Fiber-based optical sensors with the advantages of highly sensitive, label-free detection, and easy handling in complex environments have tremendously progressed in recent years. Although fibers are primarily used as light carriers, their structure can be altered elegantly, such as tapering the fiber by heating and pulling from both ends. As a result of tapering the fiber in an optical sensing setup, a considerable portion of the optical mode leaks out of the taper. The mode interacts with an analyte surrounding the tapered fiber—consequently, its optical characteristics change, which can then be correlated with the analyte properties. The need for enhanced sensitivity to detect various diseases, environmental pollutants, and contaminants for food security applications demands high optical power to be injected into tapered fibers or place tapered fibers inside optical cavities. The heat generated in a tapered fiber due to propagating modes will thermally impact probing surroundings in the tapered fiber's vicinity and also induce material-dependent refractive index changes; hence overall sensing measurements will be affected.

Various works on thermal analysis of optical fibers have been conducted primarily for fiber laser applications in the literature. However, no propagating-mode-based thermal analysis work exists on tapered fibers in general, and particularly for sensing applications. Therefore, the present work investigates the temporospatial thermal analysis of tapered fibers for sensing applications, particularly involving cavity sensors.

In this work, we develop a model based on the heat equation in cylindrical coordinates to predict temperature variations in air-clad and water-clad tapered fibers connected to a CW laser source. We apply the proposed model to optical cavities that employ tapered fibers as sensing heads for air and liquid applications. We assume that cavities comprise 99.9-99.99% reflective mirrors with 10mW-50mW of input power at 1550nm. We find that single-mode air-clad and water-clad tapered fibers experience the surface temperature changes of ≤15o and ≤1o, respectively, due to the propagating mode. We also find that steady-state times to reach these temperatures can take up to 0.5 ms and 0.9 ms, respectively. Moreover, we also determine that these temporospatial thermal effects lead to the shift in resonant wavelength by ≤140 pm and ≤6 pm for air and water surroundings, respectively, in the cavity sensor. Significantly, the current work is not only applicable to optical sensors employing tapered fibers but can also find a wide range of applications in power amplification, optical coupling, and supercontinuum generation.