Symmetry-guided modal control in elliptical femtosecond-laser-written photonic waveguides
Few-mode photonic circuits can increase functionality without multiplying waveguide paths, but bends and fabrication errors can mix their transverse modes. We investigate a strategy in which waveguide confinement and perturbation parity are engineered together in vertically elliptical, femtosecond-laser-written glass waveguides. The intended modal basis comprises the even $1S$ mode and the vertically odd $2P_y$ mode. No window-converged $2P_x$ state is resolved for a lower-confinement (LC) design, whereas a higher-confinement (HC) design guides $2P_x$, which must therefore be isolated by symmetry. In scalar beam-propagation calculations, the $1S$-$2P_y$ propagation-constant splitting predicts the optimized periods of a vertically modulated coherent modal splitter to within $1.0\%$. Horizontal S-bends remain parity-mismatched for $1S \leftrightarrow 2P_y$ coupling, while the symmetry-allowed HC $1S \rightarrow 2P_x$ transfer reaches only $0.6\%$ at the largest displacement. At a displacement of $150~μ\mathrm{m}$, the HC design retains approximately the same $2P_y$ power as the LC design retains at $40~μ\mathrm{m}$. Thermal and stochastic writing-error calculations reveal the resulting trade-off: stronger confinement improves modal-power retention, but writing jitter that breaks $x$-parity can populate the guided $2P_x$ mode. These results demonstrate how modal-basis engineering can shift part of the crosstalk-control burden from the trajectory to waveguide symmetry, supporting joint path--mode degrees of freedom in quantum photonic applications.