Abstract

The scattering and transparency properties of layered plasmonic nanoparticles are studied from the perspective of spherical transmission line theory. The advantage of this approach is that the interaction of the nanoparticle with its surroundings can be very conveniently represented as a combination of admittances. In this framework we reformulate the total impedance expression of a spherical nanoparticle, and from this we derive through a compact and intuitive methodology the two conditions that govern the resonance and transparency states of a nanoparticle. These conditions are satisfied when the particle’s input admittance becomes inductive and capacitive, respectively. The recursive relations that determine the TM admittance of an electrically small, radially inhomogeneous dielectric sphere are analyzed, and it is demonstrated that any degree of layering can be homogenized by a decomposition into successive binary mixtures. The appropriate material choice results in mixtures that exhibit multiple Lorentzian resonances that are directly mapped to the particle’s admittance, due to its small electrical size. Consequently, the particle’s admittance exhibits multiple inductive-to-capacitive switchings, and thus the resonance and transparency conditions are satisfied at multiple frequencies. This explains the well-known feature of multiple resonance–transparency pairs observed in the scattering signature of layered plasmonic nanoparticles.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
    [CrossRef]
  2. M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
    [CrossRef]
  3. J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
    [CrossRef]
  4. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989).
    [CrossRef]
  5. J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res. B 10, 441–449 (1963).
  6. M. Kerker, “Invisible bodies,” J. Opt. Soc. Am. 65, 376–379 (1975).
    [CrossRef]
  7. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  8. A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic cloaks,” Phys. Rev. Lett. 100, 113901 (2008).
    [CrossRef]
  9. F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
    [CrossRef]
  10. F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
    [CrossRef]
  11. D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Unveiling ultrasharp scattering–switching signatures of layered gold–dielectric–gold nanospheres,” J. Opt. Soc. Am. B 30, 2066–2074 (2013).
    [CrossRef]
  12. D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).
  13. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  14. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2013 (2)

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

D. Sikdar, I. D. Rukhlenko, W. Cheng, and M. Premaratne, “Unveiling ultrasharp scattering–switching signatures of layered gold–dielectric–gold nanospheres,” J. Opt. Soc. Am. B 30, 2066–2074 (2013).
[CrossRef]

2012 (2)

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

2011 (1)

M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
[CrossRef]

2010 (1)

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

2008 (1)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic cloaks,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

2005 (2)

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

1989 (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989).
[CrossRef]

1975 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1963 (1)

J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res. B 10, 441–449 (1963).

Alam, M.

M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
[CrossRef]

Alu, A.

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic cloaks,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef]

Argyropoulos, C.

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

Belov, P. A.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

Cheng, W.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Doyle, W. T.

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989).
[CrossRef]

Eleftheriades, G. V.

M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
[CrossRef]

Engheta, N.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic cloaks,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef]

Filonov, D. S.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

Greffet, J.-J.

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kerker, M.

M. Kerker, “Invisible bodies,” J. Opt. Soc. Am. 65, 376–379 (1975).
[CrossRef]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Kivshar, Y. S.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

Laroche, M.

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Marquier, F.

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Massoud, Y.

M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
[CrossRef]

Monticone, F.

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

Premaratne, M.

Rukhlenko, I. D.

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef]

Sikdar, D.

Slobozhanyuk, A. P.

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

Wait, J. R.

J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res. B 10, 441–449 (1963).

Appl. Sci. Res. B (1)

J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res. B 10, 441–449 (1963).

IEEE Trans. Microwave Theor. Tech. (1)

M. Alam, Y. Massoud, and G. V. Eleftheriades, “A time-varying approach to circuit modeling of plasmonic nanospheres using radial vector wave functions,” IEEE Trans. Microwave Theor. Tech. 59, 2595–2611 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852–9858 (1989).
[CrossRef]

Phys. Rev. E (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic cloaks,” Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef]

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

F. Monticone, C. Argyropoulos, and A. Alu, “Multilayered covers for comblike scattering response and optical tagging,” Phys. Rev. Lett. 110, 113901 (2013).
[CrossRef]

Phys. Stat. Sol. RRL (1)

D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Stat. Sol. RRL 6, 46–48 (2012).

Sci. Rep. (1)

F. Monticone, C. Argyropoulos, and A. Alu, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci. Rep. 2, 912–918 (2012).
[CrossRef]

Other (1)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Geometry of a radially inhomogeneous spherically layered structure.

Fig. 2.
Fig. 2.

(a) Input susceptance of a homogeneous silver sphere and a homogeneous sphere with εr=5, along with the susceptance conditions for resonance and transparency and (b) scattering efficiency of a homogeneous silver sphere and a homogeneous sphere with εr=5.

Fig. 3.
Fig. 3.

(a) Susceptance of the effective homogeneous core-shell particle whose material properties are computed from Eq. (21) and (b) scattering efficiency of the actual core-shell particle.

Fig. 4.
Fig. 4.

Homogenization scheme of a triple-layer spherical particle.

Fig. 5.
Fig. 5.

(a) Susceptance of the effective homogeneous triple-layer particle with material properties determined from Eq. (29) and (b) scattering efficiency of the actual triple-layer particle.

Fig. 6.
Fig. 6.

