The Effect of Length and Diameter on the Signal-to-Noise Ratio of Evanescent Field Absorption Fiber-Optic Sensors T. B. COLIN,* K.-H. YANG,*t M. A. ARNOLD, GARY W. SMALL,~ and W. C. STWALLEY*§ Department of Chemistry, University o[ Iowa, Iowa City, Iowa 52242 This paper discusses the theoretical and experimental implications of changing the length and diameter of the evanescent field sensing region of an evanescent field sensor. Particular emphasis is placed on optimizing the intensity of the evanescent field for near-infrared sensor applications. Both theoretical and experimental results show that an optimal length and diameter must be determined experimentally for each analyte sys- tem. Index Headings: Infrared; Instrumentation, sensors; Optics; Fiber op- tics. INTRODUCTION Evanescent field fiber-optic sensors have become in- creasingly popular for remote sensing applications. Gen- eral spectroscopic systems for mid-IR 1 and near-IR, 2 as well as specific biosensors 3 and distributed sensor sys- tems, 4have been developed on the basis of the evanescent field sampling technique. Since the evanescent field in- tensity is very weak in comparison to the light intensity used in conventional optical techniques, it is important to optimize the evanescent field sensor to gain full ad- vantage of its sensitivity. The focus of this paper is on the optimization of these sensors by adjustment of the length and diameter of the evanescent field sensing re- gion. THEORY Light propagation in step index multimode optical fi- bers can be described in terms of a cylindrical dielectric waveguide which has been described in detail by Snitzer2 The results of these calculations reveal that many modes of propagation are possible, each having a characteristic distribution of intensity between the core and cladding of the optical fiber. To understand the nature of the evanescent field in a multimode fiber, it is necessary to calculate how much light is propagated by each mode, and how much of the energy of each mode is propagating in the cladding, or evanescent field. The modes of interest in fiber-optic sensor development are the HE, EH, TE, and TM modes. The expressions for the intensity of light in each mode have been published previously2 The critical parameters are P~o~e and P¢~d, which represent the amounts of power propagating in the core and cladding of each mode, re- Received 21 February 1992. * Also Center for Laser Science and Engineering. t Also Department of Physics, St. Ambrose University, Davenport, IA 52803. Department of Chemistry, Ohio University, Athens, OH 45701-2979. § Also Department of Physics and Astronomy. Author to whom cor- respondence should be sent. spectively. The intensity of the evanescent field calcu- lated in these experiments is defined as the fraction of power propagating in the cladding, as shown in Eq. 1: rip "= Pchd/(Pcore 2'- Pchd)" (1) In this experiment we take advantage of the Beer's law relationship between the ~p and absorbance, which can be expressed as shown in Eq. 2: A = ~71pbc (2) where A is the absorbance, a is the absorption coefficient, b is the length of sensor, and c is the analyte concentra- tion. The intensity of the evanescent field can be cal- culated by computing a from a transmission experiment, then solving for np, expressed in ppt (parts per thousand). Length Considerations. One problem associated with optimizing evanescent field sensors is the relationship of absorbance to pathlength. Naively, one might estimate that it would be a linear relationship, as in the conven- tional Beer's law case. However, this is not even a good first approximation since, unlike the conventional case, each unit length of sensor will not provide the same absorption. Consider a theoretical optical fiber which has two al- lowed modes of propagation: HEll and HE2, A V-num- ber of approximately 3 is required to meet this criterion. The ~p for HEu is approximately 10% and for HE21 it is approximately 35%. Assume that the analyte absorbs 100% of the light available in the cladding per unit length; the amount of light present in the cladding can be cal- culated as a function of position along the length of the sensor. Each unit length of sensor results in the absorp- tion of all the available cladding energy, and a subse- quent replenishing of the cladding with energy from the TABLE I. Light distribution over a 10-cm sensor with two modes." Posi- HE~I HE21 tion (cm) Wo,.d Woo,° Wo,ad W~r. 0 0.02575 0.22420 0.08763 0.16238 1 0.02309 0.20111 0.05704 0.10533 2 0.02071 0.18040 0.03692 0.06841 3 0.01858 0.16180 0.02399 0.04445 4 0.01667 0.14510 0.01558 0.02887 5 0.01454 0.13020 0.01012 0.01875 6 0.01341 0.11680 0.00657 0.01218 7 0.01203 0.10480 0.00427 0.00791 8 0.01080 0.09400 0.00277 0.00514 9 0.00968 0.08430 0.00180 0.00334 10 0.00868 0.07560 0.00117 0.00217 a W~,~d is the light power in the cladding and Woore is the light power in the core. Volume 46, Number 7, 1992 0003-7028/92/4607-112952.00/0 APPLIED SPECTROSCOPY 1129 © 1992 Societyfor AppliedSpectroscopy