## Controlling light scattering and polarization by spherical particles with radial anisotropy |

Optics Express, Vol. 21, Issue 7, pp. 8091-8100 (2013)

http://dx.doi.org/10.1364/OE.21.008091

Acrobat PDF (1523 KB)

### Abstract

Based on full-wave electromagnetic theory, we derive the zero-forward and zero-backward scattering conditions for radially anisotropic spheres within the quasi-static limit. We find that the near-field intensity can be tuned dramatically through the adjustment of the radial anisotropy, while the far-field light scattering diagrams are similar under the zero-forward or zero-backward scattering conditions. Generalized “Brewster’s angle” for anisotropic spheres is also derived, at which the scattering light is totally polarized. In addition, the high-quality polarized scattering wave and the tunable polarization conversion can be achieved for the radially anisotropic spheres.

© 2013 OSA

## 1. Introduction

2. G. Mie, “Contributions to the optics of turbid media, particularly colloidal metal solutions,” Ann. Phys. **25**, 377–445 (1908) [CrossRef] .

5. P. Bhatia and B. D. Gupta, “Fabrication and characterization of a surface plasmon resonance based fiber optic urea sensor for biomedical applications,” Sens. Actuators B **161**, 434–438 (2012) [CrossRef] .

6. T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sctherland, and M. Kall, “Plasmonics sensing characteristis of single nanometric holes,” Nano Lett. **5**, 2335–2339 (2005) [CrossRef] [PubMed] .

7. S. Albaladejo, M. I. Marques, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of spin angular momentum of a light field,” Phys. Rev. Lett. **102**, 113602 (2009) [CrossRef] [PubMed] .

8. M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express **18**, 11428–11443 (2010) [CrossRef] [PubMed] .

9. J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express **15**, 2622–2653 (2007) [CrossRef] [PubMed] .

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

11. Z. Liu, S. Durant, H. Lee, Y. Picus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. **7**, 403–408 (2007) [CrossRef] [PubMed] .

12. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**, 1780–1782 (2006) [CrossRef] [PubMed] .

13. M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. **97**, 263902 (2006) [CrossRef] .

14. M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonance,” Phys. Rev. Lett. **100**, 043903 (2008) [CrossRef] [PubMed] .

*Q*from the small particles made of metamaterials were demonstrated such as

_{sca}*Q*∼ 1/

_{sca}*q*

^{2}(size parameter

*q*= 2

*πa*/

*λ*, where

*a*is the radius of the sphere and

*λ*is the illuminating wavelength) or

*Q*∼

_{sca}*const*under certain conditions [15

15. Z. Liu, Z. Lin, and S. T. Chui, “Electromagnetic scattering by spherically negative-refractive-index particles: low frequency resonance and localization parameters,” Phys. Rev. E **69**, 016609 (2004) [CrossRef] .

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

*et. al.*showed that the forward scattering and backward scattering can be almost suppressed if the dielectric and magnetic properties of the isotropic scatters satisfy certain relations [17

17. M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. **73**, 765–767 (1983) [CrossRef] .

*et. al.*renewed Kerker’s zero-forward scattering condition [18

18. B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, “Exception for the zero-forward-scattering theory,” J. Opt. Soc. Am. A **25**, 2875–2878 (2008) [CrossRef] .

20. B. García-Cámara, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, “Directionality in scattering by nanoparticles: Kerker’s null-scattering conditions revisited,” Opt. Lett. **36**, 728–730 (2011) [CrossRef] [PubMed] .

21. B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances in small particles with electric and magnetic properties,” J. Opt. Soc. Am. A **25**, 327–334 (2008) [CrossRef] .

*et. al.*[22

22. J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. **3**, 1171 (2012) [CrossRef] .

23. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. **4**, 1527 (2013) [CrossRef] [PubMed] .

24. S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” http://arxiv.org/abs/1212.2793v1.

25. J. Roth and M. J. Digman, “Scattering and extinction cross sections for a spherical particle coated with an oriented molecular layer,” J. Opt. Soc. Am. **63**, 308–311 (1973) [CrossRef] .

