Anal. Chem. 1999, 71, 4956-4964
Use of Analyte-Modulated Modal Power Distribution in Multimode Optical Fibers for Simultaneous Single-Wavelength Evanescent-Wave Refractometry and Spectrometry Radislav A. Potyrailo,†,‡ Vincent P. Ruddy,§ and Gary M. Hieftje*,†
Department of Chemistry, Indiana University, Bloomington, Indiana 47405, and School of Physical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
A new method is described for the simultaneous determination of absorbance and refractive index of a sample medium. The method is based on measurement of the analyte-modulated modal power distribution (MPD) in a multimode waveguide. In turn, the MPD is quantified by the far-field spatial pattern and intensity of light, i.e., the Fraunhofer diffraction pattern (registered on a CCD camera), that emerges from a multimode optical fiber. Operationally, light that is sent down the fiber interacts with the surrounding analyte-containing medium by means of the evanescent wave at the fiber boundary. The light flux in the propagating beam and the internal reflection angles within the fiber are both affected by optical absorption connected with the analyte and by the refractive index of the analyte-containing medium. In turn, these angles are reflected in the angular divergence of the beam as it leaves the fiber. As a result, the Fraunhofer diffraction pattern of that beam yields two parameters that can, together, be used to deduce refractive index and absorbance. This MPD based detection offers important advantages over traditional evanescent-wave detection strategies which rely on recording only the total transmitted optical power or its lost fraction. First, simultaneous determination of sample refractive index and absorbance is possible at a single probe wavelength. Second, the sensitivity of refractometric and absorption measurements can be controlled simply, either by adjusting the distance between the end face of the fiber and the CCD detector or by monitoring selected modal groups at the fiber output. As a demonstration of these capabilities, several weakly absorbing solutions were examined, with refractive indices in the range from 1.3330 to 1.4553 and with absorption coefficients in the range 0-16 cm-1. The new detection strategy is likely to be important in applications in which sample coloration varies and when it is necessary to compensate for variations in the refractive index of a sample. 4956 Analytical Chemistry, Vol. 71, No. 21, November 1, 1999
With optical-waveguide chemical and biochemical sensors, an analyte concentration is usually quantified by monitoring a change in amplitude, wavelength, phase, or polarization of the detected lightwave.1 However, any one of these properties often cannot, by itself, provide all the capabilities needed for a specific analytical task. As a result, it has become commonplace to combine parameters in a single measurement. For example, a broad dynamic range can be achieved with polarization interferometers,2 simple discrimination between different surface-bound species is possible with polarized fluorescence detection,3 and spatially resolved analyte mapping can be performed with optical time-offlight absorption4 or fluorescence5 detection. Unfortunately, many of these measurements require complex instrumentation and are difficult to perform in the field. We are developing alternative optical-waveguide sensors that offer a combination of attributes without sacrificing their simplicity and robustness. In the present study, we introduce a new method for signal generation in optical-waveguide chemical sensors and develop a theory for operation of such instruments. In particular, we use a multimode step-index optical fiber and, rather than to record the total optical power6-15 transmitted by the fiber or its * To whom correspondence should be addressed. Tel.: (812) 855-2189. Fax: (812) 855-0958. E-mail:
