Abstract

We compare a recently developed coherent-scattering model for the reflectance of light from a turbid colloidal suspension of particles with experimental measurements. The experimental data were obtained in an internal reflection configuration around the critical angle using a glass prism in contact with a monodisperse colloidal suspension of latex particles, and a polydisperse suspension of TiO2 particles. First, we review the coherent scattering model and extend it to the case of polydisperse suspensions in an internal reflection configuration. The experimental data is then compared with results of the coherent scattering model and results obtained assuming that the colloidal system can be treated as a homogeneous medium with an effective index of refraction. We find that the experimental results are not compatible with the effective medium model. On the other hand, good fits to the experimental curves can be obtained with the coherent scattering model.

© 2005 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Retrieving the real refractive index of mono- and polydisperse colloids from reflectance near the critical angle

Benjamin E. Reed, Roy G. Grainger, Daniel M. Peters, and Andrew J. A. Smith
Opt. Express 24(3) 1953-1972 (2016)

Rigorous theoretical framework for particle sizing in turbid colloids using light refraction

Augusto García-Valenzuela, Rubén G. Barrera, and Edahí Gutierrez-Reyes
Opt. Express 16(24) 19741-19756 (2008)

Coherent optical reflectance from a monolayer of large particles adsorbed on a glass surface

Mary Carmen Peña-Gomar, Francisco Castillo, Augusto García-Valenzuela, Rubén G. Barrera, and Elías Pérez
Appl. Opt. 45(4) 626-632 (2006)

References

  • View by:
  • |
  • |
  • |

  1. M Lax, “Multiple scattering of waves II. The effective field in dense systems” Phys. Rev. 85621 (1952).
    [Crossref]
  2. L Tsang and J A Kong, Scattering of electromagnetic waves: Advanced topics (Wiley, New York, 2001).
  3. L Tsang and J A Kong, “Effective propagation constants for coherent electromagnetic waves propagating in media embedded with dielectric scatterers” J. Appl. Phys. 53, 7162 (1982).
    [Crossref]
  4. A García-Valenzuela and R G Barrera, “Electromagnetic response of a random half-space of Mie scatterers within the effective medium approximation and the determination of the effective optical coefficients” J. Quant. Spectrosc. Radiat. Transfer 627, 79 (2003).
  5. Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
    [Crossref]
  6. C Yang, A Wax, and M S Feld, “Measurement of the anomalous phase velocity of ballistic light in a random medium by use of a novel interferometer” Opt. Lett. 26 (4), 235 (2001).
    [Crossref]
  7. R G Barrera and A Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach” J. Opt. Soc. Am. A 20 (2), 296 (2003).
    [Crossref]
  8. A Garcia-Valenzuela and R G Barrera, “Optical reflectance of a composite medium with a sparse concentration of large spherical inclusions” Phys. Status Solidi B 240, 480 (2003).
    [Crossref]
  9. R G Barrera and A Garcia-Valenzuela, “Amperian magnetism in the dynamic response of granular materials”, Developments in Mathematical and Experimental Physics, Volume B: Statistical Physics and Beyond, Edited by Macias et al. (Kluwer Academic, Plenum Publishers, 2003) pp. 147–170.
    [Crossref]
  10. A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
    [Crossref]
  11. C F Bohren, “Applicability of effective medium theories to problems of scattering and absorption by non-homogeneous atmospheric particles” J. Atmos. Sci. 43, 468 (1986).
    [Crossref]
  12. R Ruppin, “Evaluation of extended Maxwell Garnett theories” Opt. Commun. 182, 273 (2000).
    [Crossref]
  13. C F Bohren and D R Huffman, Absorption and Scattering of Light by Small Particles (J. Wiley & Sons, New York, 1983).
  14. H C van de Hulst, Light scattering by small particles (Wiley, New York, 1957).
  15. A Chou and M Kerker, “The refractive index of colloidal sols” J. Phys. Chem. 60, 562 (1956).
    [Crossref]
  16. J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
    [Crossref]
  17. K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
    [Crossref]
  18. G H Meeten and A N North , “Refractive index measurement of turbid colloidal fluids by transmission near the critical angle” Meas. Sci. Technol. 2, 441 (1991).
    [Crossref]
  19. G H Meeten and A N North , “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle” Meas. Sci. Technol. 6, 214 (1995).
    [Crossref]
  20. M Mohammadi, “Colloidal refractometry: meaning and measurement of refractive index for dispersions; the science that time forgot” Adv. Colloid & Interf Sci. 62, 17 (1995).
    [Crossref]
  21. G H Meeten, “Refraction by spherical particles in the intermediate scattering region” Opt. Comm. 134, 233 (1997).
    [Crossref]
  22. G H Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials” Meas. Sci. Technol. 8, 728 (1997).
    [Crossref]
  23. Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
    [Crossref]
  24. H Ding, J Q Lu, K M Jacobs, and X-H Hu, “Determination of refractive indices of porcine skin tissues and intralipid at eight wavelengths between 325 and 1557 nm”, J. Opt. Soc. Am. A 22 (6), 1151 (2005).
    [Crossref]
  25. A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.
  26. F Curiel, Predicción de propiedades ópticas de películas inhomogéneas por medio de modelos de transferencia radiativa y su aplicación en pinturas, Ph.D. Thesis (Instituto de Física, Universidad Nacional Autónoma de México, México D.F. (2004).