27. T. Ambjornsson, G. Mukhopadhyay, S. P. Apell, and M. Kall, “Resonant coupling between localized plasmons and anisotropic molecular coatings in ellipsoidal metal nanoparticles,” Phys. Rew. B **73**, 085412 (2006) [CrossRef] .

12. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**, 1780–1782 (2006) [CrossRef] [PubMed] .

28. L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rew. E **78**, 046609 (2008) [CrossRef] .

29. L. Gao and X. P. Xu, “Second- and third-harmonic generations for a nondilute suspension of coated particles with radial dielectric anisotropy,” Eur. Phys. J. B **55**, 403–409 (2007) [CrossRef] .

33. H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A **86**, 033825 (2012) [CrossRef] .

28. L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rew. E **78**, 046609 (2008) [CrossRef] .

34. J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. **99**, 063908 (2007) [CrossRef] [PubMed] .

## 2. Theoretical model

*a*, surrounded by the free space with permittivity

*ε*

_{0}and permeability

*μ*

_{0}. Radial anisotropy means that the permittivity (or permeability) tensor is diagonal in spherical coordinates, and the element along the radial direction differs from the one along the tangential direction [25

25. J. Roth and M. J. Digman, “Scattering and extinction cross sections for a spherical particle coated with an oriented molecular layer,” J. Opt. Soc. Am. **63**, 308–311 (1973) [CrossRef] .

*ε̿*= (

*ε*+

_{r}r̂r̂*ε*+

_{t}θ̂θ̂*ε*) and

_{t}ϕ̂ϕ̂*μ̿*= (

*μ*+

_{r}r̂r̂*μ*+

_{t}θ̂θ̂*μ*). For simplicity, we assume the polarized wave with unit amplitude to be E

_{t}ϕ̂ϕ̂*=*

_{i}*ê*exp(ik

_{x}_{0}z) with

28. L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rew. E **78**, 046609 (2008) [CrossRef] .

35. B. S. Luk’yanchuk and C. W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys. A **92**, 773–776 (2008) [CrossRef] .

*q*=

*k*

_{0}

*a*is the size parameter,

*ψ*(

_{n}*x*) and

*ξ*(

_{n}*x*) are the Ricatti-Bessel functions. The primes indicate differentiation with respect to the entire argument of the corresponding functions. From Eqs. (1) and (2), we find that all the information on the particle anisotropy is presented by the orders of spherical Bessel functions, where Ae =

*ε*/

_{t}*ε*and Am =

_{r}*μ*/

_{t}*μ*are, respectively, the electric and magnetic anisotropy ratios. For the isotropic case, Ae = Am = 1, Eqs. (1) and (2) are naturally reduced to the exact formulae of Mie theory.

_{r}*I*is composed of two polarized components [17

17. M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. **73**, 765–767 (1983) [CrossRef] .

*I*

_{1}and

*I*

_{2}are the two polarized components of the scattered intensity when the incident electric field vector is perpendicular (TE) and parallel (TM) to the scattering plane, which contains the incident direction and the direction of the scattered wave. In addition,

*λ*is the incident wavelength,

*r*is the distance to the observer, and

*ϕ*is the angle between the electric vector of the incident wave and the scattering plane. And the amplitude functions

*S*

_{⊥}and

*S*

_{||}are defined as where the angular functions

*θ*being the angle between the forward and scattering directions. Note that there are two special directions such as 0° and 180° at which the scattering does not depend on the input polarization. In this connection, we can write the reflection (backward,

*θ*= 180°)

*R*and transmission (forward,

*θ*= 0°)

*T*amplitudes,

## 3. Conditions for suppression of the scattering intensity

17. M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. **73**, 765–767 (1983) [CrossRef] .

*R*= 0) for the scattering coefficients satisfying

*a*=

_{n}*b*, whereas the scattering in the forward direction can be totally suppressed (i. e.

_{n}*T*= 0) when

*a*= −

_{n}*b*.

