OSA's Digital Library

Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 8 — Aug. 1, 2011
  • pp: 2354–2363
« Show journal navigation

Spin angular momentum transfer from TEM00 focused Gaussian beams to negative refractive index spherical particles

Leonardo A. Ambrosio and Hugo E. Hernández-Figueroa  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 8, pp. 2354-2363 (2011)
http://dx.doi.org/10.1364/BOE.2.002354


View Full Text Article

Acrobat PDF (1100 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate optical torques over absorbent negative refractive index spherical scatterers under the influence of linear and circularly polarized TEM00 focused Gaussian beams, in the framework of the generalized Lorenz-Mie theory with the integral localized approximation. The fundamental differences between optical torques due to spin angular momentum transfer in positive and negative refractive index optical trapping are outlined, revealing the effect of the Mie scattering coefficients in one of the most fundamental properties in optical trapping systems.

© 2011 OSA

1. Introduction

Since 2000, when the first papers began to appear treating the subject of constructing some artificial medium with simultaneous negative permittivity and permeability [1

1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

,2

2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

], there has been an increasing interest on the new properties and revolutionary potential applications of what has been called negative refractive index (NRI) or double-negative (DNG) metamaterials, left-handed (LH) materials or Veselago’s medium (VM), which are artificial structural-arranged materials capable of delivering a homogeneous medium with an effective negative refractive index [3

3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

5

5. A. Grbic and G. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002). [CrossRef]

]. Some of these applications overcome current positive refractive index (PRI) limitations and, together with plasmonic structures, they are promising near-future technologies and devices for both microwaves and optics, such as in lenses, transmission lines, antennas, optical cloaking, cancer treatment and so on [6

6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

14

14. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004). [CrossRef] [PubMed]

].

Recently, we have proposed the use of NRI metamaterials in optical trapping systems not only as optical devices for mechanical and lasing purposes, but as real trappable micro- or nano-particles. We have called this a “double-negative optical trapping” [15

15. L. A. Ambrosio and H. E. Hernández-Figueroa, “Double-negative optical trapping,” in Biomedical Optics (BIOMED/Digital Holography and Three-Dimensional Imaging) on CD-ROM’10/OSA, BSuD83, Miami, USA, 11–14 April 2010.

,16

16. L. A. Ambrosio and H. E. Hernández-Figueroa, “Trapping double negative particles in the ray optics regime using optical tweezers with focused beams,” Opt. Express 17(24), 21918–21924 (2009). [CrossRef] [PubMed]

] or, alternatively, “negative refractive index optical trapping” [17

17. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]

]. Radial and axial radiation pressure forces were then calculated for both Gaussian and Bessel beams using first a ray optics approach, and further the generalized Lorenz-Mie theory (GLMT) with the integral localized approximation (ILA), thus allowing an all-optical regime analysis [16

16. L. A. Ambrosio and H. E. Hernández-Figueroa, “Trapping double negative particles in the ray optics regime using optical tweezers with focused beams,” Opt. Express 17(24), 21918–21924 (2009). [CrossRef] [PubMed]

19

19. L. A. Ambrosio and H. E. Hernández-Figueroa, “Radiation pressure cross-sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams,” to appear in Appl. Opt.

]. New and interesting trapping characteristics which could never be observed for any PRI particle were revealed for homogeneous and lossless simple NRI spheres.

2. Optical Torques over NRI Spherical Particles

An arbitrary electromagnetic wave can carry both spin and orbital angular momentum, the first being associated with its state of polarization, and the second with its azimuth light pattern dependence. The mechanism by which both are transferred to a given object is well established. It is well known, for example, that off-axis particles may rotate under the influence of a plane-polarized (linearly polarized) TEM00 focused Gaussian beam due to an asymmetric linear momentum transfer [20

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

,23

23. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998). [CrossRef]

]. Also, a circularly polarized laser beam carries an SAM of σħ/photon, where σ = 0, + 1 or −1 for linear, right- and left-hand polarizations, respectively, and this AM causes a particle to rotate about its own axis, the sense of rotation being determined by the state of polarization of the beam [20

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

]. Finally, OAM of /photon is also carried by the fields, l being the topological charge or the mode index. A Laguerre-Gaussian beam, for example, has an AM of (σ + l)ħ/photon [21

21. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66(6), 063402 (2002). [CrossRef]

,22

22. K. Volke-Sepulveda, V. Garcés-Chavez, S. Chávez-Cerda, J. Arlt, and D. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4(2), S82–S89 (2002). [CrossRef]

].

