A method for measuring the concentration of a solution

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A method for measuring the concentration of a solution

Der-Chin Su*, Kun-Huang Chen, and Cheng-Chih Hsu

Institute ofElectro-Optical Engineering, National Chiao Tung University,

ABSTRACT

When a linearly polarized light beam enters a surface-plasmon-resonanse (SPR) apparatus and is incident on the boundary surface with tested solution at the resonant angle, the phase difference between s- and p- polarizations is changed with the concentration of the solution. And the phase difference can be measured accurately by the heterodyne interferometry. Based on these effects, a method for measuring the concentration of a solution is presented.

Keywords: Surface-plasmon reson ance, Heterodyne interferometry, Concentration.

SUMMARY

A schematic diagram of our method is designed and shown in Fig. 1. The heterodyne light source1 consists of a linearly polarized laser, a half-wave plate H, and an electro-optical modulator EU driven by a function generator FG. The angular frequency difference between s- and p- polarizations is co. A light beam coming from this heterodyne light source enters the SPR apparatus2 being an isosceles right-angle prism with a thin metal film deposited on the hypotenuse surface being contacted with the test solution. Ifthe light beam is incident at the resonant angle O on this boundary surface, then the reflection coefficients r and r, ofp- and s- polarizations ofthe reflected light can be derived from the Aiiy's formulas3,

and can be written as ._k

r0+re2d

i

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JJ = _q i2kd e

q

(q s),

r011 2e

wherer01andr12arethe reflection coefficients ofprism-metal boundary and metal-solution boundary. respectively, d is the

thickness of metal film, k is the wave vector in metal, q, and arethe phases of s- and p- polarizations of the reflected light., and q$ is the phase difference between s- and p- polarizations, respectively.

From these equations, it is clear that q5 is dependent on the refractive index of the tested solution and the refractive index is related to its concentration4. Consequently it can be seen that q$ is dependent on the concentration. Next the reflected light passes an analyzer AN with the transmission axis at a to the horizontal axis and is detected by a photodetector D. Then the intensity measured by D is the test signal and can be derived as

=1E11 = cos2_{a + 2 sin2 a +2rr cosasinacos(cot + q5)J} (2)

On the other hand, the electrical signal generated by the function generator FG is filtered and becomes the reference signal. It has the form as

*[email protected], phone +886-3-573-1951; fax +886-3-571-6631; National Chiao Tung Univ., 1001 Ta-Hsueh Rd., Hsin-Chu 300, Taiwan, R.O.C.

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I, =

![1

+ cos(cot)J. (3)

Both of these two sinusoidal signals aresent to a phase meter PM, q5 can be measured accurately. The concentration can be estimated from its associated data of 0withthe specified relation curve of phase difference versus concentration.

In order to demonstrate the feasibility of this method, an SPR apparatus consisting of a BK7 prism and a thin gold film of thickness 35nm to measure the concentration of glucose solution. Their refractive indices are measured with an ellipsometer and they are 1.5 15 1 and 0. 1973+i3.563 1, respectively. A high-resolution rotation stage with angular resolution 0.001° is used to mount the SPR apparatus. A phase meter with angular resolution 0.01° is used and a personal computer is used to record and analyze the data. The frequency difference of the heterodyne light source is 1 kHz and equals to 71.03°. The measured results and its fitting curve are shown in Fig. 2. And the concentration of other glucose solution can be estimated from its associated data of 0 with this fitting curve.

Because r is very small in this method, so the fast axis of the half-wave plate should be located moderately to enhance the contrast of the test sigual. Considering the angular resolution of the phase meter, second harmonic error, and polarization-mixing errors, the angular resolution is decreased to is 0.03°, the sensitivity of our method is 3.3 lx 102

(mg/mi). This method has the advantages of both the common-path interferometry and the heterodyne interferometry,

such as high stability, high resolution, and easy operation.

REFERENCES

1. D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser", Prec. Eng. 18,161-163 (1996).

2. S. Shen, T. Liu and J. Guo, "Optical phase-shift detection of surface plasmon resonance", Appl. Opt. 37, NO. 10, 1747-1751(1998).

3. P. Yeh, "Optical waves in layered media", John Wiley & Sons, Inc. ,86-88,(1988).

4. E. Kretschmann, "The determination of the optical constants of metals by excitation of surface plasnions," Z. Phys. 241, 313 (1971).

I

Measurementdata 110 10

.

.t90

80 Test 70 mnntration(rrg'mI)

Fig. 2 Measurement data of phase difference at different Fig. 1 Schematic for measuring the concentration of a solution.

concentration and the fitting curve.

H Stage Ref. AN — Fittingcurve D 0 10 a 30 40 50

Proc. of SPIE Vol. 4829 873