_{n}*q*= 2

*πa*/

*λ*≪ 1) and low-frequency (

*mq*≪ 1) limit, the higher terms for

*n*> 1 are so small that can be neglected, and the scattering efficiency is mainly characterized by the first two scattering coefficients

*a*

_{1}and

*b*

_{1}, which represent the dipole contributions. Correspondingly, the Riccati-Bessel functions with small arguments for

*n*= 1 and non-integer order

*ν*are approximately to be,

*a*

_{1}and

*b*

_{1}with small arguments are, As a consequence, we obtain the zero-backward and zero-forward scattering conditions for small particles with radial anisotropy, Here we would like to mention that Eq. (11) is reduced to Kerker’s conditions for the isotropic case with

*ν*

_{1}=

*γ*

_{1}= 1. Actually, zero-forward scattering intensity cannot be exactly obtained under the zero-forward scattering condition. The forward scattering intensity just leads to a minimum, and its magnitude is much smaller than the scattering in all other directions. The reason is that the zero-forward scattering condition is derived under the quasi-static limit, and the higher-order scattering coefficients (i.e.

*a*

_{2},

*b*

_{2}...), which definitely exist, have been omitted. In this sense, the overall scattering from the sphere is indeed low and the higher-order components of the forward scattering takes into account the extinction from the sphere, and then the optical theorem (the extinction cross section is proportional to the scattering amplitude in the forward direction) is satisfied [36

36. A. Alù and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem,” J. Nanophoton. **4**, 041590 (2010) [CrossRef] .

*ε*= −(

_{t}*ν*

_{1}+ 1) [we get

*μ*= −(

_{t}*γ*

_{1}+ 1) with the condition for zero-forward scattering], at which the localized surface plasmon resonances are excited [18

18. B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, “Exception for the zero-forward-scattering theory,” J. Opt. Soc. Am. A **25**, 2875–2878 (2008) [CrossRef] .

*μ*=

_{r}*μ*= 2, the scattering coefficient

_{t}*b*

_{1}is fully fixed. Moreover, under the zero-forward (or backward) scattering condition, one yields

*a*

_{1}= −

*b*

_{1}(or

*a*

_{1}=

*b*

_{1}) no matter what the anisotropic permittivities are chosen. As a consequence, the scattering intensity, determined mainly by the first two scattering coefficients

*a*

_{1}and

*b*

_{1}, is almost independent of the radial anisotropy.

20. B. García-Cámara, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, “Directionality in scattering by nanoparticles: Kerker’s null-scattering conditions revisited,” Opt. Lett. **36**, 728–730 (2011) [CrossRef] [PubMed] .

36. A. Alù and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem,” J. Nanophoton. **4**, 041590 (2010) [CrossRef] .

*a*

_{1}and

*b*

_{1}should be modified by, Then, the condition for zero-backward scattering is found to be the same as the first one in Eq. (11), while the condition for the zero-forward scattering is revised to be Similarly, Eq. (13) is reduced to the modified Kerker’s condition [20

20. B. García-Cámara, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, “Directionality in scattering by nanoparticles: Kerker’s null-scattering conditions revisited,” Opt. Lett. **36**, 728–730 (2011) [CrossRef] [PubMed] .

*ν*

_{1}=

*γ*

_{1}= 1 for the isotropic case. In order to fulfill Eq. (13), at least one of the anisotropic parameters should be complex with negative imaginary part if other parameters are real. The negative imaginary part of

*ε*

_{r}_{(t)}or

*μ*

_{r}_{(t)}may result in negative absorption cross section or amplification cross section. The scatters with such a property are known as gain (active) objects. On the contrary, for usual passive spheres whose imaginary parts of the permeabilities and/or permittivities are positive, the corresponding electric or magnetic polarizability cannot have opposite sign to each other [36

36. A. Alù and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem,” J. Nanophoton. **4**, 041590 (2010) [CrossRef] .

38. M. Nieto-Vesperinas, R. Gómez-Medina, and J. J. Sáenz, “Angle-supressed scattering and optical forces on submicrometer dieletric particles,” J. Opt. Soc. Am. A **28**, 54–60 (2011) [CrossRef] .

39. R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. **5**, 053512 (2011) [CrossRef] .

## 4. The polarization of the scattering wave

40. C. E. Dean and P. L. Marston, “Critical angle light scattering from bubbles: an asymptotic series approximation,” Appl. Opt. **30**, 4764–4776 (1991) [CrossRef] [PubMed] .