2005 (2)

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

H Ding, J Q Lu, K M Jacobs, and X-H Hu, “Determination of refractive indices of porcine skin tissues and intralipid at eight wavelengths between 325 and 1557 nm”, J. Opt. Soc. Am. A 22 (6), 1151 (2005).
[Crossref]

2004 (1)

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

2003 (3)

R G Barrera and A Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach” J. Opt. Soc. Am. A 20 (2), 296 (2003).
[Crossref]

A Garcia-Valenzuela and R G Barrera, “Optical reflectance of a composite medium with a sparse concentration of large spherical inclusions” Phys. Status Solidi B 240, 480 (2003).
[Crossref]

A García-Valenzuela and R G Barrera, “Electromagnetic response of a random half-space of Mie scatterers within the effective medium approximation and the determination of the effective optical coefficients” J. Quant. Spectrosc. Radiat. Transfer 627, 79 (2003).

2001 (1)

2000 (1)

R Ruppin, “Evaluation of extended Maxwell Garnett theories” Opt. Commun. 182, 273 (2000).
[Crossref]

1997 (2)

G H Meeten, “Refraction by spherical particles in the intermediate scattering region” Opt. Comm. 134, 233 (1997).
[Crossref]

G H Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials” Meas. Sci. Technol. 8, 728 (1997).
[Crossref]

1996 (1)

Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
[Crossref]

1995 (2)

G H Meeten and A N North , “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle” Meas. Sci. Technol. 6, 214 (1995).
[Crossref]

M Mohammadi, “Colloidal refractometry: meaning and measurement of refractive index for dispersions; the science that time forgot” Adv. Colloid & Interf Sci. 62, 17 (1995).
[Crossref]

1991 (1)

G H Meeten and A N North , “Refractive index measurement of turbid colloidal fluids by transmission near the critical angle” Meas. Sci. Technol. 2, 441 (1991).
[Crossref]

1986 (1)

C F Bohren, “Applicability of effective medium theories to problems of scattering and absorption by non-homogeneous atmospheric particles” J. Atmos. Sci. 43, 468 (1986).
[Crossref]

1982 (1)

L Tsang and J A Kong, “Effective propagation constants for coherent electromagnetic waves propagating in media embedded with dielectric scatterers” J. Appl. Phys. 53, 7162 (1982).
[Crossref]

1981 (1)

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

1978 (1)

J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
[Crossref]

1956 (1)

A Chou and M Kerker, “The refractive index of colloidal sols” J. Phys. Chem. 60, 562 (1956).
[Crossref]

1952 (1)

M Lax, “Multiple scattering of waves II. The effective field in dense systems” Phys. Rev. 85621 (1952).
[Crossref]

Alexander, K

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

Barrera, R G

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

A Garcia-Valenzuela and R G Barrera, “Optical reflectance of a composite medium with a sparse concentration of large spherical inclusions” Phys. Status Solidi B 240, 480 (2003).
[Crossref]

A García-Valenzuela and R G Barrera, “Electromagnetic response of a random half-space of Mie scatterers within the effective medium approximation and the determination of the effective optical coefficients” J. Quant. Spectrosc. Radiat. Transfer 627, 79 (2003).

R G Barrera and A Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach” J. Opt. Soc. Am. A 20 (2), 296 (2003).
[Crossref]

A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.