[email protected]. † Indiana University. ‡ Present address: Characterization and Environmental Technology Laboratory, Corporate Research and Development, General Electric Company, P.O. Box 8, Building K-1, Schenectady, New York 12301. § Dublin City University. (1) Boisde, G.; Harmer, A. Chemical and Biochemical Sensing With Optical Fibers and Waveguides; Artech House: Boston, MA, 1996. (2) Schlatter, D.; Barner, R.; Fattinger, C.; Huber, W.; Hubscher, J.; Hurst, J.; Koller, H.; Mangold, C.; Muller, F. Biosens. Bioelectron. 1993, 8, 109-116. (3) Potyrailo, R. A.; Conrad, R. C.; Ellington, A. D.; Hieftje, G. M. Twenty-Fourth Annual Meeting of the Federation of Analytical Chemistry and Spectroscopy Societies, Oct. 27-31, 1997, Providence, R.I.; paper 372. (4) Kharaz, A.; Jones, B. E. Sens. Actuators, A 1995, 47, 491-493. (5) Browne, C. A.; Tarrant, D. H.; Olteanu, M. S.; Mullens, J. W.; Chronister, E. L. Anal. Chem. 1996, 68, 2289-2295. (6) Kumar, A.; Subrahmanyam, T. V. B.; Sharma, A. D.; Thyagarajan, K.; Pal, B. P.; Goyal, I. C. Electon. Lett. 1984, 20, 534-535. (7) Bolin, F. P.; Preuss, L. E.; Taylor, R. C.; Ference, R. J. Appl. Opt. 1989, 28, 2297-2303. (8) Bobb, L. C.; Krumboltz, H. D.; Davis, J. P. Proc. SPIE-Int. Soc. Opt. Eng. 1988, 990, 164-169. (9) Archenault, M.; Gagnaire, H.; Goure, J. P.; Jaffrezic-Renault, N. Sens. Actuators, B 1991, 5, 173-179. 10.1021/ac990851t CCC: $18.00
© 1999 American Chemical Society Published on Web 09/30/1999
lost fraction,16,17 we collect the Fraunhofer diffraction pattern at the fiber output. This far-field spatial pattern is a direct image of the power distribution of guided modes in the optical fiber18 and provides information about both the absorption-induced attenuation in and refractive index of the medium surrounding the cladding of the fiber. These changes come about because the surrounding analyte-containing medium interacts with the evanescent wave of light propagated in the waveguide. Ordinarily, evanescent-wave optical-waveguide sensors operate by measuring the transmission of a waveguide of refractive index n1 as a function of the complex refractive index of the external medium, n2′ ) n2 + in2*, where n2 is the refractive index and n2* is the extinction coefficient of the medium. Changes in waveguide transmission caused by variations in n2 or n2* are measured, respectively, by refractometric6 or spectroscopic12 systems. Unfortunately, these methods have a fundamental shortcoming: they respond to both n2 and n2* and not to either parameter individually. Likewise, sensors based on dark-field16,19 (also known as mode-filtered light17) detection suffer from the same problem because the light level escaping from the waveguide is a function not only of n2 but also of n2*. As a result, past evanescent-wave refractometric, spectroscopic, and dark-field measurements suffer interference from the parameter whose value is assumed to be constant. To address the selectivity problem encountered with these types of sensors, several techniques can be useful. For example, moderately and highly absorbing samples can be treated by means of a Kramers-Kronig analysis20 and by time-independent perturbation theory.21 Such samples can be also studied with surfaceplasmon resonance spectroscopy, in which surface plasmons are simultaneously excited at multiple angles and multiple wavelengths.22,23 If weakly absorbing samples are being investigated, the change in refractive index can often be ignored; even anomalous dispersion that occurs in the vicinity of an absorption band is smaller than the typical (1-6) × 10-5 refractive-index resolution of most optical-waveguide refractometers.8,9,24,25 Also, the contributions of a variable refractive index and absorbance of a weakly absorbing sample can sometimes be differentiated by means, respectively, of the baseline shift and the magnitude of the absorption peak in a collected evanescent-wave spectrum.14,15 (10) Kapany, N. S.; Pontarelli, D. A. Appl. Opt. 1963, 2, 1043-1048. (11) Ruddy, V.; MacCraith, B. D.; Murphy, J. A. J. Appl. Phys. 1990, 67, 60706074. (12) Ruddy, V. Fiber Integr. Opt. 1990, 9, 142-150. (13) DeGrandpre, M. D.; Burgess, L. W. Anal. Chem. 1988, 60, 2582-2586. (14) DeGrandpre, M. D.; Burgess, L. W. Appl. Spectrosc. 1990, 44, 273-279. (15) Eberl, R.; Wilke, J. Sens. Actuators, B 1996, 32, 203-208. (16) Siva Sankara Sai, S.; Srinivasan, K. Rev. Sci. Instrum. 1994, 65, 242-246. (17) Synovec, R. E.; Sulya, A. W.; Burgess, L. W.; Foster, M. D.; Bruckner, C. A. Anal. Chem. 1995, 67, 473-481. (18) Gloge, D. Bell Syst. Tech. J. 1972, 51, 1767-1783. (19) Temple, P. A. Dark field surface inspection illumination technique. US Patent 4,297,032, 1981. (20) Zatykin, A. A.; Morshnev, S. K.; Frantsesson, A. V. Sov. J. Quantum Electron. 1983, 13, 1484-1487. (21) Dankner, Y.; Katzir, A. Appl. Opt. 1997, 36, 873-876. (22) Karlsen, S. R.; Johnston, K. S.; Jorgenson, R. C.; Yee, S. S. Sens. Actuators, B 1995, 24-25, 747-749. (23) Jung, C. C.; Jorgenson, R. C.; Morgan, C. H.; Yee, S. S. Process Control Qual. 1995, 7, 167-171. (24) Cole, C. F.; Hill, G. M.; Adams, A. J. J. Am. Oil Chem. Soc. 1994, 71, 13391342. (25) Trouillet, A.; Ronot-Trioli, C.; Veillas, C.; Gagnaire, H. Pure Appl. Opt. 1996, 5, 227-237.
