Abstract

Radiation forces exerted upon a dielectric, circular-shaped cylinder of infinite length illuminated by a non-paraxial cylindrical Gaussian beam are considered. Vectorial projections of the radiation pressure force on a dielectric, arbitrary- and circular-shaped cylinder are expressed analytically. In particular, the radiation force is expressed through coefficients of the decomposition of the non-paraxial Gaussian beam into the cylindrical functions. Using numerical examples, a possibility to optically trap a circular-shaped cylinder in a non-paraxial cylindrical Gaussian beam is demonstrated.

© 2006 Optical Society of America

1. Introduction

Diffraction of the electromagnetic wave by a homogeneous sphere can be analyzed by use of the Mie theory. The generalization of the Lorenz-Mie theory onto the diffraction of a Gaussian beam and an arbitrary-shaped beam was discussed in Refs. [17] and [8], respectively. The rigorous electromagnetic calculation of the radiation pressure force exerted on a spherical microparticle illuminated by a Gaussian beam with the fifth-order non-paraxiality was considered in Refs. [9,10]. Note that in Refs. [17] the Gaussian beam was described using different approaches: Davis-Barton theory [9], standard beams [2], and localized approximation [5]. In Refs. [5,6] all three approaches were numerically compared. Note that the waist radius of the Gaussian beam in a Davis-Barton formulation [9] was much greater than the wavelength of light used. A tightly focused Gaussian beam can be generated by a spherical lens of high numerical aperture and aberration. The calculation of the radiation force pressure on a spherical microparticle located in the lens’s focus was dealt with in Refs. [11,12]. Note, however, that in Refs. [11,12] the calculation was performed for the Rayleigh particles, that is, by use of the theory of the second-order scattering. The rigorous calculation of radiation forces exerted upon an arbitrary-radius spherical particle located in the focus of a converging beam with spherical aberration was reported in Refs. [13,14]. However, only the impact of the radiation pressure force acting along the optical axis was analyzed. Forces acting on a spherical particle located in the focus of a converging spherical wave were computer-simulated and rigorously calculated analytically in Refs. [15,16]. In Refs. [17,18], three methods for calculating the radiation pressure force were compared theoretically and numerically: geometric optics approximation, Rayleigh approximation, and rigorous method. Analytical expressions for the radiation pressure forces on a spherical particle with Kerr nonlinearity located in the focus of the Gaussian beam were derived in Ref. [19]. Transfer of the angular momentum from a plane, circularly polarized electromagnetic wave to a spherical particle was reported in Ref. [20,7]. TE-polarization-specific analytical relations to calculate the diffraction of a non-paraxial 2D Gaussian beam by a circular dielectric cylinder were derived in Refs. [21,22]. In Ref. [23] the diffraction of the 3D Gaussian beam by an infinite cylinder with arbitrary location and orientation was numerically simulated.

In the present paper, we derive analytical relations and perform computer simulation for calculating the radiation pressure force on an infinite dielectric, circular-shaped cylinder located in the neighborhood of a non-paraxial 2D cylindrical Gaussian beam. In the 2D case, it becomes possible to rigorously describe a non-paraxial cylindrical Gaussian beam as a decomposition in terms of plane waves. The results derived below also apply to cylinders of finite length, provided that the length is much greater than the cylinder’s diameter.

2. Radiation pressure force on a microobject

According to Ref. [24], the conservation of the total momentum of a system composed of the electromagnetic field and an object V limited by the surface S is given by

tV1PidV+tP0i=S1σiknkdS,

where Pi are the coordinates of the vector of the electromagnetic field momentum density (V1 and S1 are a volume and a boundary surface that envelope the object VV 1), related to the Poynting vector, P0i are the coordinates of the object momentum vector, P0it are the coordinates of vector of the radiation pressure force;

σik=ε0ε1E2+μμ0H22δikε0ε1EiEkμμ0HiHk;

σik is Maxwell’s stress tensor (σik =σki ); E, H are the vectors of the electromagnetic field strength in free space, and ε1 is the permittivity of medium.