Consider now that the scatterer is a homogeneous sphere with refractive index N = NreiNim, where Nre can be either positive or negative depending on its PRI or NRI nature, respectively, and Nim accounts for absorption. A time-dependence exp(iωt) is implicitly assumed. The absorption causes the polarization of the beam to be changed after passing through the sphere, and SAM to be transferred to it [20

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

].

3. Numerical Results and Discussion

3.1. Linear Polarization

When a linearly polarized TEM00 laser beam hits a PRI homogeneous spherical particle, no torque is observed if the particle is located at the trap focus or, equivalently, at the point of stable equilibrium, regardless of its refractive index being real or complex. However, if the particle is transversally shifted along the trapping plane (perpendicular to the optical axis of the beam and containing the trap focus), it is well-known that an optical torque can be detected, due to an asymmetrical illumination, whenever this particle has a nonzero imaginary refractive index different from that of the external medium [20

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

,23

23. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998). [CrossRef]

,30

30. 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), 4594–4602 (1989). [CrossRef]

]. This Nim ≠ 0 condition is also valid in the NRI case for achieving nonzero optical torques, as we shall see.

By looking at Fig. 1, it can be inferred that, for the parameters chosen, the magnitude of Tx for a NRI particle resemble that of the equivalent PRI particle. But significant differences in magnitude can also be expected for specific values of Nr, simply because the Mie scattering coefficients an and bn present distinct resonances for NRI and PRI particles [17

17. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]

].

Notice that, because of the ray optics characteristic a/λ ≈19.53, a significant number of Mie coefficients are necessary to account for a good description of the optical torque components. Although the MSCs can assume different complex values for PRI and NRI particles, it is only when a ~λ or a << λ that Tx for a NRI sphere presents a distinct amplitude profile relative to that of a PRI sphere. Figure 2
Fig. 2 Tx profile for an x-polarized TEM00 laser beam (λ = 1064 nm, ω 0 = 3.7 μm) and a spherical particle with a = 0.75 μm and |Nim| = 10−7. The position of the particle is (x 0,y 0,z 0) = (0,1.9,0) μm. Only the first 10 an’s and bn’s significantly contribute to the torque profiles. Resonances in the Mie coefficients are reflected in the peaks observed.
is a plot of Tx as a function of Nr for a = 750 nm, λ = 1064 nm, ω 0 = 3.7 μm, Nim = 10−7, y 0 = 1.9 μm and z 0 = 0. Now, a/λ ≈0.705, so that the size parameter ka ≈4.43 and, consequently, only n up to 10 is used in (1) in order to ensure the adequate convergence of the GLMT [26

26. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

,27

27. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

]. Peaks at distinct |Nr| can be readily seen.

3.2. Circular Polarization

In an optical tweezers system employing focused Gaussian beams for optically trapping biological molecules and PRI particles in general, SAM is transferred from the incident photons to an absorbing particle located at the trap focus leading to a nonzero longitudinal torque Tz [20

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

]. This causes the trapped particle to rotate counter- or clockwise along z depending on the handedness of the polarization.

