Abstract

On the basis of spherical vector wave functions and coordinate rotation theory, the expansion of the fields of an incident Gaussian beam with arbitrary propagation and polarization directions in terms of spherical vector wave functions is investigated, and beam shape coefficients are derived. Using the results of electromagnetic scattering by a uniaxial anisotropic sphere, the analytical expressions of the radiation force and torque exerted on a homogeneous absorbing uniaxial anisotropic sphere by the arbitrary incident Gaussian beam. We numerically analyze and discuss the following: the effects of an anisotropic absorbing dielectric on the axial and transverse radiation forces exerted by an off-axis Gaussian beam on a uniaxial anisotropic sphere; the variations in the axial, transverse, and resultant radiation forces (with incident angle β and polarization angle α) imposed by an obliquely Gaussian beam on a uniaxial anisotropic sphere; and the results on the characteristics of the three components of the radiation forces versus the center-to-center distance between the sphere and beam. Selected numerically results on the radiation torque exerted on a stationary uniaxial anisotropic transparent or absorbing sphere by a linearly polarized Gaussian beam are shown, and the results are compared with those exerted an isotropic sphere. The accuracy of the theory and code is confirmed by comparing the axial radiation forces with the results obtained from references.

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    [CrossRef]
  39. G. Gouesbet, “T-matrix formulation and generalized lozrenz-Mie theories in spherical coordinates,” Opt. Commun.283(4), 517–521 (2010).
    [CrossRef]
  40. G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A11(9), 2516–2525 (1994).
    [CrossRef]
  41. A. Doicu and T. Wriedt, “Computation of the beam-shape coefficients in the generalized Lorenz-Mie theory by using the translational addition theorem for spherical vector wave functions,” Appl. Opt.36(13), 2971–2978 (1997).
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    [CrossRef] [PubMed]
  43. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
    [CrossRef]

2011

2010

Q. K. Yuan, Z. S. Wu, and Z. J. Li, “Electromagnetic scattering for a uniaxial anisotropic sphere in an off-axis obliquely incident Gaussian beam,” J. Opt. Soc. Am. A27(6), 1457–1465 (2010).
[CrossRef] [PubMed]

G. Gouesbet, “T-matrix formulation and generalized lozrenz-Mie theories in spherical coordinates,” Opt. Commun.283(4), 517–521 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
[CrossRef]

2009

2008

M. Sluijter, D. K. G. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A25(6), 1260–1273 (2008).
[CrossRef] [PubMed]

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

2007

C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007).
[CrossRef]

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express15(2), 735–746 (2007).
[CrossRef] [PubMed]

2006

2004

2002

Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron.38(2), 131–141 (2002).
[CrossRef]

2001

2000

1998

1997

1996

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt.35(15), 2702–2710 (1996).
[CrossRef] [PubMed]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun.124(5-6), 529–541 (1996).
[CrossRef]

T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).

1995

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

R. C. Gauthier and S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of force equations,” J. Opt. Soc. Am. B12(9), 1680–1687 (1995).
[CrossRef]

1994

G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A11(9), 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994).
[CrossRef]

1993

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics47(1), 664–673 (1993).
[CrossRef] [PubMed]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J.61(2), 569–582 (1992).
[CrossRef] [PubMed]

R. Gussgard, T. Lindmo, and I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B9(10), 1922–1930 (1992).
[CrossRef]

1991

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

1990

1989

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989).
[CrossRef]

1988

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, and G. Grehan, “Light Scattering from a sphere arbitrarily located in a Gaussian beam,using a Bromwich formulation,” J. Opt. Soc. Am. A5(9), 1427–1443 (1988).
[CrossRef]

1986

1985

1984

R. D. Graglia and P. L. E. Uslenghi, “Electromagnetic Scattering from Anisotropic Materials, Part I: General Theory,” IEEE Trans. Antenn. Propag.32(8), 867–869 (1984).
[CrossRef]

1983

1980

A. Ashkin, “Applications of laser radiation pressure,” Science210(4474), 1081–1088 (1980).
[CrossRef] [PubMed]

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988).
[CrossRef]

Angelova, M. I.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun.124(5-6), 529–541 (1996).
[CrossRef]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J.61(2), 569–582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett.11(5), 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Applications of laser radiation pressure,” Science210(4474), 1081–1088 (1980).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988).
[CrossRef]

Bjorkholm, J. E.