In the 2D case of TE-polarization and for monochromatic light the time-domain averaging over the period T=2πω (ω is the cyclic frequency) yields, in place of Eq. (1) (Fx =0)

Fy=12S1{12[μμ0Hy2ε0ε1Ex2μμ0Hz2]dz+μμ0Re(HyHz*)dy},
Fz=12S1{12[μμ0Hz2ε0ε1Ex2μμ0Hy2]dy+μμ0Re(HzHy*)dy},

here S 1 is a contour that envelops the object cross-section in the YOZ-plane, µ is the permeability of medium (µ=1), and µ 0 is the permeability of vacuum. In the 2D case for TE-polarization (Hx =Ey =Ez =0), the electric field is parallel to the X-axis: Ex ≠0, z is the optical axis, with the 2D object presented by an arbitrary-shaped cylinder of infinite length along the X-axis. The YOZ-plane is where light propagates (see Fig.1).

 

Fig. 1. The Gaussian beam with focus at (- Z 0,Y 0) falls on a circular cylinder with its center at (0;0).

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3. Diffraction of a cylindrical non-paraxial Gaussian beam by a circular homogeneous cylinder

Following Ref. [18], we will consider the diffraction of a 2D non-paraxial cylindrical Gaussian beam by a circular homogeneous cylinder. It is noteworthy that in the 2D case, the diffraction problem is solved independently for TE (Ex ≠0) and TM (Hx ≠0) polarization. In homogeneous space, the fields Ex and Hx satisfy the scalar 2D Helmholtz equation. Any function that satisfies the 2D Helmholtz equation can be represented by an integral decomposition into plane waves. Therefore, for TE-polarization, when (Exi, Hyi, Hzi ) are nonzero, the electric field strength for the non-paraxial Gaussian beam can be given by

Exi(ρ,φ)=E0ω0πλexp[k2ω02q24+ik(Z0pY0q)+ikrcos(φγ)]dq,

where (ρ,φ) are the coordinates in the plane (Y,Z), γ=arcsin q, p2 +q2 =1, p=cosγ, and q=sinγ, ω 0 is the waist’s radius, E 0=const, k=2πλε1=ωcε1 is the wavenumber in the medium, c is the light speed in free space, and λ is the wavelength. The series expansion of the electric field strength (5) in terms of cylindrical harmonics is

Ex(ρ,φ)=E0n=inCnJn(kr)einφ,
Cn=ω0πλexp[k2ω02q24+ik1q2Z0ikqY0inarcsinq]dq,

where Jn(x) is the Bessel function of the n-th order. From Maxwell’s equation we go on to calculate the magnetic field strength, Hr and Hφ . Then, the magnetic field projection of the incident wave takes the form:

Hφi(r,φ)=iH0n=inCnJn(kr)einφ,Jn(kr)=dd(kr)Jn(kr),
Hri(r,φ)=H0n=innCnJn(kr)kreinφ,H0=ε1ε0μ0E0.

Similarly, the expansions of the electromagnetic fields scattered outside the cylinder (ES , Hs ) functions are:

ExS=E0n=inCnSHn(1)(kr)einφ,HφS=iH0n=inCnSHn(1)(kr)einφ,
HrS=H0n=ninCnSHn(1)(kr)kreinφ,

where CnS=anCn ,

an=k1Jn(k1R)Jn(kR)kJn(k1R)Jn(kR)k1Jn(k1R)Hn(1)(kR)kJn(k1R)Hn(1)(kR),

where also R is the radius of the cylinder’s circular cross-section, k=2πλε, ε is the permittivity of the cylinder. Substituting Eqs. (5)(11) into Eqs. (3)(4), integrating over a circumference of radius R′>R and tending the radius R′ to infinity, we can obtain an analytical expression for projections of the radiation pressure force on the circular homogeneous dielectric cylinder (µ=1):

Fy=iε0ε1E02kn=Cn(Cn+1*an+1*+Cn+1*an+
+2Cn+1*anan+1*Cn1*an1*Cn1*an2Cn1*anan1*),
Fz=ε0ε1E02kn=Cn(Cn+1*an+1*+Cn+1*an+
+2Cn+1*anan+1*+Cn1*an1*+Cn1*an+2Cn1*anan1*).