Unfortunately, all these techniques require recording of a complete spectrum of an absorption feature, including frequencies that do not undergo absorption. In contrast, a simplified detection system capable of monitoring only a single wavelength would be highly desirable in process analysis, for continuous monitoring of flowing streams, in liquid chromatography, and in other fields.26-28 The model power distribution (MPD) based signal-detection method offers a solution to this problem. We demonstrate both theoretically and experimentally that simultaneous determination of n2 and n2* is possible at a single probe wavelength. Contributions of n2 and n2* to the sensor signal are separated by means of the simultaneous monitoring of the angular width and peak intensity of the Fraunhofer diffraction pattern. In addition, MPD detection makes it possible to quantify modecoupling effects in a multimode evanescent-wave sensor, an analysis that cannot be performed with conventional evanescentwave sensors. Knowledge of the MPD in the sensing zone is essential for quantitative evanescent-wave detection and for effective design of a wide range of sensors, including those based on refractive index, absorbance, or fluorescence detection. Mode coupling,29 which is due primarily to scattering and absorption within the fiber core and at the core-cladding interface, results in a loss of some higher-order core modes into the cladding and a concentration of lower-order (on-axis) modes that increases with distance from the source.30 As a result, mode coupling in a multimode evanescent-wave sensor alters the sensitivity of the sensor and increases the analyte-independent optical loss. Finally, we show that the sensitivity of refractometric and absorption measurements can be adjusted by altering the distance from the end face of the fiber to the CCD detector or by monitoring chosen modal (off-axis) groups at the fiber output. This approach is more attractive than changing the length of the sensing region9 or the diameter of the fiber core6,8 or its bend radius31sapproaches that have been used in the past. As an example of the capability of this new sensor approach, we have investigated weakly absorbing solutions with refractive indices n2 in the range from 1.3330 to 1.4553 and extinction coefficients n2* in the range from 0 to 5 × 10-5. For weakly absorbing media, it is more common to represent the absorption of a sample by means of its absorption coefficient R than with the extinction coefficient n2*. These coefficients are related as R ) 2kn2n2*, where k is the free-space propagation constant, k ) 2π/ λ, in which λ is the wavelength of the probe radiation in a vacuum. At the wavelength used, of 560 nm, the absorption coefficient R was in the range from 0 to 16 cm-1. 1. SENSOR MODEL In a multimode step-index optical fiber, the radial electric field of an unattenuated mode guided in the core is given by (26) Braun, R. B. Introduction to Instrumental Analysis; McGraw-Hill: New York, 1987. (27) Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 54, 1174-1178. (28) Wilson, S. A.; Yeung, E. S. Anal. Chem. 1985, 57, 2611-2614. (29) Marcuse, D. Theory of Dielectric Optical Waveguides; Academic Press: New York, 1974; Section 5.6. (30) Ruddy, V.; Shaw, G. Appl. Opt. 1995, 34, 1003-1006. (31) Takeo, T.; Hattori, H. Jpn. J. Appl. Phys., Part 1 1982, 21, 1509-1512.
Analytical Chemistry, Vol. 71, No. 21, November 1, 1999
4957
ψ ) A Jl (Ur/a)
(1)
where A is the field amplitude coefficient, Jl is a Bessel function of order l, r is the radial coordinate, a is the radius of the fiber core, and U is the fiber-core parameter of the guided mode. Since the electric-field amplitude ψ′ of an unattenuated mode at the detector plane29 is a function of ψ, the intensity of the Fraunhofer diffraction pattern (far-field spatial pattern) formed by the mode U is proportional to ψ′ψ′* and can be written as
ψ′ ψ′* ∝ (
∫ R J (UR) J (kaθR)dR) 1
0
l
l
2
(2)
where θ is the radiation far-field angle and R ) r/a. This integral has nonzero values32 only when U ) kaθ. Thus, the far-field spatial pattern described by eq 2 has a sharp maximum, forming a narrow, bright ring at the detector plane at an angle given by
θ ) U/ka
Figure 1. Formation of the Fraunhofer diffraction pattern (the farfield spatial pattern) from the output of a multimode step-index optical fiber. The cladding material is modified with an absorbing medium over the length L. The external angle θ is related to the core parameter of each guided mode in the fiber as shown in eq 3.
