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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 4 — Apr. 23, 2008
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Interaction of spherical nanoparticles with a highly focused beam of light

Kürşat Şendur, William Challener, and Oleg Mryasov  »View Author Affiliations


Optics Express, Vol. 16, Issue 5, pp. 2874-2886 (2008)
http://dx.doi.org/10.1364/OE.16.002874


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Abstract

The interaction of a highly focused beam of light with spherical nanoparticles is investigated for linear and radial polarizations. An analytical solution is obtained to calculate this interaction. The Richards-Wolf theory is used to express the incident electric field near the focus of an aplanatic lens. The incident beam is expressed as an integral where the integrand is separated into transverse-electric (TE) and transverse-magnetic (TM) waves. The interaction of each TE and TM wave with a spherical nanoparticle is calculated using the Mie theory. The resulting analytical solution is then obtained by integrating the scattered waves over the entire angular spectrum. A finite element method solution is also obtained for comparison.

© 2008 Optical Society of America

1. Introduction

The Richards-Wolf theory [15

15. E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London Ser. A 253, 349–357 (1959). [CrossRef]

, 16

16. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]

] provides an accurate representation for the incident beam near the focus of an aplanatic lens. A solution for the interaction of spherical particles with incident beams described by Richards-Wolf theory is necessary for applications that utilize a highly focused beam of light. This is particularly crucial for applications that utilize metallic spheres supporting surface plasmons, since the interaction of different spectral components of the incident beam with metal plasma varies significantly.

This study addresses the interaction of spherical nanoparticles with highly focused incident beams defined by Richards-Wolf theory [15

15. E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London Ser. A 253, 349–357 (1959). [CrossRef]

, 16

16. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]

]. Both metallic and dielectric nanoparticles are investigated. Another important contribution of this paper is the utilization of both linear and radial polarizations. Analytical studies in the literature have mostly concentrated on linearly polarized light. However, more sophisticated polarizations such as radially polarized focused beams have been used extensively to excite surface plasmons in experimental studies. There has been increasing interest in radially polarized focused light due to its favorable configuration to excite surface plasmons on cylindrical particles [17

17. A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of singlewalled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003). [CrossRef] [PubMed]

]. The analytical models in this study can be used to validate complicated 3-D modeling tools, such as finite-difference time domain (FDTD) [18

18. W. A. Challener, I. K. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11, 3160–3170 (2003). [CrossRef] [PubMed]

] and finite element method (FEM) [19

19. K. Sendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96, 2743–2752 (2004). [CrossRef]

], which can later be used to model more complicated nanostructures. We also compare the results of a 3-D FEM model with the analytical model presented in this study.

This paper is organized as follows: In Sect. 2 we present the formulations for the linearly and radially polarized electric fields. Different components of the electric field vector are identified and plotted for both linear and radial polarizations. In Sect. 3, the formulation for the interaction of focused light with spherical nanoparticles is presented. A verification of the implementation is presented in Sect. 4 by comparing the analytical and FEM solutions. The results for different spherical nanoparticles are presented and discussed in Sect. 4. Concluding remarks appear in Sect. 5.

2. Focused field formulation

Many applications, such as optical storage and optical levitation, use highly focused optical beams. An accurate prediction of three-dimensional distributions of various polarizations requires proper analysis of the vector nature of the incident electromagnetic fields. Richards and Wolf developed a method for calculating the electric field semi-analytically near the focus of an aplanatic lens [15

15. E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London Ser. A 253, 349–357 (1959). [CrossRef]

, 16

16. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]

]. Using Richards-Wolf method, we can obtain both transverse and longitudinal components near the focus. As we describe below, Richards and Wolf method can be used to obtain the electric field components for different polarizations. In this study, we utilize linear and radial polarizations. A highly focused beam with a linear polarization has a stronger transverse component than a longitudinal component. Radial polarization, on the other hand, has a stronger component in the longitudinal direction than the transverse direction. Due to this difference, linearly and radially polarized focused beams interact differently with the particles that are placed around the focal region.

