Abstract

Laser induced stress on spherical water droplets is studied. At mechanical equilibrium, the body stress vanishes therefore we consider only the surface stress. The surface stress on sub-wavelength droplets is slightly weaker along the light propagation direction. For larger droplets, due to their light focusing effect, the forward stress is significantly enhanced. For a particle roughly 3 micron in radius, when it is excited at whispering gallery mode with Q ∼ 104 by a 1 Watt Gaussian beam, the stress can be enhanced by two orders of magnitude, and can be comparable with the Laplace pressure.

© 2014 Optical Society of America

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References

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2014 (2)

M. Yang, K. F. Ren, Y. Wu, and X. Sheng, “Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle,” Phys. Rev. E 89, 043310 (2014).
[Crossref]

N. Wang, W. Lu, J. Ng, and Z. Lin, “Optimized optical ‘tractor beam’ for core-shell nanoparticles,” Opt. Lett. 39, 2399–2402 (2014).
[Crossref] [PubMed]

2013 (2)

S. A. Ellingsen, “Theory of microdroplet and microbubble deformation by Gaussian laser beam,” J. Opt. Soc. Am. B 301694–1710 (2013).
[Crossref]

N. Wang, J. Chen, S. Liu, and Z. Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[Crossref]

2011 (2)

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nature Photon. 5, 318–321 (2011).
[Crossref]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nature Photon. 5, 349–356 (2011).
[Crossref]

2010 (1)

J. Ng, Z. F. Lin, and C. T Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref] [PubMed]

2009 (1)

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Optical stress on the surface of a particle: Homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[Crossref]

2008 (2)

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipunation,” Soc. Rev. 37, 42–55 (2008).
[Crossref]

J. Ng and C. T. Chan, “Size-selective optical forces for microspheres using evanescent wave excitation of whispering gallery modes,” Appl. Phys. Lett. 92, 251109 (2008).
[Crossref]

2007 (2)

M. Eichenfield, C. P. Micheal, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref] [PubMed]

2005 (6)

J. Ng and C. T. Chan, ”Strong optical force induced by morphology dependent resonances,” Opt. Lett. 30, 1956–1958 (2005).
[Crossref] [PubMed]

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[Crossref]

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

2004 (1)

A. La Porta and M. D. Wang, “Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[Crossref] [PubMed]

2003 (1)

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

2000 (1)

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alighnment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

1995 (1)

1993 (1)

1980 (1)

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[Crossref] [PubMed]

1978 (1)

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

1970 (1)

A. Ashkin, “Accelaration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980).
[Crossref] [PubMed]

A. Ashkin, “Accelaration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Barbosa, L. C.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Block, S. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nature Photon. 5, 318–321 (2011).
[Crossref]

Capasso, F.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

Carmon, T.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

Cesar, C. L.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Chan, C. T

J. Ng, Z. F. Lin, and C. T Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref] [PubMed]

Chan, C. T.

J. Ng and C. T. Chan, “Size-selective optical forces for microspheres using evanescent wave excitation of whispering gallery modes,” Appl. Phys. Lett. 92, 251109 (2008).
[Crossref]

J. Ng and C. T. Chan, ”Strong optical force induced by morphology dependent resonances,” Opt. Lett. 30, 1956–1958 (2005).
[Crossref] [PubMed]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[Crossref]

Chen, J.

N. Wang, J. Chen, S. Liu, and Z. Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[Crossref]

Chen, J. Y.

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[Crossref]

Chylek, P.

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

Constable, A.

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

de Paula, A. M.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

de Thomaz, A. A.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Dholakia, K.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipunation,” Soc. Rev. 37, 42–55 (2008).
[Crossref]

Eichenfield, M.

M. Eichenfield, C. P. Micheal, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Ellingsen, S. A.

Fazal, F. M.

F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nature Photon. 5, 318–321 (2011).
[Crossref]

Fontes, A.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alighnment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Gouesbet, G.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Optical stress on the surface of a particle: Homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[Crossref]

Grier, G.

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

Gu, M.

K. Dholakia, P. Reece, and M. Gu, “Optical micromanipunation,” Soc. Rev. 37, 42–55 (2008).
[Crossref]

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[Crossref]

Guck, J.

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[Crossref]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alighnment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Ibanescu, M.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nature Photon. 5, 349–356 (2011).
[Crossref]

Käs, J.

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Kiehl, J. T.

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

Kim, J.

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref] [PubMed]

Ko, M. K. W.

P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

La Porta, A.

A. La Porta and M. D. Wang, “Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[Crossref] [PubMed]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and Pitaevskii, Electrodynamics of Continuous Media2nd Ed. (Butterworth-Heinemann, 1984).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and Pitaevskii, Electrodynamics of Continuous Media2nd Ed. (Butterworth-Heinemann, 1984).

Lin, Z.

N. Wang, W. Lu, J. Ng, and Z. Lin, “Optimized optical ‘tractor beam’ for core-shell nanoparticles,” Opt. Lett. 39, 2399–2402 (2014).
[Crossref] [PubMed]

N. Wang, J. Chen, S. Liu, and Z. Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[Crossref]

Lin, Z. F.

