Measuring deviations from a perfectly circular cross section of an optical nanofiber at the angstrom scale

Tapered optical fibers (TOFs) with sub-wavelength-diameter waists, known as optical nanofibers, are powerful tools for interfacing quantum emitters and nanophotonics. These applications demand stable polarization of the fiber-guided light field. However, the linear birefringence resulting from Ångström-scale (Å-scale) deviations in the nanofiber's ideally circular cross section can lead to significant polarization changes within mm of light propagation. Here, we experimentally investigate such deviations using two approaches. First, we measure the resonance frequencies of hundreds of flexural modes along the nanofiber, which exhibit splitting due to the noncircular cross section. By analyzing the mean resonance frequencies of each pair and the corresponding frequency splitting, we conclude that the nanofiber can be well described as having an elliptical cross section with a mean radius of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>255.2</a:mn> <a:mo>(</a:mo> <a:mn>8</a:mn> <a:mo>)</a:mo> <a:mspace width="0.16em"/> <a:mi>nm</a:mi> </a:mrow> </a:math> , where the semiaxes differ by only about <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>2</c:mn> <c:mspace width="0.16em"/> <c:mo>Å</c:mo> </c:mrow> </c:math> . Second, we monitor the polarization of the guided light field by imaging the light scattered out of the nanofiber and observe a periodic polarization change along it. From the linear birefringence due to the elliptical cross section, we infer a comparable difference in the semiaxes as the first method, and determine the orientation of the polarization eigenaxes. Our work is crucial for any fundamental or applied study that requires a well-controlled interaction between guided light and matter, in particular for quantum memories, frequency conversion, or lasing that require a large interaction length.