γ ≈ Rθ2/[ka(n12 - n22)3/2]
Substitution of eq 6 into eq 4 gives the expression for the farfield spatial pattern
[
(3)
RL θ2 ka (n 2 - n 2)3/2 1 2
I ) Io exp This expression shows that the core parameter U of each guided mode in the fiber can be directly related to the external angle θ of the far-field distribution pattern at the detector plane (see Figure 1). The bright ring in Figure 1 has an angular width of ∆θ ∼ π/ka. Thus, the far-field radiation pattern can be used as a direct indication of the modal power distribution in an optical fiber.18 When the cladding material is modified with an absorbing species or when the cladding is replaced by an absorbing medium over a length L (cf. Figure 1), the evanescent wave experiences attenuation, and the total power in each guided mode is reduced. The power of the guided mode at the exit of the absorbing region is given by
I ) Ient exp(- γ L)
(4)
(6)
]
where Io is the maximum of the far-field spatial pattern profile at the detector plane. If we include attenuation in the diffraction analysis (eq 2) we must introduce an amplitude attenuation of
[
θ2 RL exp 2 2ka (n - n 2)3/2 1 2
]
γ ≈ R(U2/V2W)
(9)
where θ1/2 is the half width at half-maximum (HWHM) of the farfield pattern given by
θ1/2 ) (ka ln 2/R L)1/2 (n12 - n22)3/4
(10)
(5)
where V is the waveguide parameter, V ) ka (n12 - n22)1/2, W is the cladding parameter, W ) a (β2 - k2 n22)1/2, β is the mode propagation constant, β ) n1k {1 - 2∆x2}1/2, ∆ is the profile height parameter, ∆ ) (n12 - n22)/2n12, and x is the relative mode index.34 The core and cladding parameters are related to the waveguide parameter by U2 + W2 ) V2. Using eq 3 above and approximating W by V in the denominator, gives
While the ray treatment of mode-dependent attenuation (cf. eq 7) is useful for prediction of the far-field spatial pattern for angles θ * 0, it incorrectly predicts that the lowest guided mode in the fiber (when θ ) 0) propagates unattenuated through an absorbing-cladding-fiber section. In fact, the lowest-order modes will experience a finite attenuation with the evanescent wave attenuation coefficient:
γ)R (32) Gradshteyn, I. S.; Ryshik, I. M. Table of Integrals, Series, and Products; Academic Press: New York, 1980; eq 6.521.1. (33) Gloge, D.; Marcatili, E. A.; Marcuse, D.; Personick, S. D. In Optical Fiber Telecommunications; Miller, S. E., Chynoweth, A. G., Eds.; Academic Press: New York, 1979; Chapter 4. (34) Ruddy, V. Opt. Eng. 1994, 33, 3891-3894.
4958
(8)
equivalent to an apodization of the aperture function. If all guided modes reaching the sensing region have the same optical power, then the attenuation introduces a Gaussian falloff of intensity with θ in accordance with eq 7. Thus, the far-field pattern can be written as
I ) Io exp[-ln 2(θ2/θ1/22)] where Ient is the power of the guided mode at the entrance to the fiber region that has an absorbing cladding, and γ is the evanescent-wave attenuation coefficient. The attenuation of a mode due to an absorbing cladding with an absorption coefficient R is given by33
(7)
Analytical Chemistry, Vol. 71, No. 21, November 1, 1999
θmin2 ka(n12 - n22)3/2
(11)
where θmin is the smallest value of the angle θ, which can be calculated according to eq 3.
Figure 2. Schematic diagram of the measurement system.
Thus, the power of the lowest-order modes is attenuated by a factor of
[
]
RLθmin2 exp ka(n12 - n22)3/2 Combining eqs 7 and 12, we have
[
] [
(12)
]
RLθmin2 RLθ2 exp I ) Imax exp ka(n12 - n22)3/2 ka(n12 - n22)3/2
(13)
where Imax is the intensity at the peak of the far-field pattern observed with a reference sample solution (e.g., having smallest n2 and R). The first exponential term in eq 13 indicates that variation of either R or n2 causes a change in the maximum intensity of the far-field pattern. The second exponential term similarly shows a dependence of the HWHM of the far-field pattern on n2 and R. Thus, it is possible to determine simultaneously n2 and R if both parameters of the Gaussian (i.e., peak intensity and HWHM) are measured. These measurements can be accomplished with a two-dimensional array detector as shown in Figure 1. The external angle θ of the far-field spatial pattern at the detector plane is related to the spatial coordinates x and y and the distance z from the end face of the fiber to the detector plane as
θ ) tan-1((x2 + y2)/z2)1/2
(14)
2. EXPERIMENTAL SECTION Materials and Reagents. Multimode PCS (plastic-clad silica) optical fiber was purchased from Fiberguide Industries (Stirling, NJ) with core and cladding diameters of 100 and 200 µm, respectively. According to the manufacturer, the numerical aperture (NA) of the fiber drops from NA ) 0.4 for short fiber lengths (50c
600 750 0.4 20 10 115
a
36 1000 0.48 200 >50
37
37
37
104 150 0.13 21 635 1
100 150 0.5
90 120 0.156
675 0.01
12
18 55 0.144 33