The total electric field in the vicinity of the focus is given by

E(rp)=iλ0αdθsinθ02πdϕa(θ,ϕ)exp(ik·rp)
(1)

where α is the half angle of the beam, r p is the observation point

rp=xpx̂+ypŷ+zpẑ=rpcosϕpx̂+rpsinϕpŷ+zpẑ
(2)

and

k=2πλ(sinθcosϕx̂+sinθsinϕŷcosθẑ).
(3)

In Eqs. (2) and (3) λ is the wavelength in the medium, rp=xp2+yp2, and ϕp= arctan(yp/xp). In Eq. (1), a(θ,ϕ) is the weighting vector for a plane wave incident from the (θ,ϕ) direction. Here it should be noted that a(θ,ϕ) is a polarization dependent quantity. a(θi,ϕj) is given as

a(θ,ϕ)=[cosθcos2ϕ+sin2ϕcosθcosϕsinϕcosϕsinϕsinθcosϕ]cosθ,
(4)
a(θ,ϕ)=[cosθcosϕcosθsinϕsinθ]cosθ,
(5)

for linear and radial polarizations, respectively. In Eqs. (4) and (5), the cosθ factor is applied to the incident beam for energy conservation in a solid immersion lens (SIL), but no other apodization is applied.

To obtain the electric field distributions for radial and linear polarizations, Eq. (1) can be evaluated using a numerical integration. Equation (1) is discretized as

E(rp)=iλi=1Nθ+1j=1Nϕ+1ωijsinθicosθia(θi,ϕj)exp(ikij·rp)
(6)
Fig. 1. Various electric fields components for the linearly polarized focused beam at the focal plane. The results are normalized with the maximum value of the total electric field. (a) Ex (x,y), (b) Ey (x,y), (c) Ez (x,y), and (d) Et (x,y).

where ωij are the numerical quadrature coefficients,

θi=(i1)θmaxNθ,
(7)
ϕj=(j1)2πNϕ,
(8)

and

kij=2πλ(sinθicosϕjx̂+sinθisinϕjŷcosθiẑ).
(9)

Using Eq. (6) along with Eqs. (4) and (5), we can now obtain the electric field distributions around the focus. Equation (6) can also be interpreted as a summation of plane waves propagating in the k ij direction with an amplitude of iλωijsinθicosθia(θi,ϕj)). Linear and radial polarizations are distinguished by the scaling factor a(θi,ϕj) of the plane wave in the k ij direction.

Different components of the electric field are presented at the focal plane in Figs. 1 and 2 for linear and radial polarizations, respectively. In the calculations, the refractive index of the medium is 1, and the half angle of the beam is 60°. In both figures, the field quantities are normalized with the maximum value of the total electric field. For the linearly polarized focused wave, the x-component of the electric field is much stronger than the other two components as shown in Fig. 1. The radially polarized wave has a strong z-component in the focal region as shown in Fig. 2.

Fig. 2. Various electric fields components for the radially polarized focused beam at the focal plane. The results are normalized with the maximum value of the total electric field. (a) Ex (x,y), (b) Ey (x,y), (c) Ez (x,y), and (d) Et (x,y).

3. Analytical treatment of the interaction of focused light with spherical nanoparticles

In this section, the formulation for the interaction of focused light with spherical nanoparticles is presented. The incident focused light is described by Eq. (6) along with Eqs. (4) and (5) for linear and radial polarizations, respectively. In Eq. (6), a focused incident beam of light is expressed as an integral where the integrand can be separated into TE and TM polarized plane wave components. In our formulation, the interaction of each TE and TM plane wave component with a spherical nanoparticle is calculated using Mie theory. The resulting analytical solution is then obtained by integrating the scattered waves over the entire angular spectrum.