(a) Scattering efficiency comparison of a triple-layer particle and that of an effective equivalent sphere and (b) relative error in scattering efficiency calculations.

Equations (35)

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

Yi+1,n(e)=Y0,n(e)(mi+1αi+1)1Ψ(mi+1αi+1,mi+1αi)1Yi,n(e)1Y0,n(e)(mi+1α)i1Yi,n(e)+1Yext,n(e)(mi+1αi)1Ω(mi+1αi+1,mi+1αi)Yi,n(e)Y0,n(e)(mi+1αi)Yi,n(e)+Yext,n(e)(mi+1αi),
Ψ(x,y)χn(x)ψn(x)ψn(y)χn(y)
Ω(x,y)χn(x)ψn(x)ψn(y)χn(y),
Y0,n(e)(mi+1αi+1)=jmi+1ψn(mi+1αi+1)ψn(mi+1αi+1)
Yext,n(e)(mi+1αi)=mi+1jχn(mi+1αi)χn(mi+1αi).
Y1,n(e)=jm1ψn(m1α1)ψn(m1α1).
pz=6πjk03a1Ezi,
a1=ψ1(α1)ψ1(m1α1)m1ψ1(m1α1)ψ1(α1)χ1(α1)ψ1(m1α1)m1ψ1(m1α1)χ1(α1),
a1=ψ1(α1)χ1(α1)Y1,1(e)(m1α1)Y0,1(e)(α1)Y1,1(e)(m1α1)+Yext,1(e)(α1).
Z=Ezjωpz=k036πωχ1(α1)ψ1(α1)Y1,1(e)(m1α1)+Yext,1(e)(α1)Y1,1(e)(m1α1)Y0,1(e)(α1).
Y1,1(e)(m1α1)+Yext,1(e)(α1)=0.
Y1,1(e)(m1α1)Y0,1(e)(α1)=0.
Y0,1(e)(α1)=jα12+jα1320+O(jα15)
Yext,1(e)(α1)=jα1+jα13+O(jα1)4.
Qsca=4πGk02(|a1|2+|b1|2),
Y1,1(e)(m1α1)Y0jm12α12Y0=jωε0r12ε1.
Y2,1(e)=Y0,1(e)(m2α2)1Ψ(m2α2,m2α1)1Y1,1(e)1Y0,1(e)(m2α1)1Y1,1(e)+1Yext,1(e)(m2α1)1Ω(m2α2,m2α1)Y1,1(e)Y0,1(e)(m2α1)Y1,1(e)+Yext,1(e)(m2α1).
Y2,1(e)Y0jm22α221+2fjm12α12jm22α12jm12α12+jm22α11fjm12α12jm22α12jm12α12+jm22α1Y0
Y2,1(e)Y0jm22α221+2fε1ε2ε1+2ε21fε1ε2ε1+2ε2Y0=jωε0r22ε21+2fα121fα12,
α12=ε1ε2ε1+2ε2,
ε12=ε21+2fα121fα12.
Y3,1(e)=Y0,1(e)(m3α3)1Ψ(m3α3,m3α2)1Y2,1(e)1Y0,1(e)(m3α2)1Y2,1(e)+1Yext,1(e)(m3α2)1Ω(m3α3,m3α2)Y2,1(e)Y0,1(e)(m3α2)Y2,1(e)+Yext,1(e)(m3α2)
Y2,1(e)=Y0,1(e)(m2α2)1Ψ(m2α2,m2α1)1Y1,1(e)1Y0,1(e)(m2α1)1Y1,1(e)+1Yext,1(e)(m2α1)1Ω(m2α2,m2α1)Y1,1(e)Y0,1(e)(m2α1)Y1,1(e)+Yext,1(e)(m2α1).
Y2,1(e)jm22α221+2f1jm12α12jm22α12jm12α12+jm22α11f1jm12α12jm22α12jm12α12+jm22α1
Y2,1(e)jm22α221+2f1ε1ε2ε1+2ε21f1ε1ε2ε1+2ε2=jm22α221+2f1α121f1α12λ,
Y3,1(e)=jm32α321+2f2jm22α22λjm32α22jm22α22λ+jm32α21f2jm22α22λjm32α22jm22α22λ+jm32α2
Y3,1(e)Y0jm32α321+2f2ε2λε3ε2λ+2ε31f2ε2λε3ε2λ+2ε3Y0=jωε0r32ε31+2f2α1231f2α123,
α123ε2λε3ε2λ+2ε3
εe=ε31+2f2α1231f2α123.
Zi+1,n(m)=Z0,n(m)(mi+1αi+1)1Ψ(mi+1αi+1,mi+1αi)1Zi,n(m)1Z0,n(m)(mi+1αi)1Zi,n(m)+1Zext,n(m)(mi+1αi)1Ω(mi+1αi+1,mi+1αi)Zi,n(m)Z0,n(m)(mi+1αi)Zi,n(m)+Zext,n(m)(mi+1αi),
Z0,n(m)(mi+1αi+1)=mi+12Y0,n(e)(mi+1αi+1),
Zext,n(m)(mi+1αi)=mi+12Yext,n(e)(mi+1αi),
Zi,n(m)=mi2Yi,n(e),i=1
Z1,n(m)=m12Y1,n(e).
Zi+1,1(m)Z0,1(m)(mi+1αi+1).

Metrics