41. B. García-Cámara, F. González, and F. Moreno, “Linear polarization degree for detecting magnetic properties of small particles,” Opt. Lett. **35**, 4084–4086 (2010) [CrossRef] [PubMed] .

*S*

_{⊥}or

*S*

_{||}equals zero, the scattering light will be totally polarized. The angle at which

*S*

_{⊥}(or

*S*

_{||}) equals zero is defined as the generalized Brewster’s angles for the sphere [16

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

*θ*

_{⊥}(when

*S*

_{⊥}= 0) and

*θ*

_{||}(when

*S*

_{||}= 0) refer to the “Brewster’s angles” for spherical particles with radial anisotropy. Moreover, the degree of polarization

*P*of the scattered light is expressed as,

*P*shall be 1 or −1, indicating totally TE- or TM-polarized scattering light. On the other hand, for the spheres with large size parameters, we can directly resort to our generalized formalism Eqs. (5) and (6) with Eqs. (1) and (2) to present the numerical results. In Fig. 4, we plot the polarization diagram and

*P*versus

*θ*with

*q*= 0.5 for different anisotropic permeabilities and permittivities. The following features are clearly noted: (1) The polarization can be nearly 1 or −1, that is to say, totally polarized, when we adjust the electric and magnetic anisotropy ratios suitably; (2) Either TE-polarized scattering wave (see the blue short dashed and olive dash-dotted lines) or TM-polarized scattering wave (see the black solid and red dotted lines) is achieved from the radially anisotropic sphere; (3) Through tuning the anisotropy ratios it is possible to obtain high-quality polarized scattered waves in comparison with those from isotropic spheres. High-quality means the degree of polarization is larger and the range of “Brewster’s angles” are broader; (4) Tunable “Brewster’s angles” from forward (0° ∼ 90°, see the black solid line) to backward (90° ∼ 180°, see the dash-dotted olive line) directions can be achieved.

*q*= 1.0. For the isotropic case (Ae = 1 and Am = 1), increasing the size parameters while keeping the physical parameters unchanged will result in a lower degree of polarization (see the red short dotted lines in Figs. 4 and 5). However, as the radial anisotropy is taken into account, we can still get high-quality polarized scattering wave.

## 5. Conclusion

## Acknowledgments

## References and links

1. | L. Rayleigh, “On the light from the sky, its polarization and color appendix,” Philos. Mag. |

2. | G. Mie, “Contributions to the optics of turbid media, particularly colloidal metal solutions,” Ann. Phys. |

3. | C. F. Bohren and D. R. Huffman, |

4. | M. Born and E. Wolf, |

5. | P. Bhatia and B. D. Gupta, “Fabrication and characterization of a surface plasmon resonance based fiber optic urea sensor for biomedical applications,” Sens. Actuators B |

6. | T. Rindzevicius, Y. Alaverdyan, A. Dahlin, F. Hook, D. S. Sctherland, and M. Kall, “Plasmonics sensing characteristis of single nanometric holes,” Nano Lett. |

7. | S. Albaladejo, M. I. Marques, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of spin angular momentum of a light field,” Phys. Rev. Lett. |

8. | M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express |

9. | J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express |

10. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

11. | Z. Liu, S. Durant, H. Lee, Y. Picus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. |

12. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

13. | M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. |

14. | M. I. Tribelsky, S. Flach, A. E. Miroshnichenko, A. V. Gorbach, and Y. S. Kivshar, “Light scattering by a finite obstacle and Fano resonance,” Phys. Rev. Lett. |

15. | Z. Liu, Z. Lin, and S. T. Chui, “Electromagnetic scattering by spherically negative-refractive-index particles: low frequency resonance and localization parameters,” Phys. Rev. E |

16. | A. E. Miroshnichenko, “Non-Rayleigh limit of the Lorenz-Mie solution and supression of scattering by spheres of negative refractive index,” Phys. Rev. A |

17. | M. Kerker, D. S. Wang, and C. L. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. |

18. | B. García-Cámara, F. González, F. Moreno, and J. M. Saiz, “Exception for the zero-forward-scattering theory,” J. Opt. Soc. Am. A |

