Abstract

We present a quantitative experimental comparison of fiber-based, single- and few-mode dynamic light scattering with the classical pinhole-detection optics. The recently presented theory of mode-selective dynamic light scattering [Appl. Opt. 32, 2860 (1993)] predicts a collection efficiency and a signal-to-baseline ratio superior to that of a classical pinhole setup. These predictions are confirmed by our experiments. Using single-mode optical fibers with different cutoff wavelengths and commercially available mechanical components, we have constructed a mode-selective detection optics in a simple and compact dynamic light-scattering spectrometer that permits an optimal compromise between signal intensity and dynamical resolution.

© 1995 Optical Society of America

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References

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  1. J. P. McClymer, “Comparison of multimode and single-mode optical fibers for quasi-elastic light scattering,” Rev. Sci. Instrum. 61, 2001–2002 (1990).
    [CrossRef]
  2. B. Chu, Laser Light Scattering (Academic, New York, 1991).
  3. J. Rička, “Dynamic light scattering with single-mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef]
  4. R. G. Brown, “Dynamic light scattering using monomode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
    [CrossRef] [PubMed]
  5. E. G. Neumann, Single-Mode Fibers (Springer, Berlin, 1988).
  6. 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]
  7. H. S. Dhadwal, B. Chu, “A fiber-optic light scattering spectrometer,” Rev. Sci. Instrum. 60, 845–853 (1989).
    [CrossRef]
  8. K. Schätzel, R. Kalström, B. Stampa, J. Ahrens, “Correction of detection-system dead-time effects on photon-correlation functions,” J. Opt. Soc. Am. B 6, 937–947 (1989).
    [CrossRef]
  9. K. Schätzel, “Noise on photon correlation data,” Quantum Opt. 2, 287–305 (1990).
    [CrossRef]
  10. The Guinier formula, 〈J〉(Q)/〈J〉(0) = exp[−Q2RG2/3], is an approximation to the form factor of a homogeneous sphere, with a radius of gyration RG for QRG < 1.
  11. K. Suparno, P. Deurloo, R. Stamatelopoulos, R. Srivastva, J. C. Thomas, “Light scattering with single-mode fiber collimators,” Appl. Opt. 33, 7200–7205 (1994).
    [CrossRef] [PubMed]

1994 (1)

1993 (1)

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 (2)

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

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

1989 (2)

1987 (1)

Ahrens, J.

Brown, R. G.

Chu, B.

H. S. 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, 1991).

Deurloo, P.

Dhadwal, H. S.

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

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]

Kalström, R.

McClymer, J. P.

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

Neumann, E. G.

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

Ricka, J.

Schätzel, K.

Srivastva, R.

Stamatelopoulos, R.

Stampa, B.

Suparno, K.

Thomas, J. C.

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]

Appl. Opt. (3)

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. Opt. Soc. Am. B (1)

Quantum Opt. (1)

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

Rev. Sci. Instrum. (2)

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

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

Other (3)

B. Chu, Laser Light Scattering (Academic, New York, 1991).

The Guinier formula, 〈J〉(Q)/〈J〉(0) = exp[−Q2RG2/3], is an approximation to the form factor of a homogeneous sphere, with a radius of gyration RG for QRG < 1.

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

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic representation of a light-scattering experiment with a single-mode (SM) receiver. The scattering volume is illuminated by excitation beam A(r), which is intersected by observation beam B(r). The collimator lens in front of the fiber is used to modify the receiver beam characteristics such that a reasonably small effective beam radius and a suitable working distance between the receiver and the scattering volume can be realized. The polarizer may be left out for optically isotropic scattering samples. (b) Scattering geometry and coordinate system. Beam profiles A(r) and B(r) of the excitation beam and of the observation beam, respectively, are shown as cylinders whose intersection forms scattering volume V. This situation corresponds to a well-aligned setup with moderately focused beams. The polarization of the excitation beam is perpendicular to scattering plane Π spanned by the wave vectors k e and k s . Angle θ between the excitation beam and the observation beam determines scattering vector Q = k s k e . Coordinates (x, y) and (x, y′) are perpendicular to the axis of beam propagation.