Note that for TM-polarization the relationships for the force projections are identical to Eqs. (12) and (13) for TE-polarization. We only need to replace the coefficients in Eq. (11) with the similar Mie coefficients for TM-polarization.

4. Numerical simulation

To compare computation results for the radiation forces on a microcylinder derived from Eqs. (9), (10) and from Eqs. (19), (20), we computed the radiation force on a circular microcylinder near the Gaussian beam focus at the following parameters: wavelength is λ=1µm, ε=1.2, the particle diameter is 2µm, the Gaussian beam waist’s diameter is 1µm, and the power is 100 mW/m. It should be noted that in our case the confinement factor S=1/(kω0)=1/π (Ref. [5]) is not a small quantity, and, thus, the Gaussian beam can not be described in the Davis- Barton approximation [9]. Figure 2 shows the forces on a microparticle against the displacement L, acting along (Fz ) and transversely to (Fy ) the light propagation axis. The displacement L is the spacing between the beam’s waist and the cylinder’s center. At L>0, the cylinder’s center is located in the diverging beam and at L<0 the cylinder is in the converging beam (note that in Refs. [5,6] the opposite was the case). The discrepancy between the corresponding plots for the Fz is less than 5%. In calculation, all the series are truncated to the first 15 terms. Figure 2 demonstrates the optical trapping of a dielectric circular cylinder in a single Gaussian beam.

 

Fig. 2. The Z-axis (a) and Y-axis (b) projections of the pressure force on a circular cylinder ε=1.2 by the Gaussian beam (medium permittivity is ε 1=1).

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From Fig. 2(a) it is seen that the maximal absolute value of the reverse radiation pressure [5,6] is attained when L is close to the cylinder’s radius R=1 µm. This conclusion agrees with the results reported by other researchers (see Fig. 8 in [5], Fig. 4 in [6] and Table 2 in [14]). Also, from Fig. 2 it follows that for the beam power of 0.1W/m the order of the force is 10-10 N/m, which is equivalent to the 3D situation when for the beam power of 0.1W and sphere radius of R=1 µm the order of the force is 10-10 N. This is in compliance with Fig. 2 in Ref. [19].

5. Conclusions

Summing up, as a result of this work we have: (A) deduced relationships for the radiation pressure force (in particular, for a non-paraxial cylindrical Gaussian beam with TE-polarization) exerted on an infinite dielectric, circular-shaped cylinder for: an arbitrary radius of integration (Eqs. (3)(4)) and infinite radius of integration (Eqs. (12)(13)) and (B) numerically demonstrated that the dielectric circular cylinder can be optically trapped in a single cylindrical Gaussian beam, providing restrictions are imposed on the cylinder’s permittivity (Fig. 2).

Acknowledgments

The work was financially supported by the Russian-American program “Basic Research and Higher Education”, the CRDF grant REC-SA-014-02.

References and links

1. 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 A 5, 1427–1443 (1988). [CrossRef]  

2. G. Gouesbet and J.A. Lock. “A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz-Mie theory II. Off-axis beams,” J. Opt. Soc. Am A 2, 2516–2525 (1994). [CrossRef]  

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

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

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

6. H. Polaert, G. Grehan, and G. Gouesbet. “Improved standard beams with applications to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998). [CrossRef]  

7. H. Polaert, G. Grehan, and G. Gouesbet. “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun 155, 169–179 (1998). [CrossRef]  

8. G. Gouesbet. “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres,” J. Opt. Soc. Am A 16, 1641–1650 (1999). [CrossRef]  

9. J. Barton, D. Alexander, and S. Schaub. “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989). [CrossRef]  

10. R. Gussgard, T. Lindmo, and I. Brevik. “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am B 9, 1922–1930 (1992). [CrossRef]  

11. A. Rohrbach and E.H.K. Stelzer. “Optical trapping of a dielectric particle in arbitrary fields,” J. Opt. Soc. Am A 18, 839–853 (2001). [CrossRef]  