Let us again assume a first-order Davis description for a right-hand circularly polarized focused Gaussian beam with λ = 384 nm, ω 0 = 3.7 μm propagating along + z. The particle is displaced along z and (x 0,y 0) = (0,0) with parameters a = 7.5 μm and Nim = 10−7. Figures 4(a)
Fig. 4 Tz profile (due to circular polarization) for (a) PRI and (c) NRI particles with a = 7.5 μm, Nim = 10−7 and different Nr. The associated radiation pressure cross sections Cpr , z are shown in (b) and (d), respectively. In (b), the undefined region −2.8x10−4 m < z 0 < −1.0x10−4 m for Nr = 1.005 represents negative Cpr , z not shown due to the logarithmic scale. Beam parameters are λ = 384 nm and ω 0 = 3.7 μm.
and 4(b) show the optical torque Tz and the radiation pressure cross-section along z, Cpr,z, respectively, for five positive values of Nr, the same adopted in Fig. 3 plus Nr = 1.005. Radiation pressure forces along + z and -z are represented by the conditions Cpr,z > 0 and Cpr,z < 0. The additional |Nr| = 1.005 was chosen because, in the GLMT, it is known to provide a region of negative Cpr,z (the undefined region −2.8x10−4 m < z 0 < −1.0x10−4 m in Fig. 4(b)) and, therefore, a theoretical three-dimensional trap [37

37. K. R. Fen, Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques (Ph.D thesis, Faculté des Sciences de L’Université de Rouen, 1995).

]. Because radial forces are null at any point along the optical axis, points where Cpr,z = 0 in Fig. 3(b) represents the theoretical stable equilibrium points. For the parameters of Fig. 4, not a single particle with Nr < 0 would be trapped in a three-dimensional fashion, but yet a careful choice of the incident beam and the NRI particle can eventually furnishes 3D-trappable NRI particles [17

17. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]

].

Figure 6
Fig. 6 Tz profile for an right-hand circularly polarized TEM00 laser beam (λ = 1064 nm, w = 3.7 μm) and a spherical particle with a = 0.75 μm located at (x 0,y 0,z 0) = (0,0,0). Only the first 10 an and bn significantly contribute to the torque profiles. Resonances in the Mie coefficients are reflected in the peaks observed.
is a three-dimensional view of Tz as the complex refractive index of the particle is changed. The right-hand circularly polarized Gaussian beam has the same wavelength and beam waist as before, while the radius of the scatterer is fixed at a = 0.75 μm. The resonances at Nr ≈-1.480 and −1.071 for the NRI case are readily identified and, even at (x 0,y 0,z 0) = (0,0,0), a plot of Tz versus |Nr| would result in a figure very similar to Fig. 2 for Tx.

The peak amplitudes in Fig. 2 and still valid for Tz are essentially a consequence of a combination of the first ten an’s and bn’s. Suppose, for example, a NRI particle with a = 0.75 μm, Nim = 10−7 and |Nr| ≈-1.071. For this refractive index, the optical torque peak amplitude is basically due to a 7, whereas the peak for |Nr| ≈-1.48 comes from b 9, as shown in Fig. 7
Fig. 7 (a) Tz profile for an right-hand circularly polarized TEM00 laser beam (λ = 1064 nm, w = 3.7 μm) and a NRI spherical particle with a = 0.75 μm located at (x 0,y 0,z 0) = (0,0,0). (b), (c) and (d) show the Mie scattering coefficients responsible for the peaks observed in (a).
. In fact, we could say that these peaks arise from specific Mie scattering coefficients, all of them weighted by the beam shape coefficients of the incident beam.

4. Conclusions

The study of optical torques in optical trapping systems is extremely important and serves as an useful theoretical tool for predicting whether some biological particle will rotate, about some specific axis, under the presence of some arbitrary incident beam. In this way, the GLMT is an essential mathematical formulation to account for numerical optical torque calculations because it can be used to describe the linear or angular momentum transfer from any laser beam to an arbitrary particle in any optical regime. The integral localized approximation reduces computational time in the sense that it eliminates the undesirable and time consuming quadratures with double or triple integration.

The focused Gaussian beams explored here are not capable of transferring orbital angular momentum due to its azimuth symmetry, and we can naturally expect that other types of laser beams such as Laguerre-Gaussian and higher order Bessel beams, for example, will induce new optical torques in NRI particles.

Experimental verification of our results is still a challenge because of actual technological limitations in nanofabricating effective homogeneous negative refractive index spherical particles, especially in the optical regime. Although this may seem a little frustrating, it would be possible, in principle, to design a delicate experiment using macrostructures with a 2D NRI response in microwaves, small enough and with such a mass that, when impinged by a well-designed laser beam with sufficient power, it is mechanically oriented in a given plane as predicted by our recent studies.

