Abstract

Single-mode optical fibers provide the ideal receiver optics for dynamic light-scattering measurements. Theoretical analysis shows that with a single-mode fiber one can achieve a theoretical limit of 1 for the coherence factor while maintaining a high light-collection efficiency. In fact, the sensitivity of the single-mode receiver surpasses that of a classical two-pinhole setup with a coherence factor of 0.8 by a factor of 4 and the advantage increases rapidly when a still higher coherence factor is desired. In addition, a single-mode fiber receiver offers the possibility of working with an arbitrary large scattering volume and with an arbitrary working distance. All these features are also demonstrated experimentally by a remarkably simple apparatus that consists, essentially, of a commercial laser beam delivery assembly.

© 1993 Optical Society of America

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  1. G. Ramachandran, “Fluctuations of light intensity in coronae formed by diffraction,” Proc. Indian Acad. Sci. A 18, 190–200 (1943).
  2. H. Cummins, E. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973).
  3. H. Cummins, E. Pike, eds., Photon Correlation Spectroscopy and Velocimetry (Plenum, New York, 1976).
  4. B. Chu, Laser Light Scattering (Academic, New York, 1974).
  5. B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  6. E. Schulz-DuBois, ed., Photon Correlation Techniques in Fluid Mechanics (Springer-Verlag, Berlin, 1983).
  7. R. Pecora, ed., Dynamic Light Scattering (Plenum, New York, 1985).
    [CrossRef]
  8. B. Chu, ed., Selected Papers on Quasielastic Light Scattering by Macromolecular, Supramolecular and Fluid Systems (International Society for Optical Engineering, Bellingham, Wash., 1990).
  9. R. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
    [CrossRef] [PubMed]
  10. R. Brown, A. P. Jackson, “Monomode fiber components for dynamic light scattering,” J. Phys. E. 20, 1503–1506 (1987).
    [CrossRef]
  11. H. Dhadwal, B. Chu, “A fiber-optic light-scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
    [CrossRef]
  12. A. MacFadyen, B. Jennings, “Fiber-optic systems for dynamic light scattering—a review,” Opt. Laser Technol. 22, 175–187 (1990).
    [CrossRef]
  13. J. McClymer, “Comparison of multimode and single-mode optical fibers for quasi-elastic light scattering,” Rev. Sci. Instrum. 61, 2001–2002 (1990).
    [CrossRef]
  14. H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
    [CrossRef]
  15. Here we focus on literature dealing with single-mode fibers. An overview of work on general fiber-optic dynamic light scattering, including also multimode fibers, can be found in Refs. 9 and 12.
  16. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  17. A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  18. E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).
  19. It cannot be emphasized strongly enough that the transverse coherence of the guided field is not just a consequence of the tiny entrance aperture of the fiber that would select an area much smaller than a speckle from the interference pattern. A perfect selection of a single mode requires an optical cavity such as is formed by the refractive-index profile of a long fiber.
  20. J. Rička, “Coupling of a light source into a single-mode receiver,” (1992) submitted to J. Mod. Opt.
  21. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  22. J. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  23. D. Jones, The Theory of Electromagnetism (Pergamon, Oxford, 1964).
  24. J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  25. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  26. The relation of this equation to the continuum picture of the suspension becomes evident when one recalls the definition of the instantaneous number density of the particles: cn(r, t) = ΣiNδ[r − ri(t)].
  27. For another example of a single-mode receiver, a short dipole antenna, the visualization is more difficult. Unlike the launched electromagnetic field E−, H− of a dipole, which is the well-known Hertz field, the receiver field E+, H+ does not represent any physically realized solution of Maxwell equations. It is, in fact, the advanced solution.
  28. E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988), Chap. 7.
  29. Note that the integral ¼∫[j*(r, t) · E+ (r)]d3r does have the unit of energy per time. This suggests its relation with the interaction Hamiltonian of the quantum theory of light. In fact, the projection amplitude P(t) is closely related to the transition amplitude for the transfer of photons from the source j into the state characterized by E+, H+. These topics, however, are beyond the scope of this paper.
  30. J. D. Kraus, Antennas (McGraw-Hill, New York, 1988), Chap. 10.
  31. Recall that we have equipped the receiver with a polarizer in order to have a true single-mode case. Otherwise we would have to take into account the fact that the monomode fiber guides two orthogonal polarization modes equally well. Equation (7) would then consist of two terms differing only in the polarization of the receiver modes E+1 and E+2. One of the polarization directions can be freely chosen to be parallel with the polarization of the illuminating beam.
  32. M. Klein, T. Furtag, Optics (Wiley, New York, 1986), Chap. 7.
  33. P. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Cummins, E. Pike, eds. (Plenum, New York, 1976), pp. 45–141.
  34. T. Springer, Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids (Springer-Verlag, Berlin, 1972), Chap. 2.
  35. A. Guinier, “Advances in x-ray and neutron diffraction techniques,” in Diffraction and Imaging Techniques in Material Science, Vol. II, S. Amelincks, R. Gevers, J. V. Landuyt, eds. (North-Holland, Amsterdam, 1978), pp. 593– 621.
  36. A. Guinier, G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).
  37. J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975), Chap. 5.
  38. J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 7.
  39. P. Pusey, R. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985), pp. 85–171.
    [CrossRef]
  40. J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 5.
  41. E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Cummins, E. Pike, eds. (Plenum, New York, 1973), pp. 109–111.
  42. B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.
  43. E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
    [CrossRef]
  44. K. Schätzel, “Noise on photon correlation data,” Quantum Opt. 2, 287–305 (1990).
    [CrossRef]
  45. A. Lightstone, R. McIntyre, “Avalanche photodiodes for single photon detection,” IEEE Trans. Electron Devices ED-28, 1210 (1981).
    [CrossRef]
  46. R. Brown, K. Ridley, J. Rarity, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 1: passive quenching,” Appl. Opt. 25, 4122–4126 (1986).
    [CrossRef] [PubMed]
  47. R. Brown, K. Ridley, J. Rarity, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 1: active quenching,” Appl. Opt. 26, 2383–2389 (1987).
    [CrossRef] [PubMed]
  48. S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).
  49. I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.
  50. Source information available from the author.
  51. E. Elson, D. Madge, “Fluorescence correlation spectroscopy. i. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
    [CrossRef]
  52. D. Schaefer, B. J. Berne, “Light scattering from non-Gaussian concentration fluctuations,” Phys. Rev. Lett. 28, 475–478 (1972).
    [CrossRef]
  53. J. Rička, T. Binkert, “Direct measurement of a distinct correlation function by fluorescence cross correlation,” Phys. Rev. A 39, 2646–2652 (1989).
    [CrossRef]
  54. S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
    [CrossRef]
  55. J. Swift, “Four-point function and light scattering near the critical point,” Ann. Phys. 75, 1–8 (1973).
    [CrossRef]