12. A. Rohrbach and E.H.K. Stelzer. “Trapping forces, force constant, and potential depths for dielectric spheres in the presence of spherical aberration,” Appl. Opt. 41, 2494–2507 (2002). [CrossRef]   [PubMed]  

13. J.A. Lock. “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration,” Appl. Opt. 43, 2532–2544 (2004). [CrossRef]   [PubMed]  

14. J.A. Lock. “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force,” Appl. Opt. 43, 2545–2554 (2004). [CrossRef]   [PubMed]  

15. D. Ganic, X. Gan, and M. Gu. “Exact radiation trapping force calculation based on vectorial diffraction theory,” Opt. Express 12, 2670–2675 (2004). [CrossRef]   [PubMed]  

16. T.A. Nieminen, N.R. Heckenberg, and H. Rubinstein-Dunlop. “Computational modeling of optical tweezers,” Proceedings of SPIE , 5514, 514–523 (2004). [CrossRef]  

17. A. Mazolli, P.A. Maia Neto, and H.M. Nussenzveig. “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. , 459, 3021–3041 (2003). [CrossRef]  

18. Y.K. Nahmias and D.J. Oddl. “Analysis of radiation forces in laser trapping and laser-guided direct writing application,” IEEE J. daunt. Electr. , 38–2, 1–10 (2002).

19. R. Pobre and C. Saloma. “Radiation forces on nonlinear microsphere by a tightly focused Gaussian beam,” Appl. Opt. , 41-36, 7694–7701 (2002). [CrossRef]  

20. P.L. Marston and J.H. Crichton. “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A. , 30-5, 2508–2516 (1984). [CrossRef]  

21. E. Zimmerman, R. Dandliner, and N. Souli. “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A , 12, 398–403 (1995). [CrossRef]  

22. Z. Wu and L. Guo. “Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm,” Progress in electromagnetics research, PIER , 18, 317–333, (1998). [CrossRef]  

23. L. Mees, K.F. Ren, G. Grehan, and G. Gouesbet. “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results,” Appl. Opt. , 38, 1867–1876 (1999). [CrossRef]  

24. L. D. Landau and E. M. Lifshitz, “Brief course in theoretical physics. Mechanics. Electrodynamics,” Moscow, Nauka Publishers, Book 1, (1969).

