living cells using fluorescence lifetime imaging microscopy,” Biophys. J. 94(8), L67–L69 (2008).
[Crossref] [PubMed]

Chem. Biol. (1)

S. Vyawahare, A. D. Griffiths, and C. A. Merten, “Miniaturization and parallelization of biological and chemical assays in microfluidic devices,” Chem. Biol. 17(10), 1052–1065 (2010).
[Crossref] [PubMed]

Clin. Cancer Res. (1)

W. J. Allard, J. Matera, M. C. Miller, M. Repollet, M. C. Connelly, C. Rao, A. G. Tibbe, J. W. Uhr, and L. W. Terstappen, “Tumor cells circulate in the peripheral blood of all major carcinomas but not in healthy subjects or patients with nonmalignant diseases,” Clin. Cancer Res. 10(20), 6897–6904 (2004).
[Crossref] [PubMed]

J. Biophotonics (2)

J. W. Chan, “Recent advances in laser tweezers Raman spectroscopy (LTRS) for label-free analysis of single cells,” J. Biophotonics 6(1), 36–48 (2013).
[Crossref] [PubMed]

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

J. Eur. Opt. Soc. (1)

M. M. van Leest, F. Bernal Arango, and J. Caro, “Optical forces and trapping potentials of a dual-waveguide trap based on multimode solid-core waveguides,” J. Eur. Opt. Soc. 6, 11022 (2011).
[Crossref]

J. Extracell. Vesicles (2)

Z. J. Smith, C. Lee, T. Rojalin, R. P. Carney, S. Hazari, A. Knudson, K. Lam, H. Saari, E. L. Ibañez, T. Viitala, T. Laaksonen, M. Yliperttula, and S. Wachsmann-Hogiu, “Single exosome study reveals subpopulations distributed among cell lines with variability related to membrane content,” J. Extracell. Vesicles 4(1), 28533 (2015).
[Crossref] [PubMed]

I. Tatischeff, E. Larquet, J. M. Falcón-Pérez, P. Y. Turpin, and S. G. Kruglik, “Fast characterisation of cell-derived extracellular vesicles by nanoparticles tracking analysis, cryo-electron microscopy, and Raman tweezers microspectroscopy,” J. Extracell. Vesicles 1(1), 19179 (2012).
[Crossref] [PubMed]

Lab Chip (2)

O. G. Hellesø, P. Løvhaugen, A. Z. Subramanian, J. S. Wilkinson, and B. S. Ahluwalia, “Surface transport and stable trapping of particles and cells by an optical waveguide loop,” Lab Chip 12(18), 3436–3440 (2012).
[Crossref] [PubMed]

S. Dochow, M. Becker, R. Spittel, C. Beleites, S. Stanca, I. Latka, K. Schuster, J. Kobelke, S. Unger, T. Henkel, G. Mayer, J. Albert, M. Rothhardt, C. Krafft, and J. Popp, “Raman-on-chip device and detection fibres with fibre Bragg grating for analysis of solutions and particles,” Lab Chip 13(6), 1109–1113 (2013).
[Crossref] [PubMed]

Nano Lett. (1)

P. M. Bendix and L. B. Oddershede, “Expanding the optical trapping range of lipid vesicles to the nanoscale,” Nano Lett. 11(12), 5431–5437 (2011).
[Crossref] [PubMed]

Nat. Cell Biol. (1)

J. Skog, T. Würdinger, S. van Rijn, D. H. Meijer, L. Gainche, M. Sena-Esteves, W. T. Curry, B. S. Carter, A. M. Krichevsky, and X. O. Breakefield, “Glioblastoma microvesicles transport RNA and proteins that promote tumour growth and provide diagnostic biomarkers,” Nat. Cell Biol. 10(12), 1470–1476 (2008).
[Crossref] [PubMed]

Nat. Methods (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Nature (1)

S. A. Melo, L. B. Luecke, C. Kahlert, A. F. Fernandez, S. T. Gammon, J. Kaye, V. S. LeBleu, E. A. Mittendorf, J. Weitz, N. Rahbari, C. Reissfelder, C. Pilarsky, M. F. Fraga, D. Piwnica-Worms, and R. Kalluri, “Glypican-1 identifies cancer exosomes and detects early pancreatic cancer,” Nature 523(7559), 177–182 (2015).
[Crossref] [PubMed]

Oncotarget (1)

A. Nanou, F. A. W. Coumans, G. van Dalum, L. L. Zeune, D. Dolling, W. Onstenk, M. Crespo, M. S. Fontes, P. Rescigno, G. Fowler, P. Flohr, C. Brune, S. Sleijfer, J. S. de Bono, and L. W. M. M. Terstappen, “Circulating tumor cells, tumor-derived extracellular vesicles and plasma cytokeratins in castration-resistant prostate cancer patients,” Oncotarget 9(27), 19283–19293 (2018).
[Crossref] [PubMed]

Opt. Commun. (1)

P. Zemánek, A. Jonaš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151(4–6), 273–285 (1998).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Pharmacol. Rev. (1)

E. van der Pol, A. N. Böing, P. Harrison, A. Sturk, and R. Nieuwland, “Classification, functions, and clinical relevance of extracellular vesicles,” Pharmacol. Rev. 64(3), 676–705 (2012).
[Crossref] [PubMed]

Proc. SPIE (1)

J. Ježek, P. Zemánek, A. Jonáš, M. Šery, P. Pokorny, and M. Liška, “Behavior of nanoparticle and microparticle in the standing wave trap,” Proc. SPIE 4356, 318–326 (2001).
[Crossref]

Sci. Rep. (1)

M. Y. Wu, D. X. Ling, L. Ling, W. Li, and Y. Q. Li, “Stable optical trapping and sensitive characterization of nanostructures using standing-wave Raman tweezers,” Sci. Rep. 7(18042), 42930 (2017).
[Crossref] [PubMed]

Sensors (Basel) (1)

G. Luka, A. Ahmadi, H. Najjaran, E. Alocilja, M. DeRosa, K. Wolthers, A. Malki, H. Aziz, A. Althani, and M. Hoorfar, “Microfluidics integrated biosensors: a leading technology towards lab-on-a-chip and sensing applications,” Sensors (Basel) 15(12), 30011–30031 (2015).
[Crossref] [PubMed]

Other (5)

TriPleX is a trademark for the waveguide technology of LioniX International BV.

