Abstract

We present two electromagnetic frameworks to compare the surface stresses on spheroidal particles in the optical stretcher (a dual-beam laser trap that can be used to capture and deform biological cells). The first model is based on geometrical optics (GO) and limited in its applicability to particles that are much greater than the incident wavelength. The second framework is more sophisticated and hinges on the generalized Lorenz–Mie theory (GLMT). Despite the difference in complexity between both theories, the stress profiles computed with GO and GLMT are in good agreement with each other (relative errors are on the order of 1–10%). Both models predict a diminishing of the stresses for larger wavelengths and a strong increase of the stresses for shorter laser-cell distances. Results indicate that surface stresses on a spheroid with an aspect ratio of 1.2 hardly differ from the stresses on a sphere of similar size. Knowledge of the surface stresses and whether or not they redistribute during the stretching process is of crucial importance in real-time applications of the stretcher that aim to discern the viscoelastic properties of cells for purposes of cell characterization, sorting, and medical diagnostics.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).
  4. A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).
  5. A. Ekpenyong, C. Posey, J. Chaput, A. Burkart, M. Marquardt, T. Smith, and M. Nichols, “Determination of cell elasticity through hybrid ray optics and continuum mechanics modeling of cell deformation in the optical stretcher,” Appl. Opt. 48, 6344–6354 (2009).
    [CrossRef]
  6. J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
    [CrossRef]
  7. K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).
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    [CrossRef]
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    [CrossRef]
  10. K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
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2012

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

2011

L. Boyde, K. Chalut, and J. Guck, “Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics,” Appl. Opt. 50, 1023–1033 (2011).
[CrossRef]

Z. Wang, P. Wang, and Y. Xu, “Crucial experiment to resolve Abraham-Minkowski controversy,” Optik 122, 1994–1996 (2011).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Near- and far-field scattering from arbitrary three- dimensional aggregates of coated spheres using parallel computing,” Phys. Rev. E 83, 026701 (2011).

2010

X. Sun, H. Wang, and H. Zhang, “Scattering of Gaussian beam by a conduction spheroidal particle with confocal dielectric coating,” J. Infrared Millimeter Terahertz Waves 31, 1100–1108 (2010).

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

2009

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

A. Ekpenyong, C. Posey, J. Chaput, A. Burkart, M. Marquardt, T. Smith, and M. Nichols, “Determination of cell elasticity through hybrid ray optics and continuum mechanics modeling of cell deformation in the optical stretcher,” Appl. Opt. 48, 6344–6354 (2009).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Interaction of Gaussian beam with near-spherical particle: an analytic-numerical approach for assessing scattering and stresses,” J. Opt. Soc. Am. A 26, 1814–1826 (2009).
[CrossRef]

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

H. Sosa-Martínez and J. Gutíerrez-Vega, “Optical forces on a Mie spheroidal particle arbitrarily oriented in a counter-propagating trap,” J. Opt. Soc. Am. B 26, 2109–2116 (2009).
[CrossRef]

2007

2006

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

2005

H. Zhang and Y. Han, “Scattering by a confocal multi-layer spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

2004

W. Sun, N. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the fdtd and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

2002

C. Rinaldi and H. Brenner, “Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?” Phys. Rev. E 65, 036615 (2002).
[CrossRef]

2001

Y. Han and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509(2001).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

2000

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

1993

1979

1977

B. Sinha and R. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

1975

1970

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

Ananthakrishnan, R.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

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

R. Ananthakrishnan, “On the structural response of eukaryotic cells,” Ph.D. dissertation (University of Texas at Austin, 2003).

Ananthakrishnanan, R.

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

Asano, S.

Ashkin, A.

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

Bareil, P.

Beil, M.

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

Bilby, C.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Boyde, L.

L. Boyde, K. Chalut, and J. Guck, “Near- and far-field scattering from arbitrary three- dimensional aggregates of coated spheres using parallel computing,” Phys. Rev. E 83, 026701 (2011).

L. Boyde, K. Chalut, and J. Guck, “Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics,” Appl. Opt. 50, 1023–1033 (2011).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Interaction of Gaussian beam with near-spherical particle: an analytic-numerical approach for assessing scattering and stresses,” J. Opt. Soc. Am. A 26, 1814–1826 (2009).
[CrossRef]

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

L. Boyde, A. Ekpenyong, G. Whyte, and J. Guck, “Elastic theory for the deformation of a homogeneous or layered spheroid under axisymmetric loading,” Acta Mech. (submitted).

