## Materials and Methods  
### Sample Production and Etching  
Approximately 15 cm of single crystal sapphire optical fiber (optical \(c\)-axis) with an original diameter of 125 \(\upmu\)m was cut from a 100 cm segment from Micromaterials, Inc. (Tampa, FL, USA). Early experiments found signal-scattering deposits comprised of aluminum sulfate and aluminum phosphate would form and adhere strongly to the surface of an immersed sapphire fiber during etching, concentrated near the air-acid interface. To prevent adherence of these deposits at this region, a protective borosilicate glass tube with an internal diameter of 140 \(\upmu\)m and length of around 5 cm was collapsed over one end of the sapphire fiber using an oxyhydrogen torch, leaving 10 cm of sapphire fiber to be etched. Less than 1 cm of the borosilicate tube was collapsed to reduce any \"cladding\" effect this region may have; with this seal formed, the acid solution would be prevented from wicking up along the fiber and producing deposits. Accordingly, the shielded 5 cm-length of the sapphire fiber retained its 125 \(\upmu\)m diameter throughout, while etching reduced the diameter of the remaining 10 cm exposed length.  
A ferrule connector/physical contact (FC/PC) connector was mounted, secured and polished on one end of the sapphire fiber which would remain outside the etching solution; attaching the connector before etching ensured that measurements could be taken between etching sessions without inadvertently altering input conditions.  
The etching solution was a 3:1 molar ratio mixture of sulfuric acid (98%, Sigma Aldrich, St. Louis, MO, USA) and phosphoric acid (85%, VWR). This solution was contained within a fused quartz tube with an inner diameter of 1.25\({}^{\prime\prime}\). One end of this 8\({}^{\prime\prime}\)-long tube was collapsed using an oxyhydrogen torch, then placed within custom-made porous aluminosilicate rings to improve thermal distribution during heating. Holes were drilled longitudinally through these rings and resistance heating wire (80% nickel, 20% chromium, 20 gauge, OMEGA Engineering, Norwalk, CT, USA) was wound throughout. This resistance heating wire was connected to a variable transformer (Variac, Cleveland, UK, USA) so that the temperature could be controlled by adjusting to the proper voltage setting. These heating rings were finally enclosed in a polycrystalline alumina tube (Coorstek, Golden, CO, USA) and padded with alumina fiber insulation. Figure 1 illustrates the etching apparatus in simplified form.  
To initiate etching, a thermocouple probe (Omega) was inserted into a small sealed fused quartz tube upon which the sapphire components were previously mounted, and this assembly was immersed in the acid solution at room temperature. The opening of the vessel was enclosed with Teflon tape (with a small outlet for pressure relief), and the voltage was increased to a value optimized to quickly heat the solution without causing rapid boiling of the sulfuric acid component. Etching would typically be allowed to occur for 8-10 h at a time before the sapphire sample was removed for analysis and the etching solution was refreshed, during which the temperature was recorded every 15 s using a Digisense datalogging digital thermocouple reader (Davis Instruments, Vernon Hills, IL, USA).