The technique summarized in this section is based on the Mie series solution for TE and TM plane waves. The interaction of plane waves with spheres has been thoroughly studied [20

20. G. Mie, “Beiträge zur optik truber medien, speziell kolloida ler metallösungen” Ann. d. Physik 25, 377- (1908). [CrossRef]

, 21

21. M. Born and E. Wolf, Principles of Optics 5th ed. (Pergamon Press, Oxford, 1975), section 13.5. [PubMed]

] in the literature. In this study, we will not give explicit expressions for the Mie scattering problem, since it is well documented in the literature. However, we will utilize the results of Mie scattering problem to extend the formulations to scattering problems where the incident beam is defined by Richards-Wolf theory.

The most common solution for the Mie scattering solution has been given in the literature for a simple plane wave. A linearly polarized (in the x-direction) plane wave can be expressed as

Eincx(r)=x̂exp(ik·r).
(10)

The presence of a spherical particle generates scattered fields. The solution of this problem is expressed as a total (incident + scattered) electric field E x tot (r). Explicit expressions for the E x tot (r) are given in the literature [21

21. M. Born and E. Wolf, Principles of Optics 5th ed. (Pergamon Press, Oxford, 1975), section 13.5. [PubMed]

] as a summation of spherical harmonics, and will not be repeated here.

The TEinc and TMinc polarized incident plane waves, shown in Fig. 3, can be expressed as

EincTE(r)=(sinϕincx̂+cosϕincŷ)exp(ik·r),
(11)
Fig. 3. Spherical particle illuminated by (a) TM polarized plane wave, and (a) TE polarized plane wave.

and

EincTM(r)=(cosθinccosϕincx̂+cosθincsinϕincŷ+sinθincẑ)exp(ik·r),
(12)

respectively. The incident E TEinc (r) and E TMinc (r) polarized plane waves in Eqs. (11) and (12) can be obtained from E xinc(r) in Eq. (10) by simple coordinate transformations. E TMinc (r) is obtained from E xinc(r) by subsequent θ=θinc, and ϕ=ϕinc transformations. Similarly, E TEinc (r) is obtained from E xinc(r) by subsequent ϕ=-π/2, θ=θinc, and ϕ=ϕinc transformations. Since the incident fields E TMinc (r) and E TEinc (r) can be obtained from linear transformations of E xinc(r), the total fields E TMtot (r) and E TEtot (r) can be obtained from E xtot (r) by the same transformations due to the linearity of the system. In summary, the total electric fields due to the presence of the sphere E TMtot (r) and E TEtot (r) are obtained as

EtotTM(r)=[cosθcosϕsinϕsinθcosϕcosθsinϕcosϕsinθsinϕsinθ0cosθ]Etotx(r)
(13)
EtotTE(r)=[sinϕcosθsinϕsinθcosϕcosϕcosθsinϕsinθsinϕ0sinθcosθ]Etotx(r)
(14)

So far, we have established how to obtain E TMtot (r) and E TEinc (r) starting from the expression in the literature. Equations (13) and (14) will be utilized to find the solution scattering from spherical particles when the incident field is given by Richards-Wolf theory. In Eq. (1), a highly focused incident beam of light is expressed as an integral where the integrand is a plane wave propagating in the k direction. A linearly polarized incident focused wave

Einclin(r)=iAπ0αdθ02πdϕsinθcosθexp(ik·r)[cosθcos2ϕ+sin2ϕcosθcosϕsinϕcosϕsinϕsinθcosϕ]
(15)

can be rearranged to obtain

Einclin(r)=iAπ0αdθ02πdϕsinθcosθ[cosϕexp(ik·r)[cosθcosϕcosθsinϕsinθ]
sinϕexp(ik·r)[sinϕcosϕ0]]
(16)

The first and second terms in brackets in Eq. (16) can be recognized as TMinc and TEinc incident plane waves, respectively. We can write the total (incident + scattered) electric field due to scattering from spherical particles when the incident field is given by Eq. (15) as

Etotlin(r)=iAπ0αdθ02πdϕsinθcosθ[cosϕEtotTM(r)sinϕEtotTE(r)]
(17)

where E TMtot (r) and E TEtot (r) are defined in Eqs. (13) and (14), respectively.