Brenner, H.

C. Rinaldi and H. Brenner, “Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?” Phys. Rev. E 65, 036615 (2002).
[CrossRef]

Bruel, A.

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

Burkart, A.

Chalut, K.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics,” Appl. Opt. 50, 1023–1033 (2011).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Near- and far-field scattering from arbitrary three- dimensional aggregates of coated spheres using parallel computing,” Phys. Rev. E 83, 026701 (2011).

L. Boyde, K. Chalut, and J. Guck, “Interaction of Gaussian beam with near-spherical particle: an analytic-numerical approach for assessing scattering and stresses,” J. Opt. Soc. Am. A 26, 1814–1826 (2009).
[CrossRef]

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

Chaput, J.

Chen, Y.

Chilvers, E.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

Chiou, A.

Ciric, I.

Clarke, E.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

Clegg, W.

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

Cooray, M.

Cunningham, C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

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

Dietrich, J.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

Ebert, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Ekpenyong, A.

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

A. Ekpenyong, C. Posey, J. Chaput, A. Burkart, M. Marquardt, T. Smith, and M. Nichols, “Determination of cell elasticity through hybrid ray optics and continuum mechanics modeling of cell deformation in the optical stretcher,” Appl. Opt. 48, 6344–6354 (2009).
[CrossRef]

L. Boyde, A. Ekpenyong, G. Whyte, and J. Guck, “Elastic theory for the deformation of a homogeneous or layered spheroid under axisymmetric loading,” Acta Mech. (submitted).

Erickson, H.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Falloon, P.

P. Falloon, “Theory and computation of spheroidal harmonics with general arguments,” master’s thesis (University of Western Australia, 2001).

Fiddler, C.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

Flammer, C.

C. Flammer, Spheroidal Wave Functions, 1st ed. (Stanford, 1957).

Foja, C.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Franze, K.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Fu, Q.

W. Sun, N. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the fdtd and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

Gan, X.

Gouesbet, G.

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

Grosche, J.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Gu, M.

Guck, J.

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

L. Boyde, K. Chalut, and J. Guck, “Near- and far-field scattering from arbitrary three- dimensional aggregates of coated spheres using parallel computing,” Phys. Rev. E 83, 026701 (2011).

L. Boyde, K. Chalut, and J. Guck, “Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics,” Appl. Opt. 50, 1023–1033 (2011).
[CrossRef]

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

L. Boyde, K. Chalut, and J. Guck, “Interaction of Gaussian beam with near-spherical particle: an analytic-numerical approach for assessing scattering and stresses,” J. Opt. Soc. Am. A 26, 1814–1826 (2009).
[CrossRef]

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

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

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

L. Boyde, A. Ekpenyong, G. Whyte, and J. Guck, “Elastic theory for the deformation of a homogeneous or layered spheroid under axisymmetric loading,” Acta Mech. (submitted).

Gutíerrez-Vega, J.

Han, Y.

H. Zhang and Y. Han, “Scattering by a confocal multi-layer spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Y. Han and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509(2001).
[CrossRef]

Höpfler, M.

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

Kääs, J.

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

Kang, X.

L. Li, X. Kang, and M. Leong, Spheroidal Wave Functions in Electromagnetic Theory (Wiley, 2001).

Käs, J.

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

Keyser, U.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

Kuriakose, S.

Langer, R.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

Lautenschläger, F.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

Lenz, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Leong, M.

L. Li, X. Kang, and M. Leong, Spheroidal Wave Functions in Electromagnetic Theory (Wiley, 2001).

Li, L.

L. Li, X. Kang, and M. Leong, Spheroidal Wave Functions in Electromagnetic Theory (Wiley, 2001).

Lincoln, B.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Lock, J.

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

Loeb, N.

W. Sun, N. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the fdtd and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

MacPhie, R.

B. Sinha and R. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

Maloney, J.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

Marquardt, M.

Martinez-Arias, A.

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

Melhuish, I.

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

Mitchell, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Moon, P. H.

P. H. Moon and D. E. Spencer, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. (Springer Verlag, 1988).

Moon, T.

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

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

Nichols, M.

Nikova, D.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

Pagliara, S.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

Paschke, S.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

Posey, C.

Reichenbach, A.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Remmerbach, T.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

Rinaldi, C.

C. Rinaldi and H. Brenner, “Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?” Phys. Rev. E 65, 036615 (2002).
[CrossRef]

Romeyke, M.

