Abstract

This paper proposes a novel approach for estimating the utilization efficiency of metal particles to increase light energy absorption by a medium with a nonzero imaginary part of a medium refractive index. This method is implemented for spherical Ag and Au nanoparticles embedded in muscle tissue. Numerical calculations for spheres in absorbing media show that the utilization efficiency of metal particles increases with the decreasing absorbability of the medium.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009

R. A. Dynich, A. N. Ponyavina, and V. V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76, 705–710 (2009).
[CrossRef]

R. A. Dynich and A. N. Ponyavina, “Effect of metallic nanoparticle sizes on the local field near their surface,” J. Appl. Spectrosc. 75, 832–838 (2009).
[CrossRef]

2006

2005

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

2003

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

2001

1999

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

1996

M. Quinten and J. Rostalski, “Lorenz–Mie theory for sphere immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

1990

1979

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221(1979).
[CrossRef]

1977

1974

1972

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

1951

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246(1951).
[CrossRef]

Aden, A. L.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246(1951).
[CrossRef]

Altenkirch, R. A.

Anderson, R. R.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221(1979).
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Christy, R. W.

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

Chylek, P.

Decraemer, W. F.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Dirckx, J. J. J.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Dynich, R. A.

R. A. Dynich, A. N. Ponyavina, and V. V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76, 705–710 (2009).
[CrossRef]

R. A. Dynich and A. N. Ponyavina, “Effect of metallic nanoparticle sizes on the local field near their surface,” J. Appl. Spectrosc. 75, 832–838 (2009).
[CrossRef]

Filippov, V. V.

R. A. Dynich, A. N. Ponyavina, and V. V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76, 705–710 (2009).
[CrossRef]

Fu, Q.

Gartz, M.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

Gilra, D. P.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221(1979).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Joe, E. K.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Johnson, P. B.

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

Kerker, M.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246(1951).
[CrossRef]

Kreibig, U.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

Kuypers, L. C.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Lebedev, A. N.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

Lin, C. P.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Mackowski, D. W.

Menguc, M. P.

Mundy, W. C.

Pilon, L.

Pitsillides, C. M.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Ponyavina, A. N.

R. A. Dynich, A. N. Ponyavina, and V. V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76, 705–710 (2009).
[CrossRef]

R. A. Dynich and A. N. Ponyavina, “Effect of metallic nanoparticle sizes on the local field near their surface,” J. Appl. Spectrosc. 75, 832–838 (2009).
[CrossRef]

Quinten, M.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for sphere immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Rostalski, J.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for sphere immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Roux, J. A.

Smith, A. M.

Stenzel, O.

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

Sudiarta, I. W.

I. W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
[CrossRef]

I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

Sun, W.

Wei, X.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Yin, J.

Appl. Opt.

Biophys J.

C. M. Pitsillides, E. K. Joe, X. Wei, R. R. Anderson, and C. P. Lin, “Selective cell targeting with light-absorbing microparticles and nanoparticles,” Biophys J. 84, 4023–4032(2003).
[CrossRef] [PubMed]

Eur. Phys. J. D

A. N. Lebedev, M. Gartz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
[CrossRef]

J. Appl. Phys.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246(1951).
[CrossRef]

J. Appl. Spectrosc.

R. A. Dynich and A. N. Ponyavina, “Effect of metallic nanoparticle sizes on the local field near their surface,” J. Appl. Spectrosc. 75, 832–838 (2009).
[CrossRef]

R. A. Dynich, A. N. Ponyavina, and V. V. Filippov, “Local field enhancement near spherical nanoparticles in absorbing media,” J. Appl. Spectrosc. 76, 705–710 (2009).
[CrossRef]

J. Biomed. Opt.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, “Refractive index of tissue measured with confocal microscopy,” J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

J. Colloid Interface Sci.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221(1979).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

Part. Part. Syst. Charact.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for sphere immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Phys. Rev. B

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

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (8)

Fig. 1
Fig. 1

Partition of the spherical surface with radius R into annular zones Δ ζ i . (a) Rings Δ S i are projections of annular zones on the plane x y . (b) The difference between the outer and inner radii of each ring is invariable and equal to Δ y . S P , Poynting vector; e r , outward unit vector normal to the spherical surface; and E 0 in , electric field amplitude at the beginning of the coordinate system.