A similar procedure can be applied when the incident beam is radially polarized, which is given by

Eincrad(r)=iAπ0αdθ02πdϕsinθcosθexp(ik·r)[cosθcosϕcosθsinϕsinθ].
(18)

In this equation, the expression (cosθinc cosϕinc+cosθinc sinϕincŷ+sinθinc)exp(i k · r) is a representation of the TM polarized incident plane waves. Using the linearity of the integration operation, we can write the total field due to the radially polarized focused light as

Etotrad(r)=iAπ0αdθ02πdϕsinθcosθEtotTM(r)
(19)

where E TMtot (r) is defined in Eqs. (13).

In addition to the analytical solution, a three-dimensional finite element method (FEM) based solution is also obtained to calculate the response of spherical nanoparticles when they are illuminated with a focused beam of light. The FEM based solution will be validated using the analytical solution given in Section 3. The finite element method (FEM) is a well-known numerical algorithm for the solution of Maxwell’s equations [22

22. J. M. Jin, The Finite Element Method in Electomagnetics (John Wiley & Sons, New York, NY, 2000).

]. In this study, a frequencydomain based FEM is used for the solution of Maxwell’s equations. Tetrahedral elements are used to discretize the computational domain, which allow modeling of arbitrarily shaped threedimensional geometries. Over the tetrahedral elements, edge basis functions and second-order interpolation functions are used to expand the functions. Adaptive mesh refinement is employed to improve the coarse solution regions with high field intensities and large field gradients. To represent the focused incident beam, Eq. (6) along with Eqs. (4) and (5) are used with the FEM.

Fig. 4. Interaction of a radially polarized focused beam with a silver sphere with a 50 nm radius. The total electric field is plotted on the x̂-ẑ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.

4. Results

In this section, we provide the results based on the methods outlined in Section 3. The analytical results are first compared with the FEM. Near-field electric field distributions of various dielectric and metallic spherical nanoparticles are investigated for highly focused linearly and radially polarized beams. The optical properties of materials in this section are taken from the literature [23

23. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, CA, 1998).

].

To compare the results of the analytical solution with the FEM, three different spheres are considered: silver spheres with 50 and 250 nm radii, and a dielectric sphere with a 250 nm radius. The comparison of the results for the metallic spheres is crucial when investigating surface plasmons. Electromagnetic fields do not penetrate much into metallic spheres due to the small skin-depth of metal. Therefore, metallic sphere do not provide strong fields within the particles for comparison. Since electromagnetic fields penetrate better into a dielectric sphere, a comparison involving dielectric spheres provides an opportunity to validate the results within the sphere. Therefore, we will obtain the results for a dielectric sphere in addition to silver spheres. The wavelength for the calculations is 700 nm. The refractive index of the silver at this wavelength is taken from the literature [23

23. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, CA, 1998).

] as 0.14+i×4.523. The wavelength is selected around the plasmonic resonances of larger nanoparticles. However, no particular attempt is made to optimize the response of the nanoparticles as a function of wavelength when they are illuminated with a focused beam of light.

Fig. 5. Interaction of a linearly polarized focused beam with a silver sphere with a 50 nm radius. The total electric field is plotted on the x̂-ẑ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.

In all simulations, the light propagates in the + direction. In Figs. 4 and 5, the results of a silver sphere with a 50 nm radius are presented for radial and linear polarizations, respectively. The half beam angle of the optical lens is 60°. In Figs. 4 and 5, |Ex|2 and |Ez|2 are plotted. The |Ey|2 component was negligible for both linear and radial polarization. The Mie series solution agrees well with the FEM results. For the 50 nm sphere the results for radial polarization and linear polarization are very similar, except for a 90° rotation, which is consistent with the direction of the incident field at the focus, as shown in Figs. 1 and 2. In this case the sphere is too small to interact with field components in other directions.