1991 (1)

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

1990 (3)

A. MacFadyen, B. Jennings, “Fiber-optic systems for dynamic light scattering—a review,” Opt. Laser Technol. 22, 175–187 (1990).
[CrossRef]

J. McClymer, “Comparison of multimode and single-mode optical fibers for quasi-elastic light scattering,” Rev. Sci. Instrum. 61, 2001–2002 (1990).
[CrossRef]

K. Schätzel, “Noise on photon correlation data,” Quantum Opt. 2, 287–305 (1990).
[CrossRef]

1989 (2)

J. Rička, T. Binkert, “Direct measurement of a distinct correlation function by fluorescence cross correlation,” Phys. Rev. A 39, 2646–2652 (1989).
[CrossRef]

H. Dhadwal, B. Chu, “A fiber-optic light-scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
[CrossRef]

1987 (4)

R. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
[CrossRef] [PubMed]

R. Brown, A. P. Jackson, “Monomode fiber components for dynamic light scattering,” J. Phys. E. 20, 1503–1506 (1987).
[CrossRef]

R. Brown, K. Ridley, J. Rarity, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 1: active quenching,” Appl. Opt. 26, 2383–2389 (1987).
[CrossRef] [PubMed]

S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).

1986 (1)

1981 (1)

A. Lightstone, R. McIntyre, “Avalanche photodiodes for single photon detection,” IEEE Trans. Electron Devices ED-28, 1210 (1981).
[CrossRef]

1974 (1)

E. Elson, D. Madge, “Fluorescence correlation spectroscopy. i. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

1973 (1)

J. Swift, “Four-point function and light scattering near the critical point,” Ann. Phys. 75, 1–8 (1973).
[CrossRef]

1972 (1)

D. Schaefer, B. J. Berne, “Light scattering from non-Gaussian concentration fluctuations,” Phys. Rev. Lett. 28, 475–478 (1972).
[CrossRef]

1971 (1)

E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
[CrossRef]

1943 (2)

G. Ramachandran, “Fluctuations of light intensity in coronae formed by diffraction,” Proc. Indian Acad. Sci. A 18, 190–200 (1943).