References

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  1. 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 A 5, 1427-1443 (1988).
    [CrossRef]
  2. G.   Gouesbet and J. A. Lock, "A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz-Mie theory II. Off-axis beams," J. Opt. Soc. Am A 2, 2516-2525 (1994).
    [CrossRef]
  3. F. Ren, G.   Grehan, and G.   Gouesbet, "Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
    [CrossRef]
  4. G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
    [CrossRef]
  5. K. F. Ren, G. Grehan, and G. Gouesbet, "Prediction of reverse radiation pressure by generalized Lorenz-Mie theory," Appl. Opt. 35, 2702-2710 (1996).
    [CrossRef] [PubMed]
  6. H. Polaert, G. Grehan, and G. Gouesbet, "Improved standard beams with applications to reverse radiation pressure," Appl. Opt. 37, 2435-2440 (1998).
    [CrossRef]
  7. H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
    [CrossRef]
  8. G. Gouesbet, "Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres," J. Opt. Soc. Am A 16, 1641-1650 (1999).
    [CrossRef]
  9. J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
    [CrossRef]
  10. R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
    [CrossRef]
  11. A. Rohrbach and E. H. K.  Stelzer, "Optical trapping of a dielectric particle in arbitrary fields," J. Opt. Soc. Am A 18, 839-853 (2001).
    [CrossRef]
  12. A. Rohrbach, and E. H. K. Stelzer, "Trapping forces, force constant, and potential depths for dielectric spheres in the presence of spherical aberration," Appl. Opt. 41, 2494-2507 (2002).
    [CrossRef] [PubMed]
  13. J. A. Lock, "Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration," Appl. Opt. 43, 2532-2544 (2004).
    [CrossRef] [PubMed]
  14. J. A. Lock, "Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force," Appl. Opt. 43, 2545-2554 (2004).
    [CrossRef] [PubMed]
  15. D.  Ganic, X.  Gan, and M. Gu, "Exact radiation trapping force calculation based on vectorial diffraction theory," Opt. Express 12, 2670-2675 (2004).
    [CrossRef] [PubMed]
  16. T. A.   Nieminen, N. R.   Heckenberg, and H.   Rubinstein-Dunlop, "Computational modeling of optical tweezers," in Optical Trapping and Optical Micromanipulation; K. Dholakia, and G. C. Spalding, eds., Proc. SPIE 5514, 514-523 (2004).
    [CrossRef]
  17. A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
    [CrossRef]
  18. Y. K.   Nahmias, and D. J. Oddl. "Analysis of radiation forces in laser trapping and laser-guided direct writing application," IEEE J. Qauntum. Electron., 38-2, 1-10 (2002).
  19. R.   Pobre, and C.   Saloma. "Radiation forces on nonlinear microsphere by a tightly focused Gaussian beam," Appl. Opt., 41-36, 7694-7701 (2002).
    [CrossRef]
  20. P. L.  Marston, and J. H.  Crichton. "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A., 30-5, 2508-2516 (1984).
    [CrossRef]
  21. E. Zimmerman, R. Dandliner, and N. Souli. "Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach," J. Opt. Soc. Am. A,  12, 398-403 (1995).
    [CrossRef]
  22. Z. Wu, and L. Guo. "Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm," Prog. Electromagn. Res. 18, 317-333, (1998).
    [CrossRef]
  23. L. Mees, K. F. Ren, G. Grehan, and G. Gouesbet. "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results," Appl. Opt.,  38, 1867-1876 (1999).
    [CrossRef]
  24. L. D. Landau, and E. M. Lifshitz, "Brief course in theoretical physics. Mechanics. Electrodynamics," (Moscow, Nauka Publishers, Book 1, 1969).

2004 (3)

2003 (1)

A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
[CrossRef]

2002 (1)

2001 (1)

A. Rohrbach and E. H. K.  Stelzer, "Optical trapping of a dielectric particle in arbitrary fields," J. Opt. Soc. Am A 18, 839-853 (2001).
[CrossRef]

1999 (2)

G. Gouesbet, "Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres," J. Opt. Soc. Am A 16, 1641-1650 (1999).
[CrossRef]

L. Mees, K. F. Ren, G. Grehan, and G. Gouesbet. "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results," Appl. Opt.,  38, 1867-1876 (1999).
[CrossRef]

1998 (3)

H. Polaert, G. Grehan, and G. Gouesbet, "Improved standard beams with applications to reverse radiation pressure," Appl. Opt. 37, 2435-2440 (1998).
[CrossRef]

Z. Wu, and L. Guo. "Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm," Prog. Electromagn. Res. 18, 317-333, (1998).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
[CrossRef]

1996 (1)

1995 (2)

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

E. Zimmerman, R. Dandliner, and N. Souli. "Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach," J. Opt. Soc. Am. A,  12, 398-403 (1995).
[CrossRef]

1994 (2)

G.   Gouesbet and J. A. Lock, "A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz-Mie theory II. Off-axis beams," J. Opt. Soc. Am A 2, 2516-2525 (1994).
[CrossRef]

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

1992 (1)

R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

1989 (1)

J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

1988 (1)

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 A 5, 1427-1443 (1988).
[CrossRef]

Alexander, D.

J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Angelova, M. A.

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

Barton, J.

J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Brevik, I.

R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

Dandliner, R.

Gan, X.

Ganic, D.

Gouesbet, G.

L. Mees, K. F. Ren, G. Grehan, and G. Gouesbet. "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results," Appl. Opt.,  38, 1867-1876 (1999).
[CrossRef]

G. Gouesbet, "Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres," J. Opt. Soc. Am A 16, 1641-1650 (1999).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Improved standard beams with applications to reverse radiation pressure," Appl. Opt. 37, 2435-2440 (1998).
[CrossRef]

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

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

G.   Gouesbet and J. A. Lock, "A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz-Mie theory II. Off-axis beams," J. Opt. Soc. Am A 2, 2516-2525 (1994).
[CrossRef]

F. Ren, G.   Grehan, and G.   Gouesbet, "Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
[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 A 5, 1427-1443 (1988).
[CrossRef]

Grehan, G.

