Abstract

Chiral resolution is a fundamental problem in pharmaceutics or agrochemicals, so a great effort has been made to generate experimental techniques capable of producing mechanical separation of a mixture of enantiomers. Unlike other techniques that are usually employed, such as chiral resolving agents or chiral chromatography, we propose a new technique which is directly applicable in solution and without further processing. This technique is based on optical forces, since we show that with the proper design of the polarization states of the incident beams and temporal dephasing, a chiral sensitive optical conveyor can be obtained that is able to transport enantiomers in opposite directions. The implementation of such an optical conveyor with the required focused optical fields produces a well-defined trapping region for each enantiomer, since theoretical simulations over a large number of chiral particle trajectories show that it is possible to reach values of enantiomeric excess of over 99%.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (2)

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photonics 3, 304–309 (2016).
[Crossref]

D. E. Fernandes and M. G. Silveirinha, “Single-beam optical conveyor belt for chiral particles,” Phys. Rev. Appl. 6, 014016 (2016).
[Crossref]

2015 (5)

D. S. Bradshaw and D. L. Andrews, “Laser optical separation of chiral molecules,” Opt. Lett. 40, 677–680 (2015).
[Crossref] [PubMed]

L. Carretero, P. Acebal, C. Garcia, and S. Blaya, “Periodic trajectories obtained with an active tractor beam using azimuthal polarization: Design of particle exchanger,” IEEE Photonics J. 7, 3400112 (2015).
[Crossref]

L. Carretero, P. Acebal, C. Garcia, and S. Blaya, “Helical tractor beam: analytical solution of rayleigh particle dynamics,” Opt. Express 23, 20529–20539 (2015).
[Crossref] [PubMed]

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” P. Natl. Acad. Sci. USA 112, 13190–13194 (2015).
[Crossref]

M. H. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

2014 (8)

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

G. Tkachenko and E. Brasselet, “Optofluidic sorting of material chirality by chiral light,” Nat. Commun. 5, 3577 (2014).
[Crossref] [PubMed]

G. Tkachenko and E. Brasselet, “Helicity-dependent three-dimensional optical trapping of chiral microparticles,” Nat. Commun. 5, 4491 (2014).
[Crossref] [PubMed]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[PubMed]

D. B. Ruffner and D. G. Grier, “Universal, strong and long-ranged trapping by optical conveyors,” Opt. Express 22, 26840–26849 (2014).
[Crossref]

L. Carretero, P. Acebal, and S. Blaya, “Three-dimensional analysis of optical forces generated by an active tractor beam using radial polarization,” Opt. Express 22, 3284–3295 (2014).
[Crossref] [PubMed]

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref] [PubMed]

D. S. Bradshaw and D. L. Andrews, “Chiral discrimination in optical trapping and manipulation,” New J. Phys. 16, 103021 (2014).
[Crossref]

2013 (4)

A. Eilam and M. Shapiro, “Spatial separation of dimers of chiral molecules,” Phys. Rev. Lett. 110, 213004 (2013).
[Crossref] [PubMed]

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

2012 (3)

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109, 163903 (2012).
[Crossref] [PubMed]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

A. Novitsky, C.-W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref] [PubMed]

2011 (4)

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

M. Tencer and R. Bielski, “Mechanical resolution of chiral objects in achiral media: Where is the size limit?” Chirality 23, 144–147 (2011).
[Crossref]

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2006 (3)

A. E. Cohen and W. Moerner, “Suppressing brownian motion of individual biomolecules in solution,” P. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[Crossref]

A. W. Garrison, “Probing the enantioselectivity of chiral pesticides,” Envir. Sci. Tech. Lib. 40, 16–23 (2006).
[Crossref]

D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Optics 45, 880–887 (2006).
[Crossref]

2005 (1)

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

E. J.G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308–1316 (2003).
[Crossref] [PubMed]

2000 (1)

1991 (1)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Effective properties of a sparse random distribution of non-interacting small chiral spheres in a chiral host medium,” J. Phys. D Appl. Phys. 24, 1–10 (1991).
[Crossref]

1986 (1)

1959 (2)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems 2. structure of the image field in an aplanatic system,” P. Roy. Soc. A- Mat. Phy. 253, 358–379 (1959).
[Crossref]

E. Wolf, “Electromagnetic diffraction in optical systems 1. an integral representation of the image field,” P. Roy. Soc. A- Mat. Phy. 253, 349–457 (1959).
[Crossref]

Acebal, P.