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Berne, B.

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Berne, B. J.

D. Schaefer, B. J. Berne, “Light scattering from non-Gaussian concentration fluctuations,” Phys. Rev. Lett. 28, 475–478 (1972).
[CrossRef]

Binkert, T.

J. Rička, T. Binkert, “Direct measurement of a distinct correlation function by fluorescence cross correlation,” Phys. Rev. A 39, 2646–2652 (1989).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Brown, R.

Chandrasekhar, S.

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Chu, B.

H. Dhadwal, B. Chu, “A fiber-optic light-scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
[CrossRef]

B. Chu, Laser Light Scattering (Academic, New York, 1974).

Cova, S.

S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).

Cowley, J.

J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975), Chap. 5.

Dhadwal, H.

H. Dhadwal, B. Chu, “A fiber-optic light-scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
[CrossRef]

Elson, E.

E. Elson, D. Madge, “Fluorescence correlation spectroscopy. i. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

Fournet, G.

A. Guinier, G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Furtag, T.

M. Klein, T. Furtag, Optics (Wiley, New York, 1986), Chap. 7.

Guinier, A.

A. Guinier, “Advances in x-ray and neutron diffraction techniques,” in Diffraction and Imaging Techniques in Material Science, Vol. II, S. Amelincks, R. Gevers, J. V. Landuyt, eds. (North-Holland, Amsterdam, 1978), pp. 593– 621.

A. Guinier, G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Hamal, K.

I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.

Hansen, J.

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 5.

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 7.

Höbel, M.

I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.

Horn, D.

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Jackson, A. P.

R. Brown, A. P. Jackson, “Monomode fiber components for dynamic light scattering,” J. Phys. E. 20, 1503–1506 (1987).
[CrossRef]

Jackson, J.

J. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Jakeman, E.

E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
[CrossRef]

E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Cummins, E. Pike, eds. (Plenum, New York, 1973), pp. 109–111.

Jennings, B.

A. MacFadyen, B. Jennings, “Fiber-optic systems for dynamic light scattering—a review,” Opt. Laser Technol. 22, 175–187 (1990).
[CrossRef]

Jones, D.

D. Jones, The Theory of Electromagnetism (Pergamon, Oxford, 1964).

Kerker, M.

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

Klein, M.

M. Klein, T. Furtag, Optics (Wiley, New York, 1986), Chap. 7.

Kraus, J. D.

J. D. Kraus, Antennas (McGraw-Hill, New York, 1988), Chap. 10.

Lacaita, A.

S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).

Lightstone, A.

A. Lightstone, R. McIntyre, “Avalanche photodiodes for single photon detection,” IEEE Trans. Electron Devices ED-28, 1210 (1981).
[CrossRef]

Love, J.

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

MacFadyen, A.

A. MacFadyen, B. Jennings, “Fiber-optic systems for dynamic light scattering—a review,” Opt. Laser Technol. 22, 175–187 (1990).
[CrossRef]

Madge, D.

E. Elson, D. Madge, “Fluorescence correlation spectroscopy. i. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

McClymer, J.

J. McClymer, “Comparison of multimode and single-mode optical fibers for quasi-elastic light scattering,” Rev. Sci. Instrum. 61, 2001–2002 (1990).
[CrossRef]

McDonald, I.

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 7.

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 5.

McIntyre, R.

A. Lightstone, R. McIntyre, “Avalanche photodiodes for single photon detection,” IEEE Trans. Electron Devices ED-28, 1210 (1981).
[CrossRef]

Neumann, E.

E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988), Chap. 7.

E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).

Pecora, R.

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Pike, E.

E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
[CrossRef]

Procházka, I.

I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.

Pusey, P.

P. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Cummins, E. Pike, eds. (Plenum, New York, 1976), pp. 45–141.

P. Pusey, R. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985), pp. 85–171.
[CrossRef]

Ramachandran, G.

G. Ramachandran, “Fluctuations of light intensity in coronae formed by diffraction,” Proc. Indian Acad. Sci. A 18, 190–200 (1943).

Rarity, J.

Ricka, J.