L. Mees, K. F. Ren, G. Grehan, and G. Gouesbet. "Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation, numerical results," Appl. Opt.,  38, 1867-1876 (1999).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Improved standard beams with applications to reverse radiation pressure," Appl. Opt. 37, 2435-2440 (1998).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
[CrossRef]

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

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

F. Ren, G.   Grehan, and G.   Gouesbet, "Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorenz-Mie theory and associated resonance effects," Opt. Commun. 108, 343-354 (1994).
[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 A 5, 1427-1443 (1988).
[CrossRef]

Gu, M.

Guo, L.

Z. Wu, and L. Guo. "Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm," Prog. Electromagn. Res. 18, 317-333, (1998).
[CrossRef]

Gussgard, R.

R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

Lindmo, T.

R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

Lock, J. A.

Maheu, B.

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 A 5, 1427-1443 (1988).
[CrossRef]

Maia Neto, P. A.

A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
[CrossRef]

Martinet-Lagarde, G.

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

Mazolli, A.

A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
[CrossRef]

Mees, L.

Nussenzveig, H. M.

A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
[CrossRef]

Polaert, H.

H. Polaert, G. Grehan, and G. Gouesbet, "Improved standard beams with applications to reverse radiation pressure," Appl. Opt. 37, 2435-2440 (1998).
[CrossRef]

H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
[CrossRef]

Pouligny, B.

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

Ren, F.

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

Ren, K. F.

Rohrbach, A.

Schaub, S.

J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

Souli, N.

Stelzer, E. H. K.

Wu, Z.

Z. Wu, and L. Guo. "Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm," Prog. Electromagn. Res. 18, 317-333, (1998).
[CrossRef]

Zimmerman, E.

Appl. Opt. (6)

J. Appl. Phys. (1)

J.   Barton, D.   Alexander, and S.   Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594-4602 (1989).
[CrossRef]

J. Opt. Soc. Am A (4)

G. Gouesbet, "Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz-Mie theory for spheres," J. Opt. Soc. Am A 16, 1641-1650 (1999).
[CrossRef]

A. Rohrbach and E. H. K.  Stelzer, "Optical trapping of a dielectric particle in arbitrary fields," J. Opt. Soc. Am A 18, 839-853 (2001).
[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 A 5, 1427-1443 (1988).
[CrossRef]

G.   Gouesbet and J. A. Lock, "A rigorous justification of the localized approximation to the beam-shape coefficients in the generalized Lorenz-Mie theory II. Off-axis beams," J. Opt. Soc. Am A 2, 2516-2525 (1994).
[CrossRef]

J. Opt. Soc. Am B (1)

R. Gussgard, T.   Lindmo, and I.   Brevik, "Calculation of the trapping force in a strongly focused laser beam," J. Opt. Soc. Am B 9, 1922-1930 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun (1)

H. Polaert, G. Grehan, and G. Gouesbet, "Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam," Opt. Commun 155, 169-179 (1998).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (1)

Proc. R. Soc. London (1)

A. Mazolli, P. A.  Maia Neto, and H. M.  Nussenzveig. "Theory of trapping forces in optical tweezers," Proc. R. Soc. London 459, 3021-3041 (2003).
[CrossRef]

Prog. Electromagn. Res. (1)

Z. Wu, and L. Guo. "Electromagnetic scattering from a multilayered cylinder arbitrarily located in a Gaussian beam, a new recursive algorithm," Prog. Electromagn. Res. 18, 317-333, (1998).
[CrossRef]

Pure Appl. Opt. (1)

G. Martinet-Lagarde, B. Pouligny, M. A. Angelova, G. Grehan, and G. Gouesbet, "Trapping and levitation of a dielectric sphere with off-centered Gaussian beams, II-GLMT analysis," Pure Appl. Opt. 4, 571-585 (1995).
[CrossRef]

Other (5)

T. A.   Nieminen, N. R.   Heckenberg, and H.   Rubinstein-Dunlop, "Computational modeling of optical tweezers," in Optical Trapping and Optical Micromanipulation; K. Dholakia, and G. C. Spalding, eds., Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

Y. K.   Nahmias, and D. J. Oddl. "Analysis of radiation forces in laser trapping and laser-guided direct writing application," IEEE J. Qauntum. Electron., 38-2, 1-10 (2002).

