## 5 Conclusions  
In this work, very low modal volume was observed in an air-clad single-crystal sapphire optical fiber, with single-mode behavior observed for the first time at laser wavelengths of 783 nm and 983 nm. The stability of far-field mode profile measurements for the 6.5 \(\upmu\)m-diameter sapphire fiber was demonstrated through the alteration of input conditions, bolstering confidence in the observed low modal volume. It is possible that some higher order modes are yet supported by sapphire optical fiber of this diameter but are simply too leaky to propagate for substantial lengths; this consideration will be the subject of continued experimentation. For the practical purposes of distributed sensing applications, however, this work has demonstrated that dominant power in a 6.5 \(\upmu\)m-diameter sapphire optical fiber is coupled in the lowest order modes in the wavelength range of 532 nm-983 nm.  
It was also demonstrated that modal volume calculations using weakly-guiding approximations are inaccurate at these fiber diameters if the theoretical numerical aperture is input, but accuracy is greatly improved if the effective numerical aperture is measured and substituted for the theoretical \(NA\) using weakly-guiding approximations. Finally, the discovery that single-mode behavior is exhibited at sapphire fiber diameters on the microscale rather than the nanoscale predicted using original assumptions is of huge benefit to the extreme-environment sensing community; sapphire microfibers  
Figure 9: The predicted maximum air-clad sapphire optical fiber radius that will support only a single mode changes significantly when the measured effective numerical aperture (0.090) is substituted for the theoretical numerical aperture (1.4) in step-index approximations. The predicted single-mode cutoff using the measured \(NA_{\text{eff}}\) in these approximations agreed with experimental observations.  
are much more easily manufactured, handled, and deployed than nanofibers, and the power capacity of a microfiber will be exponentially greater than a nanofiber. Additionally, detection resolutions may be increased in distributed sensors and sensing schemes requiring low modal volume or single mode behavior (such as Bragg gratings) are now enabled in sapphire.  
The authors wish to acknowledge financial support from the National Energy Technology Lab (NETL) at the U.S. Department of Energy (DOE) under contract DE-FE0012274. Publication fees were generously provided by the Virginia Tech Open Access Subvention Fund.  
[PERSON] and [PERSON] guided experimental design and provided refining feedback throughout the research. [PERSON] and [PERSON] lended experimental assistance, especially regarding optical analysis setup and execution. [PERSON] and [PERSON] evaluated experimental data and suggested additional validating techniques. [PERSON] performed the experiments, sample characterization and analysis, and wrote the paper.  
The authors declare no conflict of interest. _Disclaimer_. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by tradename, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.