The results for a silver sphere with a 250 nm radius is illustrated in Figs. 6 and 7 for radial and linear polarizations, respectively. The results again show agreement. The electromagnetic field distributions and the locations of maxima and minima are similar, especially for radially polarized wave. The amplitude of the electromagnetic field is in agreement both in the -direction and the -direction for radially polarized light. Although the amplitude of the electromagnetic wave in -direction is similar for linear polarization, there is some difference in the amplitude of the -component for linear polarization.

Fig. 6. Interaction of a radially polarized focused beam with a silver sphere with a 250 nm radius. The total electric field is plotted on the x̂-ẑ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.
Fig. 7. Interaction of a linearly polarized focused beam with a silver sphere with a 250 nm radius. The total electric field is plotted on the x̂-zĮ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.

Fig. 8. Interaction of a radially polarized focused beam with a dielectric sphere with a 250 nm radius. Dielectic index of the sphere is 2. The total electric field is plotted on the x̂-ẑ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.

5. Conclusion

In this study, the interaction of spherical nanoparticles with highly focused incident beams was modeled using Richards-Wolf theory, which provides an accurate representation for a highly focused beam near the focus of an aplanatic lens. Both analytical and FEM-based models were developed to study this interaction. Formulations were given for both linearly and radially polarized focused beams. Analytical model and results in this study can be used by other scientists to validate more complicated 3-D modeling tools, such as FDTD and FEM involving linear and radial polarizations. In this study, the analytical model was also utilized to validate a 3-D FEM solution. There has been increasing interest in radially polarized focused beams to excite surface plasmons on nanoparticles. The tools developed in this study are crucial to validate and analyze the interaction of particles with linear and radial polarizations.

Fig. 9. Interaction of a linearly polarized focused beam with a dielectic sphere with a 250 nm radius. Dielectic index of the sphere is 2. The total electric field is plotted on the x̂-ẑ plane. (a) Solution using Mie series for |Ex (x,y)|2, (b) FEM solution for |Ex (x,y)|2, (c) Solution using Mie series for |Ez (x,y)|2, (d) FEM solution for |Ez (x,y)|2. |Ey (x,y)|2 components for both solutions are negligible.

References and links

1.

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

2.

C. Godefroy and M. Adjouadi, “Particle sizing in a flow environment using light scattering patterns,” Part. Part. Syst. Charact. 17, 47–55 (2000). [CrossRef]

3.

A. C. Eckbreth, “Effects of laser-modulated particulate incandescence on Raman scattering diagnostics,” J. Appl. Phys. 48, 4473–4479 (1977). [CrossRef]

4.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Yakanishi, “Scattering of a beam by a spherical object,” IEEE Trans. Antennas Propag. 16, 724–727 (1968). [CrossRef]

5.

W.-C. Tsai and R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical objects,” J. Opt. Soc. Am. A 65, 1457–1463 (1975). [CrossRef]

6.

W. G. Tam and R. Corriveau, “Scattering of electromagnetic beams by spherical objects,” J. Opt. Soc. Am. 68, 763–767 (1978). [CrossRef]

7.

J. S. Kim and S. S. Lee, “Scattering of laser beams and the optical potential well for a homogeneous sphere,” J. Opt. Soc. Am. 73, 303–312 (1983). [CrossRef]

8.

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, 1632–1639 (1988). [CrossRef]

9.

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

10.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989). [CrossRef]

11.

J. P. Barton and D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundemental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989). [CrossRef]

12.

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, 4594–4602 (1989). [CrossRef]

13.

J. P. Barton, “Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects,” Appl. Opt. 36, 1303–1311 (1997). [CrossRef] [PubMed]

14.

J. P. Barton, “Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering,” Appl. Opt. 37, 3339–3344 (1998). [CrossRef]

15.

