Fiber optics in laser light-scattering spectroscopy, spatial coherence considerations

Fiber Optics in Laser Light-Scattering Spectroscopy, Spatial Coherence Considerations An analysis of the coherence angle required for efficient optical mixing by means of fiber optics in laser light-scattering spectroscopy is presented. © 1987AcademicPress,Inc. INTRODUCTION The optical fiber, of the type designed for communications, is now near the theoretical limit of fabrication and is rapidly finding applications outside the communications area. In this short note we are primarily concerned with outlining one of the pitfalls to be avoided when using optical fibers for static and dynamic light scattering. Optical fibers offer compactness, remote sensing, and miniaturization capabilities to the experimenter in the field of light scattering. Indeed, the first experimental use of an optical fiber was described by Tanaka and Benedek (1). This was followed by the fiber-optic Doppler anemometer (FODA) designed by Dyott (2) and more recently by Auweter and Horn (3). Experimental setups of Dyott and of Auweter and Horn, representing a backscattering heterodyne detection system, make use of a single multimode fiber which is used for both transmitting the laser light to the scattering medium and detecting the scattered laser light. SPATIAL COHERENCE CONSIDERATIONS Optical fibers, whether multimode or bundles, are basicaly incoherent, that is, the coherence properties of the optical field entering one end of the fiber cannot be related to the coherence properties of the optical field emanating

NA OF INCIDENT LIGHT CONE LESS THAN NA OF FIBER

from the other end of the fiber. This can be readily understood in terms of the numerical aperture, NA, of the optical fiber, which defines a cone of light guided by the optical fiber without significant attenuation, as shown Fig. 1. The consequence of this incoherence is that light entering one end of the fiber, at any numerical aperture, always exits at the other end of the fiber at the full numerical aperture. This necessarily dictates that, in order to take the spatial considerations into account, the angular aperture of the detection system should be controlled before the scattered light is allowed to enter the fiber and not after it has exited the other end, except in the backscattering mode (discussion to follow). A typical multimode optical fiber with a step-graded refractive index profile (2) has a numerical aperture of 0.15 in air and a corresponding critical acceptance angle of 6.4 ° in water. We know that a detection system with an uncertainty in the scattering angle of 6.4 ° is generally useless as far as dynamic light scattering is concerned. However, the required coherence angle (A(0))coh is a function of the scattering volume (Lx, Ly, L=) and the scattering angle 0. If the incident laser beam is propagating in the z direction with polarization in the x direction, as shown in Fig. 2a, then the coherence angle in the scattering plane y - z is (4) X (A(0))coh [1] 2(Lzsin(O) + Lrcos(O)) '

OPTICAL FIBER

NA OF EXITING LIGHT CONE EQUAL TO NA OF FIBER

A--, CLADDING

n2

CORE

nI OUTPUT

INPUT

n 3

FIG. 1. Optical fiber waveguide. NA--numerical aperture; 0o--critical acceptance angle; and nl,/'/2, n3-refractive indices of the core, cladding, and scattering medium. 561 0021-9797/87 $3.00 Journal of Colloid andlnterface Science, Vol. 115, No. 2, February 1987

Copyright © 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

562

NOTES b

10.0

a

Lz

"-,..,,,

Z

~

1.0'

0.1 60

120

180

S C A T T E R I N G ANGLE, 0 IN D E G R E E S

FIG. 2. Calculations of the coherence angle, (A(0))coh.(a) Coordinate system--incident beam is propagating in the z direction with polarization in the x direction. (b) Plot of (A(0))~h based on Eq. [2] with Lx = Lr = DA = 50 um and X = 0.475 ~m.

where X is the laser light wavelength in the scattering medium. If the detection system has an aperture, DA, then Lz = DA/sin(0), and Eq. [ 1] is reduced to (m(0))eoh

X 2(DA + Lrcos(0))"

[21

Figure 2b shows a plot of (A(0))coh as a function of 0 for DA = Ly = 50 /~m, as is the case for the experimental arrangements described by Dyott and by Auweter and Horn. From the plot we see that when using the optical fiber in the backscatter configuration, the spatial coherence

requirements on (A(0))~ohare very favorable in this direction. For example, the critical acceptance angle of 6.4 ° is smaller than the required coherence angle of 7.9 ° at a scattering angle of 165 °. However, it should be noted that for real fiber-optic backscatter probes, L~ does not increase indefinitely with increasing 0 but approaches a limiting value of about one hundred times the core diameter of the optical fiber (2). Thus, in practice, the coherence angle may be considerably smaller in the backscatter direction than indicated by Fig. 2b. This explains why Dyott's FODA and the optical arrangement reported by Auweter and Horn worked very well for dynamic light scattering. Thus