Braat, J. J. M.

Brevik, I.

Capsalis, C. N.

Chai, L.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Chang, S.

Chaumet, P. C.

Chu, S.

de Boer, D. K. G.

de Grooth, B. G.

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

Doicu, A.

Dziedzic, J. M.

Gao, B. Z.

Gauthier, R. C.

Geng, Y. L.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004).
[CrossRef] [PubMed]

Gouesbet, G.

G. Gouesbet, “T-matrix formulation and generalized lozrenz-Mie theories in spherical coordinates,” Opt. Commun.283(4), 517–521 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
[CrossRef]

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt.35(15), 2702–2710 (1996).
[CrossRef] [PubMed]

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A11(9), 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A7(6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, B. Maheu, and G. Grehan, “Light Scattering from a sphere arbitrarily located in a Gaussian beam,using a Bromwich formulation,” J. Opt. Soc. Am. A5(9), 1427–1443 (1988).
[CrossRef]

Graglia, R. D.

R. D. Graglia and P. L. E. Uslenghi, “Electromagnetic Scattering from Anisotropic Materials, Part I: General Theory,” IEEE Trans. Antenn. Propag.32(8), 867–869 (1984).
[CrossRef]

Gréha, G.

K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994).
[CrossRef]

Grehan, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

G. Gouesbet, B. Maheu, and G. Grehan, “Light Scattering from a sphere arbitrarily located in a Gaussian beam,using a Bromwich formulation,” J. Opt. Soc. Am. A5(9), 1427–1443 (1988).
[CrossRef]

Gréhan, G.

Greve, J.

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

Guan, B. R.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004).
[CrossRef] [PubMed]

Gussgard, R.

Han, G. X.

Han, Y. P.

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
[CrossRef]

Y. P. Han, H. Y. Zhang, and G. X. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express15(2), 735–746 (2007).
[CrossRef] [PubMed]

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun.124(5-6), 529–541 (1996).
[CrossRef]

Hesselink, G.

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

Kim, J. S.

Lang, L. Y.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Lee, S. S.

Li, H.-Y.

Li, L. W.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004).
[CrossRef] [PubMed]

Li, Z. J.

Lindmo, T.

Lock, J.

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

Lock, J. A.

Maheu, B.

Mao, F. L.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Mao, S. C.

Martinot-Lagarde, G.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

Nahmias, Y. K.

Y. K. Nahmias, B. Z. Gao, and D. J. Odde, “Dimensionless parameters for the design of optical traps and laser guidance systems,” Appl. Opt.43(20), 3999–4006 (2004).
[CrossRef] [PubMed]

Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron.38(2), 131–141 (2002).
[CrossRef]

Nemoto, S.

Nevière, M.

Nieto-Vesperinas, M.

Odde, D. J.

Y. K. Nahmias, B. Z. Gao, and D. J. Odde, “Dimensionless parameters for the design of optical traps and laser guidance systems,” Appl. Opt.43(20), 3999–4006 (2004).
[CrossRef] [PubMed]

Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron.38(2), 131–141 (2002).
[CrossRef]

Papadakis, S. N.

Peng, Y.

Pereda, J. A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

Popov, E.

Pouligny, B.

G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
[CrossRef]

Prieto, A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

Qiu, C. W.

C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007).
[CrossRef]

Razek, A.

C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007).
[CrossRef]

Ren, K. F.

K. F. Ren, G. Gréhan, and G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt.35(15), 2702–2710 (1996).
[CrossRef] [PubMed]

K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994).
[CrossRef]

Ren, W.

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics47(1), 664–673 (1993).
[CrossRef] [PubMed]

Rohrbach, A.