J. Rička, T. Binkert, “Direct measurement of a distinct correlation function by fluorescence cross correlation,” Phys. Rev. A 39, 2646–2652 (1989).
[CrossRef]

I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.

J. Rička, “Coupling of a light source into a single-mode receiver,” (1992) submitted to J. Mod. Opt.

Ridley, K.

Ripamonti, G.

S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).

Saleh, B.

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.

Schaefer, D.

D. Schaefer, B. J. Berne, “Light scattering from non-Gaussian concentration fluctuations,” Phys. Rev. Lett. 28, 475–478 (1972).
[CrossRef]

Schätzel, K.

K. Schätzel, “Noise on photon correlation data,” Quantum Opt. 2, 287–305 (1990).
[CrossRef]

Snyder, A.

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Springer, T.

T. Springer, Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids (Springer-Verlag, Berlin, 1972), Chap. 2.

Stratton, J.

J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Swain, S.

E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
[CrossRef]

Swift, J.

J. Swift, “Four-point function and light scattering near the critical point,” Ann. Phys. 75, 1–8 (1973).
[CrossRef]

Tough, R.

P. Pusey, R. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985), pp. 85–171.
[CrossRef]

Wiese, H.

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Ann. Phys. (1)

J. Swift, “Four-point function and light scattering near the critical point,” Ann. Phys. 75, 1–8 (1973).
[CrossRef]

Appl. Opt. (3)

Biopolymers (1)

E. Elson, D. Madge, “Fluorescence correlation spectroscopy. i. Conceptual basis and theory,” Biopolymers 13, 1–27 (1974).
[CrossRef]

IEEE Trans. Electron Devices (1)

A. Lightstone, R. McIntyre, “Avalanche photodiodes for single photon detection,” IEEE Trans. Electron Devices ED-28, 1210 (1981).
[CrossRef]

J. Chem. Phys. (1)

H. Wiese, D. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex dispersions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

J. Phys. A (1)

E. Jakeman, E. Pike, S. Swain, “Statistical accuracy in the digital autocorrelation of photon counting fluctuations,” J. Phys. A 4, 517–534 (1971).
[CrossRef]

J. Phys. E. (1)

R. Brown, A. P. Jackson, “Monomode fiber components for dynamic light scattering,” J. Phys. E. 20, 1503–1506 (1987).
[CrossRef]

Nuclear Instrum. Methods (1)

S. Cova, G. Ripamonti, A. Lacaita, “Avalanche semiconductor detector for single optical photons with a time resolution of 60 ps,” Nuclear Instrum. Methods A253, 482–487 (1987).

Opt. Laser Technol. (1)

A. MacFadyen, B. Jennings, “Fiber-optic systems for dynamic light scattering—a review,” Opt. Laser Technol. 22, 175–187 (1990).
[CrossRef]

Phys. Rev. A (1)

J. Rička, T. Binkert, “Direct measurement of a distinct correlation function by fluorescence cross correlation,” Phys. Rev. A 39, 2646–2652 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

D. Schaefer, B. J. Berne, “Light scattering from non-Gaussian concentration fluctuations,” Phys. Rev. Lett. 28, 475–478 (1972).
[CrossRef]

Proc. Indian Acad. Sci. A (1)

G. Ramachandran, “Fluctuations of light intensity in coronae formed by diffraction,” Proc. Indian Acad. Sci. A 18, 190–200 (1943).

Quantum Opt. (1)

K. Schätzel, “Noise on photon correlation data,” Quantum Opt. 2, 287–305 (1990).
[CrossRef]

Rev. Mod. Phys. (1)

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Rev. Sci. Instrum. (2)

J. McClymer, “Comparison of multimode and single-mode optical fibers for quasi-elastic light scattering,” Rev. Sci. Instrum. 61, 2001–2002 (1990).
[CrossRef]

H. Dhadwal, B. Chu, “A fiber-optic light-scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
[CrossRef]

Other (37)

I. Procházka, K. Hamal, J. Rička, M. Höbel, “An all solid state picosecond photon counting system for spectroscopy,” in Ultrafast Processes in Spectroscopy, Section II, No. 126 of the Institute of Physics Conference Series (Institute of Physics, Bristol, England, 1992), p. 147.

Source information available from the author.