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Schild, D.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Schinkinger, S.

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Sheng, Y.

Siegman, A.

A. Siegman, Lasers (University Science, 1986).

Sinha, B.

B. Sinha and R. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Skatchkov, S.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Smith, T.

Sosa-Martínez, H.

Spencer, D. E.

P. H. Moon and D. E. Spencer, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. (Springer Verlag, 1988).

Sun, W.

W. Sun, N. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the fdtd and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

Sun, X.

X. Sun, H. Wang, and H. Zhang, “Scattering of Gaussian beam by a conduction spheroidal particle with confocal dielectric coating,” J. Infrared Millimeter Terahertz Waves 31, 1100–1108 (2010).

Travis, K.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Tropea, C.

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

Uckermann, O.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Ulvick, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Van De Hulst, H.

H. Van De Hulst, Light Scattering by Small Particles (Dover, 1982).

Van Vliet, K.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

Wang, H.

X. Sun, H. Wang, and H. Zhang, “Scattering of Gaussian beam by a conduction spheroidal particle with confocal dielectric coating,” J. Infrared Millimeter Terahertz Waves 31, 1100–1108 (2010).

Wang, P.

Z. Wang, P. Wang, and Y. Xu, “Crucial experiment to resolve Abraham-Minkowski controversy,” Optik 122, 1994–1996 (2011).
[CrossRef]

Wang, Z.

Z. Wang, P. Wang, and Y. Xu, “Crucial experiment to resolve Abraham-Minkowski controversy,” Optik 122, 1994–1996 (2011).
[CrossRef]

Whyte, G.

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

L. Boyde, A. Ekpenyong, G. Whyte, and J. Guck, “Elastic theory for the deformation of a homogeneous or layered spheroid under axisymmetric loading,” Acta Mech. (submitted).

Wittekind, C.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

Wottawah, F.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Wu, Z.

Xu, F.

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

Xu, Y.

Z. Wang, P. Wang, and Y. Xu, “Crucial experiment to resolve Abraham-Minkowski controversy,” Optik 122, 1994–1996 (2011).
[CrossRef]

Yamamoto, G.

Zhang, H.

X. Sun, H. Wang, and H. Zhang, “Scattering of Gaussian beam by a conduction spheroidal particle with confocal dielectric coating,” J. Infrared Millimeter Terahertz Waves 31, 1100–1108 (2010).

H. Zhang and Y. Han, “Scattering by a confocal multi-layer spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Appl. Opt.

Biophys. J.

J. Maloney, D. Nikova, F. Lautenschläger, E. Clarke, R. Langer, J. Guck, and K. Van Vliet, “Mesenchymal stem cell mechanics from the attached to the suspended state,” Biophys. J. 99, 2479–2487 (2010).
[CrossRef]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81, 767–784 (2001).
[CrossRef]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88, 3689–3698 (2005).
[CrossRef]

Cancer Res.

T. Remmerbach, F. Wottawah, J. Dietrich, B. Lincoln, C. Wittekind, and J. Guck, “Oral cancer diagnosis by mechanical phenotyping,” Cancer Res. 69, 1728–1732 (2009).
[CrossRef]

IEEE Trans. Antennas Propag.

H. Zhang and Y. Han, “Scattering by a confocal multi-layer spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Integr. Biol.

K. Chalut, A. Ekpenyong, W. Clegg, I. Melhuish, and J. Guck, “Quantifying cellular differentiation by physical phenotype using digital holographic microscopy,” Integr. Biol. 4, 280–284 (2012).
[CrossRef]

J. Infrared Millimeter Terahertz Waves

X. Sun, H. Wang, and H. Zhang, “Scattering of Gaussian beam by a conduction spheroidal particle with confocal dielectric coating,” J. Infrared Millimeter Terahertz Waves 31, 1100–1108 (2010).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Quant. Spectrosc. Radiat. Transfer

W. Sun, N. Loeb, and Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the fdtd and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

J. Theor. Biol.

R. Ananthakrishnanan, J. Guck, F. Wottawah, S. Schinkinger, B. Lincoln, M. Romeyke, T. Moon, and J. Käs, “Quantifying the contribution of actin networks to the elastic strength of fibroblasts,” J. Theor. Biol. 242, 502–516 (2006).
[CrossRef]

Opt. Express

Optik

Z. Wang, P. Wang, and Y. Xu, “Crucial experiment to resolve Abraham-Minkowski controversy,” Optik 122, 1994–1996 (2011).
[CrossRef]

Phys. Rev. A

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

Phys. Rev. E

C. Rinaldi and H. Brenner, “Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?” Phys. Rev. E 65, 036615 (2002).
[CrossRef]

L. Boyde, K. Chalut, and J. Guck, “Near- and far-field scattering from arbitrary three- dimensional aggregates of coated spheres using parallel computing,” Phys. Rev. E 83, 026701 (2011).