Alizadeh, M. H.

M. H. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

Andrews, D. L.

D. S. Bradshaw and D. L. Andrews, “Laser optical separation of chiral molecules,” Opt. Lett. 40, 677–680 (2015).
[Crossref] [PubMed]

D. S. Bradshaw and D. L. Andrews, “Chiral discrimination in optical trapping and manipulation,” New J. Phys. 16, 103021 (2014).
[Crossref]

Ashkin, A.

Barnett, S. M.

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref] [PubMed]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

Bielski, R.

M. Tencer and R. Bielski, “Mechanical resolution of chiral objects in achiral media: Where is the size limit?” Chirality 23, 144–147 (2011).
[Crossref]

Bjorkholm, J. E.

Blaya, S.

Bohren, F.

D. R. H. Craig and F. Bohren, Absorption and Scattering of Light by Small Particles (WILEY-VCH, 1998).

Bradshaw, D. S.

D. S. Bradshaw and D. L. Andrews, “Laser optical separation of chiral molecules,” Opt. Lett. 40, 677–680 (2015).
[Crossref] [PubMed]

D. S. Bradshaw and D. L. Andrews, “Chiral discrimination in optical trapping and manipulation,” New J. Phys. 16, 103021 (2014).
[Crossref]

Brasselet, E.

G. Tkachenko and E. Brasselet, “Optofluidic sorting of material chirality by chiral light,” Nat. Commun. 5, 3577 (2014).
[Crossref] [PubMed]

G. Tkachenko and E. Brasselet, “Helicity-dependent three-dimensional optical trapping of chiral microparticles,” Nat. Commun. 5, 4491 (2014).
[Crossref] [PubMed]

Brown, T. G.

Brzobohaty, O.

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

Cameron, R. P.

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref] [PubMed]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

Canaguier-Durand, A.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Capasso, F.

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” P. Natl. Acad. Sci. USA 112, 13190–13194 (2015).
[Crossref]

Carretero, L.

Chan, C. T.

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[PubMed]

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

Chantada, L.

Chaumet, P. C.

Chen, J.

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

Chu, S.

Cipparrone, G.

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Cizmar, T.

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

Cohen, A. E.

A. E. Cohen and W. Moerner, “Suppressing brownian motion of individual biomolecules in solution,” P. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[Crossref]

Craig, D. R. H.

D. R. H. Craig and F. Bohren, Absorption and Scattering of Light by Small Particles (WILEY-VCH, 1998).

Dholakia, K.

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

Dionne, J. A.

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photonics 3, 304–309 (2016).
[Crossref]

Dziedzic, J. M.

Ebbesen, T. W.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Eilam, A.

A. Eilam and M. Shapiro, “Spatial separation of dimers of chiral molecules,” Phys. Rev. Lett. 110, 213004 (2013).
[Crossref] [PubMed]

Fernandes, D. E.

D. E. Fernandes and M. G. Silveirinha, “Single-beam optical conveyor belt for chiral particles,” Phys. Rev. Appl. 6, 014016 (2016).
[Crossref]

Ferrari, A. C.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Garces-Chavez, V.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

Garcia, C.

L. Carretero, P. Acebal, C. Garcia, and S. Blaya, “Periodic trajectories obtained with an active tractor beam using azimuthal polarization: Design of particle exchanger,” IEEE Photonics J. 7, 3400112 (2015).
[Crossref]

L. Carretero, P. Acebal, C. Garcia, and S. Blaya, “Helical tractor beam: analytical solution of rayleigh particle dynamics,” Opt. Express 23, 20529–20539 (2015).
[Crossref] [PubMed]

Garrison, A. W.

A. W. Garrison, “Probing the enantioselectivity of chiral pesticides,” Envir. Sci. Tech. Lib. 40, 16–23 (2006).
[Crossref]

Genet, C.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Gittes, F.

E. J.G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308–1316 (2003).
[Crossref] [PubMed]

Gomez-Medina, R.

Grier, D. G.

D. B. Ruffner and D. G. Grier, “Universal, strong and long-ranged trapping by optical conveyors,” Opt. Express 22, 26840–26849 (2014).
[Crossref]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109, 163903 (2012).
[Crossref] [PubMed]

D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Optics 45, 880–887 (2006).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Gucciardi, P. G.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Hayat, A.

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” P. Natl. Acad. Sci. USA 112, 13190–13194 (2015).
[Crossref]

Hernandez, R. J.

