Development of an Analytical Model for a Fiber Optic Evanescent Wave Sensor

Abstract

Spectroscopy in the near infrared range is a powerful tool for the qualitative and quantitative analysis of a variety of materials in the gas liquid or solid phases. The use of optical fibers as a means of performing cost effective in-situ spectroscopic analysis has gained a lot of attention in many fields in the past three decades. Intensity based fiber optic sensors, which rely on variations in transmission power at a fixed wavelength for the characterization of material, are relatively inexpensive to fabricate and provide an easy to read signal. The objective of this thesis will be to present an analytical model developed for a multimode fiber optic evanescent wave sensor (FOEWS) capable of monitoring the charge cycle of a lithium-ion battery cell. The sensor is fabricated by partial removal of the cladding material surrounding the core of a multimode fiber optic. The thinned cladding section allows for transmission loss via evanescing waves which radiate power out from the core as a function of the external environment. In contrast to FOEWS designs which use a single mode optical fiber, the use of a multimode fiber causes difficulty in numerical modeling of the system. Single mode optical fibers have core diameters which are small relative to the wavelength of light propagating within. As such, solving for the transmission response of a single mode fiber can be accomplished using a numerical solver. By using a multimode optical fiber the fiber core diameter is orders of magnitude larger than the wavelength of propagating light. Attempting to accurately mesh a multimode optical fiber requires an unmanageably large mesh which cannot be solved in a reasonable time frame. Alternative approaches for the modeling of a multimode FOEWS have been proposed in the past. However, these methods make use of effective attenuation coefficients to estimate the transmission coefficient of the sensor and thus, they do not include a direct analysis of the electromagnetic field solutions of the thin cladding region. An analytical method for accurately solving the attenuation coefficient using the transfer matrix method is presented. Adoption of the analytical method extends the theoretical description of FOEWS model allowing for more accurate prediction of the sensor behavior by directly accounting for cladding thickness without the use of empirically determined attenuation coefficients. FOEWS fabricated using commercially available step index multimode fibers etched with buffered hydrofluoric acid were used to verify predictions of the newly modified model. Model predictions are matched with experimental tests performed using known index of refraction samples of glycerol and calibrated thermal optic oil ranging from 1.451 to 1.466. The experimentally observed intensity variations are compared to model predictions for verification. The fabricated FOEWS was determined to have a cladding thickness of 0.485±0.1 µm. Comparison with direct measurement under scanning electron microscope (SEM) place the variations of the model from the experimental results within one standard deviation of the fabrication tolerances of the optical fiber. Building on the increased capabilities of the transfer matrix method to analytically model the thin film reflection coefficient, a method is put forth to simulate the partial contact of a solid analyte with a FOEWS. A case study is presented which investigates the FOEWS response behavior to a solid lithium-ion graphite anode held in partial contact to the fiber. SEM images of lithium-ion anode materials held in sensing contact with a fabricated FOEWS are analyzed to determine the fractional contact area of the fiber optic sensing region with the solid anode. A statistical average of the fractional contact area as well as mean depth of non-contact regions is determined. The presence of partial contact between the fiber thin cladding and anode material creates a fourth thin film region which is filled with electrolyte liquid from the cell. The addition of a fourth thin film region is added to the transfer matrix method analysis of the sensing region of the FOEWS to account for the presence of liquid electrolyte between the fiber sensing region and anode bed. By splitting the model analysis of the sensing region into two separate sections representing the fractional full and fractional partial contact regions effects of partial is then studied using simulated results. In summary, the ability to directly model thin film cladding effects using the transfer matrix method has been added to pre-existing FOEWS models. This new functionality is tested against fabricated devices using solutions of various index of refraction. The model is then used to predict the effect of partial contact of the sensor with a solid anode analyte from a lithium-ion cell.