Phys. Rev. Lett.

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

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

PLOS ONE

A. Ekpenyong, G. Whyte, K. Chalut, S. Pagliara, F. Lautenschläger, C. Fiddler, S. Paschke, U. Keyser, E. Chilvers, and J. Guck, “Viscoelastic properties of differentiating blood cells are fate- and function-dependent,” PLOS ONE 7e45237 (2012).

Proc. Nat. Acad. Sci.

F. Lautenschläger, S. Paschke, S. Schinkinger, A. Bruel, M. Beil, and J. Guck, “The regulatory role of cell mechanics for migration of differentiating myeloid cells,” Proc. Nat. Acad. Sci. 106, 15696–15701 (2009).

Proc. Natl. Acad. Sci.

K. Franze, J. Grosche, S. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, “Müller cells are living optical fibers in the vertebrate retina,” Proc. Natl. Acad. Sci. 104, 8287–8292 (2007).
[CrossRef]

Radio Sci.

B. Sinha and R. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Other

H. Van De Hulst, Light Scattering by Small Particles (Dover, 1982).

K. Chalut, M. Höpfler, L. Boyde, A. Martinez-Arias, and J. Guck, “Chromatin decondensation and nuclear softening accompany Nanog downregulation in embryonic stem cells,” Biophys. J. (to be published).

L. Li, X. Kang, and M. Leong, Spheroidal Wave Functions in Electromagnetic Theory (Wiley, 2001).

P. H. Moon and D. E. Spencer, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. (Springer Verlag, 1988).

C. Flammer, Spheroidal Wave Functions, 1st ed. (Stanford, 1957).

R. Ananthakrishnan, “On the structural response of eukaryotic cells,” Ph.D. dissertation (University of Texas at Austin, 2003).

A. Siegman, Lasers (University Science, 1986).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999).

P. Falloon, “Theory and computation of spheroidal harmonics with general arguments,” master’s thesis (University of Western Australia, 2001).

L. Boyde, A. Ekpenyong, G. Whyte, and J. Guck, “Elastic theory for the deformation of a homogeneous or layered spheroid under axisymmetric loading,” Acta Mech. (submitted).

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Figures (5)

Fig. 1.
Fig. 1.

Definition of prolate spheroidal coordinates ξ, η, and ϕ. Values for the radial coordinate ξ=const. are surfaces of confocal ellipsoids of revolution around the z axis with ξ[1,]. Values for the angular coordinate η=const. constitute surfaces of confocal hyperboloids of revolution with η[1,1]. The angle, ϕ, of rotation around the z axis is not shown in the diagram. The unit vectors eξ and eη are orientated perpendicular to surfaces of constant ξ and η, respectively. The unit vector eϕ (not indicated) points out of the plane.

Fig. 2.
Fig. 2.

Cross section of a dielectric, spheroidal particle with semi-axes a and b aligned parallel and perpendicular to the optical axis of a laser beam. Incident light (blue arrows) with a Gaussian intensity distribution is divergent (with the spatially varying divergence angle marked as α1). Light is reflected and refracted at the interfaces between regions I and II (with refractive indices nI and nII). Dashed lines are normal to the surface of the spheroid and make angles α2 and γ2 with the optical axis. The points P(x,z) and Q(x,z) where light rays enter or exit the spheroid appear under the angles θ (front) and θ (back) as measured from the center of the spheroid.

Fig. 3.
Fig. 3.

Comparison of normal surface stresses exerted on particle by dual-beam laser trap computed with geometrical optics (GO, purple) and generalized Lorenz–Mie theory (GLMT, blue). Left: Object is a sphere with radius a=b=5.0μm. Right: Object is a prolate spheroid with semi-axes a=6.0μm and b=5.0μm. The refractive indices of the surrounding medium and the particle are nI=1.335 and nII=1.370, respectively. Incident laser light has power of P=1W per fiber, a wavelength of λ0=1064nm, and a distance from the fiber to the particle center of z0=50μm.