R G Barrera and A Garcia-Valenzuela, “Amperian magnetism in the dynamic response of granular materials”, Developments in Mathematical and Experimental Physics, Volume B: Statistical Physics and Beyond, Edited by Macias et al. (Kluwer Academic, Plenum Publishers, 2003) pp. 147–170.
[Crossref]

Bohren, C F

C F Bohren, “Applicability of effective medium theories to problems of scattering and absorption by non-homogeneous atmospheric particles” J. Atmos. Sci. 43, 468 (1986).
[Crossref]

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

Capek, I

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Champion, J V

J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
[Crossref]

Chou, A

A Chou and M Kerker, “The refractive index of colloidal sols” J. Phys. Chem. 60, 562 (1956).
[Crossref]

Curiel, F

F Curiel, Predicción de propiedades ópticas de películas inhomogéneas por medio de modelos de transferencia radiativa y su aplicación en pinturas, Ph.D. Thesis (Instituto de Física, Universidad Nacional Autónoma de México, México D.F. (2004).

de Hulst, H C van

H C van de Hulst, Light scattering by small particles (Wiley, New York, 1957).

Ding, H

Feld, M S

Garcia-Valenzuela, A

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

A Garcia-Valenzuela and R G Barrera, “Optical reflectance of a composite medium with a sparse concentration of large spherical inclusions” Phys. Status Solidi B 240, 480 (2003).
[Crossref]

R G Barrera and A Garcia-Valenzuela, “Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach” J. Opt. Soc. Am. A 20 (2), 296 (2003).
[Crossref]

A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.

R G Barrera and A Garcia-Valenzuela, “Amperian magnetism in the dynamic response of granular materials”, Developments in Mathematical and Experimental Physics, Volume B: Statistical Physics and Beyond, Edited by Macias et al. (Kluwer Academic, Plenum Publishers, 2003) pp. 147–170.
[Crossref]

García-Valenzuela, A

A García-Valenzuela and R G Barrera, “Electromagnetic response of a random half-space of Mie scatterers within the effective medium approximation and the determination of the effective optical coefficients” J. Quant. Spectrosc. Radiat. Transfer 627, 79 (2003).

Hu, X-H

Huffman, D R

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

Jacobs, K M

Janícková, S

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Kerker, M

A Chou and M Kerker, “The refractive index of colloidal sols” J. Phys. Chem. 60, 562 (1956).
[Crossref]

Killey, A

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

Konecníková, A

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Kong, J A

L Tsang and J A Kong, “Effective propagation constants for coherent electromagnetic waves propagating in media embedded with dielectric scatterers” J. Appl. Phys. 53, 7162 (1982).
[Crossref]

L Tsang and J A Kong, Scattering of electromagnetic waves: Advanced topics (Wiley, New York, 2001).

Kostic, I

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Kuga, Y

Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
[Crossref]

Lax, M

M Lax, “Multiple scattering of waves II. The effective field in dense systems” Phys. Rev. 85621 (1952).
[Crossref]

Lu, J Q

Matay, L

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Meeten, G H

G H Meeten, “Refraction by spherical particles in the intermediate scattering region” Opt. Comm. 134, 233 (1997).
[Crossref]

G H Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials” Meas. Sci. Technol. 8, 728 (1997).
[Crossref]

G H Meeten and A N North , “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle” Meas. Sci. Technol. 6, 214 (1995).
[Crossref]

G H Meeten and A N North , “Refractive index measurement of turbid colloidal fluids by transmission near the critical angle” Meas. Sci. Technol. 2, 441 (1991).
[Crossref]

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
[Crossref]

Mohammadi, M

M Mohammadi, “Colloidal refractometry: meaning and measurement of refractive index for dispersions; the science that time forgot” Adv. Colloid & Interf Sci. 62, 17 (1995).
[Crossref]

North, A N

G H Meeten and A N North , “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle” Meas. Sci. Technol. 6, 214 (1995).
[Crossref]

G H Meeten and A N North , “Refractive index measurement of turbid colloidal fluids by transmission near the critical angle” Meas. Sci. Technol. 2, 441 (1991).
[Crossref]

Reyes-Coronado, A

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.

Rice, D

Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
[Crossref]

Ruppin, R

R Ruppin, “Evaluation of extended Maxwell Garnett theories” Opt. Commun. 182, 273 (2000).
[Crossref]

Sánchez-Pérez, C

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.

Sarov, Y

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Sarova, V

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Senior, M

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
[Crossref]

Tsang, L

L Tsang and J A Kong, “Effective propagation constants for coherent electromagnetic waves propagating in media embedded with dielectric scatterers” J. Appl. Phys. 53, 7162 (1982).
[Crossref]

L Tsang and J A Kong, Scattering of electromagnetic waves: Advanced topics (Wiley, New York, 2001).