J. Ng, Z. F. Lin, and C. T Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref] [PubMed]

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
[Crossref]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[Crossref]

Liu, S.

N. Wang, J. Chen, S. Liu, and Z. Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
[Crossref]

Lock, J. A.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Optical stress on the surface of a particle: Homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
[Crossref]

Loncar, M.

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
[Crossref]

Lu, W.

Mervis, J.

Micheal, C. P.

M. Eichenfield, C. P. Micheal, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Moon, T. J.

J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Käs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84, 5451–5454 (2000).
[Crossref] [PubMed]

Moreira, W. L.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Neves, A. A. R.

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
[Crossref]

Ng, J.

N. Wang, W. Lu, J. Ng, and Z. Lin, “Optimized optical ‘tractor beam’ for core-shell nanoparticles,” Opt. Lett. 39, 2399–2402 (2014).
[Crossref] [PubMed]

J. Ng, Z. F. Lin, and C. T Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref] [PubMed]

J. Ng and C. T. Chan, “Size-selective optical forces for microspheres using evanescent wave excitation of whispering gallery modes,” Appl. Phys. Lett. 92, 251109 (2008).
[Crossref]

J. Ng and C. T. Chan, ”Strong optical force induced by morphology dependent resonances,” Opt. Lett. 30, 1956–1958 (2005).
[Crossref] [PubMed]

J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
[Crossref]

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alighnment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
[Crossref]

Painter, O.

M. Eichenfield, C. P. Micheal, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
[Crossref]

Perahia, R.

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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
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Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Fontes, A. A. R. Neves, W. L. Moreira, A. A. de Thomaz, L. C. Barbosa, C. L. Cesar, and A. M. de Paula, “Double optical tweezers for ultrasensitive force spectroscopy in microsphere Mie scattering,” Appl. Phys. Lett. 87, 221109 (2005).
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J. Biomed. Opt. (1)

J. T. Yu, J. Y. Chen, Z. F. Lin, L. Xu, P. N. Wang, and M. Gu, “Surface stress on the erythrocyte under laser irradiation with finite-difference time-domain calculation,” J. Biomed. Opt. 10, 064013 (2005).
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J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

M. Eichenfield, C. P. Micheal, R. Perahia, and O. Painter, “Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces,” Nat. Photonics 1, 416–422 (2007).
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Nature (2)

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F. M. Fazal and S. M. Block, “Optical tweezers study life under tension,” Nature Photon. 5, 318–321 (2011).
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M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nature Photon. 5, 349–356 (2011).
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Opt. Exp. (1)

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators,” Opt. Exp. 13, 8286–8295 (2005).
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Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (3)

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Optical stress on the surface of a particle: Homogeneous sphere,” Phys. Rev. A 79, 053808 (2009).
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N. Wang, J. Chen, S. Liu, and Z. Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87, 063812 (2013).
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J. Ng, Z. F. Lin, C. T. Chan, and P. Sheng, “Photonic clusters formed by dielectric microspheres: numerical simulations,” Phys. Rev. B 72, 085130 (2005).
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Phys. Rev. E (1)

M. Yang, K. F. Ren, Y. Wu, and X. Sheng, “Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle,” Phys. Rev. E 89, 043310 (2014).
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J. Ng, Z. F. Lin, and C. T Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
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Figures (4)

Fig. 1
Fig. 1 Light induced surface stress on water droplets. (a) Droplet of different sizes illuminated by an circularly polarized incident plane wave. (b) Droplet with a radius a = 0.5λ illuminated by a linearly polarized (E on the ϕ = 0° plane) plane wave. Different color curves correspond to different azimuthal angles.
Fig. 2
Fig. 2 Radiation pressure acting on a spherical droplet illuminated by a circularly polarized plane wave. The radii of the two sharp peaks, denoted by b 44 1 and a 44 1, respectively, are 5.93895λ and 6.00526λ.
Fig. 3
Fig. 3 Light induced stress for (a) whispering gallery modes and (b) off resonance case where a = 6λ. The incident wave is a circular polarized plane wave.
Fig. 4
Fig. 4 Light induced surface stress for a droplet excited at the a 44 1 mode. (a) A Gaussian beam is focused on the droplet center and (b) the droplet is displaced perpendicularly to the beam axis, along 90°. The incident circularly polarized Gaussian beam has a power of 1 W and a numerical aperture of 0.9.

Equations (6)

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

T ¯ water = 1 2 ε w ε 0 E E * + 1 2 μ 0 H H * 1 4 [ ε w ε 0 E E * + μ 0 H H * ] I ¯
σ = [ T ¯ air ( at outer boundary ) T ¯ water ( at inner boundary ) ] e r
σ = ε 0 4 ( ε w 1 ) ( | E t | 2 + | E r | 2 ε w ) e r
E i = ( e x + i e y ) E 0 e i k z / 2
E s = 1 4 π ε 0 [ 3 e r ( e r p ) p ] 1 a 3
σ = ε 0 8 ( ε w 1 ) [ ( 1 + cos 2 θ ) | 1 α 4 π ε 0 a 3 | 2 + 1 ε w sin 2 θ | 1 + α 2 π ε 0 a 3 | 2 ] E 0 2 e r

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