Fig. 4.
Fig. 4.

Comparison of normal surface stresses exerted on a sphere (left) or prolate spheroid (right) by dual-beam laser trap computed with geometrical optics (GO, purple) and generalized Lorenz–Mie theory (GLMT, blue). The distance between the fiber end and particle center is z0=100μm; all other parameters are identical to Fig. 3.

Fig. 5.
Fig. 5.

Comparison of normal surface stresses exerted on a sphere (left) or prolate spheroid (right) by dual-beam laser trap computed with geometrical optics (GO, purple) and generalized Lorenz–Mie theory (GLMT, blue). The incident laser wavelength is λ0=800nm; all remaining parameters are identical to Fig. 3.

Tables (1)

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Table 1. Stresses on the Optical Axis of a Spherical (a=5μm) or Spheroidal (a=6μm) Particle for Different Wavelengths, λa

Equations (38)

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x=f(ξ21)12(1η2)12cosϕ,
y=f(ξ21)12(1η2)12sinϕ,
z=fξη.
F(a,b,θ)=ab(asinθ)2+(bcosθ)2.
I=I0exp[2(x2+z2)sin2θw2].
R=(z+z0)[1+(zRz+z0)2],
F=ΔpΔt=Pc0Q,
Q=nII(1R)cosβnI(1+R)cos(α).
σξξ=Ic0Qcosα.
Πmn(j)(h;ξ,η,ϕ)=Smn(h;η)Rmn(j)(h;ξ)eimϕ,
ddη[(1η2)dSmndη]+[λmnh2η2m21η2]Smn=0,
ddξ[(ξ21)dRmn(j)dξ][λmnh2ξ2+m2ξ21]Rmn(j)=0,
Rmn(j)(h;ξ)=l=0,1almn(h)ξm(ξ21)m2zm+l(j)(hξ),
Smn(h;η)=l=0,1dlmn(h)Pm+l(m)(η).
λmn=λmn,
Rmn(j)=Rmn(j),
Smn=(1)m(nm)!(n+m)!Smn.
E(i)=n=0m=n+n[Pmnnmn(1)(ξ,η,ϕ)+Qmnmmn(1)(ξ,η,ϕ)],
E(s)=n=0m=n+n[Amnnmn(3)(ξ,η,ϕ)+Bmnmmn(3)(ξ,η,ϕ)],
E(c)=n=0m=n+n[Cmnnmn(1)(ξ,η,ϕ)+Dmnmmn(1)(ξ,η,ϕ)].
Eη(i)+Eη(s)=Eη(c),
Eϕ(i)+Eϕ(s)=Eϕ(c),
Pn(m)(cosθ)zn(j)(kr)=l=m,m+1αlmnRml(j)(ξ)Sml(η),
αlmn=1Nlm2iln2n+1(n+m)!(nm)!dnmml,
Nlm=r=0,12(r+2m)!(2r+2m+1)r!(drml)2.
Mmn(j)(r,θ,ϕ)=l=m,m+1αlmnmml(j)(h;ξ,η,ϕ),
Nmn(j)(r,θ,ϕ)=l=m,m+1αlmnnml(j)(h;ξ,η,ϕ).
pmn=+(1)m(n+m)!(nm)!pmn,
qmn=(1)m(n+m)!(nm)!qmn.
E(i)(r,θ,ϕ)=n=1m=0+n[pmn(Nmn(1)+Nmn(1)*)+qmn(Mmn(1)Mmn(1)*)]n=1[p0nN0n(1)+q0nM0n(1)].
αlmn=(l+m)!(lm)!(nm)!(n+m)!αl+mnform>0,
E(i)(ξ,η,ϕ)=n=0,1l=1m=0l[pmlαnml(nmn(1)+nmn(1)*)+qmlαnml(mmn(1)mmn(1)*)]n=0,1l=1[p0lαn0ln0n(1)+q0lαn0lm0n(1)].
Pmn=r=0,1αnmr+mpmr+m,
Qmn=r=0,1αnmr+mqmr+m,
Pmn=+(1)m(n+m)!(nm)!Pmn,
Qmn=(1)m(n+m)!(nm)!Qmn.
f=12Re{εEξE*+μHξH*12(εE2+μH2)eξ}.
σξξ=14Re{ε0(εrI|nInII|4εrII)EξI2ε0(εrIεrII)(EηI2+EϕI2)}.

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