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Hutchison, J. A.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Jones, P. H.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Lakhtakia, A.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Effective properties of a sparse random distribution of non-interacting small chiral spheres in a chiral host medium,” J. Phys. D Appl. Phys. 24, 1–10 (1991).
[Crossref]

Lavrinenko, A.

A. Novitsky, C.-W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref] [PubMed]

Lin, Z. F.

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

Marago, O. M.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Mazzulla, A.

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Moerner, W.

A. E. Cohen and W. Moerner, “Suppressing brownian motion of individual biomolecules in solution,” P. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[Crossref]

Mueller, J. P. B.

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” P. Natl. Acad. Sci. USA 112, 13190–13194 (2015).
[Crossref]

Ng, J.

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

Nieto-Vesperinas, M.

Novitsky, A.

A. Novitsky, C.-W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref] [PubMed]

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[Crossref] [PubMed]

Pane, A.

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Peterman, E. J.G.

E. J.G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308–1316 (2003).
[Crossref] [PubMed]

Qiu, C.-W.

A. Novitsky, C.-W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref] [PubMed]

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[Crossref] [PubMed]

Rahmani, A.

Reinhard, B. M.

M. H. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems 2. structure of the image field in an aplanatic system,” P. Roy. Soc. A- Mat. Phy. 253, 358–379 (1959).
[Crossref]

Roichman, Y.

D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Optics 45, 880–887 (2006).
[Crossref]

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, “Universal, strong and long-ranged trapping by optical conveyors,” Opt. Express 22, 26840–26849 (2014).
[Crossref]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109, 163903 (2012).
[Crossref] [PubMed]

Saenz, J. J.

Saleh, A. A. E.

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photonics 3, 304–309 (2016).
[Crossref]

Schmidt, C. F.

E. J.G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308–1316 (2003).
[Crossref] [PubMed]

Shapiro, M.

A. Eilam and M. Shapiro, “Spatial separation of dimers of chiral molecules,” Phys. Rev. Lett. 110, 213004 (2013).
[Crossref] [PubMed]

Silveirinha, M. G.

D. E. Fernandes and M. G. Silveirinha, “Single-beam optical conveyor belt for chiral particles,” Phys. Rev. Appl. 6, 014016 (2016).
[Crossref]

Steinhilber, Dieter

G. F. Theodor Dingermann and Dieter Steinhilber, Molecular Biology in Medicinal Chemistry (John Wiley & Sons, 2006).

Tencer, M.

M. Tencer and R. Bielski, “Mechanical resolution of chiral objects in achiral media: Where is the size limit?” Chirality 23, 144–147 (2011).
[Crossref]

Theodor Dingermann, G. F.

G. F. Theodor Dingermann and Dieter Steinhilber, Molecular Biology in Medicinal Chemistry (John Wiley & Sons, 2006).

Tkachenko, G.

G. Tkachenko and E. Brasselet, “Helicity-dependent three-dimensional optical trapping of chiral microparticles,” Nat. Commun. 5, 4491 (2014).
[Crossref] [PubMed]

G. Tkachenko and E. Brasselet, “Optofluidic sorting of material chirality by chiral light,” Nat. Commun. 5, 3577 (2014).
[Crossref] [PubMed]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Effective properties of a sparse random distribution of non-interacting small chiral spheres in a chiral host medium,” J. Phys. D Appl. Phys. 24, 1–10 (1991).
[Crossref]

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Effective properties of a sparse random distribution of non-interacting small chiral spheres in a chiral host medium,” J. Phys. D Appl. Phys. 24, 1–10 (1991).
[Crossref]

Volke-Sepulveda, K.

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Volpe, G.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Wang, H.

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[Crossref] [PubMed]

Wang, S. B.

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems 2. structure of the image field in an aplanatic system,” P. Roy. Soc. A- Mat. Phy. 253, 358–379 (1959).
[Crossref]

E. Wolf, “Electromagnetic diffraction in optical systems 1. an integral representation of the image field,” P. Roy. Soc. A- Mat. Phy. 253, 349–457 (1959).
[Crossref]

Yao, A. M.

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref] [PubMed]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

Youngworth, K. S.

Zemanek, P.

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

Zhao, Y.