H. Cummins, E. Pike, eds., Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973).

H. Cummins, E. Pike, eds., Photon Correlation Spectroscopy and Velocimetry (Plenum, New York, 1976).

B. Chu, Laser Light Scattering (Academic, New York, 1974).

B. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

E. Schulz-DuBois, ed., Photon Correlation Techniques in Fluid Mechanics (Springer-Verlag, Berlin, 1983).

R. Pecora, ed., Dynamic Light Scattering (Plenum, New York, 1985).
[CrossRef]

B. Chu, ed., Selected Papers on Quasielastic Light Scattering by Macromolecular, Supramolecular and Fluid Systems (International Society for Optical Engineering, Bellingham, Wash., 1990).

Here we focus on literature dealing with single-mode fibers. An overview of work on general fiber-optic dynamic light scattering, including also multimode fibers, can be found in Refs. 9 and 12.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

A. Snyder, J. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988).

It cannot be emphasized strongly enough that the transverse coherence of the guided field is not just a consequence of the tiny entrance aperture of the fiber that would select an area much smaller than a speckle from the interference pattern. A perfect selection of a single mode requires an optical cavity such as is formed by the refractive-index profile of a long fiber.

J. Rička, “Coupling of a light source into a single-mode receiver,” (1992) submitted to J. Mod. Opt.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

J. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

D. Jones, The Theory of Electromagnetism (Pergamon, Oxford, 1964).

J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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

The relation of this equation to the continuum picture of the suspension becomes evident when one recalls the definition of the instantaneous number density of the particles: cn(r, t) = ΣiNδ[r − ri(t)].

For another example of a single-mode receiver, a short dipole antenna, the visualization is more difficult. Unlike the launched electromagnetic field E−, H− of a dipole, which is the well-known Hertz field, the receiver field E+, H+ does not represent any physically realized solution of Maxwell equations. It is, in fact, the advanced solution.

E. Neumann, Single-Mode Fibers (Springer-Verlag, Berlin, 1988), Chap. 7.

Note that the integral ¼∫[j*(r, t) · E+ (r)]d3r does have the unit of energy per time. This suggests its relation with the interaction Hamiltonian of the quantum theory of light. In fact, the projection amplitude P(t) is closely related to the transition amplitude for the transfer of photons from the source j into the state characterized by E+, H+. These topics, however, are beyond the scope of this paper.

J. D. Kraus, Antennas (McGraw-Hill, New York, 1988), Chap. 10.

Recall that we have equipped the receiver with a polarizer in order to have a true single-mode case. Otherwise we would have to take into account the fact that the monomode fiber guides two orthogonal polarization modes equally well. Equation (7) would then consist of two terms differing only in the polarization of the receiver modes E+1 and E+2. One of the polarization directions can be freely chosen to be parallel with the polarization of the illuminating beam.

M. Klein, T. Furtag, Optics (Wiley, New York, 1986), Chap. 7.

P. Pusey, “Statistical properties of scattered radiation,” in Photon Correlation Spectroscopy and Velocimetry, H. Cummins, E. Pike, eds. (Plenum, New York, 1976), pp. 45–141.

T. Springer, Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids (Springer-Verlag, Berlin, 1972), Chap. 2.

A. Guinier, “Advances in x-ray and neutron diffraction techniques,” in Diffraction and Imaging Techniques in Material Science, Vol. II, S. Amelincks, R. Gevers, J. V. Landuyt, eds. (North-Holland, Amsterdam, 1978), pp. 593– 621.

A. Guinier, G. Fournet, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

J. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1975), Chap. 5.

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 7.

P. Pusey, R. Tough, “Particle interactions,” in Dynamic Light Scattering, R. Pecora, ed. (Plenum, New York, 1985), pp. 85–171.
[CrossRef]

J. Hansen, I. McDonald, Theory of Simple Liquids (Academic, London, 1976), Chap. 5.

E. Jakeman, “Photon correlation,” in Photon Correlation and Light Beating Spectroscopy, H. Cummins, E. Pike, eds. (Plenum, New York, 1973), pp. 109–111.

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.

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Figures (5)

Fig. 1
Fig. 1

Simple apparatus for dynamic light scattering. The light source is a He–Ne laser (Spectra-Physics 127-35) with a beam diameter of 0.95 mm. The receiving optics consists of a commercial single-mode fiber assembly (Laser Optik Technologie, Darmstadt) equipped with a collimator lense. (The fact that the collimator is optimized for a wavelength of 514 nm does not impair performance.) The sample is a glass of Lambrusco wine. Not shown is the detector, a commercial solid-state photon-counting module (RCA SPCM-100).

