Abstract

We describe a method for obtaining the refractive index (RI), size, and concentration of nonabsorbing nanoparticles in suspension from relatively simple optical measurements. The method requires measuring the complex effective RI of two dilute suspensions of the particles in liquids of different refractive indices. We describe the theoretical basis of the proposed method and provide experimental results validating the procedure.

© 2014 Optical Society of America

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  1. M. Nakagaki and W. Heller, J. Appl. Phys. 27, 975 (1956).
    [CrossRef]
  2. C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).
  3. I. Niskanen, J. Räty, and K.-E. Peiponen, Appl. Opt. 49, 3428 (2010).
    [CrossRef]
  4. I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
    [CrossRef]
  5. M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
    [CrossRef]
  6. B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).
  7. A. García-Valenzuela, H. Contreras-Tello, J. A. Olivares, and F. L. S. Cuppo, J. Opt. Soc. Am. A 30, 1328 (2013).
    [CrossRef]
  8. C. F. Bohren, J. Atmos. Sci. 43, 468 (1986).
    [CrossRef]
  9. J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
    [CrossRef]
  10. S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
    [CrossRef]

2013

I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
[CrossRef]

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

A. García-Valenzuela, H. Contreras-Tello, J. A. Olivares, and F. L. S. Cuppo, J. Opt. Soc. Am. A 30, 1328 (2013).
[CrossRef]

2011

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

2010

2008

B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).

2007

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

1997

J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

1986

C. F. Bohren, J. Atmos. Sci. 43, 468 (1986).
[CrossRef]

1956

M. Nakagaki and W. Heller, J. Appl. Phys. 27, 975 (1956).
[CrossRef]

Bali, L. M.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Bali, S.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Barrera, R. G.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

Bohren, C. F.

C. F. Bohren, J. Atmos. Sci. 43, 468 (1986).
[CrossRef]

Calhourn, W. R.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Contreras-Tello, H.

Cuppo, F. L. S.

Dong, M. L.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Flores-Flores, J. O.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

García-Valenzuela, A.

A. García-Valenzuela, H. Contreras-Tello, J. A. Olivares, and F. L. S. Cuppo, J. Opt. Soc. Am. A 30, 1328 (2013).
[CrossRef]

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

Goyal, K. G.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Heller, W.

M. Nakagaki and W. Heller, J. Appl. Phys. 27, 975 (1956).
[CrossRef]

Ivanov, C. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

Kasarova, S. N.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

Khanadeev, V. A.

B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).

Khlebtsov, B. N.

B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).

Khlebtsov, N. G.

B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).

Köser, J.

J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Makkar, S. S.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Nakagaki, M.

M. Nakagaki and W. Heller, J. Appl. Phys. 27, 975 (1956).
[CrossRef]

Nikolov, I. D.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

Niskanen, I.

I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
[CrossRef]

I. Niskanen, J. Räty, and K.-E. Peiponen, Appl. Opt. 49, 3428 (2010).
[CrossRef]

Olivares, J. A.

Peiponen, K. E.

I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
[CrossRef]

Peiponen, K.-E.

Räty, J.

I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
[CrossRef]

I. Niskanen, J. Räty, and K.-E. Peiponen, Appl. Opt. 49, 3428 (2010).
[CrossRef]

Rheims, J.

J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Sánchez-Pérez, C.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

Sato-Berrú, R. Y.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

Sultanova, N. G.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

Worth, B. W.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

Wriedt, T.

J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

M. Nakagaki and W. Heller, J. Appl. Phys. 27, 975 (1956).
[CrossRef]

J. Atmos. Sci.

C. F. Bohren, J. Atmos. Sci. 43, 468 (1986).
[CrossRef]

J. Biomed. Opt.

M. L. Dong, K. G. Goyal, B. W. Worth, S. S. Makkar, W. R. Calhourn, L. M. Bali, and S. Bali, J. Biomed. Opt. 18, 087003 (2013).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys.

C. Sánchez-Pérez, A. García-Valenzuela, R. Y. Sato-Berrú, J. O. Flores-Flores, and R. G. Barrera, J. Phys. 274, 012064(2011).

Langmuir

B. N. Khlebtsov, V. A. Khanadeev, and N. G. Khlebtsov, Langmuir 4, 16 (2008).

Meas. Sci. Technol.

J. Rheims, J. Köser, and T. Wriedt, Meas. Sci. Technol. 8, 601 (1997).
[CrossRef]

Opt. Mater.

S. N. Kasarova, N. G. Sultanova, C. D. Ivanov, and I. D. Nikolov, Opt. Mater. 291481 (2007).
[CrossRef]

Talanta

I. Niskanen, J. Räty, and K. E. Peiponen, Talanta 115, 68 (2013).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Transmittance spectra T and imaginary part of the effective RI Δn for samples C1, C2, C3, and C4 in water (solid line) and glycerin/water (dashed line) matrices. Arrows indicate the corresponding y axis for each curve.

Fig. 2.
Fig. 2.

Particle RI dispersions obtained for C1, C2, C3, and C4 latex suspensions (symbol curves) and nominal RI curves for water, glycerin, polystyrene, and PMMA. In the inset, the retrieved curves together with the nominal curve for PMMA are plotted in a smaller scale.

Tables (1)

Tables Icon

Table 1. Data for Particle Calculations at λ=589nm

Equations (10)

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

neff=nm(1+i32S(0)xm3)f,
Δneffneffnm,
Δneff=32nmχfandΔneff=nmχ2xm3f,
Y1=Δn1Δn1Z=Δn1Δn2.
Y1=23χ1(n1k0a)3andZ=n14χ12n24χ22,
np=b±b24c2,
b=[(2n12n22)n12(2n22n12)/(n22Z1/2)]1n12/(n22Z1/2)andc=2n22n12.
a=1n1k0(3Y12χ1)1/3.
f=Δn1(2)n1(2)χ1(2)2x1(2)3.
Δn1(2)(λ)=λ4πdln(T1(2)).

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