Acknowledgments

The authors wish to thank FAPESP – Fundação de Amparo à Pesquisa do Estado de São Paulo – under contracts 2009/54494-9 (L. A. Ambrosio’s post doctorate grant) and CePOF, Optics and Photonics Research Center, 2005/51689-2 for supporting this work.

References and links

1.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]

2.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

3.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

4.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001). [CrossRef] [PubMed]

5.

A. Grbic and G. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002). [CrossRef]

6.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

7.

N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005). [CrossRef]

8.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]

9.

N. Engheta and R. Ziolkowski, Metamaterials – Physics and Engineering Explorations (IEEE Press, Wiley-Interscience, John Wiley & Sons, 2006).

10.

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (IEEE Press, Wiley-Interscience, John Wiley & Sons, 2006).

11.

S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modelling, Applications (Springer, NATO, 2008).

12.

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67(19), 193106 (2003). [CrossRef]

13.

A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-material plate,” Phys. Rev. Lett. 92(7), 077401 (2004). [CrossRef] [PubMed]

14.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004). [CrossRef] [PubMed]

15.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Double-negative optical trapping,” in Biomedical Optics (BIOMED/Digital Holography and Three-Dimensional Imaging) on CD-ROM’10/OSA, BSuD83, Miami, USA, 11–14 April 2010.

16.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Trapping double negative particles in the ray optics regime using optical tweezers with focused beams,” Opt. Express 17(24), 21918–21924 (2009). [CrossRef] [PubMed]

17.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]

18.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime,” Opt. Express 18(23), 24287–24292 (2010). [CrossRef] [PubMed]

19.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Radiation pressure cross-sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams,” to appear in Appl. Opt.

20.

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

21.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66(6), 063402 (2002). [CrossRef]

22.

K. Volke-Sepulveda, V. Garcés-Chavez, S. Chávez-Cerda, J. Arlt, and D. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4(2), S82–S89 (2002). [CrossRef]

23.

H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998). [CrossRef]

24.

G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908). [CrossRef]

25.

C. F. Bohren and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, John Wiley & Sons, 1983).

26.

G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).

27.

B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).

28.

K. F. Ren, G. Gréhan, 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]

29.

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]

30.

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), 4594–4602 (1989). [CrossRef]

31.

L. A. Ambrosio and H. E. Hernández-Figueroa, “Optical torque analysis of double-negative optical trapping with focused Gaussian beams,” in Latin America Optics and Photonics on CD-ROM’10/OSA, Tu05, Recife, Brazil, 27–30 September 2011.

32.

K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998). [CrossRef] [PubMed]

33.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979). [CrossRef]

34.

A. Wunsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9(5), 765–774 (1992). [CrossRef]

35.

J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. on-axis beams,” J. Opt. Soc. Am. A 11(9), 2503–2515 (1994). [CrossRef]

36.

J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A 11(9), 2516–2525 (1994). [CrossRef]

37.

K. R. Fen, Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques (Ph.D thesis, Faculté des Sciences de L’Université de Rouen, 1995).

38.

A. E. Miroshnichenko, “Non-Rayleigh limit of the Lorenz-Mie solution and suppression of scattering by spheres of negative refractive index,” Phys. Rev. A 80(1), 013808 (2009). [CrossRef]

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(290.4020) Scattering : Mie theory
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Traps, Manipulation, and Tracking

History
Original Manuscript: May 2, 2011
Revised Manuscript: July 21, 2011
Manuscript Accepted: July 22, 2011
Published: July 22, 2011

Citation
Leonardo A. Ambrosio and Hugo E. Hernández-Figueroa, "Spin angular momentum transfer from TEM00 focused Gaussian beams to negative refractive index spherical particles," Biomed. Opt. Express 2, 2354-2363 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-8-2354