Fig. 2
Fig. 2

Chart to help determine the number of eigenmodes that can be propagated through a given fiber at a given operating wavelength, calculated by the use of theoretical expressions for step-index fibers.5 The vertical axis indicates single-mode cutoff wavelength λ c of the given fiber. For example, a fiber with λ c = 488 nm propagates only the fundamental LP01 mode when the operating wavelength exceeds 488 nm. The dashed horizontal lines represent λ c of five commercially available fibers, and the two dashed vertical lines correspond to two common laser lines. The solid curves separate regions with one, three, and six propagating modes. For example, when a fiber with λ c = 633 nm is operated at 514 nm, it will propagate three LP modes. Note that with real fibers the borders between the different regions are not as perfectly sharp as suggested by the chart. The open circles schematically indicate the amplitude profiles of the LP lm modes and illustrate the meaning of the indices l and m: the first index is the azimuthal mode number, i.e., the number of maxima encountered when circling around the fiber axis, and the second index indicates the number of maxima counted in the radial direction.

Fig. 3
Fig. 3

DLS setup used to compare the classical pinhole and a fiber-optic receiver. The laser beam is expanded vertically by cylindrical lens L to approximate the limit of a laterally homogeneous source. In the classical pinhole receiver the scattering volume is imaged by the combination of the apertures PL and PD and the lens onto the photomultiplier tube (PM). In the fiber-optic receiver the scattering volume and the direction of the received mode is defined by the very small numerical aperture of the GRIN lens, which is used to couple the scattered light into fiber F. In both cases the photomultiplier signal is fed into correlator C.

Fig. 4
Fig. 4

Comparison of mode-selective and classical detection setup. Coherence factor f(N) of the normalized intensity autocorrelation function is plotted versus the normalized average signal N. The open circles represent the experimental data measured with the pinhole setup. The solid curve was calculated by the use of proportionality factor KJ 0, obtained by the fit of the experimental data to Eq. (23). All experiments were performed with the same photomultiplier. The prediction for the coherence factor and the average signal for the fiber-optic detection at different cutoff wavelengths (resulting in different numbers of guided modes) is represented by the filled circles. The dashed curve serves as a guide to the eye. Triangles show experimental data measured with fibers of different cutoff wavelengths.

Fig. 5
Fig. 5

Fiber-optic spectrometer. The excitation beam is launched by a Dantec fiber through a polarizer (left) onto the sample inserted in the cylindrical index-matching vat. The receiver optics (right) consists of a polarizer and an optical fiber mounted on the goniometer arm of the rotational stage. The entire optical components of the spectometer are mounted on an aluminum plate 57 cm long and 30 cm wide.

Fig. 6
Fig. 6

Normalized intensity autocorrelation functions g (2)(τ) at θ = 90°, measured with the fiber-optic goniometer setup described in Subsection 3.B. The sample was a dilute suspension of polysty-rene latex spheres of 91 nm diameter. Fibers with cutoff wavelengths of 488, 633, 780, and 1060 nm were used. Each correlation function is the average of five individual measurements of a duration of 600 s.

Tables (2)

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Table 1 Parameters of the Fiber Assemblies

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Table 2 Comparison of the Different Fibers in the Experimental Realization

Equations (24)

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B ( r ) = B ( x , y ) = exp [ - ( x 2 + y 2 ) / 2 a 0 2 ] ,
A ( r ) = A ( x , y ) = exp [ - ( x 2 + y 2 ) / 2 a e 2 ] ,
J = R ( θ ) I e Ω 0 V 0 ( θ ) .
I e = J e π a e 2             where π a e 2 = A ( x , y ) 2 d x d y .
Ω 0 = λ 2 π a 0 2             where π a 0 2 = B ( x , y ) 2 d x d y .
V 0 = B ( r ) A ( r ) 2 d 3 r .
V 0 ( θ ) = π 3 / 2 sin θ ( a e 4 a 0 4 a e 2 + a 0 2 ) 1 / 2 .
J = J e R ( θ ) λ π sin θ ( λ 2 a e 2 + a 0 2 ) 1 / 2 .
B i ( x , y ) B j * ( x , y ) d x d y = π a i 2 δ i j ,
J = i = 0 N - 1 J i .
J = i = 0 N - 1 J i = R ( θ ) I e i = 0 N - 1 Ω i V i .
J = J 0 N             where     N = 1 Ω 0 V 0 i = 0 N - 1 Ω i V i .
N N .
N = N .
J = J 0 N             where     J 0 = J e R ( θ ) λ π sin θ λ a e .
G ( τ ) = i , j = 0 N - 1 G i j ( τ ) = i , j = 0 N - 1 J i ( 0 ) J j ( τ ) .
f = 1 N 2 i , j = 0 N - 1 W i j 2 ,
W i j = a 0 2 V i j a i a j V 0             where     V i j = A ( r ) 2 B i ( r ) B j * ( r ) d 3 r .
f = 1 N .
1 N f 1 N .
J = J 0 N ,
N = A D A coh .
f = 1 / ( N + 1 ) .
J C = K J 0 N ,

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