R.   Pobre, and C.   Saloma. "Radiation forces on nonlinear microsphere by a tightly focused Gaussian beam," Appl. Opt., 41-36, 7694-7701 (2002).
[CrossRef]

P. L.  Marston, and J. H.  Crichton. "Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave," Phys. Rev. A., 30-5, 2508-2516 (1984).
[CrossRef]

L. D. Landau, and E. M. Lifshitz, "Brief course in theoretical physics. Mechanics. Electrodynamics," (Moscow, Nauka Publishers, Book 1, 1969).

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Figures (2)

Fig. 1.
Fig. 1.

The Gaussian beam with focus at (- Z 0,Y 0) falls on a circular cylinder with its center at (0;0).

Fig. 2.
Fig. 2.

The Z-axis (a) and Y-axis (b) projections of the pressure force on a circular cylinder ε=1.2 by the Gaussian beam (medium permittivity is ε 1=1).

Equations (16)

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

t V 1 P i d V + t P 0 i = S 1 σ i k n k d S ,
σ i k = ε 0 ε 1 E 2 + μ μ 0 H 2 2 δ i k ε 0 ε 1 E i E k μ μ 0 H i H k ;
F y = 1 2 S 1 { 1 2 [ μ μ 0 H y 2 ε 0 ε 1 E x 2 μ μ 0 H z 2 ] d z + μ μ 0 Re ( H y H z * ) d y } ,
F z = 1 2 S 1 { 1 2 [ μ μ 0 H z 2 ε 0 ε 1 E x 2 μ μ 0 H y 2 ] d y + μ μ 0 Re ( H z H y * ) d y } ,
E x i ( ρ , φ ) = E 0 ω 0 π λ exp [ k 2 ω 0 2 q 2 4 + i k ( Z 0 p Y 0 q ) + i k r cos ( φ γ ) ] d q ,
E x ( ρ , φ ) = E 0 n = i n C n J n ( k r ) e in φ ,
C n = ω 0 π λ exp [ k 2 ω 0 2 q 2 4 + i k 1 q 2 Z 0 i k q Y 0 in arcsin q ] d q ,
H φ i ( r , φ ) = i H 0 n = i n C n J n ( k r ) e in φ , J n ( k r ) = d d ( k r ) J n ( k r ) ,
H r i ( r , φ ) = H 0 n = i n n C n J n ( k r ) k r e i n φ , H 0 = ε 1 ε 0 μ 0 E 0 .
E x S = E 0 n = i n C n S H n ( 1 ) ( k r ) e i n φ , H φ S = i H 0 n = i n C n S H n ( 1 ) ( k r ) e i n φ ,
H r S = H 0 n = n i n C n S H n ( 1 ) ( k r ) k r e i n φ ,
a n = k 1 J n ( k 1 R ) J n ( k R ) k J n ( k 1 R ) J n ( k R ) k 1 J n ( k 1 R ) H n ( 1 ) ( k R ) k J n ( k 1 R ) H n ( 1 ) ( k R ) ,
F y = i ε 0 ε 1 E 0 2 k n = C n ( C n + 1 * a n + 1 * + C n + 1 * a n +
+ 2 C n + 1 * a n a n + 1 * C n 1 * a n 1 * C n 1 * a n 2 C n 1 * a n a n 1 * ) ,
F z = ε 0 ε 1 E 0 2 k n = C n ( C n + 1 * a n + 1 * + C n + 1 * a n +
+ 2 C n + 1 * a n a n + 1 * + C n 1 * a n 1 * + C n 1 * a n + 2 C n 1 * a n a n 1 * ) .

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