W. Lee, Optical Sciences, University of Twente, Drienerloolaan 5, Enschede 7500 AE, The Netherlands, A. Nanou, L.G. Rikkert, F.A.W. Coumans, C. Otto, L.W.M.M. Terstappen and H.L. Offerhaus are preparing a manuscript to be called “Label-free prostate cancer detection by characterization of extracellular vesicles using Raman spectroscopy.”

Lumerical FDTD Solutions, Inc., http://www.lumerical.com/tcad-products/fdtd/ (accessed June 26, 2018).

The expression for the gradient force goes back to Eq. (2) of [16], the pioneering work of A. Ashkin. The difference with Eq. (2) in [16] involves typographic errors and our prefactor π instead of (1/2). Further, our equation has no minus sign and gives the direction of the force vector. Finally, we use SI units.

F. Schreuder, LioniX International BV, Hengelosestraat 500, 7521 AN Enschede, The Netherlands (personal communication, 2018).

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Figures (6)

Fig. 1
Fig. 1 (a) Cross section of the composite SiO2−Si3N4 waveguide, the building block of the dual-waveguide trap. The material inside and outside the square box with Si3N4 walls is SiO2. (b) Three-dimensional impression of the dual-waveguide trap. The waveguide facets, with separation w, are part of the walls of the fluidic channel. The origin of the coordinate system is the trap centre, where in the figure an EV is located with a core-shell structure.
Fig. 2
Fig. 2 (a) Profile of the TE mode of the waveguide in Fig. 1(a), for a wavelength of 785 nm. The colors indicate intensity, red (blue) meaning high (low), and do not relate to the scale bar to the right. (b) Energy density of the optical field in the xy-plane, both in the waveguide and the water, obtained from a FDTD simulation. The horizontal dashed line is the beam axis. Vertical dashed lines indicate the facet position and are the transverse lines for which in (d) beam profiles are plotted. The color bar defines the energy-density values. (c) Longitudinal energy-density profile on the beam axis. (d) Transverse beam profiles on the axes in (b).
Fig. 3
Fig. 3 Time averaged energy density in the yx-plane for dual-waveguide traps with a facet separation of 5, 10 and 15 μm. The total power supplied to each trap is 1 W. The 5 μm trap has one global hot region centred between the facets. The 10 and 15 μm traps have two global hot regions, each near a facets. The color bar defines the energy-density values.
Fig. 4
Fig. 4 Force curves for the 5 and 15 µm traps, calculated using the volumetric technique. The black dots have been obtained using Eq. (2). The legends in (a) define EV size and EV index model (homogeneous vs. core-shell) and apply to each panel. (a) Transverse force F y (y) for the 5 µm trap. (b) Transverse force F z (z) for the 5 µm trap. (c) Longitudinal force F x (x) for the 5 µm trap. (d) Longitudinal force F x (x) for the 15 µm trap, with part of the x-axis omitted to obtain the same horizontal scale as in (a-c). The curves in (a-d) are piecewise cubic spline interpolations between the data points. F y (y) and F z (z) curves have 15 data points. F x (x) curves have 33 data points per µm.
Fig. 5
Fig. 5 Normalized trapping potentials for the 5 and 15 µm traps for 100 mW of optical power supplied to the traps, calculated from the force curves in Fig. 4. The legends in (a) define EV sizes and the EV index model (homogeneous versus core-shell) and apply to each panel. (a) transverse potential U y (y)/kT for the 5 µm. (b). Longitudinal potential U x (x)/kT for the 5 µm trap. (c) Longitudinal potential U x (x)/kT for the 15 µm trap, with part of the x-axis omitted to obtain the same horizontal scale as in (a) and (b).
Fig. 6
Fig. 6 (a)-(c) Potential wells for the 5 µm trap in case of stable trapping under conditions as indicated above the panels. (a) The transverse well U y /kT. The indicated knee points limit the confined Brownian motion, as discussed in the text. (b) The deepest local well of U x /kT. (c) The global well U x /kT. (d)-(f) Stability curves for the three wells as mentioned in the panels. The legends in (d) define the trap sizes and the EV index model (homogeneous versus core-shell) and apply to each of the stability curves in (d), (e) and (f).

Tables (1)

Tables Icon

Table 1 Normalized trap stiffnesses κ x and κ y of the strongest trapping sites for the three traps for diameters of core-shell EVs as indicated. The quantities d EV , w, κ x(y) denote EV diameter, facet separation of the trap, and stiffnesses for the x(y)-direction, respectively.

Equations (4)

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

< f >= ε 0 ε b ( < E > )< E >+iω ε 0 ( ε EV ε b )< E >×< B >.
< F >= π ε 0 ε b d EV 3 8 ( m 2 1 m 2 +2 )< | E | 2 >,m= ε EV / ε b .
U y ( x 0 , y 0 ,0)= y 0 < F x 0 ,y,0 (y)> dy.
U x ( x 0 )U( x 0 ,0,0)= x 1 x 0 < F x (x)> dx.

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