Fig. 2
Fig. 2

Lambrusco: Correlogram obtained with setup from Fig. 1 from a glass of Lambrusco wine. I have to admit that the sample is not ideally prepared. There is quite a lot of stray light, and the correlogram is distorted by convection. Most of the signal originates from scattering on tiny gas bubbles found so often in this slightly frizzante Italian wine. But who would degas Lambrusco…? Latex: Performance of the same setup with a better-defined sample, i.e., the usual (and, compared with Lambrusco, perhaps somewhat boring) dilute suspension of polystyrene latex. A rectangular sample cell was used without an index matching vessel. Because of residual stray light, the theoretical limit of 1 for the amplitude of the correlation function is not quite reached.

Fig. 3
Fig. 3

Schematics of the single-mode fiber setup: A(r), profile of the probing beam; B(r), profile of the observation beam; Vs, scattering volume; X(r) = A*(r)B(r), profile of the scattering volume.

Fig. 4
Fig. 4

Schematics of conventional QLS receiving optics with 1:1 imaging geometry. AL, lens aperture with radius wL; AD, detector aperture with radius wD. A point source (a scatterer) at r close to the object plane O creates an Airy pattern B(ρ, δ) centered at δim in the detector plane D. Source coordinates transverse to the optical axis of observation are denoted by ρ.

Fig. 5
Fig. 5

Two examples of linearly polarized fiber modes. Field profiles B(ρ) [ρ = (y, z)]. The notation follows Ref. 18. LP10, fundamental (Gaussian) mode with B(ρ) ∝ exp(−ρ2/w02); LP11, a mode with B(ρ) ∝ y exp(−ρ2/w02). Since the LP11 mode is an odd function of y, the overlap integral of LP10 and LP11 vanishes. These two modes are orthogonal.

Equations (81)