Wax, A

West, R D

Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
[Crossref]

Yang, C

Adv. Colloid & Interf Sci. (1)

M Mohammadi, “Colloidal refractometry: meaning and measurement of refractive index for dispersions; the science that time forgot” Adv. Colloid & Interf Sci. 62, 17 (1995).
[Crossref]

AIP Conference Proceedings (1)

A Garcia-Valenzuela, C Sánchez-Pérez, A Reyes-Coronado, and R G Barrera, “Optical Characterization of a turbid colloid by light reflection around the critical angle” Materials Science and Applied Physics, 2nd Mexican Meeting on Mathematical and Experimental Physics, Eds. J L Hernández-Pozos and R Olayo-González, AIP Conference Proceedings 759, 62 (2005).
[Crossref]

IEEE Trans. Antennas Propag. (1)

Y Kuga, D Rice, and R D West, “Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium” IEEE Trans. Antennas Propag. 44 (3), 326 (1996).
[Crossref]

J. Appl. Phys. (1)

L Tsang and J A Kong, “Effective propagation constants for coherent electromagnetic waves propagating in media embedded with dielectric scatterers” J. Appl. Phys. 53, 7162 (1982).
[Crossref]

J. Atmos. Sci. (1)

C F Bohren, “Applicability of effective medium theories to problems of scattering and absorption by non-homogeneous atmospheric particles” J. Atmos. Sci. 43, 468 (1986).
[Crossref]

J. Chem. Soc, Faraday Trans. (1)

J V Champion, G H Meeten, and M Senior, “Refractive index of particles in the colloidal state” J. Chem. Soc, Faraday Trans. 74, 1319 (1978).
[Crossref]

J. Chem. Soc. Farday Trans. (1)

K Alexander, A Killey, G H Meeten, and M Senior, “Refractive index of concentrated colloidal dispersions” J. Chem. Soc. Farday Trans. 77, 361 (1981).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Phys. Chem. (1)

A Chou and M Kerker, “The refractive index of colloidal sols” J. Phys. Chem. 60, 562 (1956).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

A García-Valenzuela and R G Barrera, “Electromagnetic response of a random half-space of Mie scatterers within the effective medium approximation and the determination of the effective optical coefficients” J. Quant. Spectrosc. Radiat. Transfer 627, 79 (2003).

Meas. Sci. Technol. (3)

G H Meeten and A N North , “Refractive index measurement of turbid colloidal fluids by transmission near the critical angle” Meas. Sci. Technol. 2, 441 (1991).
[Crossref]

G H Meeten and A N North , “Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle” Meas. Sci. Technol. 6, 214 (1995).
[Crossref]

G H Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials” Meas. Sci. Technol. 8, 728 (1997).
[Crossref]

Opt. Comm. (1)

G H Meeten, “Refraction by spherical particles in the intermediate scattering region” Opt. Comm. 134, 233 (1997).
[Crossref]

Opt. Commun. (1)

R Ruppin, “Evaluation of extended Maxwell Garnett theories” Opt. Commun. 182, 273 (2000).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

M Lax, “Multiple scattering of waves II. The effective field in dense systems” Phys. Rev. 85621 (1952).
[Crossref]

Phys. Status Solidi B (1)

A Garcia-Valenzuela and R G Barrera, “Optical reflectance of a composite medium with a sparse concentration of large spherical inclusions” Phys. Status Solidi B 240, 480 (2003).
[Crossref]

Vacuum (1)

Y Sarov, I Capek, S Janíčková, I Kostič, A Konečníková, L Matay, and V Sarova, “Properties of nano-scaled disperse media investigated by refractometric measurements” Vacuum 76, 231 (2004).
[Crossref]

Other (6)

A Garcia-Valenzuela, C Sánchez-Pérez, R G Barrera, and A Reyes-Coronado, “Surface effects on the coherent reflection of light from a polydisperse colloid”, to be submitted.

F Curiel, Predicción de propiedades ópticas de películas inhomogéneas por medio de modelos de transferencia radiativa y su aplicación en pinturas, Ph.D. Thesis (Instituto de Física, Universidad Nacional Autónoma de México, México D.F. (2004).