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photonics 3, 304–309 (2016).
[Crossref]

ACS Photonics (2)

M. H. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photonics 3, 304–309 (2016).
[Crossref]

Appl. Optics (1)

D. G. Grier and Y. Roichman, “Holographic optical trapping,” Appl. Optics 45, 880–887 (2006).
[Crossref]

Appl. Phys. Lett. (1)

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

Biophys. J. (1)

E. J.G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84, 1308–1316 (2003).
[Crossref] [PubMed]

Chirality (1)

M. Tencer and R. Bielski, “Mechanical resolution of chiral objects in achiral media: Where is the size limit?” Chirality 23, 144–147 (2011).
[Crossref]

Envir. Sci. Tech. Lib. (1)

A. W. Garrison, “Probing the enantioselectivity of chiral pesticides,” Envir. Sci. Tech. Lib. 40, 16–23 (2006).
[Crossref]

IEEE Photonics J. (1)

L. Carretero, P. Acebal, C. Garcia, and S. Blaya, “Periodic trajectories obtained with an active tractor beam using azimuthal polarization: Design of particle exchanger,” IEEE Photonics J. 7, 3400112 (2015).
[Crossref]

J. Phys. Chem. A (1)

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref] [PubMed]

J. Phys. D Appl. Phys. (1)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “Effective properties of a sparse random distribution of non-interacting small chiral spheres in a chiral host medium,” J. Phys. D Appl. Phys. 24, 1–10 (1991).
[Crossref]

Lab Chip (1)

R. J. Hernandez, A. Mazzulla, A. Pane, K. Volke-Sepulveda, and G. Cipparrone, “Attractive-repulsive dynamics on light-responsive chiral microparticles induced by polarized tweezers,” Lab Chip 13, 459–467 (2013).
[Crossref]

Laser Phys. Lett. (1)

T. Cizmar, O. Brzobohaty, K. Dholakia, and P. Zemanek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

Nat. Commun. (3)

G. Tkachenko and E. Brasselet, “Optofluidic sorting of material chirality by chiral light,” Nat. Commun. 5, 3577 (2014).
[Crossref] [PubMed]

G. Tkachenko and E. Brasselet, “Helicity-dependent three-dimensional optical trapping of chiral microparticles,” Nat. Commun. 5, 4491 (2014).
[Crossref] [PubMed]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[PubMed]

Nat. Nanotechnol. (1)

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

J. Chen, J. Ng, Z. F. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics 5, 531–534 (2011).
[Crossref]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

New J. Phys. (4)

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

D. S. Bradshaw and D. L. Andrews, “Chiral discrimination in optical trapping and manipulation,” New J. Phys. 16, 103021 (2014).
[Crossref]

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

P. Natl. Acad. Sci. USA (2)

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” P. Natl. Acad. Sci. USA 112, 13190–13194 (2015).
[Crossref]

A. E. Cohen and W. Moerner, “Suppressing brownian motion of individual biomolecules in solution,” P. Natl. Acad. Sci. USA 103, 4362–4365 (2006).
[Crossref]

P. Roy. Soc. A- Mat. Phy. (2)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems 2. structure of the image field in an aplanatic system,” P. Roy. Soc. A- Mat. Phy. 253, 358–379 (1959).
[Crossref]

E. Wolf, “Electromagnetic diffraction in optical systems 1. an integral representation of the image field,” P. Roy. Soc. A- Mat. Phy. 253, 349–457 (1959).
[Crossref]

Phys. Rev. Appl. (1)

D. E. Fernandes and M. G. Silveirinha, “Single-beam optical conveyor belt for chiral particles,” Phys. Rev. Appl. 6, 014016 (2016).
[Crossref]

Phys. Rev. Lett. (4)

A. Eilam and M. Shapiro, “Spatial separation of dimers of chiral molecules,” Phys. Rev. Lett. 110, 213004 (2013).
[Crossref] [PubMed]

A. Novitsky, C.-W. Qiu, and H. Wang, “Single gradientless light beam drags particles as tractor beams,” Phys. Rev. Lett. 107, 203601 (2011).
[Crossref] [PubMed]

A. Novitsky, C.-W. Qiu, and A. Lavrinenko, “Material-independent and size-independent tractor beams for dipole objects,” Phys. Rev. Lett. 109, 023902 (2012).
[Crossref] [PubMed]

D. B. Ruffner and D. G. Grier, “Optical conveyors: A class of active tractor beams,” Phys. Rev. Lett. 109, 163903 (2012).
[Crossref] [PubMed]

Other (3)

S. Ahuja, ed., Chiral Separation Methods for Pharmaceutical and Biotechnological Products (John Wiley & Sons, Inc., 2011).