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. Roy. Soc. London Ser. A 253, 349–357 (1959). [CrossRef]

16.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]

17.

A. Hartschuh, E. J. Sánchez, X. S. Xie, and L. Novotny, “High-resolution near-field Raman microscopy of singlewalled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003). [CrossRef] [PubMed]

18.

W. A. Challener, I. K. Sendur, and C. Peng, “Scattered field formulation of finite difference time domain for a focused light beam in dense media with lossy materials,” Opt. Express 11, 3160–3170 (2003). [CrossRef] [PubMed]

19.

K. Sendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96, 2743–2752 (2004). [CrossRef]

20.

G. Mie, “Beiträge zur optik truber medien, speziell kolloida ler metallösungen” Ann. d. Physik 25, 377- (1908). [CrossRef]

21.

M. Born and E. Wolf, Principles of Optics 5th ed. (Pergamon Press, Oxford, 1975), section 13.5. [PubMed]

22.

J. M. Jin, The Finite Element Method in Electomagnetics (John Wiley & Sons, New York, NY, 2000).

23.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, CA, 1998).

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(240.6680) Optics at surfaces : Surface plasmons
(290.4020) Scattering : Mie theory

ToC Category:
Scattering

History
Original Manuscript: January 7, 2008
Revised Manuscript: February 11, 2008
Manuscript Accepted: February 12, 2008
Published: February 15, 2008

Virtual Issues
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Kursat Sendur, William Challener, and Oleg Mryasov, "Interaction of spherical nanoparticles with a highly focused beam of light," Opt. Express 16, 2874-2886 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-5-2874


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References

  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
  2. C. Godefroy and M. Adjouadi, "Particle sizing in a flow environment using light scattering patterns," Part. Part. Syst. Charact. 17, 47-55 (2000). [CrossRef]
  3. A. C. Eckbreth, "Effects of laser-modulated particulate incandescence on Raman scattering diagnostics," J. Appl. Phys. 48, 4473-4479 (1977). [CrossRef]
  4. N. Morita, T. Tanaka, T. Yamasaki, and Y. Yakanishi, "Scattering of a beam by a spherical object," IEEE Trans. Antennas Propag. 16, 724-727 (1968). [CrossRef]
  5. W.-C. Tsai and R. J. Pogorzelski, "Eigenfunction solution of the scattering of beam radiation fields by spherical objects," J. Opt. Soc. Am. A 65, 1457-1463 (1975). [CrossRef]
  6. W. G. Tam and R. Corriveau, "Scattering of electromagnetic beams by spherical objects," J. Opt. Soc. Am. 68, 763-767 (1978). [CrossRef]
  7. J. S. Kim and S. S. Lee, "Scattering of laser beams and the optical potential well for a homogeneous sphere," J. Opt. Soc. Am. 73, 303-312 (1983). [CrossRef]
  8. 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, 1632-1639 (1988). [CrossRef]
  9. L. W. Davis, "Theory of electromagnetic beams," Phys. Rev. A 19, 1177-1179 (1979). [CrossRef]
  10. J. P. Barton, D. R. Alexander, and S. A. Schaub, "Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance," J. Appl. Phys. 65, 2900-2906 (1989). [CrossRef]
  11. J. P. Barton and D. R. Alexander, "Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam," J. Appl. Phys. 66, 2800-2802 (1989). [CrossRef]
  12. 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, 4594-4602 (1989). [CrossRef]
  13. J. P. Barton, "Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects," Appl. Opt. 36, 1303-1311 (1997). [CrossRef] [PubMed]
  14. J. P. Barton, "Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering," Appl. Opt. 37, 3339-3344 (1998). [CrossRef]
  15. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Proc. Roy. Soc. London Ser. A 253, 349-357 (1959). [CrossRef]
  16. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. Roy. Soc. London Ser. A 253, 358-379 (1959). [CrossRef]
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