Fig. 2
Fig. 2

Dependence of A ( R ) / A str ( R ) on a radius of a spherical layer R. The radius of the silver particle is 10 nm , the wavelength is 405 nm , and the medium refractive index is m r = 1.3 (1), 1.5 (2), and m i = 0.05 .

Fig. 3
Fig. 3

Tridimensional diagrams for coefficient k eff on λ 0 and R / a . An absorbing medium has a real part of the refractive index m r = 1.5 and an imaginary part (a) m i = 0.05 , (b) 0.1, and (c) 0.2. The radius of the spherical Ag particle is 10 nm .

Fig. 4
Fig. 4

Spectral dependencies of absorption efficiency Q abs of the spherical Ag particle with a radius of 10 nm in an absorbing medium.

Fig. 5
Fig. 5

Tridimensional diagrams for k eff . Spherical Ag particle with a = 10 nm embedded in an absorbing medium with a real part of the refractive index m r = 1.3 and an imaginary part (a) m i = 0.05 , (b) 0.1, and (c) 0.2.

Fig. 6
Fig. 6

Tridimensional diagrams for k eff on λ 0 and a of spherical (a) silver and (b) gold nanoparticles embedded in biological tissue with a refractive index of 1.382 + i 0.004 . A spherical layer surrounding the particle has the outer radius of R = 1.5 a .

Fig. 7
Fig. 7

Normalized energy absorbed by a medium in a spherical layer with (a), (b) a = 10 nm and (c), (d) 30 nm in the (a), (c) absence and presence of (b) Ag and (d) Au particles. Particle radii are 10 (Ag) and 30 nm (Au). An absorbing medium is a biological tissue with a refractive index of 1.382 + i 0.004 .

Fig. 8
Fig. 8

Utilization efficiency of silver and gold nanoparticles with radii of (a) 10 and (b) 30 nm , respectively. A medium in which embedded nanoparticles is biological tissue with a refractive index of 1.382 + i 0.004 .

Tables (1)

Tables Icon

Table 1 Values of k eff max for Spherical Metal Particles in an Absorbing Medium

Equations (12)

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

A m ( R ) = W m ( R ) .
W m ( R ) = 1 / 2 Re [ ζ ( E in × H in * ) e r d ζ ] ,
W m = W m 1 + W m 2 .
W m 2 = 2 π R 2 η R 2 I 0 [ 1 + ( η R 1 ) exp ( η R ) ] .
A m ( R ) = 2 π R 2 η R 2 I 0 [ ( η R 1 ) exp ( η R ) + ( η R + 1 ) exp ( η R ) ] .
A m s = A m ( R ) A m ( a ) ,
A s = A ( R ) A p ( a ) ,
W p ( a ) = 1 / 2     Re 0 π 0 2 π ( E × H * ) e r a 2 sin θ d θ d φ ,
A p ( a ) = π | E 0 in | 2 ω μ Re [ 1 k n = 1 i ( 2 n + 1 ) ( ψ n * ψ n ψ n ψ n * a n ψ n * ξ n a n * ψ n ξ n * + b n ψ n * ξ n + b n * ψ n ξ n * + | a n | 2 ξ n ξ n * | b n | 2 ξ n ξ n * ) ] ,
W ( R ) = 1 / 2     Re 0 π 0 2 π ( E × H * ) e r R 2 sin θ d θ d φ .
k eff = A s A m s ,
Q abs = A p ( a ) / A 0 ,

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