Rosin, A.

T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988).
[CrossRef]

Schut, T. C. B.

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

Shang, Q. C.

Sluijter, M.

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, “Optical trapping of dielectric particle in arbitrary fields,” J. Opt. Soc. Am. A18(4), 839–853 (2001).
[CrossRef]

T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).

Stout, B.

Togo, H.

Tropea, C.

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

Uslenghi, P. L. E.

R. D. Graglia and P. L. E. Uslenghi, “Electromagnetic Scattering from Anisotropic Materials, Part I: General Theory,” IEEE Trans. Antenn. Propag.32(8), 867–869 (1984).
[CrossRef]

Uzunoglu, N. K.

Vegas, A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

Vielva, L. A.

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

Wallace, S.

Wang, J. J.

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
[CrossRef]

Wang, K.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Wang, Q. Y.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Wohland, T.

T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).

Wriedt, T.

Wu, X. B.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004).
[CrossRef] [PubMed]

Wu, Z. S.

Xing, Q. R.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Xu, F.

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

Yuan, Q. K.

Zhang, H. Y.

Zouhdi, S.

C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007).
[CrossRef]

Appl. Opt.

Biophys. J.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J.61(2), 569–582 (1992).
[CrossRef] [PubMed]

Cytometry

T. C. B. Schut, G. Hesselink, B. G. de Grooth, and J. Greve, “Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,” Cytometry12(6), 479–485 (1991).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

Y. K. Nahmias and D. J. Odde, “Analysis of Radiation Forces in Laser Trapping and Laser-Guided Direct Writing Applications,” IEEE J. Quantum Electron.38(2), 131–141 (2002).
[CrossRef]

IEEE Trans. Antenn. Propag.

R. D. Graglia and P. L. E. Uslenghi, “Electromagnetic Scattering from Anisotropic Materials, Part I: General Theory,” IEEE Trans. Antenn. Propag.32(8), 867–869 (1984).
[CrossRef]

J. A. Pereda, L. A. Vielva, A. Vegas, and A. Prieto, “FDTD Analysis of Magnetized Ferrites: Application to the Calculation of Dispersion Characteristics of Ferrite-Loaded Waveguides,” IEEE Trans. Antenn. Propag.43(2), 350–357 (1995).

C. W. Qiu, S. Zouhdi, and A. Razek, “Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells,” IEEE Trans. Antenn. Propag.55(12), 3515–3523 (2007).
[CrossRef]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys.64(4), 1632–1639 (1988).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys.66(10), 4594–4962 (1989).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

G. Gouesbet, B. Maheu, and G. Grehan, “Light Scattering from a sphere arbitrarily located in a Gaussian beam,using a Bromwich formulation,” J. Opt. Soc. Am. A5(9), 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, and B. Maheu, “Localized interpretation to compute all the coefficients gmn in the generalized Lorentz-Mie theory,” J. Opt. Soc. Am. A7(6), 998–1007 (1990).
[CrossRef]

B. Stout, M. Nevière, and E. Popov, “Mie scattering by an anisotropic object. Part I. Homogeneous sphere,” J. Opt. Soc. Am. A23(5), 1111–1123 (2006).
[CrossRef] [PubMed]

G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A11(9), 2516–2525 (1994).
[CrossRef]

S. N. Papadakis, N. K. Uzunoglu, and C. N. Capsalis, “Scattering of a plane wave by a general anisotropic dielectric ellipsoid,” J. Opt. Soc. Am. A7(6), 991–997 (1990).
[CrossRef]

M. Sluijter, D. K. G. de Boer, and J. J. M. Braat, “General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media,” J. Opt. Soc. Am. A25(6), 1260–1273 (2008).
[CrossRef] [PubMed]

Z. S. Wu, Q. K. Yuan, Y. Peng, and Z. J. Li, “Internal and external electromagnetic fields for on-axis Gaussian beam scattering from a uniaxial anisotropic sphere,” J. Opt. Soc. Am. A26(8), 1778–1788 (2009).
[CrossRef]