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
  3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
  4. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001). [CrossRef] [PubMed]
  5. A. Grbic and G. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002). [CrossRef]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  7. N. Engheta and R. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005). [CrossRef]
  8. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]
  9. N. Engheta and R. Ziolkowski, Metamaterials – Physics and Engineering Explorations (IEEE Press, Wiley-Interscience, John Wiley & Sons, 2006).
  10. C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (IEEE Press, Wiley-Interscience, John Wiley & Sons, 2006).
  11. S. Zouhdi, A. Sihvola, and A. P. Vinogradov, Metamaterials and Plasmonics: Fundamentals, Modelling, Applications (Springer, NATO, 2008).
  12. Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67(19), 193106 (2003). [CrossRef]
  13. A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-material plate,” Phys. Rev. Lett. 92(7), 077401 (2004). [CrossRef] [PubMed]
  14. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209(2), 171–176 (2004). [CrossRef] [PubMed]
  15. L. A. Ambrosio and H. E. Hernández-Figueroa, “Double-negative optical trapping,” in Biomedical Optics (BIOMED/Digital Holography and Three-Dimensional Imaging) on CD-ROM’10/OSA, BSuD83, Miami, USA, 11–14 April 2010.
  16. L. A. Ambrosio and H. E. Hernández-Figueroa, “Trapping double negative particles in the ray optics regime using optical tweezers with focused beams,” Opt. Express 17(24), 21918–21924 (2009). [CrossRef] [PubMed]
  17. L. A. Ambrosio and H. E. Hernández-Figueroa, “Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory,” Biomed. Opt. Express 1(5), 1284–1301 (2010). [CrossRef] [PubMed]
  18. L. A. Ambrosio and H. E. Hernández-Figueroa, “Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime,” Opt. Express 18(23), 24287–24292 (2010). [CrossRef] [PubMed]
  19. L. A. Ambrosio and H. E. Hernández-Figueroa, “Radiation pressure cross-sections and optical forces over negative refractive index spherical particles by ordinary Bessel beams,” to appear in Appl. Opt.
  20. P. L. Marston and J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic beam,” Phys. Rev. A 30(5), 2508–2516 (1984). [CrossRef]
  21. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66(6), 063402 (2002). [CrossRef]
  22. K. Volke-Sepulveda, V. Garcés-Chavez, S. Chávez-Cerda, J. Arlt, and D. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4(2), S82–S89 (2002). [CrossRef]
  23. H. Polaert, G. Gréhan, and G. Gouesbet, “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1-3), 169–179 (1998). [CrossRef]
  24. G. Mie, “Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. 330(3), 377–445 (1908). [CrossRef]
  25. C. F. Bohren and D. R. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, John Wiley & Sons, 1983).
  26. G. Gouesbet and G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. (Paris) 13, 97–103 (1982).
  27. B. Maheu, G. Gouesbet, and G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
  28. K. F. Ren, G. Gréhan, 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]
  29. 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]
  30. 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), 4594–4602 (1989). [CrossRef]
  31. L. A. Ambrosio and H. E. Hernández-Figueroa, “Optical torque analysis of double-negative optical trapping with focused Gaussian beams,” in Latin America Optics and Photonics on CD-ROM’10/OSA, Tu05, Recife, Brazil, 27–30 September 2011.
  32. K. F. Ren, G. Gouesbet, and G. Gréhan, “Integral localized approximation in generalized lorenz-mie theory,” Appl. Opt. 37(19), 4218–4225 (1998). [CrossRef] [PubMed]
  33. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177–1179 (1979). [CrossRef]
  34. A. Wunsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9(5), 765–774 (1992). [CrossRef]
  35. J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. on-axis beams,” J. Opt. Soc. Am. A 11(9), 2503–2515 (1994). [CrossRef]
  36. J. A. Lock and G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. off-axis beams,” J. Opt. Soc. Am. A 11(9), 2516–2525 (1994). [CrossRef]
  37. K. R. Fen, Diffusion des Faisceaux Feuille Laser par une Particule Sphérique et Applications aux Ecoulements Diphasiques (Ph.D thesis, Faculté des Sciences de L’Université de Rouen, 1995).
  38. A. E. Miroshnichenko, “Non-Rayleigh limit of the Lorenz-Mie solution and suppression of scattering by spheres of negative refractive index,” Phys. Rev. A 80(1), 013808 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited