A rigorous theoretical model of fluorescence-based fiber optic sensors: application to D-shaped fibers

We develop a comprehensive theoretical model for fluorescence-based fiber optic sensors that accounts for multimodal excitation, incoherent emission from a homogeneously distributed ensemble of individually treated dipole emitters, and multimodal fluorescence capture. Unlike previous models based on bulk excitation and emission, our approach starts from single-dipole physics and extends to a continuous emitter distribution, enabling accurate modeling of spatial interference effects and fluorescence collection. Using this model, a fiber optics sensor, consisting of a D-shaped fiber sandwiched between an input and output fiber, is simulated to investigate the effects of core size, excitation modes, and polishing depth on fluorescence output, thereby identifying configurations that optimize sensor performance. The results indicate that, for fundamental mode excitation, polishing the fiber to approximately halfway through the core diameter enhances the fluorescence output. Additionally, smaller core fibers demonstrate stronger fluorescence output, and excitation with higher-order modes consistently produces greater fluorescence than fundamental mode excitation. This effect is especially pronounced in larger core fibers. These findings suggest that the fluorescence collection limitations in larger core fibers can be mitigated by higher-order mode excitation. Moreover, higher-order mode excitation enables optimal fluorescence output at shallower polishing depths, making it especially advantageous for large-core fibers in practical applications.