S. C. Mao, Z. S. Wu, and H.-Y. Li, “Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions,” J. Opt. Soc. Am. A26(11), 2282–2291 (2009).
[CrossRef] [PubMed]

Q. K. Yuan, Z. S. Wu, and Z. J. Li, “Electromagnetic scattering for a uniaxial anisotropic sphere in an off-axis obliquely incident Gaussian beam,” J. Opt. Soc. Am. A27(6), 1457–1465 (2010).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, “Optical trapping of dielectric particle in arbitrary fields,” J. Opt. Soc. Am. A18(4), 839–853 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

G. Gouesbet, “T-matrix formulation and generalized lozrenz-Mie theories in spherical coordinates,” Opt. Commun.283(4), 517–521 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz-Mie theories through rotations of coordinate systems,” Opt. Commun.283(17), 3218–3225 (2010).
[CrossRef]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun.124(5-6), 529–541 (1996).
[CrossRef]

K. F. Ren, G. Gréha, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects,” Opt. Commun.108(4-6), 343–354 (1994).
[CrossRef]

Opt. Express

Opt. Laser Technol.

F. L. Mao, Q. R. Xing, K. Wang, L. Y. Lang, L. Chai, and Q. Y. Wang, “Calculation of axial optical forces exerted on medium-sized particles by optical trap,” Opt. Laser Technol.39(1), 34–39 (2007).
[CrossRef]

Opt. Lett.

Optik (Stuttg.)

T. Wohland, A. Rosin, and E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttg.)102(4), 181–190 (1996).

Phys. Rev. A

F. Xu, J. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A78(1), 013843 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

Y. L. Geng, X. B. Wu, L. W. Li, and B. R. Guan, “Mie scattering by a uniaxial anisotropic sphere,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(5), 056609 (2004).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

W. Ren, “Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics47(1), 664–673 (1993).
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G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, and G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centred Gaussian beams. II. GLMT analysis,” Pure Appl. Opt.4(5), 571–585 (1995).
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[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

(a) Uniaxial anisotropic sphere is illuminated by an incident Gaussian beam with arbitrary directions of propagation and polarization. (b) Rotation relationships of two coordinate system.

Fig. 2
Fig. 2

Comparison of the axial RF from the theory when the obliquely incident Gaussian beam is reduced to an on-axis incident Gaussian beam with the results in reference [36].

Fig. 3
Fig. 3

Effects of absorbing electric anisotropy on axial RF exerted. (a) the imaginary part of ε t “A” increases. (b) the imaginary part of permittivity tensor elements ε z “B” increases.

Fig. 4
Fig. 4

(a) Effects of absorbing electric anisotropy on transverse RF Fx. (b) Effects of absorbing electric anisotropy on transverse RF Fy.

Fig. 5
Fig. 5

RF versus the incident angle β. (1) (a) is plotted the three components of the RF and the resultant RF versus β; (2) (b) is plotted the direction of the resultant RF.

Fig. 6
Fig. 6

RF versus the incident angle β. (1) (a) is plotted the three components of the RF and the resultant RF versus β; (2) (b) is plotted the direction of the resultant RF.

Fig. 7
Fig. 7

Variation of RF with polarization angle α for different incident angles β. (a) Transverse RF Fx. (b) Transverse RF Fy. (c) Axial RF Fz.

Fig. 8
Fig. 8

(a) Variation of RF with -x0 for different incident angle β. (b) Variation of RF with -z0 for different incident angle β.

Fig. 9
Fig. 9

Torque about z-axis Tx versus the location of the beam center along y axis.

