Identify the sapphire crystal axis orientation in the measured vapor cell

Determine the crystallographic axis orientation of the sapphire cube in the rubidium-filled sapphire vapor cell relative to the c-axis for the measurement orientation used in the stripline experiments, in order to reconcile the measured dielectric constant with sapphire’s anisotropy.

Background

The authors measured an effective dielectric constant of approximately 9 for the sapphire portion of a rubidium-filled sapphire vapor cell and noted this value is consistent with sapphire’s bulk properties. However, sapphire is anisotropic, and the measured permittivity depends on the crystal axis orientation relative to the applied field.

Only one orientation was measured, and the authors did not determine the actual orientation; they speculate it is likely perpendicular to the c-axis given the lower dielectric constant. Precisely identifying the orientation would clarify the interpretation of the permittivity measurement.

References

Note that only one orientation of the sapphire axis is measured, and while the axis is unknown, it is likely perpendicular to the major c-axis given the lower dielectric constant.

— Extraction of Effective Electromagnetic Material Properties for Rydberg Electrometer Vapor Cells from 10-300 MHz  (2604.11785 - Richardson et al., 13 Apr 2026) in Subsection 'S-parameter Measurement and Permittivity Determination'