G. F. Theodor Dingermann and Dieter Steinhilber, Molecular Biology in Medicinal Chemistry (John Wiley & Sons, 2006).

D. R. H. Craig and F. Bohren, Absorption and Scattering of Light by Small Particles (WILEY-VCH, 1998).

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Figures (4)

Fig. 1
Fig. 1 Points denote the numerical simulation of the enantiomers’ trajectories (red points negative χR, blue points positive χR) obtained solving the Eq. (17) with parameter values: σ1=10−3m/s, β=0.01, θ=15°, λ=1070 10−9m and ξ=10 Hz. Continuous lines denote the analytic trajectories of the two enantiomers given by Eq. (22) with the same parameters.
Fig. 2
Fig. 2 Schematic representation of the proposed set-up for the chiral discrimination of enantiomers.
Fig. 3
Fig. 3 Distribution of final (after 5 seconds) and initial particle positions (black circles) for the two enantiomers (blue circles negative χR enantiomers and red filled circles positive χR enantiomers) plotted over the density plot of the potential energy distribution for one of the enantiomers.
Fig. 4
Fig. 4 Temporal evolution of the enantiomeric excess in the region between −19 μm and −9 μm of the z coordinate and between 0 and 0.75 μm for the radial coordinate (red curve) and in the region from 5 to 15 μm for axial coordinate and between 0 and 0.75 μm for the radial coordinate (blue curve). Inset shows the trajectories obtained for the axial coordinate of 128 particles (positive χR enantiomer in red and negative χR particles in blue).

Equations (62)