R G Barrera and A Garcia-Valenzuela, “Amperian magnetism in the dynamic response of granular materials”, Developments in Mathematical and Experimental Physics, Volume B: Statistical Physics and Beyond, Edited by Macias et al. (Kluwer Academic, Plenum Publishers, 2003) pp. 147–170.
[Crossref]

L Tsang and J A Kong, Scattering of electromagnetic waves: Advanced topics (Wiley, New York, 2001).

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

H C van de Hulst, Light scattering by small particles (Wiley, New York, 1957).

Supplementary Material (1)

» Media 1: MOV (2467 KB)     

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 (7)

Fig. 1.
Fig. 1.

Coherent reflection and transmission of light from a random system of particles. a) Half-space formed by a semi-infinite pile of thin slabs, and b) coherent reflection and transmission from an isolated thin slab.

Fig. 2.
Fig. 2.

Illustration of the reflection of the coherent wave from the compound interface: incident-medium - matrix and matrix - composite-matrix interface.

Fig.3.
Fig.3.

Schematic of the experimental setup. [Media 1]

Fig. 4.
Fig. 4.

Reflectance results for a TE polarization using a suspension of latex particles. Experimental data for opex-13-18-6723-i001 water and ● particle suspension. Theoretical curves are calculated with: n p =1.48, n m =1.3313, a =120.5 nm,. (a)f= 2.75 %, (b)f= 4.9 %, (c)f= 6.4 %, and (d)f= 14.0%, for opex-13-18-6723-i002 CSM,opex-13-18-6723-i003IEMM and opex-13-18-6723-i004 pure water.

Fig. 5.
Fig. 5.

Reflectance results for a TM polarization using a suspension of latex particles. Experimental data for opex-13-18-6723-i005 water and ● particle suspension. Theoretical curves are calculated with: n p =1.47, n m =1.3313, a =186.5 nm. (a) f = 2.9 %, (b) f = 4.9 %, (c) f = 7.2 %, and (d)f = 12.0%, for opex-13-18-6723-i006 CSM,opex-13-18-6723-i007IEMM and opex-13-18-6723-i008 pure water.

Fig. 6.
Fig. 6.

Reflectance results for a TE polarization using a suspension of Ti02 particles. Experimental data for opex-13-18-6723-i009 water and ● particle suspension. Theoretical curves are calculated with: n p =2.73, n m =1.3313, a o =126.6 nm, σ=1.23, a)f= 0.38 %, b)f= 0.705 % and c)f= 1.2 %, for opex-13-18-6723-i010 CSM, opex-13-18-6723-i011 IEMM and opex-13-18-6723-i012 pure water.

Fig.7.
Fig.7.

Reflectance results for a TM polarization using a suspension of Ti02 particles. Experimental data for opex-13-18-6723-i013 water and ● particle suspension. Theoretical curves are calculated with: n p =2.73, n m =1.3313, a o =107.6 nm, σ = 1.23, a) f = 0.4 %, and b) f = 2.1 %, for opex-13-18-6723-i014 CSM, opex-13-18-6723-i015 IEMM and opex-13-18-6723-i016 pure water.

Equations (13)

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

E s = E m { α d exp ( i k + m · r ) e ̂ m + for z > d β d sinc ( k z m d ) exp ( i k m · r ) e ̂ m for z < 0 ,
α = 2 πρ k m 2 cos θ m S ( 0 ) , β = 2 πρ k m 2 cos θ m S j ( π 2 θ m ) .
r hs = β i ( k z eff + k z m ) + α ,
k z eff = ( k z m ) 2 2 i α k z m + β 2 α 2 ,
n ̃ eff n m ( 1 + i 2 π k m 3 ρ S ( 0 ) ) .
α = 2 π k m 2 cos θ m 0 ρ ( a ) S a ( 0 ) da ,
β = 2 π k m 2 cos θ m 0 ρ ( a ) S a , j ( π 2 θ m ) da .
n ( a ) = 1 a 2 π ln σ exp ( ln 2 ( a a 0 ) 2 ln 2 σ ) ,
ρ T = 3 f 4 π a 0 3 exp [ 1 2 ( 3 ln σ ) 2 ] .
n ̃ eff n m ( 1 + i 2 π k m 3 0 ρ ( a ) S a ( 0 ) da ) .
r = r 12 Fresnel + r hs ( θ m ) exp ( 2 i n m k 0 cos θ m z s ) 1 + r 12 Fresnel r hs ( θ m ) exp ( 2 i n m k 0 cos θ m z s ) ,
θ m = arcsin ( n 1 n m sin θ i ) ,
ρ ( a , z ) = U ( z a ) ρ ( a ) ,

Metrics