Fig. 10
Fig. 10

Torque about y-axis Ty versus the incident angle β, the permittivity and permeability tensors elements are εt = εz = 2ε0, μt = μz = 1μ0 in case1; εt = 2ε0, εz = 4ε0, μt = μz = μ0 in case2; εt = (2 + 0.01i)ε0, εz = (4 + 0.01i)ε0, μt = μz = μ0 in case3; εt = 2ε0, εz = 4ε0, μt = 2μ0, μz = 2.8μ0 in case4; εt = (2 + 0.01i)ε0, εz = (4 + 0.01i)ε0, μt = (2 + 0.01i)μ0, μz = (2.8 + 0.01i)μ0 in case5; εt = 2ε0, εz = 4ε0, μt = μz = μ0 in case6, respectively.

Equations (23)

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E i = E 0 n=1 m=n n [ i g n,TE m M mn (1) ( r , k 0 )+ g n,TM m N mn (1) ( r , k 0 ) ] , H i = E 0 k 0 ω μ 0 n=1 m=n n [ g n,TE m N mn (1) ( r , k 0 )i g n,TM m M mn (1) ( r , k 0 ) ] ,
[ g n,TM m i g n,TE m ]= (1) m1 C nm K nm ψ 0 e i k 0 z 0 1 2 [ e i(m1) φ 0 J m1 (2 Q ¯ 0 ρ 0 ρ n w 0 2 )± e i(m+1) φ 0 J m+1 (2 Q ¯ 0 ρ 0 ρ n w 0 2 ) ],
ψ 0 =i Q ¯ 0 exp(i Q ¯ 0 ρ 0 2 / w 0 2 )exp(i Q ¯ 0 (n+0.5) 2 / k 0 2 w 0 2 ), Q ¯ 0 = (i2 z 0 /( k 0 w 0 2 )) 1 ρ 0 = x 0 2 + y 0 2 , ρ n = (n+0.5) / k 0 , φ 0 =arctan( x 0 / y 0 ),
C nm ={ i n1 2n+1 n(n+1) , m0 (1) | m | (n+| m |)! (n| m |)! i n1 2n+1 n(n+1) ,m<0 , K nm ={ (i) | m | i (n+0.5) | m |1 ,m0 n(n+1) n+0.5 ,m=0 .
( x 0 y 0 z 0 )=( cosβ 0 sinβ 0 1 0 sinβ 0 cosβ )( cosα sinα 0 sinα cosα 0 0 0 1 )( x 0 y 0 z 0 ).
(M,N) mn (1) ( r , k 0 )= s=n n ρ( m,s,n ) (M,N) sn (1) ( r, k 0 ),
ρ(m,s,n)= (1) s+m e isα [ (n+m)!(ns)! (nm)!(n+s)! ] 1/2 u sm (n) (β),
u sm (n) (β)= [ (n+s)!(ns)! (n+m)!(nm)! ] 1/2 σ ( n+m nsσ ) ( nm σ ) (1) nsσ (cos β 2 ) 2σ+s+m (sin β 2 ) 2n2σsm .
E i = E 0 n=1 m=n n [ a mn i M mn (1) (r, k 0 )+ b mn i N mn (1) (r, k 0 ) ] , H i = E 0 k 0 iω μ 0 n=1 m=n n [ a mn i N mn (1) (r, k 0 )+ b mn i M mn (1) (r, k 0 ) ] ,
( a mn i , b mn i )= s=n n ρ(s,m,n) C ns ( i g n,TE s , g n,TM s ).
E s = E 0 n=1 m=n n [ A mn s M mn (3) (r, k 0 ) + B mn s N mn (3) (r, k 0 )], H s = E 0 k 0 iωμ n=1 m=n n [ A mn s N mn (3) (r, k 0 ) + B mn s M mn (3) (r, k 0 )].
ε ¯ =[ ε t 0 0 0 ε t 0 0 0 ε z ] , μ ¯ =[ μ t 0 0 0 μ t 0 0 0 μ z ].
A mn s = 1 h n (1) ( k 0 a) [ n =1 2π G m n q q=1 2 0 π A mnq e j n ( k q a) P n m (cos θ k ) k q 2 sin θ k d θ k a mn i j n ( k 0 a) ],