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γ r ˙ ( t ) = F ( r ( t ) ) + W ( t )
F = 1 2 ( p ( E * ) + μ 0 ( m H * ) k 4 3 n η ( p × m * ) )
p = 4 π 0 ( α e E + j η χ H )
m = 4 π ( α m H j χ / η E )
F = π 0 ( α e , R | E | 2 2 η χ R ( E H * ) )
E i = A exp ( j ( k i r ) ) e ^ i
H i = A k η exp ( j ( k i r ) ) ( k i × e ^ i )
k 1 = { 0 , k sin ( θ ) , k cos ( θ ) } k 2 = { 0 , k sin ( θ ) , k cos ( θ ) }
F 2 = 4 π 0 A 2 k cos ( θ ) α e , R sin ( φ 2 k z cos ( θ ) )
z ˙ ( t ) = σ d sin ( φ 2 k z cos ( θ ) )
F z = 8 π 0 A 2 k cos ( θ ) sin 2 ( θ ) χ R sin ( φ 2 k z cos ( θ ) )
z ˙ ( t ) = σ c sin ( φ 2 k z cos ( θ ) )
e 1 = { exp [ 2 j φ ] , j b 1 cos ( θ ) , j b 1 sin ( θ ) }
e 2 = { b 2 , j cos ( θ ) , j sin ( θ ) }
F z = ( Λ 1 sin ( φ 2 k z cos ( θ ) ) + Λ 2 sin ( φ + 2 k z cos ( θ ) ) )
Λ 1 = 4 π 0 A 2 k cos ( θ ) b 1 ( α e , R cos ( 2 θ ) + 2 b 2 χ R sin ( θ ) ) Λ 2 = 4 π 0 A 2 k cos ( θ ) ( b 2 α e , R + 2 χ R sin 2 ( θ ) )
z ˙ ( t ) = σ 1 sin ( φ 2 k z cos ( θ ) ) + σ 2 sin ( φ + 2 k z cos ( θ ) )
z ˙ ( t ) = σ 0 sin ( ξ t 2 k z cos ( θ ) + ArcTan ( ζ sin ( 2 ξ t ) ( 1 ζ cos ( 2 ξ t ) ) ) )
σ 0 = σ 1 1 + ζ 2 2 ζ cos ( 2 ξ t )
v p = v ( 1 ζ 2 ) 1 + ζ 2 2 ζ cos ( 2 ξ t )
ζ = 1 1 cos ( 2 θ ) 4 β 2 sin 4 ( θ )
z ( t ) = z ( 0 ) + v ξ arctan ( ζ + 1 1 ζ tan ( ξ t ) )
E 1 = ϑ exp [ j k c z ] ( exp [ 2 j ξ t ] e ^ ρ + j B 1 e ^ ϕ )
E 2 = ϑ exp [ j k c z ] Exp [ j ξ t ] ( B 2 ( M . e ^ ρ ) j e ^ ϕ )
F = 1 2 ( p ( E * ) + μ 0 m ( H * ) k 4 3 n η ( p × m * ) )
p = 4 π 0 ( α e E + j η χ H )
m = 4 π ( α m H j χ / η E )
F 1 = 4 π 0 α e , R 4 | E | 2
F 2 = 4 π 0 α m , R 4 η 2 | H | 2
F 3 = 4 π 0 χ R 2 η ( E H * )
F 4 = 4 π 0 α e , I 2 ( ( E ( E * ) )
F 5 = 4 π 0 α m , I 2 η 2 ( H ( H * ) )
F 6 = 4 π 0 χ I 2 η ( × ( E × H * ) )
F 7 = 4 π 0 χ I 2 k μ E × E * j
F 8 = 4 π 0 χ I 2 k η 2 H × H * j
F 9 = 4 π 0 k 4 3 × ( α e α m * ) η ( E × H * )
F 10 = 4 π 0 k 4 3 ( α e α m * ) η ( E × H * )
F 11 = 4 π 0 k 4 3 | χ | 2 η ( E × H * )
F 12 = 4 π 0 k 4 3 j ( χ α m * ) η 2 ( H × H * )
F 13 = 4 π 0 k 4 3 j ( χ α e * ) ( E × E * )
E 1 = ϑ exp ( j k c z ) ( exp ( 2 j ξ t ) e ^ r + j B 1 e ^ ϕ )
E 2 = ϑ exp ( j k c z ) exp ( j ξ t ) ( B 2 ( M . e ^ r ) j e ^ ϕ )
H 1 = ϑ η exp ( j k c z ) ( exp ( 2 j ξ t ) e ^ ϕ j B 1 e ^ r )
H 2 = ϑ η exp ( j k c z ) exp ( j ξ t ) ( B 2 e ^ ϕ j ( M . e ^ r ) )
U = π 0 ( α e , R | E | 2 2 η χ R ( E H * ) )
U = U t + U c 1 cos ( 2 k c z + ξ t ) + U c 2 cos ( 2 k c z ξ t )
U t = π 0 α e , R ϑ 2 ( J 1 2 C j 1 + J 0 2 C j 0 )
C j 1 = ( 1 β 2 ( 1 + c 2 ) ( 1 + cos ( 2 ξ t ) q ) + β 2 q 2 ( 1 + q 2 c 2 ) )
C j 0 = ( 2 s 2 ( 1 β 2 ( 1 + cos ( 2 ξ t ) q ) ) )
U c 1 = 2 π 0 α e , R ϑ 2 β ( ± J 1 2 + ( c 2 J 1 2 + s 2 J 0 2 ) ( 1 1 ) )
U c 2 = 2 π 0 α e , R ϑ 2 β q ( J 1 2 ± ( J 1 2 + J 0 2 ) β 2 s 2 )
p = 4 π 0 ( α e E + j η χ H )
m = 4 π ( α m H j χ / η E )
α e = 3 j 2 k 0 3 n d 1 , χ = 3 2 k 0 3 n 2 g 1 , α m = 3 j 2 k 0 3 n 3 y 1
d 1 = V 1 ( R ) D 1 ( L ) + V 1 ( L ) D 1 ( R ) W 1 ( L ) V 1 ( R ) + W 1 ( R ) V 1 ( L )
y 1 = G 1 ( R ) W 1 ( L ) + G 1 ( L ) W 1 ( R ) W 1 ( L ) V 1 ( R ) + W 1 ( R ) V 1 ( L )
g 1 = j D 1 ( L ) W 1 ( R ) W 1 ( L ) D 1 ( R ) W 1 ( L ) V 1 ( R ) + W 1 ( R ) V 1 ( L )
W 1 ( J ) = m ψ 1 ( m J x ) ξ 1 ( x ) ξ 1 ( x ) ψ 1 ( m J x )
V 1 ( J ) = ψ 1 ( m J x ) ξ 1 ( x ) m ξ 1 ( x ) ψ 1 ( m J x )
D 1 ( J ) = m ψ 1 ( m J x ) ψ 1 ( x ) ψ 1 ( x ) ψ 1 ( m J x )
G 1 ( J ) = ψ 1 ( m J x ) ψ 1 ( x ) m ψ 1 ( x ) ψ 1 ( m J x )
m L = k L k 0 n = N L n , m R = k R k 0 n = N R n , m = 2 m R m L m R + m L

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