19. | B. Garcia-Camara, J. M. Saiz, F. Gonzalez, and F. Moreno, “Nanoparticles with unconventional scattering properties: size effects,” Opt. Commun. |

20. | B. García-Cámara, R. Alcaraz de la Osa, J. M. Saiz, F. González, and F. Moreno, “Directionality in scattering by nanoparticles: Kerker’s null-scattering conditions revisited,” Opt. Lett. |

21. | B. García-Cámara, F. Moreno, F. González, J. M. Saiz, and G. Videen, “Light scattering resonances in small particles with electric and magnetic properties,” J. Opt. Soc. Am. A |

22. | J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. |

23. | Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. |

24. | S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” http://arxiv.org/abs/1212.2793v1. |

25. | J. Roth and M. J. Digman, “Scattering and extinction cross sections for a spherical particle coated with an oriented molecular layer,” J. Opt. Soc. Am. |

26. | V. L. Sukhorukov, G. Meedt, M. Kurschner, and U. Zimmermann, “A single-shell model for biological cells extended to account for the dielectric anisotropy of the plasma membrane,” J. Electrost. |

27. | T. Ambjornsson, G. Mukhopadhyay, S. P. Apell, and M. Kall, “Resonant coupling between localized plasmons and anisotropic molecular coatings in ellipsoidal metal nanoparticles,” Phys. Rew. B |

28. | L. Gao, T. H. Fung, K. W. Yu, and C. W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rew. E |

29. | L. Gao and X. P. Xu, “Second- and third-harmonic generations for a nondilute suspension of coated particles with radial dielectric anisotropy,” Eur. Phys. J. B |

30. | X. Fan, Z. Shen, and B. S. Luk’yanchuk, “Huge light scattering from anisotropic spherical particles,” Opt. Express |

31. | C. W. Qiu and B. S. Luk’yanchuk, “Peculiarities in light scattering by spherical particles with radial anisotropy,” J. Opt. Soc. Am. A |

32. | Y. X. Ni, L. Gao, A. E. Miroshnichenko, and C. W. Qiu, “Non-Rayleigh scattering behavior for anisotropic Rayleigh particles,” Opt. Lett. |

33. | H. L. Chen and L. Gao, “Anomalous electromagnetic scattering from radially anisotropic nanowires,” Phys. Rev. A |

34. | J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. |

35. | B. S. Luk’yanchuk and C. W. Qiu, “Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials,” Appl. Phys. A |

36. | A. Alù and N. Engheta, “How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem,” J. Nanophoton. |

37. | C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alu, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. |

38. | M. Nieto-Vesperinas, R. Gómez-Medina, and J. J. Sáenz, “Angle-supressed scattering and optical forces on submicrometer dieletric particles,” J. Opt. Soc. Am. A |

39. | R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophoton. |

40. | C. E. Dean and P. L. Marston, “Critical angle light scattering from bubbles: an asymptotic series approximation,” Appl. Opt. |

41. | B. García-Cámara, F. González, and F. Moreno, “Linear polarization degree for detecting magnetic properties of small particles,” Opt. Lett. |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(260.5430) Physical optics : Polarization

(290.4020) Scattering : Mie theory

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Scattering

**History**

Original Manuscript: February 7, 2013

Revised Manuscript: March 14, 2013

Manuscript Accepted: March 18, 2013

Published: March 27, 2013

**Virtual Issues**

Vol. 8, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Y. X. Ni, L. Gao, A. E. Miroshnichenko, and C. W. Qiu, "Controlling light scattering and polarization by spherical particles with radial anisotropy," Opt. Express **21**, 8091-8100 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8091

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### References

- L. Rayleigh, “On the light from the sky, its polarization and color appendix,” Philos. Mag.41, 107–120 (1871).
- G. Mie, “Contributions to the optics of turbid media, particularly colloidal metal solutions,” Ann. Phys.25, 377–445 (1908). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light, 7th (expanded) ed. (Cambridge, 1999).
- P. Bhatia and B. D. Gupta, “Fabrication and characterization of a surface plasmon resonance based fiber optic urea sensor for biomedical applications,” Sens. Actuators B161, 434–438 (2012). [CrossRef]
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