B mn s = 1 h n (1) ( k 0 a) [ iωμ k 0 q=1 2 n =1 2π G m n q 0 π A mnq h j n ( k q a) P n m (cos θ k ) k q 2 sin θ k d θ k b mn i j n ( k 0 a) ].
F= 1 2 Re 0 2π 0 π [ ε E r E+μ H r H 1 2 ( ε 0 E 2 + μ 0 H 2 ) e ^ r ] r 2 sinθ dθdϕ | r>a .
F= 1 2 Re 0 2π 0 π 1 2 [ε( E θ i E θ i* + E θ i E θ s* + E θ s E θ i* + E θ s E θ s* + E ϕ i E ϕ i* + E ϕ i E ϕ s* + E ϕ s E ϕ i* + E ϕ s E ϕ s* ) +μ( H θ i H θ i* + H θ i H θ s* + H θ s H θ i* + H θ s H θ s* + H ϕ i H ϕ i* + H ϕ i H ϕ s* + H ϕ s H ϕ inc* + H ϕ s H ϕ s* )] r 2 sinθ dθdϕ | r>a .
F x +i F y = 4 n 0 P 0 c k 0 2 w 0 2 n=1 m=n n [ (n+m+1)! (2n+1)(nm1)! ( a mn i B m+1n s* + b mn i A m+1n s* + B mn s a m+1n i* + A mn s b m+1n i* +2 A mn s B m+1n s* +2 B mn s A m+1n s* ) i(n1)(n+1)(n+m)! (2n1)(2n+1)(nm2)! N mn 1 N m+1n1 1 ( a mn i A m+1n1 s* + b mn i B m+1n1 s* + A mn s a m+1n1 i* + B mn s b m+1n1 i* +2 A mn s A m+1n1 s* +2 B mn s B m+1n1 s* ) in(n+2)(n+m+2)! (2n+1)(2n+3)(nm)! ( a mn i A m+1n+1 s* + b mn i B m+1n+1 s* + A mn s a m+1n+1 i* + B mn s b m+1n+1 i* +2 A mn s A m+1n+1 s* +2 B mn s B m+1n+1 s* )],
F z = 8 n 0 P 0 c k 0 2 w 0 2 Re n=1 m=n n [i n(n+2)(n+m+1)! (2n+1)(2n+3)(nm)! ( a mn+1 i A mn s * + A mn+1 s a mn i* + b mn+1 i B mn s* + B mn+1 s b mn i* +2 A mn+1 s A mn s* +2 B mn+1 s B mn s* ) m(n+m)! (2n+1)(nm)! ( a mn i B mn s* + b mn i A mn s* +2 A mn s B mn s* )].
T= 1 2 Re S n ^ ([εE E * +μH H * 1 2 ε | E | 2 I 1 2 μ | H | 2 I ]×r)dS ,
T= 1 2 Re 0 2π 0 π [( ε 0 E r E ϕ * + μ 0 H r H ϕ * ) e ^ θ ( ε 0 E r E θ * + μ 0 H r H θ * ) e ^ ϕ ] r 3 sinθ dθdϕ | r>a .
T x = 4n P 0 k 0 3 c w 0 2 n=1 m=n n n(n+1) 2n+1 (n+m+1)! (nm1)! ×Re[( a mn i a m+1n s* + b mn i b m+1n s* ) +( a mn s a m+1n i* + b mn s b m+1n i* )+2( a mn s a m+1n s* + b mn s b m+1n s* )],
T y = 4n P 0 k 0 3 c w 0 2 n=1 m=n n n(n+1) 2n+1 (n+m+1)! (nm1)! ×Im[( a mn i a m+1n s* + b mn i b m+1n s* ) +( a mn s a m+1n i* + b mn s b m+1n i* )+2( a mn s a m+1n s* + b mn s b m+1n s* )],
T z = 8n P 0 c k 0 3 w 0 2 n=1 m=n n mn(n+1) 2n+1 (n+m)! (nm)! [Re( a mn i a mn s* + b mn i b mn s* )+(| a mn s | 2 +| b mn s | 2 )] .

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