Origin of the secondary intensity peak in integrated-waveguide addressing

Determine the origin of the secondary intensity peak observed near an axial ion position of 110 micrometres in the Rabi-frequency measurements of the 729-nanometre femtosecond-laser-written waveguide, and explain why the peak is absent from the corresponding camera-based beam profile.

Background

The paper characterizes the spatial intensity profile emitted by an integrated femtosecond-laser-written waveguide by shuttling a trapped 40Ca+ ion along the trap axis and measuring the local Rabi frequency of the 729-nanometre qubit transition. The authors compare this ion-based profile with a beam profile obtained using a camera. Although the main peak agrees reasonably well between the two measurements, the ion-based data contain an additional peak near x = 110 micrometres that does not appear in the camera data.

The authors suggest that local intensity variations may result from surface imperfections on the manually cleaved waveguide out-coupling facet, which could perturb the emitted wavefront and generate interference effects. However, this explanation does not resolve the specific discrepancy between the two measurement methods, leaving the origin of the secondary peak unresolved.

References

A notable discrepancy is the secondary peak observed in the ion data around $x=110~\si{\micro\meter}$, which is not fully understood, as it is absent in the camera profile.

— Ion trap on borosilicate substrate with integrated femtosecond-laser-written waveguide  (2608.13207 - Wahl et al., 13 Aug 2026) in Section 5.3, “Integrated addressing of a trapped ion”