SCATTERING VOLUME INCIDENT OPTICS

EYEPIECE

FIG. 3. A schematic of the fiber-optic eyepiece detection system: S--slit of diameter, Ds; F---fixed optical fiber of diameter, D~, located at the conjugate plane; FB--fiber bundle positioned in the eyepiece in order to transmit the light from F to the remotely placed photomultiplier tube; fl--input lens, and f2--output lens. Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

NOTES

563

TABLE I Spatial Coherence Effects of the Fiber-Optic Detection System Shown in Fig. 3 D , = 0.178 m r n . A0 = 0.03 °

D~ = 0.508 m m A0 = 0.08 °

Df = 0 . 7 0 0 m m

Dr = 0 . 4 5 0 r a m

Df = 0.700 m m

Df = 0 . 4 5 0 m m

0

(zx(0))~

~

(A(0))=h

;~

(A(0))~h

~

(a(0))=h

30 45 60 90

0.006 0.006 0.006 0.006

0.022 0.024 0.026 0.028

0.008 0.009 0.009 0.009

0.044 0.046 0.045 0.044

0.006 0.006 0.006 0.006

0.11 0.12 0.11 0.14

0.008 0.009 0.009 0.009

Note. Values o f

(A(0))coh,,

in units of degrees, are based on Eq. [2] with X = 0.366 #m and DA =

0.15 0.14 0.14 0.15

2.5Df.

we can conclude that the optical fiber, without additional modifications, is not a suitable probe for dynamic light scattering at angles slightly below backscatter.

particularly high and indicate a need for a modified detection configuration based on the formulation presented here.

SOME EXPERIMENTAL RESULTS USING FIBER BUNDLES

CONCLUSION

From our discussion we see clearly that optical fibers can be used in dynamic light scattering provided we take care of the angular uncertainty of our detection system. This, of course, can be done in a number of ways. We, however, have chosen a commercially available fiber optic eyepiece, made by Gamma Scientific, in order to illustrate this idea. The eyepiece has an optical fiber of diameter, Df, positioned on the optical axis to gather the scattered light and a fiber-optic bundle to transmit the light to a photodetector. The experimental arrangement used, as shown in Fig. 3, has an angular aperture, A0 = tan -1 (Ds/2X), where Ds is the diameter of the slit. A dilute aqueous suspension (C ~ 10-5 g/ml) of latex particles (nominal diameter 170 nm) was used to make dynamic light-scattering measurements at various scattering angles for two different eyepieces, each having a different fiber diameter, and for slit diameters of 0.508 and 0.178 mm. The spatial coherence factor, /3, was extracted from the measured correlation data, where the intensity-intensity correlation function has the form G(2)(r) = A(1 +/3[g°)(r)[2) with A, r, and [g~'(r)[ being the background, delay time, and electric field correlation function, respectively. The results are tabulated in Table I. Also included in Table I are the coherence angle requirements for the various configurations. Ideally, the angular aperture of the detection system should be matched as closely as possible to the coherence angle--this was not the case. We were, however, able to show, as expected, that decreasing the diameter of the slit drops the total signal strength and has a dramatic effect on the value of/3. We also observed that 13increases with decreasing fiber diameter. The values of/3 are not

We have shown that there are no foreseen difficulties in utilizing optical fibers for dynamic light scattering, provided we can satisfy the angular aperture requirements for efficient spatial correlation at the input end of the optical fiber. ACKNOWLEDGMENTS We gratefully acknowledge support of this research by the U.S. Army Research Office (DAAG2985K0067) and the Department of Energy (DEFG0286ER452 37A000). We wish to thank Wu Chi who did the actual light-scattering measurements. REFERENCES 1. Tanaka, T., and Benedek, G. B., Appl. Opt. 14, 189 (1975). 2. Dyott, R. B., Microwaves, Opt. Acoust. 2, 13 (1978). 3. Auweter, H., and Horn, D., J. Colloid Interface Sci. 105, 399 (1985). 4. Chu, B., "Laser Light Scattering," Academic Press, New York, 1974. H. S. DHADWAL* B. CHU?

*Department of Electrical Engineering and ?Department of Chemistry State University of New York at Stony Brook Stony Brook, New York 11794 Received January 23, 1986; accepted May 8, 1986

Journal of Colloid and Interface Science, Vol.

115, N o . 2, F e b r u a r y 1987