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E f ( r f ) = P E + ( r f ) .
j ( r , t ) = ( r , t ) .
P ( r , t ) = χ ( r , t ) E l ( r , t ) ,
P ( r , t ) = i N δ [ r r i ( t ) ] p i ( t ) .
p i ( t ) = α i E e ( r i ) exp ( i ω t ) ,
j ( r , t ) = i ω α i N δ [ r r i ( t ) ] E e ( r ) exp ( i ω t ) .
J ( t ) = P ( t ) P * ( t ) P ,
P ( t ) = { 1 4 [ j * ( r , t ) · E + ( r ) ] d 3 r } / P .
J ( t ) = ω 2 α 2 16 | i δ [ r r i ( t ) ] E e * ( r ) · E + ( r ) d 3 r | 2 = ω 2 α 2 16 | i E e * ( r i ) · E + ( r i ) | 2 .
E e ( r ) = C e A ( r ) exp ( i k e · r ) , E + ( r ) = C + B ( r ) exp ( i k s · r ) .
C + 2 = 2 c 1 [ W ] π w 0 2 , π w 0 2 = | B ( ρ ) | 2 d 2 ρ .
C e 2 = 2 c J e π w e 2 , π w e 2 = | A ( ρ e ) | 2 d 2 ρ e ,
C e 2 = 2 c I e , I e = I e ( r ) | A ( r ) | 2 = J e π w e 2 ,
J ( t ) = ω 2 α 2 16 C e 2 C + 2 × | i δ [ r r i ( t ) ] X ( r ) exp ( i Qr ) d 3 r | 2 .
σ d = [ ( 2 π λ ) 2 α 4 π ] 2 .
K = σ d I e Ω , Ω = λ 2 π w 0 2 .
J ( t ) = K i , j X [ r i ( t ) ] X * [ r j ( t ) ] exp { i Q · [ r i ( t ) r j ( t ) ] } .
J ( t ) = K ( i | X [ r i ( t ) ] | 2 + i j X [ r i ( t ) ] X * [ r j ( t ) ] exp { i Q · [ r i ( t ) r j ( t ) ] } )
J = K { i | X ( r i ) | 2 + i j X ( r i ) X * ( r j ) exp [ i Q · ( r i r j ) ] } .
J s = K c n V s , V s = | X ( r ) | 2 d 3 r .
V c = h ( Δ r ) d 3 Δ r .
J d = K c n 2 [ | X ( r ) exp ( i Q · r ) d 3 r | 2 + X ( r ) X * ( r Δ r ) h ( Δ r ) × exp ( i Q · Δ r ) d 3 r d 3 Δ r ] .
J = σ d I e Ω c n V s S ( Q ) , S ( Q ) = [ 1 + c n h ( Q ) ] .
J = σ d J e c n λ 2 V s π w e 2 π w 0 2 S ( Q ) .
J = σ d J e c n λ 2 π w e S ( Q ) ,
J = σ d J e c n λ 2 1 π w e S ( Q ) .
G ( τ ) = J 2 [ 1 + 1 V s 2 | X ( r ) X * ( r + v τ ) d 3 r | 2 ] .
G ( τ ) = J 2 [ 1 + exp ( 2 Q 2 D τ ) ] .
G ( τ ) = J 2 { 1 + [ F ( Q , τ ) S ( Q ) ] 2 } .
G ( τ ) = J 2 { 1 + | g ( 1 ) ( τ ) | 2 } ,
E ( r i , δ ) = C A * ( r i ) B ( r i , δ ) exp ( i Q · r i ) = C X ( r i , δ ) exp ( i Q · r i ) .
B ( r , δ ) = B ( ρ , δ ) = 2 J 1 ( | ρ + δ | 2 π w L / λ R ) | ρ + δ | 2 π w L / λ R .
c 2 | E ( r i , δ ) | 2 d 2 δ = σ d I e ( r i ) Ω , Ω = π w L 2 R 2 .
C 2 = 2 c σ d I e Ω 1 π w 0 2 , π w 0 2 = | B ( δ ) | 2 d 2 δ = λ 2 R 2 π w L 2 .
I ( δ , t ) = K 1 π w 0 2 i , j X [ r i ( t ) , δ ] X * [ r j ( t ) , δ ] × exp { i Q · [ r i ( t ) r j ( t ) ] } ,
J ( t ) = T D ( δ ) I ( δ , t ) d 2 δ .
I ( δ ) = K c n | X ( r , δ ) | 2 d 3 r π w 0 2 S ( Q ) ,
J = σ d I e Ω c n V s S ( Q ) , V s = T D ( δ ) | X ( r , δ ) | 2 d 3 r d 2 δ π w 0 2 .
V s = π w e T D ( δ ) | B ( ρ + δ ) | 2 d 2 ρ d 2 δ π w 0 2 ,
V s = π w e π w D 2 , π w D 2 = T D ( δ ) d 2 δ .
J = N σ d I e c n λ 2 π w e S ( Q ) , N = π w D 2 π w L 2 λ 2 R 2 .
N = A / A coh , A coh = λ 2 R 2 / π w L 2 .
J ( 0 ) J ( τ ) = T D ( δ ) T D ( δ ) I ( δ , 0 ) I ( δ , τ ) d 2 δ d 2 δ .
I ( δ , 0 ) I ( δ , τ ) i , j , k , l X [ r i ( 0 ) , δ ] X * [ r j ( 0 ) , δ ] X [ r k ( τ ) , δ ] X * [ r l ( τ ) , δ ] × exp { i Q · [ r i ( 0 ) r j ( 0 ) + r k ( τ ) r l ( τ ) ] } .
I s ( δ , 0 ) I s ( δ , τ ) = K 2 c n 2 ( 1 π w 0 2 ) 2 [ | X ( r , δ ) | 2 d 3 r ] [ | X ( r , δ ) | 2 d 3 r ] .
I d ( δ , 0 ) I d ( δ , τ ) = K 2 c n 2 ( 1 π w 0 2 ) 2 | X ( r , δ ) X * ( r , δ ) d 3 r | 2 exp ( 2 Q 2 D τ ) .
G ( τ ) = J 2 [ 1 + f ( A ) exp ( 2 Q 2 D τ ) ] .
f ( A ) = T D ( δ ) T D ( δ ) | X ( r , δ ) X * ( r , δ ) d 3 r | 2 d 2 δ d 2 δ [ T D ( δ ) | X ( r , δ ) | 2 d 3 r d 2 δ ] 2 .
f ( A ) = T D ( δ ) T D ( δ ) | B ( ρ + δ ) B * ( ρ + δ ) d 2 ρ | 2 d 2 δ d 2 δ [ T D ( δ ) | B ( ρ + δ ) | 2 d 2 ρ d 2 δ ] 2 .
f ( A ) = 1 A / A coh + 1 = 1 N + 1 .
J classical = N J fiber .
N = 1 f ( A ) 1 .
J classical = ¼ J fiber .
B δ ( ρ ) B δ * ( ρ ) d 2 ρ δ δ π w δ 2 .
J ( t ) = δ T δ J δ ( t ) .
J = σ d I e c n S ( Q ) δ T δ Ω δ V s δ ,
J = N σ d I e c n λ 2 π w e S ( Q ) , N = δ T δ .
J ( 0 ) J ( τ ) = δ , δ T δ T δ J δ ( 0 ) J δ ( τ ) .
J δ s ( 0 ) J δ s ( τ ) = ( σ d I e λ 2 c n ) 2 | X δ ( r ) | 2 d 3 r π w δ 2 | X δ ( r ) | 2 d 3 r π w δ 2 .
J δ d ( 0 ) J δ d ( τ ) = ( σ d I e λ 2 c n ) 2 | X δ ( r ) X δ * ( r ) d 3 r | 2 π w δ 2 π w δ 2 exp ( 2 Q 2 D τ ) .
G ( τ ) = J 2 [ 1 + f ( N ) exp ( 2 Q 2 D τ ) ] ,
f ( N ) = [ δ , δ T δ T δ | X δ ( r ) X δ * ( r ) d 3 r | 2 π w δ 2 π w δ 2 ] / [ δ T δ | X δ ( r ) | 2 d 3 r π w δ 2 ] 2 .
f ( N ) = δ T δ 2 ( δ T δ ) 2 = δ T δ 2 N 2 .
f ( N ) = 1 N .
J ( 0 ) J ( τ ) = J s ( 0 ) J s ( τ ) + J s ( 0 ) J d ( τ ) + J d ( 0 ) J s ( τ ) + J d ( 0 ) J d ( τ ) .
J s ( 0 ) J s ( τ ) = K 2 i , j | X [ r i ( 0 ) ] | 2 | X [ r j ( τ ) ] | 2 .
J s ( 0 ) J s ( τ ) = J s 2 [ 1 + g n ( τ ) c n V e ] .
J s ( 0 ) J d ( τ ) i , k l | X [ r i ( 0 ) ] | 2 X [ r k ( τ ) ] X * [ r l ( τ ) ] × exp { i Q · [ r k ( τ ) r l ( τ ) ] }
X ( r ) exp ( i Q · r ) = ( 1 / V ) X ( r ) exp ( i Q · r ) d 3 r .
J d ( 0 ) J d ( τ ) i j , k l X [ r i ( 0 ) ] X * [ r j ( 0 ) ] X [ r k ( τ ) ] X * [ r l ( τ ) ] × exp { i Q · [ r i ( 0 ) r j ( 0 ) + r k ( τ ) r l ( τ ) ] }
p [ r i ( 0 ) , r j ( 0 ) , r i ( τ ) , r j ( τ ) ] = p [ r i ( 0 ) , r i ( τ ) ] p [ r j ( 0 ) , r j ( τ ) ] .
X [ r ( 0 ) ] X [ r ( τ ) ] exp { i Q · [ r ( τ ) + r ( 0 ) ] } = ( 1 / V ) X ( r ) X ( r + Δ r ) exp ( i 2 Q · r ) × p ( Δ r , τ ) exp ( i Q · Δ r ) d 3 r d 3 Δ r .
J d ( 0 ) J d ( τ ) = K 2 c n 2 | X ( r ) X * ( r + Δ r ) p ( Δ r , τ ) × exp ( i Q · Δ r ) d 3 r d 3 Δ r | 2 .
J d ( 0 ) J d ( τ ) flow = K 2 c n 2 | X ( r ) X * ( r + v τ ) d 3 r | 2 .
J d 2 flow = J 2 .
p ( Δ r , τ ) = ( 1 π 4 D τ ) 3 / 2 exp [ ( Δ r ) 2 / 4 D τ ] .
J d ( 0 ) J d ( τ ) brown = K 2 c n 2 V s 2 | p ( Δ r , τ ) exp ( i Q · Δ r ) d 3 Δ r | 2 = J 2 | p ( Q , τ ) | 2 .
p ( Q , τ ) = exp ( Q 2 D τ ) .
G ( τ ) = J 2 [ 1 + | g ( 1 ) ( τ ) | 2 ] .
| g ( 1 ) ( τ ) | = 1 V s | X ( r ) X * ( r + v τ ) d 3 r | ,
| g ( 1 ) ( τ ) | = p ( Q , τ ) = exp ( Q 2 D τ ) .

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